Citation
Proton-transfer kinetics and equilibria in concentrated mineral acids

Material Information

Title:
Proton-transfer kinetics and equilibria in concentrated mineral acids
Added title page title:
Equilibria in concentrated mineral acids
Added title page title:
Mineral acids
Creator:
Vogt, Brian Stanley, 1956-
Publication Date:
Language:
English
Physical Description:
vii, 150 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
4-Quinolones ( jstor )
Acidity ( jstor )
Fluorescence ( jstor )
Ionization ( jstor )
Molecules ( jstor )
pH ( jstor )
Protons ( jstor )
Titration ( jstor )
Wavelengths ( jstor )
Xanthones ( jstor )
Acid-Base Equilibrium ( mesh )
Acids ( mesh )
Acridines ( mesh )
Kinetics ( mesh )
Protons ( mesh )
Quinolines ( mesh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida.
Bibliography:
Includes bibliographical references (leaves 143-148).
General Note:
Photocopy of typescript.
General Note:
Vita.
Statement of Responsibility:
by Brian Stanley Vogt.

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
10196779 ( OCLC )
ocm10196779
0029406716 ( ALEPH )

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Full Text











PROTON-TRANSFER KINETICS AND EQUILIBRIA
IN CONCENTRATED MINERAL ACIDS





By

BRIAN STANLEY VOGT


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1983






























This dissertation is lovingly dedicated to my dear

wife, Carla. Her continual love, patience, and

encouragement were instrumental in the completion of this

work.














ACKNOWLEDGEMENTS

I would first like to thank Dr. S.G. Schulman,

chairman of my supervisory committee, for his patient

guidance throughout my graduate career. His perception,

experience, and advice were indispensable in the completion

of the research which culminated in this dissertation. I

would also like to thank the other members of my supervisory

committee, Dr. F.A. Vilallonga, Dr. K.B. Sloan, Dr. J.H.

Perrin, and Dr. J. D. Winefordner, for their suggestions

and support.

I would also like to thank the other members of the

research group not only for their friendship, but also for

the many thought-provoking discussions and heated

arguments which helped all those involved to gain a clearer

perspective on the strengths and weaknesses of their

scientific understandings. Michael Lovell was

particularly helpful in these regards.

Finally, I would like to thank my parents, Stanley and

Blanche Vogt, for the understanding and wisdom with which

they have encouraged me. They have played an important role

in the years of success that I have been privileged to.


iii














TABLE OF CONTENTS


ACKNOWLEDGEMENTS ....... .........................iii

ABSTRACT ................... .......................... vi

CHAPTER PAGE

I INTRODUCTION .......................................1

Bronsted-Lowry Acid-Base Chemistry in
Ground Electronic States........................ 3
Prototropic Reactivity in Electronically
Excited States ................... .............. 7
The Effects of Protonation on
Electronic Spectra.............................. 9
The F6rster Cycle.................................. 10
Steady-State Kinetics of Excited-State
Proton-Transfer Reactions........................ 20
Summary ......................... ..... ......... 25

II EXPERIMENTAL ...................................... 27

Reagents and Chemicals ........................... 27
Absorption and Fluorescence Studies.............. 29
Measurements of Acidity.......................... 33
Titration Methods.................................. 33
Computation.................................... .. 35

III GROUND- AND EXCITED-STATE PROTON TRANSFER
IN ACRIDONE AND XANTHONE.......................... 37

Introduction ..................................... 37
Results and Discussion............................ 41

IV EXCITED-STATE PROTON TRANSFER IN
2-QUINOLONE AND 4-QUINOLONE........................ 67

Introduction............ ......................... 67
Results and Discussion............................ 71

V EQUILIBRIUM EXCITED-STATE PROTON TRANSFER
IN 1-ISOQUINOLONE.................................. 99

Introduction........ ..............................99
Results and Discussion........................... 100










VI NONEQUILIBRIUM EXCITED-STATE PROTON
TRANSFER IN 3-AMINOACRIDINE .................... 112

Introduction... ............................... 112
Results and Discussion ......................... 114

VII SUMMARY........ ............................... 131

APPENDICES

A SIMPLE LINEAR LEAST-SQUARES REGRESSION
ANALYSIS ......................................... 135

B MULTIPLE LINEAR LEAST-SQUARES REGRESSION
ANALYSIS.......... .............................138

REFERENCES............. ................................ 143

BIOGRAPHICAL SKETCH .................................... 149














Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial
Fulfillment of the Requirements for the
Degree of Doctor of Philosophy


PROTON-TRANSFER KINETICS AND EQUILIBRIA
IN CONCENTRATED MINERAL ACIDS

By

BRIAN STANLEY VOGT

August, 1983


Chairman: Stephen G. Schulman, Ph.D
Major Department: Pharmacy

Ultraviolet-visible absorption and fluorescence

spectroscopy were used to study ground- and excited-state

proton-transfer reactions. A transition-state reaction

scheme was used to propose a model to quantitate the

kinetics of excited-state proton transfer in

concentrated acid. The Hammett acidity function, H was

used as a measure of acidity. The model thus derived

included r, the number of water molecules which enter into

the excited-state deprotonation reaction of the test

compound. Also included was n, the number of water

molecules which enter into the ground-state deprotonation

reaction of the indicator used to define that range of the

H scale over which the excited-state ionization of the

test compound occurred. The model successfully described









the excited-state ionizations of several aromatic lactams

in H2SO4 or HC1O4. Modification of the model to describe

the excited-state ionization of an H+ type molecule was

successful.

It was found that one of the molecules studied

demonstrated excited-state prototropic equilibrium. While

pKa could be determined, neither the rate constants for the

reactions steps nor n and r could be determined. The model

predicted that these limitations would apply to all excited-

state prototropic equilibria occurring in concentrated acid.

The other molecules exhibiting excited-state ionizations in

concentrated acid demonstrated nonequilibrium excited-state

proton transfer. Values of pKa, the rate constants for the

reaction steps, and n and r were determined.

Also devised was a general method of determining the

rate constants of the excited-state reaction steps when the

ground-state ionization occurs in concentrated acid but the

excited-state ionization occurs in dilute solution. This

method was successfully applied to several H type molecules.

Ground-state ionizations occurring in concentrated acid

were successfully described by a modified Henderson-

Hasselbach equation. This equation accounted for n and also

for r the number of water molecules which enter into the

ground-state deprotonation of the test compound.

For all but one of the compounds studied, the F6rster

successfully related pKa to pK .


vii














CHAPTER I
INTRODUCTION

The physical and chemical properties (solubility, pKa,

rates of hydrolysis, etc.) of drugs are usually measured in

dilute, aqueous solution. It is frequently assumed that

these measurements reflect the correct values of these same

properties of the drugs when they are found in vivo.

However, the experimental solution media are idealized

compared to the environments found in vivo. For example,

plasma is an approximately 8% solution of proteins,

electrolytes, lipids, sugars, amino acids, hormones, and

metabolic wastes (1), and hence plasma is not a dilute,

aqueous solution. Lymphatic fluid and interstitial fluid

are similar to plasma (except that they contain less

proteins). Cell interiors are another example of media

which do not act as dilute solutions, for somewhere between

10% and 60% of the total volume of cells may be water which

is "bound up" by cell constituents (2). Indeed, it has been

shown that the properties of water in dilute, aqueous

solution are dramatically different from the properties of

water in cells (2) and around hydrophobic solutes (3).

Furthermore, the acidity of aqueous solutions may be

enhanced by the addition of neutral electrolytes. For

example, a 1 M solution of NaCl (approximately 6% NaCI)

made up in 0.01 M







2

HC1 (pH = 2) has pH = 0.2 (4), and hence the acidity of the

solution is changed by almost two orders of magnitude by

the addition of the neutral salt. It is conceivable that

the presence of high concentrations of solutes in some body

fluids could lead to unexpectedly high acidities and low

activities of water in those fluids. A study of the

physicochemical properties of molecules in concentrated

electrolytic media could be useful, for such a study could

shed light on whether or not it is legitimate to use

properties measured at infinite dilution in water to

predict the behavior of the molecules in media which

significantly deviate from ideality.

The acid-base properties of functionally substituted

aromatic molecules in electronically excited states are

frequently thermodynamically and kinetically quite different

from these properties in ground electronic states. Because

of this, the ground- and excited-state ionizations may occur

in media which radically differ from each other insofar as

their electrolyte (acidic and/or neutral) compositions are

concerned. When the ionizable group is bonded directly to

an aromatic ring, UV-visible absorption and fluorescence

spectroscopy may be used as tools to study ground- and

excited-state proton-transfer reactions. The author has

used absorption and fluorescence spectroscopy to study

proton-transfer reactions in both dilute, aqueous solutions









and in concentrated electrolytic media. Before discussing

the author's research, however, a review of ground- and

excited-state acid-base chemistry is in order.

Bronsted-Lowry Acid-Base Chemistry in Ground Electronic States

We shall restrict ourselves to the Bronsted-Lowry

definitions (5,6) of acid and base (an acid is a species

which can donate a proton and a base is a species which can

accept a proton). The acid-base properties of a given

organic molecule are a consequence of the presence of one

or more electronegative atoms (usually nitrogen, oxygen,

or sulfur) in that molecule. In a Br~nsted-Lowry acid, at

least one of these atoms is present and has covalently

bonded to it a hydrogen atom. Sufficiently strong

interaction between the solvent and the hydrogen atom results

in the loss of the hydrogen atom from the molecule to form

a solvated proton and the conjugate base of the organic

acid. Bronsted-Lowry bases contain at least one

electronegative atom with at least one pair of unshared

electrons (lone pair). Protonation (ionization) is the

formation of a coordinate-covalent bond between the lone

pair on the base and a proton (which may come from the

solvent, if it is sufficiently acidic, or from some other

source of protons). The conjugate acid of the organic base

and the solvent lyate anion (when the solvent is the proton

donor) are formed when protonation of the base occurs. The







4

molecules which we shall consider have conjugate acids and

bases which react according to the mechanism

k
BH + SH '-B + SH (1),
kb

where B is the conjugate base, BH is the conjugate acid,

SH is the solvent, and SH2 is the solvent lyonium ion. The

rate constants ka and kb are, respectively, the pseudo-

first-order rate constant for deprotonation of BH+ and the

second-order rate constant for bimolecular protonation of B.

In aqueous solution, SH is water and SH2 is the hydronium

ion, and then reaction (1) becomes


BH + H20 ka B + H0 (2).
kb


It is also possible to have a conjugate acid that is so

weakly acidic that solvent lyate anions must be present for

the deprotonation reaction to occur, in which case the

reaction will be described by
k'
BH + S- a B + SH (3),

b

where S- is the solvent lyate anion ( in water this is the

hydroxide ion) and k' and kb are, respectively, the

second-order rate constant for bimolecular deprotonation of

BH+ and the pseudo-first-order rate constant for protonation

of B. The research presented in this dissertation, however,







5


deals only with molecules which react according to mechanism

(2), and hence we shall restrict ourselves to a discussion

of that mechanism.

The acid-dissociation equilibrium constant, Ka, for

reaction (2) is defined as
k aa B +
ka aBaH
K = (4),
Sakb aBH+ aw

where aB and aBH+ are the activities of the conjugate base

and acid, respectively, and aH+ and a are the activities

of proton and water, respectively. In dilute, aqueous

solution a = 1, and then
w
aBaH+ [B]f aH+
K = B = (5),
a aBH+ [BH]fBH +

where [B] and fB are, respectively, the equilibrium molar

concentration and activity coefficient of B, and [BH ] and

f BH+ are, respectively, the equilibrium molar concentration

and activity coefficient of BH At infinite dilution,

fB = 1 and f BH+ = 1, and then equation (5) may be

transformed into the familiar Henderson-Hasselbach

equation (7,8):
pK = pH log [B](6).
a [ BH (

In concentrated acidic solutions equation (6) cannot

be used. The acidity of the medium (pH < 1) cannot be

measured with a pH meter, but it can be measured with the

Hammett acidity function (9). This acidity scale is based










upon the spectrophotometrically measured conjugate base/acid

ratios of a series of primary nitroaniline indicators which

behave according to the reaction

HIn+ + nH20 ( ) In + H+ (7),

where In and HIn+ are, respectively, the conjugate base and

acid of the indicator, and n is the number of water molecules

which react with the hydrated conjugate acid to form the

hydrated conjugate base and hydrated proton. The activity

of proton is related to the Hammett acidity, H (where

Ho = -log h ), by

fI
aH+ = h aw" (8),
o
0

where f' and f' are the activity coefficients of HIn+ and
+ o
In, respectively. In concentrated acid a < 1, and hence

a cannot be eliminated from equation (8). The acid-base
w
reaction of the test compound of interest is then

BH+ + r H20 0 B + H+ (9),
g 2

where rg is the number of water molecules which react with

hydrated, ground-state BH+ to form hydrated, ground-state B

and the hydrated proton. The equilibrium constant for this

reaction is defined as

[B]f a +
K = (10).
a [BH+ f + arg










Equations (8) and (10) may be combined and put into the

logarithmic form


pKa = H- log[B] (n-rg)loga logB ,f (11).
([BH ] BH 0

Lovell and Schulman (10-12) have successfully applied

equation (11) to the prototropic reactions of a series of

unsubstituted and substituted carboxamides and to a series

of tertiary anilines, which all ionized in concentrated acid.

On the basis of similarity in size and charge of the species

involved, they assumed that fBf =fBH+fo, so that equation

(11) reduces to

pKa = H log[B] (n-r )logaw (12).
a o [BH+]

It remains to be seen whether or not equation (12) is

generally applicable.

Prototropic Reactivity in Electronically Excited States

The study of the acid-base chemistry of electronically

excited aromatic acids and bases began formally in 1949,

when F6rster (13) elaborated upon Weber's earlier

observation (14) that the fluorescence spectrum of

l-naphthylamine-4-sulfonate exhibits pH dependence different

from the pH dependence of its absorption spectrum. Years

of subsequent research have shed much light on this subject.

Electronic excitation of an aromatic molecule results

in a change in electronic distribution in that molecule.

This difference in electronic distribution results in










differences between ground- and excited-state prototropic

reactivities. Those functional groups which have lone pairs

from which electronic charge is donated to the aromatic

system upon molecular excitation become more acidic in the

excited state. In the excited state, electronic charge is

delocalized from the functional group to the aromatic i

system, and hence the electrostatic attraction between the

functional group and the proton is lower in the excited

state than it is in the ground state. The proton may thus

be lost more easily in the excited state, and hence

pKa < pKa (where pKa is the negative logarithm of the

acid-dissociation equilibrium constant for the reaction as

it occurs in the excited state). Examples of excited-state

electronic charge donating groups include -OH, -0 -OH2,

-SH, -S-, -SH2, -NH2, -NH-, -NH+, and pyrrolic nitrogens.

Functional groups that have vacant low-lying i

orbitals can accept electronic charge upon molecular

excitation. These groups include -COOH, -COO -COOH2,

-CONH2, -CONH-, -CONH3, -COSH, -COS-, and -COSH2. In the

excited state, electronic charge is delocalized from the

aromatic ir system to the vacant orbital of the functional

group, and the resulting increase in electrostatic

attraction between the functional group and the proton

results in pKa > pKa. Pyridinic nitrogens are

excited-state electronic charge acceptors even though they

possess a lone pair but not any vacant low-lying i










orbitals. This is a consequence of the electronegativity

of the nitrogen being higher than that of the carbons to

which it is bonded, and in the excited state charge is

localized on the nitrogen. The lone pair projects out in

the plane of the ring and is perpendicular to the aromatic

T system. This perpendicularity prevents the lone pair from

interacting with the aromatic system.

It should be mentioned that excited-state proton

transfer can be either intramolecular or intermolecular.

Intramolecular excited-state proton transfer has been

reviewed (15), and this dissertation is concerned only

with intermolecular proton transfer. Furthermore, the

excited state of interest can be either an electronically

excited singlet or triplet state. The principles of

excited-triplet-state proton transfer are the same as those

for the singlet state (see references (16-26) for examples),

but the research under consideration deals only with proton

transfer in ground and excited singlet states.

The Effects of Protonation on Electronic Spectra

Protonation of a functional group which is intimately

coupled to an aromatic system may have a profound effect

upon the absorption and fluorescence spectra of that

molecule. This is a result of the electronic charge

stabilization incurred by the presence of the proton at the

functional group.










As we have seen, there is a greater degree of charge

localization at an excited-state charge accepting group in

the excited state than there is at that group in the ground

state. Consequently, there will be a greater amount of

electrostatic attraction between the proton and the

functional group in the excited-state molecule than in the

ground-state molecule. Protonation of the excited-state

group, therefore, stabilizes the excited state more than

protonation of the ground-state group stabilizes the ground

state. Since protonation stabilizes the excited state

relative to the ground state, the fluorescence and longest

wavelength absorption bands shift to longer wavelength

(redshift) when the ionizable group is protonated.

Excited-state electronic charge donating groups,

however, are possessed of a greater degree of charge

localization in the ground state than they are in the

excited state. Protonation of these groups, therefore,

stabilizes the ground state relative to the excited state,

and hence the fluorescence and longest wavelength absorption

bands will shift to shorter wavelength (blueshift) when the

functional group is protonated.

The F6rster Cycle

In 1950, F6rster (27) proposed that the energies of

the spectral shifts incurred by protonation of an aromatic

base could be quantitatively related to the difference









*
between pKa and pK This relationship has come to be

known as the F6rster cycle, a schematic diagram of which is

shown in Figure 1-1.

Since the energy terms in Figure 1-1 correspond to

thermodynamic state functions, it is correct to write

EA + AH* = EB + AH (13).
d +Hd
F5rster (27) assumed that the entropies of the ground- and

excited-state proton-transfer reactions are identical, in

which case equation (13) can be changed to
A B
AG AG = E E (14),
*
where AG and AG are the Gibbs free energies of

protonation in the ground and excited states, respectively.

Furthermore, E and E can be given by E = Nhc9v and

EB = Nhcv-, respectively, where N is Avagadro's number, h

is Planck's constant, c is the speed of light, and vA and

vB are, respectively, the frequencies (in wavenumbers) of
*
the A--A and B-B transitions. It is also true that

pKa=AG/2.303RT and pKa=AG /2.303 RT, where R is the universal

gas constant and T is the absolute temperature. Equation

(14) can then be transformed into

=* Nhc B) (15)
ApK = pKa pKa = 2.303RT(VA ) (15)

In principle, the F6rster cycle can be used only when

the 0-0 energies (vA and YB) are known. These energies

correspond to transitions between ground and excited states

which are both vibrationally relaxed and thermally




























Figure 1-1
*
The F6rster cycle. A, B, A and B refer to the conjugate
acid and base molecules in their ground and excited
states, respectively. EA and EB are the energies of the
*
A-A and B-B transitions, respectively. AHd and AHd are,
respectively, the enthalpies of protolytic dissociation in
the ground and excited states.
























S--EA -
EA


*
A


A v


AHd










equilibrated. While both fluorescence and absorption

originate from vibrationally relaxed and thermally

equilibrated electronic states, they frequently terminate

in Franck-Condon electronic states (28). Figure 1-1,

therefore, is not an accurate representation of the

transitions of interest. Figure 1-2 shows a modified

Forster cycle which includes Franck-Condon ground and

excited states. It can be seen from Figure 1-2 that

absorption may occur at higher energy than the 0-0 energy,

and fluorescence may occur at energy lower than the 0-0

energy. Both vA and V-B, therefore, may be estimated from

the fluorescence and longest wavelength absorption maxima

of the conjugate pair, but they will not necessarily

reflect the true 0-0 energies.

From Figure 1-2 we see that


EA AH + AH B = Es+AH- AH (16)
abs te d abs d te

and A AHA +AH = B B
f1 H + td +Ef1 AHd AHt (17).
fl te d fl d te

Still assuming that the entropies of protonation in the

ground and excited states are identical, equations (16) and

(17) may be transformed into equations (18) and (19),

respectively.
*
Nhc -abs abs AH HA (18) A
ApK = 2.303RT(vA -B te te


Nhc -fl -fl AB
A pK (v v )+ A AH (19)
2.303RT A B te te






















Figure 1-2
*
Modified F6rster cycle. A te, B te, Ate, and Bte refer to
the thermally equilibrated conjugate acid and base
molecules in their ground and excited states, respectively.
Afc, Bfc, Afc, and Bfc refer to the conjugate acid and base
in their Franck-Condon ground and excited states,
respectively. AHA and AH are the enthalpies of
equilibration from the Franck-Condon ground states to the
thermally equilibrated ground states of the conjugate acid
A* B*
and base, respectively. AHe and AHte are the enthalpies
of equilibrium from the Franck-Condon excited states to
the thermally equilibrated excited states of the conjugate
acid and base, respectively. EAbs, Ef1, Eabs and E f
refer to the energies of absorption and fluorescence of the
conjugate acid and base, respectively. AHd and AHd are,
respectively, the enthalpies of protolytic dissociation
in the ground and excited states.















*
AH B
te


Bte


AHd


AH
te


f
/


Ate
t--e


- -- -


A
Efl


Bf
Ell


Bfc-


Afc











A
abs














Ateo


I- fc


AHA
te


AHd
I------------------------ -


fc























EB
abs


J %Bte


AH B
te


Ir










Customarily, it is assumed that AHB = AHA and
te te
AHB = AHA ,so that equations (18) and (19) reduce to
te te

Nhc -abs -abs
ApK = (RTA VB ) (20)
2.303RT A B


and

Nhc -fl --fl (21)
ApK = (2.V303RT V ) (21)
2.303RT(A B

respectively. If pKa is known, and fluorescence or

longest wavelength absorption maxima are also known, and if

AHt = AH and AHA = AHe then one can estimate pK .
te te te te a
When the fluorescence spectrum (as a function of

energy) of a molecule is an approximate mirror image of its

longest wavelength absorption band, then the vibrational

spacings in the ground and excited states are roughly the

same (29). In this case the absorption and fluorescence

spectra will be equally displaced from the 0-0 energy. It

would then be reasonable to estimate VA and VB by
-abs -fl
A = A A (22)
A 2

and
-abs -f 1
S- B + B (23),
7B = 2

in which case

A EA + EA AH + AH
E = abs fl te te (24)
2


and











B EB + E H + H
EB = abs fl te te (25).
2

It may then be assumed that AHA = AHA and
te te
B* B
AH = AH This is at least safer than assuming that

AH = AH and AH = AHA because any difference
te te te te
between AH. and AHA will be cut in half in the
te te
B
denominator of equation (24) (the same is true of AH and
te
B
AHte in equation (25)). Thus, it is preferable to estimate

vA and vB from equations (22) and (23).
*
The accuracy of a pKa calculated with the F'rster

cycle is, of course, dependent upon to what extent the

assumptions inherent in the F6rster cycle are adhered to

and upon how accurately pKa, A. and -B are known (some of

the inaccuracy in the latter two arises from errors in

positioning the monochromators in the spectrophotometer

and fluorimeter). Many molecules have excited-state

geometries and solvation cages which are similar to their

ground-state geometries and solvation cages. Because of

this, it is reasonable to assume that the ground- and

excited-state entropies of protonation are similar, and

then the precision of a pKa calculated with the Forster

cycle can be as small as 0.2 (30). This error and the

error in vA and v give typical uncertainties of about
A\ B
*
0.3 in F6rster cycle pK 's (31). When the assumptions in

the Forster cycle are not correct, however, it is not










possible to determine how much uncertainty will be present
*
in a pK calculated with the F6rster cycle. These
a
assumptions have been reviewed in depth (17,26,30,32-39),

and any further elaboration upon them here would serve no

useful purpose.
*
The F6rster cycle has been used to calculate pK 's

more than any other method (15,17,26,40-44). These

calculations have been performed for excited-state

ionizations which occur in dilute, aqueous solution and also

for some which occur in concentrated acid. Unfortunately,

the F6rster cycle gives no information concerning the rates

of excited-state proton transfer. A method that could give

such information could be used to determine not only Ka'
*
but also ka and kb. The resulting value of pKa could be

compared to that calculated with the Forster cycle, and

hence the results of each method could be used to confirm

or challenge the results of the other. While fluorescence

spectroscopy which is time-resolved on the nanosecond and

picosecond time scale has been used to determine the rate

constants for some excited-state protonation and

deprotonation reactions, this technique requires

instrumentation that is both very sophisticated and very

expensive, and also requires the extensive use of computers

for the complicated data reduction that is necessary. We

shall restrict ourselves to a discussion of










steady-state kinetics. Representative examples of

time-resolved studies of excited-state proton-transfer

kinetics may be found in references (45-55).

Steady-State Kinetics of Excited-State Proton-
Transfer Reactions

The kinetic equations for excited-state proton-

transfer reactions in dilute, aqueous solution were first

derived by Weller (56). The excited-state reaction which

we are concerned with is

k k k'
+ a f f
BH+ BH+ a H + B B (26),
kd kb kd

where kf and k' are the rate constants for the fluorescences

of BH+* and B respectively, and kd and kd are the sums of

the rate constants for all nonradiative processes

deactivating BH+* and B respectively. The fluorescence
*
lifetime of the conjugate acid (present when pH << pKa) in

the absence of excited-state proton transfer is

To = 1/(kf + kd), and that of the conjugate base (present

when pH >> pKa) in the absence of excited-state proton

transfer is To =1/(k + kA). Prior to integration, the
+* *
rate expressions for the disappearance of BH and B from

the excited state may be put into the forms


-BH d[BH+] =-f](l/To+kb[H+])[B*]dt+fka[BH+*]dt (27)


and












-f Bd[B ] = f (1/To+kb [H])[B ]dt-f ka [BH +*]dt (28),

+*
where [B ] and [BH ] are, respectively, the probabilities
+
of finding a [B [or [BH molecule in the excited state at
+.* *
time t. Since the fluorescences of BH+* and B are being

excited and monitored under steady-state conditions, the

right sides of equations (27) and (28) are to be

integrated over all time (t = 0 to t = -). The lower

limits of integration of [BH +*] and [B*] are aBH+ and

a respectively, where cBH+ is the fraction of the

ground-state population which is found as the conjugate

acid and aB is the fraction found as the conjugate base.

In spectrophotometric terms,

EH+[BH ]
a + = BH (29)
BH H +[BH ] + B[B]

and

B [B]
a = B (30),
SBH+[BH ] + e[B]

where eB and BH+ are the molar absorptivities of the

conjugate base and acid, respectively, at the wavelength of

excitation. In terms of Kai


a BH+ = BH (31)
E B+[H+] + B K










and


Ba
a =a (32).
e E +(H ] + E Ka
EBH+[H ] Ba

If the rate of attainment of steady-state conditions for the

excited-state proton-transfer reaction is much higher than

the rates of photophysical deactivation of B and BH ,

then [B*1 = e-t/T' and [BH+*] = e-t/T (57). The

fluorescence lifetimes T and T' are the lifetimes of the

conjugate acid and base, respectively, in the presence of

excited-state proton transfer, where T = 1/(kf + kd + ka)

and T' = 1/(ki + kd + kb[ H+]). The expressions for [B*]

and [BH ] may be integrated from t = 0 to t = and

then


f'[B*]dt = fe t/dt = T' (33)
0 0

and


f [BH+*dt = fIe- t/dt = T (34).
o 0

The quantum yields of fluorescence of the conjugate acid in

the absence and presence of excited-state proton transfer

are, respectively, 4 = k T0 and = k T. The relative

quantum yield of fluorescence of the conjugate acid, p/ ,0

is thus related to T and T by

T = T (35).
o base may be used to

Analogous reasoning for the conjugate base may be used to









show that

T' = T' (36),

where (' and (' are the quantum yields of fluorescence of

the conjugate base in the absence and presence of

excited-state proton transfer, respectively, and 4'/4o is

the relative quantum yield of fluorescence of the conjugate

base. Combination of equation (33) with (35) and of

equation (34) with (36) shows that

fl[B*]dt = T' L (37)
o o 4

and

0 [BH+*]dt = T ---
0 0 0 (38).

Therefore, integration of equations (27) and (28) results in

a + =- + k T o- kb T[H+] (39)
BH 4 ao 4 bo o,
0 0 0

and

aB + k '[] kTO (40).
0o 0 00

Equations (39) and (40) can be solved simultaneously for

0/40 and ,'/4' to yield

a BH + + k b'[H H+1]
S BHbo(41)
ao 1 + kT + kb T'[H+
a o bo


and











aB + k T
B a = B ao (42).
1 i+ k T + k T' [H+]
o ao b ot

It is thus seen that
a + aBH+ = 1, equations (41) and (42) can be combined to

give

/o4 1 kbT' '/kT
0 + o O[H] H 0 (43).
S- B ao ao -

A plot of ()#/4 )/(4'/4) -a ) versus ([H] 4'/4')/(4o'/' -a )

should, therefore, be a straight line with an ordinate

intercept of 1/k T and a slope of kbTo/kaTo. When To and T'
ao b ao 0
can be measured or estimated, then ka, kb, and K = ka/kb

can be calculated.

Equation (43) was derived assuming that the excited-

state proton-transfer reaction attains steady-state
+*
conditions before photophysical deactivation of B or BH

can occur. When this is not true, then equation (43) will

not rigorously describe the chemistry of interest. A more

sophisticated treatment has been derived (58) which

accounts for situations where steady-state conditions are
*
not achieved before photophysical deactivation of B and

BH+* takes place. Use of that treatment will give more

accurate values of ka and kb when nonsteady-state

considerations are significant, but equation (43) will

suffice in many situations. It should be noted, however,

that the observable rate constants ka and kb are subject









to medium effects, and hence equation (43) will not be

applicable to an excited-state proton-transfer reaction which

occurs in concentrated acid, where the medium is

different from one part of the titration inflection region

to another. The hypothetical, medium-independent rate

constants for the reaction in concentrated acid are k a(0)

and kb(0), which correspond to the deprotonation and

protonation steps, respectively, for the reaction as it

would occur in infinitely dilute, aqueous solution. The

author's research represents the first attempt to

quantitate k a(0) and kb(0).

Summary

Proton transfer in both ground and excited states has

been thoroughly studied and quantitated for those acid-base

reactions which occur at or close to infinite dilution and

where 1 < pH < 13. However, up to the time when the

author began his research, no attempts had been made to

quantitate the kinetics and equilibria of excited-state

proton-transfer reactions in concentrated electrolytic media.

It was the goal of the author to develop a successful model

for these reactions in concentrated acidic media (pH < 1).

The author also wished to see if equation (12) has more

general application than it has had to date. Finally, the

author desired to see if there exists a fundamental

relationship between the thermodynamics and kinetics of







26

proton transfer in dilute, aqueous solution and the

thermodynamics and kinetics of proton transfer in

concentrated acid.














CHAPTER II
EXPERIMENTAL

Reagents and Chemicals

The water that was used was either deionized, distilled

water or doubly deionized water. Sulfuric acid, perchloric

acid, chloroform, methanol, ammonium hydroxide, sodium

hydroxide, sodium bromide, and potassium hydrogen phthalate

were all ACS reagent grade and were purchased from either

Fisher Scientific Company (Fair Lawn, NJ) or Scientific

Products (McGaw Park, IL). Ethanol was 95% and was

purchased locally from hospital stores (J. Hillis Miller

Health Center, Gainesville, FL). Thin-layer

chromatography plates were fluorescent-indicator

impregnated, 250 micron thick silica gel plates and were

purchased from Analabs (North Haven, CT). Dry silica gel

(100-200 mesh) for atmospheric pressure column

chromatography was purchased from Fisher Scientific

Company. All acid solutions were standardized against

standard NaOH (the NaOH was standardized against potassium

acid phthalate). All reagents were checked for spurious

absorption and emission prior to their being used for

spectroscopic studies.

All weighing were performed on a Mettler Type B6

electronic analytical balance.










Acridone (9-(10H)-acridanone) and 1-isoquinolone

(isocarbostyril) were purchased from Aldrich Chemical

Company (Milwaukee, WI). Both 2-quinolone and 4-quinolone

were purchased from K&K Labs (Plainview, NY). Xanthone

(xanthen-9-one) was purchased from Eastman Organic

Chemicals (Rochester, NY). The sample of 3-aminoacridine

that was used was synthesized and identified by L.S.

Rosenberg (59) after the method of Martin and Tong (60).

Acridone was recrystallized three times from

EtOH:H20 (1:1). Xanthone was purified with column

chromatography on silica gel using CHC13 as the mobile

phase. Purity was confirmed with TLCon silica gel using

CHC13 as the mobile phase and UV light from a handheld UV

lamp as the method of spot visualization (short wavelength

UV light excited the fluorescent indicator in the silica,

revealing both fluorescent and nonfluorescent spots, while

long wavelength UV light visualized only fluorescent spots).

Both 2-quinolone and 4-quinolone were recrystallized three

times from EtOH:H20 (1:3). Crystalline 1-isoquinolone was

used as received from Aldrich. Purity was confirmed by

TLC on silica gel using three different mobile phases (CHC13,

1:9 MeOH:CHCl3, and 1:4 MeOH:CHCl3). Impure

3-aminoacridine was purified with column chromatography on

silica gel. Pure 3-aminoacridine was gradient eluted with

MeOH:CHC13 (the composition of which varied from 1:19 to

2:3) as the mobile phase. Purity was confirmed with TLC









using MeOH:CHCl3 (1:19) as the mobile phase, which was

alkalinized by the addition of one drop of NH4OH. The

presence of isosbestic points in the absorption spectra of

these compounds further confirmed their purity.
-4
Stock solutions of the compounds were =10 M to

=10-2 M and were made up in either H20 or MeOH. The stock

solutions were accurately diluted (by a factor of 100) and

the absorbances of the resulting solutions measured at

appropriate analytical wavelengths. These absorbances were

used in conjunction with published molar absorptivities to

calculate the concentrations of the stock solutions. Molar

absorptivities of acridone, 2-quinolone, 4-quinolone, and

1-isoquinolone may be found in reference (61). The molar

absorptivity of 3-aminoacridine may be found in reference

(59). A carefully weighed sample of pure xanthone was

used to prepare the stock solution, and hence its

concentration was calculated.

Absorption and Fluorescence Studies

Absorption spectra were taken on either a Beckman

DB-GT, Beckman Model 25, or Varian Cary 219

spectrophotometer. The Cary 219 was equipped with a cell

compartment thermostatted at 25.00.2C. The cell

compartment in the DB-GT was thermostatted at 25.00.2 0C

when a constant temperature bath (Brinkmann Lauda K-2/R) was

available. The Model 25 had no provision for temperature

control. All spectra taken in instruments with







30

unthermostatted cell compartments were taken at room

temperature, which was found to be 2420C.

All fluorescence spectra were uncorrected for

instrumental response and were taken on a Perkin-Elmer

MPF-2A steady-state fluorescence spectrophotometer. This

fluorimeter was equipped with a thermostatted cell

compartment, which, when a constant temperature bath was

available, was kept thermostatted at 25.00.20C. When the

ground- and excited-state proton-transfer reactions

overlapped, fluorescence was excited at an isosbestic

point (at which eB = CBH+), and hence equations (31) and

(32) reduced to

+ = [H+] (44)
BH [H+] + K
a

and


a = a (45),
[H+] + K
a

respectively. The quantities c/po and #'/o' were

calculated in terms of fluorescence intensities. The

fluorescence intensity, F, at any point on the titration

inflection region is, for a given analytical wavelength,

given by


F=2.3qIoBH+[BH+]1 + 2.3pI 0 B[B]l +

2.3l'I e [B11 + 2.3 'I E BH+[BH +] (46),









where 1 is the optical depth of the sample and I is the
o
intensity of the exciting light. The first and second

terms on the right side of equation (46) correspond to the

fluorescence from directly excited conjugate acid and that

from the conjugate acid formed by excited-state protonation

of the conjugate base, respectively. The third and fourth

terms on the right side of equation (46) correspond to the

fluorescence from directly excited conjugate base and that

from the conjugate base formed by excited-state deprotonation

of the conjugate acid, respectively. When pH >> pKa and
*
pH >> pKa, then F = FB = 2.3'I eoBCBl, from which it is

seen that


2.3IoBE = (47),
o B

where CB = [B] + [BH+] and FB is the fluorescence intensity

of the isolated conjugate base. When pH << pKa and

pH << pK then F = FBH+ = 2.34 IeBH+CB 1, and then

F +
BH
2.31 E +1 = o GB (48),


where FBH+ is the fluorescence intensity of the isolated

conjugate acid. Combination of equations (47) and (48)

with (46) yields


([BH ] ^ [B] #' [B] '[BH ]
F = F + F [B] + F [B] + F (49)
B C BH+ C B='C Bo' C
0 B oB OB o B









When fluorescence is excited at an isosbestic point, then

equations (29) and (30) reduce to caBH+ = [BH+]/CB and

aB = [B]/CB respectively. Equation (49) then becomes


F = F + + FH +-a + F -T + F aBH+ (50).


Since aB + a BH+ = 1 and 0#/o + #'/' = 1, equation (50)

can be reduced to
F F
(51),
0 FBH+ FB

and it then follows that

._' FB+- F
F BH+- FB (52).
F BH+ F B

When the ground- and excited-state proton-transfer reactions

do not overlap, then aB-l and a BH+-0 or a B0 and a BH+l, and

in either case equations (51) and (52) still follow from (50).

Fluorescence lifetimes were measured at room

temperature with a TRW model 75A decay-time fluorimeter

without excitation or emission filters. This instrument

was equipped with a TRW model 31B nanosecond spectral

source and was used with an 18 watt deuterium lamp, which

was thyratron-pulsed at 5kHz. A TRW model 32A analog decay

computer was used to deconvolute the fluorescence decay time

of the analyte from the experimentally measured fluorescence

decay, which was actually an instrumentally distorted

convolution of the lamp pulse and the analyte fluorescence.

The TRW instruments were interfaced to a Tektronix model 556










dual-beam oscilloscope, on which the convoluted fluorescence

decay from the sample was displayed. Lifetimes >1.7 ns were

measurable with this apparatus.

Measurements of Acidity

All pH measurements were made at room temperature with

a Markson ElektroMark pH meter equipped with a silver/silver-

chloride combination glass electrode. The pH meter was

standardized against Fisher Scientific Company pH buffers

or Markson Scientific Inc. (Del Mar, CA) pH buffers at

room temperature. These buffers were accurate to 0.02

pH unit and were of pH 1.00, 4.00, 7.00, and 10.00. The

precision of the pH meter was estimated to be 0.01 pH

unit, and it was used for the measurement of pH > 1.

The Hammett acidity function was used as a measure of

the acidity of solutions in which pH < 1. This acidity

scale may be used to quantitate the acidity of media when

the species involved have neutral conjugate bases and

singly charged conjugate acids. Values of H in HC104 and

H2SO4 may be found in references (62-64). Values of a in

the same media may be found in references (65-69).

Titration Methods

Solutions for absorption and fluorescence studies were

put into UV-visible quartz cuvettes with pathlengths of

10 mm and volume capacities of =4 mls. Absorption spectra

were taken against a reference solution of composition










identical to that which the sample was put in (that is,

the reference solution was either water or acid).

Aliquots of stock solution (=200O1) were injected

into a series of 10 ml volumetric flasks and the flasks

filled to the lines with either water or acid (the stock

solution solvent was first evaporated under dry nitrogen

when the stock solution was methanolic) and the concentration

of acid corrected for any dilution. For titrations where

pH > 1, 2 mls of the aqueous solution were placed in the

sample cuvette, the spectrum recorded, and the pH

measured and recorded immediately after recording the

spectrum. An aliquot of an acidic solution of the analyte

was then added to the cuvette with a micropipette, the

spectrum recorded, and the pH again measured and recorded.

Very small changes in pH (=0.1 unit) were effected by

dipping the end of a heat-fused Pasteur pipette into an

acidic solution of the analyte and then into the aqueous

solution in the cuvette (submicroliter volumes of titrant

were added in this way). The formal concentration of the

analyte was, therefore, constant throughout the titration.

The pH was varied until no further significant changes in

the spectrum were observed.

For titrations where pH < 1, 2.000 mls of an acid

solution of the analyte were put into a cuvette. The

spectrum of the analyte and the molarity of the acid were

recorded. An accurately known volume of a solution of







35

the analyte in a solution of different acid concentration

was then added to the 2 mls of solution already in the

cuvette. The solution was then stirred with a fine glass

rod. The resulting acid concentration was calculated, and

then the spectrum of the analyte and the acid molarity

were recorded. The acid solutions which were mixed were

prepared so as to differ by two or fewer molar units in

order to minimize partial molar volume effects and

temperature changes due to heat of mixing and heat of

dilution. This procedure was repeated with different

initial and final concentrations of acid until no further

significant changes in the spectrum were observed.

Solutions for all titrations were prepared immediately prior

to their being used to minimize the possibility of

degradation of the test compound.

Analytical wavelengths were chosen to be at or as close

to a peak maximum as possible while still yielding the

greatest difference between the spectra of the conjugate

acid and base. This was done to maximize analytical

sensitivity, accuracy, and precision.

Computation

Routine calculations (and sometimes simple linear

regression analysis--see Appendix A) were performed on a

card-programmable calculator (Texas Instruments TI-59).

Complex calculations (simple and multiple linear regression

analyses--see Appendices A and B) were performed on either







36

an International Business Machines IBM 4341 or on a

Digital Equipment Corporation DEC VAX 11/780. All

computer programs were written in BASIC (beginners

all-purpose symbolic instruction code) by the author. The

BASIC language on the IBM 4341 was used through MUSIC

(McGill University system for interactive computing), while

BASIC on the VAX 11/780 was used through DEC VMS (DEC

virtual memory system).














CHAPTER III
GROUND- AND EXCITED-STATE PROTON-TRANSFER
IN ACRIDONE AND XANTHONE

Introduction

The titration behavior of molecules which become much

more basic (or much less acidic) in the excited state than

they are in the ground state will be described by a

simplified form of equation (43). Since pKa >> pK, aB -l,

and then equation (43) can be reduced and rearranged (70) to



-= k[H '] (53).
='/4' 1 + kaTO (53).

Even if T and T' are known, there is no linear form
0 o
equation (53) can be put into such that ka, kb, and Ka can

be extracted from the data of a single fluorimetric

titration. A method (71-73) of titration involving the use

of HC1 has been developed which, in favorable

circumstances, does permit the used of a linear plot to

extract ka and kb from a single titration. In this

method, the fluorescence of the conjugate acid is quenched

by Cl while the proton transfer is effected by H where

both the Cl- and H+ come from the HC1. However, this

method is limited in its application to those molecules

which ionize at pH such that the rate of proton transfer is

approximately the same as the rate of quenching of the









conjugate acid fluorescence. Furthermore, #/o and #'/c '

must be calculated independently of each other, and hence

the fluorescence spectra of the conjugate acid and base

must be well resolved from each other. These conditions

must all be met before the HC1 method can be used. It was

desirable, therefore, to devise a more generally applicable

method of determine ka and kb-

It can be seen from equation (53) that the slope, m,

of a plot of (#/4 )/(0'/10) versus [H ] will be



m = 1 + kT(54),
ao

which can be rearranged to

T' 1 k
+ a (55).
m k kb 0o

If a quencher can be added to the titration medium that

will quench the fluorescence of the conjugate acid so that

(1 + ka T o) will vary with quencher concentration relative to

kb To' then m will be a function of quencher concentration.

A series of titrations, each with a different constant

concentration of quencher in the titration medium, should

then yield a different value of m and T for each

titration (if the fluorescence of the conjugate base is also

quenched, then different values of To will also be obtained).

According to equation (55), a plot of T'/m versus T should
00









be a straight line with an ordinate intercept of 1/kb and

a slope of ka/kb. Values of ka, kb, and Ka could thus be

derived from the series of titrations of the molecule of

interest.

Acridone (Figure 3-1) is a molecule in which

pKa >>pKa (31,74), and hence its fluorimetric titration

behavior should be described by equation (53).

Furthermore, since the ground-state ionization occurs in

relatively dilute solution (pKa = -0.32) (75), the media

in which the ground- and excited-state ionizations occur

are not appreciably different. Since the assumptions

inherent in the Forster cycle are normally correct for

ionizations which occur in dilute, aqueous solution, the
*
pKa of acridone calculated according to equation (55)

should agree with the value of its pKa calculated with the

F6rster cycle. Such a comparison could be used to

determine whether or not equation (55) correctly describes

the excited-state chemistry of interest. If it does, then

equation (55) could be used with confidence to determine the

pKa of a molecule in which the ground-state ionization

occurs in concentrated acid. The Fbrster cycle could then

be used to see if the excited-state ionization (which

occurs in dilute, aqueous solution) can be related to the

ground-state ionization (which occurs in concentrated acid).
















0





I
H

Figure 3-1
Structure of acridone.










Results and Discussion

The fluorescence lifetimes of neutral and protonated

acridone are presented as a function of the molarity of

Br (derived from NaBr) in Table 3-1. Since T varies

with [Br ] but TO is invariant, equation (55) should be

applicable to the titration data. Figure 3-2 shows a

quenching curve for protonated acridone (this was used in

the calculation of T in the presence of quencher--see note

b of Table 3-1 for details). Figure 3-3 shows fluorimetric

titration curves for acridone in the presence of different

concentrations of Br It is of interest to note that the

titration curve shifts to higher pH as T decreases. This

occurs because the rate of the dissociation reaction

decreases when T decreases. This shift to higher pH is

predicted by equation (53), which shows that [H ] at the

inflection point (the pH where /-o = V'/o = 0.5) will

decrease when m increases (values of m as a function of

[Br-] are also shown in Table 3-1). Figure 3-4 shows a

plot of T-/m versus T for acridone. As predicted by

equation (55), the plot is linear. Values of ka, kb and

pKa calculated from the slope and intercept of the line in

Figure 3-4 are presented in Table 3-2 along with pK a(F.C.)

calculated from the F6rster cycle (31). It can be seen

from equation (55) that, for any two different pairs of

values of m, T', and T ,









Table 3-1

Variation with bromide ion concentration of T', T and
m for acridone. o o


[Br] M


To, ns
o0


T ns


0 14.80.5 26.00.4 131c
5.0 X 10-3 14.80.5 18.7 338
1.0 x 10~o 14.80.5 15.6 403
3.0 X 10 14.80.5 9.7 593
5.0 X 10 14.80.5 6.7 715
1.0 X 10 1 14.80.5 3.7 1049
4.0 X 10 14.80.5 0.59 1696
5.0 X 10 14.80.5 0.45 1759


aThe lifetime
at pH = 7.0.


of neutral acridone was measured in water


bThe lifetime of protonated acridone was calculated as

To = ( o/co) X Ta, where /Po is the relative quantum
yield of fluorescence at the bromide ion concentration
of interest (values of and Ta is the fluorescence lifetime of protonated
acridone in the absence of quencher (measured in 2.3
M HC104, Ho = -1.0).


cTaken from reference (31).




















Figure 3-2

Variation with bromide ion concentration of the relative quantum yield of
fluorescence (W/< ) of 5 X 10-6 M protonated acridone. Analytical
wavelength = 456 nm. Excitation wavelength = 350 nm.








1.0


0.8





0.6





0.4





0.2 _





0.0 ( I I I
0.0 0.1 0.2 0.3 0.4 0.5
Bromide ion concentration, M

















Figure 3-3

Variation of the relative quantum yield of fluorescence (<'/4') of 5 X 10-6 M
neutral acridone with pH at various bromide ion concentrations. (A) [Br-] = 0,
(B) [Br-] = 5.0 X 10-3 M, (C) [Br-] = 5.0 X 10-2 M, (D) [Br-] = 1.0 X 10-1 M,
-1
(E) [Br-] = 5.0 X 10- M. Analytical wavelength = 440 nm. Excitation
wavelength = 350 nm.












0.8


B

0.6. C
D
/40
E
0.4




0.2.




4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.50.
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5


0.0































Figure 3-4

Plot of T'/m versus T for acridone.
0 0


































0
x 20



-0
E-*


0 5 10 15 20 25
T x 109, s
o









Table 3-2


Rate constants and pKa for the excited-state proton
transfer between neutral and protonated acridone.


ka, s
al


kb, M-s1


*
pK


2.7 X 108a 1.4 X 1010a 1.71a

2.90.3 X 108b 1.50.1 X 1010b 1.710.04b

1.60.3c

aDetermined graphically from Figure 3-3.

bCalculated from the data in Table 3-1.

c *
pK (F.C.), taken from the F6rster cycle calculation in
reference (31).












1 o k
= T (56)
kb m1 kb 01

and
1 'r
1 0o2 k
2_ a
-=- T (57)
kb m2 kb 02

Equations (56) and (57) may be combined to yield

k /k= (T/m1 T2/m2) ) (58),
a/b 0(1 0 2 2 0 1 0 2

so that only two titrations are needed to estimate K a. This

value of Ka can then be used in conjunction with equation

(55) to determine kb, and then ka can be calculated.

Values of ka, kb, and pKa calculated in this way are also

presented in Table 3-2. The excellent agreement between
*
pKa and pKa(F.C.) suggests that equations (55-58) may be
*
used with confidence to determine pKa when the excited-

state reaction occurs according to mechanism (26) and

when pKa >> pKa-

Xanthone (Figure 3-5) has a ground-state ionization in

concentrated acid (76,77) and an excited-state ionization

in dilute, aqueous solution (76,77). While pKa has been

estimated using the Hammett acidity function without

including a (76), it has not been seen whether equation

(12) is applicable or not. Furthermore, pKa has been






















0









Figure 3-5

Structure of xanthone.









estimated (76), but it was assumed that pKa = pH at the

inflection point. Equation (53) shows that this

assumption is incorrect.

In terms of absorbances, equation (12) is


pK = HO log A AH (n-r )log a (59),
a o AB A g w

where A is the absorbance anywhere on the inflection region

of the titration, and ABH+ and AB are, respectively, the

absorbances of the isolated conjugate acid and base at the

analytical wavelength of interest. Equation (59) may be

put into antilogarithmic form and rearranged to


KAB KA
A = H+ + h n-rg (60),
BH an-r han-r


from which it is seen that a multiple linear regression (see

Appendix B) may be used to fit for ABH+, KaAB, and Ka, and

then AB may also be calculated. A computer program to

perform this type of fit was written by the author. The

program was constructed to vary integral values of (n-r )

until a good fit was obtained. The fit was judged to be

good when the fitted ABH+ and AB agreed with the

measured ABH+ and AB and when the coefficient of multiple

determination approximated unity. Figure 3-6 shows a

spectrophotometric titration curve of xanthone. The

titration was fitted using equation (60), and the best fit

was obtained with (n-r ) = 0, which yielded pKa = -4.170.03.
ga





















Figure 3-6

Plot of absorbance versus H for 6.5 X 106 M xanthone in H 2SO4.
Analytical wavelength = 329 nm.










0.12





0.10


0.08


0.06 -





0.04 *




0.02 II---
-7 -6 -5 ,, -4 -3 -2 -1







55

This value of pKa agrees with the value of pK = -4.1

published in reference (76). When (n-r ) = 0, the fit

amounts to fitting the data with the Hammett acidity

function without including a because then a n-rg = 1.
w w
It is not surprising, therefore, that the pKa determined

in this work agrees with that already published. This does

not say that the data should not be fitted with equation

(60): it only means that, in this case, n = r .

Figure 3-7 shows the variation of T and T' with

[Br ]. Since T significantly varies while T' remains

constant, the titration behavior of xanthone should be

similar to that of acridone. Figure 3-8 shows that this is

the case, for the titration curve of xanthone shifts to

higher pH with increasing Br- concentration. Table 3-3

presents m (as well as T and T') for xanthone as a

function of [Br-], and Figure 3-9 shows a plot of T'/m

versus T for xanthone. Once again, the plot is linear,

which indicates that equation (55) is being obeyed. It is

possible, therefore, that equation (55) will find general

application to molecules of the type under consideration.

This method is limited to molecules where T can be varied,

but no limitations concerning pH or spectral overlap are

apparent at this time.

Table 3-4 presents the absorption and fluorescence

maxima of neutral and protonated xanthone. The value of

pK (F.C.) calculated with the value of pKa = -4.17 is
a a



























Figure 3-7

Plot of the fluorescence lifetime of 2 X 10-6 M xanthone
versus bromide ion concentration. (A) To (protonated
xanthone), (B) T' (neutral xanthone).
o





























































0.02


0.03


0.04


Bromide ion concentration, M


25







20







15
44






10


0.00


0.01


0.05


















Figure 3-8

Variation of the relative quantum yield of fluorescence (#'/p') of 2 X 10-6
neutral xanthone with H at various bromide ion concentrations. (A) [Br-] = 0,
-3 -3 2
(B) [Br ] = 2.5 X 10 M, (C) [Br-] = 5.0 X 10-3 M, (D) [Br-] = 1.0 X 10-2 M,
-2
(E) [Br-] = 2.5 X 10-2 M. The molecule was titrated with H 2SO. Analytical
wavelength = 358 nm. Excitation wavelength = 326 nm.













0.8 ,





0.6 .





0.4





0.2




0.0 -
-1.0


1.0


0.0 0.5 1.0 1.5 2.0 2.5


-0.50









Table 3-3


Variation with bromide ion
for xanthone.


[Br-], M


a


concentration of T T and m


T ns
o


0 3.40.1 31.80.8 5.30.2
2.5 X 10 3.4c 23.3 6.50.1
-3c
5.0 X 102 3.40.1 18.20.4 7.40.1
1.0 X 10 2 3.40.2 11.80.3 9.690.08
2.5 X 10- 3.50.2 6.50.4 12.80.1


aDetermined


in water, pH = 5.5.


bDetermined in 4.0 M H2SO4, H = -1.7.


CEstimated from Figure 3-7.




















Figure 3-9

Plot of T'/m versus T for xanthone.
O0





















U)


0
H
0





-o
H-


0 5 10 15 20 25 30

T X 109, s
o








63

Table 3-4

Fluorescence (f) and longest wavelength absorption (va)
maxima of neutral and protonated xanthone.


xanthone species


7- -
Va, cm
a


Vf, cm-


neutral 2.91 X 104 2.60 X 104
cation 2.57 X 10- 2.25 X 10







64
presented in Table 3-5 along with ka, kb, and pKa

estimated graphically from Figure 3-9. This value of pKa

does not agree with pKa(F.C.). It was observed that the

absorption spectrum of isolated neutral xanthone shifts to

shorter wavelength (by =3 nm) as the medium (H2SO4) was

changed to more dilute H2SO4. This solvent effect on the

spectrum of neutral xanthone introduces significant error

into the estimation of its 0-0 energy, and hence pKa(F.C.)

will also be inaccurate. It thus seems likely that a
*
substantial amount of the discrepancy between pKa and

pK a(F.C.) in Table 3-5 is due to the solvent-effect-

induced failure of the F6rster cycle. The nature of the

solvent effect is not known. Since the activity of water in

the sulfuric acid in which the solvent effect occurs

deviates significantly from unity (65,66), it is possible

that the state of hydration of neutral xanthone changes

when the medium changes. If a hydration change of this

type affects the absorption spectrum, then this explains

the solvent effect. If the hydration change is occurring

but does not affect the spectrum, then the solvent effect

remains unexplained. To date, no experiment has been done

which could confirm or disprove the change-in-hydration

hypothesis.

It is not possible, therefore, at least in the case of

xanthone, to use the Fbrster cycle to relate the

thermodynamics of proton transfer in dilute, aqueous solution









Table 3-5

Ground-state acid-dissociation constant of protonated
xanthone and rate constants and pKa for the excited-state
proton transfer between neutral and protonated xanthone.

pK k s-I k, M-1 s pKa


-4.170.03a 8.30.6 X 107b 5.60.3 X 109b 1.830.22b
3.20.3


aDetermined spectrophotometrically in this work with
(n r ) = 0.

bDetermined graphically from Figure 3-9.

c *
pK (F.C.), estimated from the F6rster cycle.
a










to the thermodynamics of proton transfer in concentrated

acid. If this is a consequence of changes in hydration of

a given reactant, then the standard state of that reactant

is different in the ground- and excited-state reactions.

If this is the case, then it may not even be

thermodynamically correct to predict the value of pKa (or

pKa, if the F6rster cycle is used in reverse) in one

medium based upon measurements in another. However, it will

be seen from other data presented in this dissertation

that the F6rster cycle is generally quite successful in

predicting pKa, even when the ground- and excited-state

ionizations occur in media of substantially different

acid composition. The behavior of xanthone does, however,

suggest that the prediction of the behavior of a molecule

in one medium based upon measurements in a different

medium should be done only with caution.














CHAPTER IV
EXCITED-STATE PROTON TRANSFER IN
2-QUINOLONE AND 4-QUINOLONE

Introduction

Some molecules become so acidic in their excited states

that their excited-state ionizations occur in concentrated

acid. As has already been seen in Chapter I, equation (43)

will not correctly describe the excited-state proton-

transfer reactions of these molecules because ka and kb are

usually medium-dependent. Therefore, equation (43) must be

modified to include the medium-independent rate constants

ka (0) and kb(0) before the kinetics of excited-state

proton transfer in concentrated acid can be quantitated.

The mechanism of the excited-state proton transfer of

interest can be written as


BH+*(H20)x + rH204 X X -+-B (H20) + H (H2O)z (61),

where x, y, and z are the numbers of water molecules

hydrating BH +*, B and H +, respectively, and X4 is the

transition-state species common to both the protonation and

deprotonation reactions. The coefficient r is the number of

water molecules which react with hydrated BH+* to form X+.

By mass balance it is seen that r = y + z x, and it is

assumed that x, y, z, and r remain constant over the

inflection region of a given titration. It is then simpler









to write equation (61) as

BH+* + rH20 X--- -* + H (62).

If X4 is the transition-state subspecies formed by the

combination of BH with r water molecules and Xb is the
b
transition-state subspecies formed by the combination of B

and H then the equilibrium constants for the formation of

X4 and X are, respectively, defined as


Ka +* (63)
a [BH+]f a r

and

[X If
Kb a x (64),
[B ]foa H+

where [X4], [BH+*], [Xb], and [B*] are the equilibrium

concentrations of X ,BH X, and B respectively. The

activity coefficients f+ and f0 correspond to BH+* and B ,

respectively. It is assumed that the activity coefficients

of X4 and X are identical. These coefficients are both

designated as f The rate of production of BH *, rb, and

the rate of production of B ra are given by

+*
rb = k[X] kBH+*] [BH ] (65)
a To

and


r = kt(X] kb[H+]B* (66),
To










where kt is the rate constant for the dissociation of XT in

the direction of the conjugate base and kt is the rate

constant for the rearrangment of X in the direction of the

conjugate acid. Equation (64) may be combined with (65) to

yield


rb = -Kb*] aH+ ka[BH+] [BH+*] (67),
x 0
which becomes

r = k(0)[B a+ k [BH+*] [BH ] (68).
x o
Equations (63) and (66) may be combined to give

f + r + [B*]
ra = k K [BH*]aw kb[H][B] (69),
x o
which becomes

r f + r + [B]
ra = ka(0) [BH *]aw- kb[H] [B ] (70).
x o
It is seen from reaction (26) that ra and rb may also be

given by

ra = ka [BH] kb[H+][B* [B (71)
To

and


rb = kb[H+][B ] ka[BH*] BH+*] (72).

Combination of equation (70) with (71) yields


k+ r a (73),
a a= f w
x









while combination of equations (68) and (72) gives

f
kb = kb(0)a H+f (74).
x

Equation (8) may be combined with equation (74) to yield

fif
kb = kb(O)hoaw fr (75).
x o

The medium-dependent rate constants ka and kb are thus

related to the medium-independent rate constants ka (0) and

kb(0) by equations (73) and (75), respectively.

Substitution of these equations into equation (43) results

in

/o r 1 k (0)T' ON'/o f'f
a, + b h(O)ha n fB (76).
No Bw k (0)T + k (0) o W B f
a of- a o x w o
x

The activity coefficients f+, f+, and f all correspond to

singly charged species of similar size while f and f'
o
correspond to uncharged species of similar size. These

similarities in size and identities in charge make it

reasonable to assume that f /fx = ff /f+ f = 1, in which

case equation (76) becomes


V/oo r 1 k (0)Tr' '/n
o r _aw =_____ + -h a (77),
'/o w k (0)T k (0)T o w ,/#o-aB
a o a o 0









which should correctly describe the excited-state proton-

transfer kinetics of reactions which occur in

concentrated acid. A plot of ((q/p )/(40'/o'-a))aw r

versus h a ( )/('/-B) should be a straight line

with an ordinate intercept of 1/ka(0)T0 and a slope of

kb(O)To/k a(0)To

Several molecules (78) which have excited ionizations

which occur in acid such that the inflection points are

found at pH < 1 are 2-quinolone (Figure 4-1) and

4-quinolone (Figure 4-2). It is of interest to see

whether or not these ionizations are described by

equation (77).

Results and Discussion

The absorption and fluorescence maxima of neutral and

protonated 2-quinolone, as well as their fluorescence

lifetimes, are presented in Table 4-1. The

spectrophotometric titration of 2-quinolone is shown in

Figure 4-3. These titration data were best fitted

according to equation (60) with (n-r ) = 4, which yielded

pKa = -0.300.03.

Figure 4-4 shows the fluorimetric titration curve of

2-quinolone. Figures 4-5 and 4-6 show plots of

((4 )/('/-aB))awr versus ho awn( '/)/(0'/ -aB) for
2-quinolone with various values of r and n = 3 (Figure 4-5)

or n = 4 (Figure 4-6). Values of ('/go for both 2-quinolone

and 4-quinolone were calculated according to the























N 0
1
H

Figure 4-1


Structure of 2-quinolone.




















0




1N

H

Figure 4-2
Structure of 4-quinolone.










Table 4-1

Fluorescence ( f) and longest wavelength absorption (v )
maxima and fluorescence lifetimes of neutral and
protonated 2-quinolone.


2-quinolone
species


Scm-1
v cm
a


Vf, cm


fluorescence
lifetime, ns


neutral 3.12 X 104 2.72 X 104 2.110.2a
cation 3.33 X 10 2.65 X 10 10.40.5b


a'I, measured in water, pH = 2.0.

T measured in 7.5 M H2SO4, H = -4.0.
o 2~ 4 ox























Figure 4-3
-4
Plot of absorbance versus H for 1 X 10 M 2-quinolone in H2SO4. Analytical
wavelength = 269 nm.








0.8




0.7


0.6



0.5


0.4 1




0.3 I I I I I
0.3
-4 -3 -2 -1 0 1 2 3


























Figure


Plot


of the relative


of 3 X 10-5
of 3 X 10


quantum


protonated


yield


2-quinolone


of fluorescence


in HC1O4


versu!


(s/o)
0


Analytical
280 nm (is


wavelength


osbestic


= 370 nm.


Excitation wavelength =


point).


4-4


















1.0


0.9


0.8


0.7


0.6


0.5



0.4


0.3


0.2



0.1



-5


-4 -3 -2 -1 0 1





















Figure 4-5

Plot of ((/4o)/( '/-B))awr versus hoa n'/)/('/-B) for 2-quinolone with
n = 3. (A) r = 1, (B) r = 2, (C) r = 3, (D) r = 4, (E) r = 5.



















_ _o r
0 B


10 20 30 40 50 60 70


ha 3 v'/
h w a '/'-a




















Figure 4-6

Plot of ((M/4 )/(4'/'o-a ))a r versus h 'a / '/-B) for 2-quinolone with
n = 4. (A) r = 1, (B) r = 2, (C) r = 3, (D) r = 4, (E) r = 5, (F) r = 6.

















0
oBo
'/~o-B w


5 10 15 20 25 30


h a 4"'
0 w (('/ )'-aB


35 40









relationship ='/po = 1 /co because the fluorescence

spectra of the protonated species overlap and eclipse those

of the neutral species. It can be seen that most

combinations of n and r result in curved plots. The best

fit to a straight line (chosen on the basis of the highest

linear least-squares correlation coefficient--see Appendix

A) was obtained with n = 3 and r = 4 (plot D in Figure 4-5).

The linearity of plot D in Figure 4-5 suggests several

things. In the first place, the titration data of

2-quinolone in concentrated acid are fitted well with equation

(77), which suggests that the model is valid. Secondly,

the assumption that f+/fx = o/f x = 1 is probably a

good assumption. Thirdly, the value of n in reaction (7)

for this region of acidity is n = 3 and the value of r in

reaction (62) is r = 4 for 2-quinolone. These observations

are consistent with the values of n = 3 and n = 4 proposed

by Teng and Lenzi (79) and by Bascombe and Bell (80) for

solutions in which Ho > -3.5. Values of ka(0), kb(0), and

pKa(0) = -log(ka (0)/kb(0)) are presented in Table 4-2,

along with pKa(F.C.) and pKa-

The fluorescence lifetimes and spectral maxima of

neutral and protonated 4-quinolone are presented in Table

4-3. The fluorescence lifetime, T', of neutral 4-quinolone

was estimated with the Strickler-Berg equation (81). The

ratio of the radiative lifetimes of protonated and neutral

4-quinolone (estimated with the Strickler-Berg equation),







84

Table 4-2

Ground-state acid-dissociation constant of protonated
*
2-quinolone and rate constants and pKa for the excited-
state proton transfer between neutral and protonated
2-quinolone.
M-1-1 *
pKa k (0), s-1 k (0), M s pKa
a a b a


-0.300.03a 41 X 10 1.00.3 X 10 -1.580.06
-1.80.3d


aDetermined spectrophotometrically in this work with
(n r ) = 4.

bDetermined graphically from Figure 4-5 with n = 3 and
r = 4.

CpK(0), determined graphically from Figure 4-5 with
n = 3 and r = 4.

d *
pK (F.C.), estimated with the F6rster cycle.
a










Table 4-3

Fluorescence (vf) and longest wavelength absorption (va)
maxima and fluorescence lifetimes of neutral and
protonated 4-quinolone.


4-quinolone
species


- -1
va cm
a


Vf, cm1


fluorescence
lifetime, ns


neutral 3.04 X 104 2.98 X 104 0.790.04a
cation 3.32 X 104 2.76 X 104 21lb


aTo, estimated with the Strickler-Berg equation.
b
T measured in 5.9 M HClO4, HO = -2.8.










the ratio of their quantum yields, and the measured value of

T were used in this calculation. The absorption and

fluorescence spectra of 4-quinolone exhibit a fairly good

mirror-image relationship and a small Stokes shift; hence,

the value of T' estimated with the Strickler-Berg

equation is reasonably accurate (82-84).

Figure 4-7 shows the spectrophotometric titration of

4-quinolone. This ground-state ionization occurs in dilute,

aqueous solution, and hence the titration data were fitted

using equation (60) with a = 1, in which equation (60)

reduces to an antilogarithmic form of the Henderson-

Hasselbach equation. This analysis yielded pKa = 2.220.01.

The fluorimetric titration curve of 4-quinolone is

shown in Figure 4-8. The small step in the titration curve

at pH = 2 is probably the result of a vanishingly small rate

of protonation of the excited neutral molecule at that

pH and higher pH (56). The titration data of 4-quinolone

plotted according to equation (77) are shown for n = 3 in

Figure 4-9 and n = 4 in Figure 4-10, with r taking various

values in each figure. The activity of water

significantly deviates from unity only in the most acidic

portion of the fluorimetric titration of 4-quinolone, and

hence it is expected that the inclusion of a in the kinetic

treatment will not make as dramatic a difference as it did

with 2-quinolone. This is the case; indeed, plots B

(n = 4, r = 3) and C (n = 4, r = 4) in Figure 4-10 are






























Figure 4-7
-4
Plot of absorbance versus pH for 1 X 10 M 4-quinolone in
water. Analytical wavelength = 327 nm.






















































0 1 2 3 4 5


0.8



0.7



0.6




0.5


0.4



0.3




0.2


0.1


0.0


























Figure 4-8

Plot of the relative quantum yield of fluorescence (#/o )
-5
of 3 X 10- M protonated 4-quinolone versus H The
molecule was titrated with HC1O4. Analytical wavelength =
360 nm. Excitation wavelength = 302 nm (isosbestic point).


















1.0


0.9


0.8


0.7


0.6

0
V/o

0.5


0.4



0.3


0.2


0.1


0.0,


























Figure 4-9

Plot of ((/4 o)/(#'/'-a ) )) ar versus
h a w('/ N)/(o'/'-a ) for 4-quinolone with n = 3.
(A) r = 1, (B) r = 2, (C) r = 3, (D) r = 4, (E) r = 5.






















































0.5 1.0 1.5 2.0 2.5


hoaw '/o-aB


7




6




5



4



0K13




2



1


0.0


3.0
























Figure 4-10

Plot of ((/)/('/Io-B))aw r versus
h a w( n'/c )/(O'/)'-ac) for 4-quinolone with n = 4.
(A) r = 2, (B) r = 3, (C) r = 4, (D) r = 5, (E) r = 6.




Full Text
Absorbance


Absorbance
o
O
O
O
o
o
o







N3
u>
JS-
U1
O'!
1
00
frOT


Figure 5-4
Plot of ( (4/0) / ( ) awr versus hQawn ('/4>) / (<> '/4>-aB) for
1-isoquinolone with n = 2 and r = 2.


11
k
between pK and pK This relationship has come to be
known as the Forster cycle, a schematic diagram of which is
shown in Figure 1-1.
Since the energy terms in Figure 1-1 correspond to
thermodynamic state functions, it is correct to write
EA + AH* = EB + AHd (13) .
Forster (27) assumed that the entropies of the ground- and
excited-state proton-transfer reactions are identical, in
which case equation (13) can be changed to
AG AG* = EA EB (14) ,
k
where AG and AG are the Gibbs free energies of
protonation in the ground and excited states, respectively.
A n
Furthermore, E and E can be given by E = Nhcv^ and
D
E = Nhcv_,, respectively, where N is Avagadro' s number, h
is Planck's constant, c is the speed of light, and vA and
v_ are, respectively, the frequencies (in wavenumbers) of
B
*
the A->-A and B-HB transitions. It is also true that
k k
pK =AG/2.303RT and pK =AG /2.303 RT, where R is the universal
a a
gas constant and T is the absolute temperature. Equation
(14) can then be transformed into
k Mil C
ApK = pKa pKa = 2.303RT(VA VB) (15)*
In principle, the Forster cycle can be used only when
the 0-0 energies (v,. and v_) are known. These energies
correspond to transitions between ground and excited states
which are both vibrationally relaxed and thermally


144
18.Jackson, G., and Porter, G., Proc. Roy. Soc. London A,
260 (1961), 13.
19. Grabowska, A., and Pakula, B., Chem. Phys. Letts., 1
(1967),369.
20. Bulska, H., Chodkowska, A., Grabowska, A., and Pakula,
B., J. Lumin., 10 (1975), 39.
21. Herbich, J., and Grabowska, A., Chem. Phys. Letts.,
46 (1977), 372.
22. Bulska, H., and Kotlicka, J., Pol. J. Chem., 53
(1979), 2103.
23. Paul, W.L., Kovi, P.J., and Schulman, S.G., Spec.
Letts., 6 (1973), 1.
24. Capellos, G., and Porter, G., J. Chem. Soc. Faraday
Trans. II, 70 (1974), 1159.
25. Peterson, S.H., and Demas, J.N., J. Am. Chem. Soc., 101
(1979), 6571.
26. Ireland, J.F., and Wyatt, P.A.H., Adv. Phys. Org. Chem.,
12 (1976), 131.
27. Forster, T., Z. Phys. Chem. Frankfurt am Main, 54
(1950), 42.
28. Lippert, E., Accts. Chem. Res., 3^ (1970), 74.
29. Levschin, W.L., Z. Phys., 43 (1927), 230.
30. Schulman, S.G., and Capomacchia, A.C., Spetrochim.
Acta, 28A (1972), 1.
31.Schulman, S.G., and Underberg, W.J.M., Anal. Chim.
Acta, 107 (1979), 411.
32. Schulman, S.G., in Modern Fluorescence Spectroscopy,
v. 2, ed. E.L. Wehry, New York, Plenum, 1976,
chapter 6.
33. Grabowski, Z.R., and Grabowska, A., Z. Phys. Chem. N. F.,
101 (1976), 197.
Rosenberg, J.L., and Brinn, I., J. Phys. Chem., 76
(1972), 3558.
34.


52
estimated (76) but it was assumed that pK^ = pH at the
inflection point. Equation (53) shows that this
assumption is incorrect.
In terms of absorbances, equation (12) is
A ~ A3H+
pKa = Ho lo9 Ag A where A is the absorbance anywhere on the inflection region
of the titration, and Ag^+ and Ag are, respectively, the
absorbances of the isolated conjugate acid and base at the
analytical wavelength of interest. Equation (59) may be
put into antilogarithmic form and rearranged to
A =
+ +
K A
a
- n-r,,
ha 9
o w
, n-r,,
ha 9
o w
(60) ,
from which it is seen that a multiple linear regression (see
Appendix B) may be used to fit for AgH+, KaAg / and K^, and
then Ag may also be calculated. A computer program to
perform this type of fit was written by the author. The
program was constructed to vary integral values of (n-r )
g
until a good fit was obtained. The fit was judged to be
good when the fitted Ag^t and Ag agreed with the
measured AgH+ and Ag and when the coefficient of multiple
determination approximated unity. Figure 3-6 shows a
spectrophotcmetric titration curve of xanthone. The
titration was fitted using equation (60), and the best fit
was obtained with (n-r^) = 0, which yielded pK^
-4.170.03.


55
This value of pK agrees with the value of pK = -4.1
cl 3
published in reference (76). When (n-r ) =0, the fit
amounts to fitting the data with the Hammett acidity
function without including a because then a n r It is not surprising, therefore, that the pK determined
in this work agrees with that already published. This does
not say that the data should not be fitted with equation
(60) : it only means that, in this case, n = r .
Figure 3-7 shows the variation of x and x' with
o o
[Br ]. Since xq significantly varies while x^ remains
constant, the titration behavior of xanthone should be
similar to that of acridone. Figure 3-8 shows that this is
the case, for the titration curve of xanthone shifts to
higher pH with increasing Br concentration. Table 3-3
presents m (as well as x and x') for xanthone as a
o o
function of [Br ], and Figure 3-9 shows a plot of x'/m
o
versus xq for xanthone. Once again, the plot is linear,
which indicates that equation (55) is being obeyed. It is
possible, therefore, that equation (55) will find general
application to molecules of the type under consideration.
This method is limited to molecules where xq can be varied,
but no limitations concerning pH or spectral overlap are
apparent at this time.
Table 3-4 presents the absorption and fluorescence
maxima of neutral and protonated xanthone. The value of
*
pK (F.C.) calculated with the value of pK = -4.17 is
a a


Figure 5-3
_5
Plot of the relative quantum yield of fluorescence of 2.5 X 10 M
protonated 1-isoquinolone in I^SO^ versus Hq. Analytical wavelength = 360 nm.
Excitation wavelength = 252 nm (isosbestic point).


40
0
Figure 3-1
Structure of acridone.


19
possible to determine how much uncertainty will be present
*
in a pK calculated with the Forster cycle. These
assumptions have been reviewed in depth (17,26,30,32-39),
and any further elaboration upon them here would serve no
useful purpose.
*
The Forster cycle has been used to calculate PKa1s
more than any other method (15,17,26,40-44). These
calculations have been performed for excited-state
ionizations which occur in dilute, aqueous solution and also
for some which occur in concentrated acid. Unfortunately,
the Forster cycle gives no information concerning the rates
of excited-state proton transfer. A method that could give
k
such information could be used to determine not only K ,
cl

but also k and k, The resulting value of pK could be
cl D cl
compared to that calculated with the Forster cycle, and
hence the results of each method could be used to confirm
or challenge the results of the other. While fluorescence
spectroscopy which is time-resolved on the nanosecond and
picosecond time scale has been used to determine the rate
constants for some excited-state protonation and
deprotonation reactions, this technique requires
instrumentation that is both very sophisticated and very
expensive, and also requires the extensive use of computers
for the complicated data reduction that is necessary. We
shall restrict ourselves to a discussion of


34
identical to that which the sample was put in (that is,
the reference solution was either water or acid).
Aliquots of stock solution (^200yl) were injected
into a series of 10 ml volumetric flasks and the flasks
filled to the lines with either water or acid (the stock
solution solvent was first evaporated under dry nitrogen
when the stock solution was methanolic) and the concentration
of acid corrected for any dilution. For titrations where
pH > 1, 2 mis of the aqueous solution were placed in the
sample cuvette, the spectrum recorded, and the pH
measured and recorded immediately after recording the
spectrum. An aliquot of an acidic solution of the analyte
was then added to the cuvette with a micropipette, the
spectrum recorded, and the pH again measured and recorded.
Very small changes in pH (==0.1 unit) were effected by
dipping the end of a heat-fused Pasteur pipette into an
acidic solution of the analyte and then into the aqueous
solution in the cuvette (submicroliter volumes of titrant
were added in this way). The formal concentration of the
analyte was, therefore, constant throughout the titration.
The pH was varied until no further significant changes in
the spectrum were observed.
For titrations where pH < 1, 2.000 mis of an acid
solution of the analyte were put into a cuvette. The
spectrum of the analyte and the molarity of the acid were
recorded. An accurately known volume of a solution of


148
90. Spiegel, M.R., Theory and Problems of Statistics,
New York, McGraw-Hill, 1961, chapters 13-14.
91. Youden, N.J., Statistical Methods for Chemists, New
York, John Wiley & Sons, 1951, chapter 5.
92. Wolberg, J., Prediction Analysis, Princeton, D. Van
Nostrand, 1967, chapters 3-4.
93. Afifi, A.A., and Azen, S.P., Statistical Analysis;
A Computer Oriented Approach, New York, Academic,
1973, chapter 3.


116
Table 6-1
Fluorescence (vf) and longest wavelength absorption (v )
H cl
maxima and fluorescence lifetimes of monoprotonated and
diprotonated 3-aminoacridine.
3-aminoacridine v cm ^ v^, cm ^ fluorescence
species lifetime, ns
monocation 2.20 X 104 1.91 X 104 4.120.08b
. a .a
dication 2.32 X 10 2.13 X 10 26.0 0.3C
These energies were estimated from strongly pronounced
(but not well resolved) vibrational features in the
spectra.
bT^, measured in 3.1 M H2SC>4, H+ = -1.6.
ctq, measured in 16.3 M H2S04, H+ = -8.7.


31
where 1 is the optical depth of the sample and I is the
o
intensity of the exciting light. The first and second
terms on the right side of equation (46) correspond to the
fluorescence from directly excited conjugate acid and that
from the conjugate acid formed by excited-state protonation
of the conjugate base, respectively. The third and fourth
terms on the right side of equation (46) correspond to the
fluorescence from directly excited conjugate base and that
from the conjugate base formed by excited-state deprotonation
of the conjugate acid, respectively. When pH >> pK and
cl
*
pH >> pK then F = F_ = 2.3' I e^C-l, from which it is
a. o O O o £5
seen that
^ As '
B
o B Ca
O B
(47) ,
where CL, = [B] + [BH ] and Fn is the fluorescence intensity
O O
of the isolated conjugate base. When pH << pK and
a.
k
pH << pK then F = FotJ+ = 2.3c¡> I 1, and then
a. or O O oil o
, 4.1 FBH +
o£bh (48) ,
where Fot,+ is the fluorescence intensity of the isolated
Oil
conjugate acid. Combination of equations (47) and (48)
with (46) yields
, [BH~I~] (j> [B] tj>' [B] y [BH+]
BH^o C3 BH+(!)oCb B^Cb B* C3
F
(49) .


30
25
20
15
10
5
0
57
B
-L
-L
0.02 0.03 0.04
Bromide ion concentration, M
00
0.01
0.05


Figure 4-6
Plot of ((4>/ ) / (4)'/

O O ti w
= 4. (A) r = 1, (B) r = 2, (C) r =
for
3, (D) r = 4, (E) r = 5, (F)
2-quinolone
r =
with
n
6.


26
proton transfer in dilute, aqueous solution and the
thermodynamics and kinetics of proton transfer in
concentrated acid.


BIOGRAPHICAL SKETCH
Brian Stanley Vogt was born on April 29, 1956, in the
Clover Hill Hospital in Lawrence, Massachusetts,to Stanley
and Blanche Vogt. He is their second son and has one
brother and one sister.
He attended kindergarten, elementary school, junior
high school, and high school in the Andover, Massachusetts,
public system between the years of 1961 and 1974. He
became a member of the National Honor Society in the
1973-1974 school year.
Subsequent to graduation from high school in 1974,
he attended Bob Jones University in Greenville, South
Carolina. He had a double major (biology/chemistry), and
graduated cum laude with a Bachelor of Science in 1979.
The science faculty at Bob Jones University selected him as
the outstanding biology graduate in the 1979 graduating
class.
He participated in the sports of fencing, soccer, and
table tennis while in undergraduate school. He also
enjoys fishing, bicycling, photography, birdwatching,
classical music, and woodworking.
When he was young, he made a personal committment to
the Lord Jesus Christ. He has read and studied the Bible,
and has used the principles found therein to guide his
149


6
upon the spectrophotometrically measured conjugate base/acid
ratios of a series of primary nitroaniline indicators which
behave according to the reaction
HIn+ + nH20 In + H+ (7) ,
where In and HIn+ are, respectively, the conjugate base and
acid of the indicator, and n is the number of water molecules
which react with the hydrated conjugate acid to form the
hydrated conjugate base and hydrated proton. The activity
of proton is related to the Hammett acidity, Hq (where
Ho = log hQ)' by
a+ = ha
H o w
n
f;
(8)
o
where f_J_ and f' are the activity coefficients of HIn+ and
In, respectively. In concentrated acid aw < 1, and hence
a cannot be eliminated from equation (8). The acid-base
w
reaction of the test compound of interest is then
BH+ + r H^O B + H+ (9)
g 2
/
where r is the number of water molecules which react with
g
hydrated, ground-state BH+ to form hydrated, ground-state B
and the hydrated proton. The equilibrium constant for this
reaction is defined as
K
a
^ fBaH+
BH+1fBH+ ^
(10) .


68
to write equation (61) as
.+*
BH
+ rH2 -
:x
t
+
-B + H
(62) .
If X+ is the transition-state subspecies formed by the
combination of BH
+*
with r water molecules and x is the
b
transition-state subspecies formed by the combination of B
and H then the equilibrium constants for the formation of
4
X' and xj are, respectively, defined as
K
+ =
[XT] f
a x
+ r
[BH ]fa
+ w
(63)
and
4-
i4]fx
lB*lfoV
(64) ,
4= +* *
where [XJ] [BH ], [X], and [B ] are the equilibrium
a. D
concentrations of X', BH
a'
+* *
, Xj, and B respectively. The
*
activity coefficients f+ and f correspond to BH and B ,
respectively. It is assumed that the activity coefficients
of xj and xj are identical. These coefficients are both
designated as f The rate of production of BH
X
*
the rate of production of B r are given by
cl
, rb, and
*-+, -
rb = ktxS]
k [BH+*] -
(65)
and
= k+[XT] -
a L a
[H+] [B*] -
(66) ,


Figure 4-3
-4
Plot of absorbance versus H for 1 X 10 M 2-quinolone in H^SO,.
wavelength = 269 nm.
Analytical


CHAPTER V
EQUILIBRIUM EXCITED-STATE PROTON TRANSFER
IN 1-ISOQUINOLONE
Introduction
When the rates of the excited-state protonation and
deprotonation reactions are equal, the excited-state
reaction is at prototropic equilibrium. It has been
shown (85) that 1/k (0)t ->-0 when this condition is met.
ci O
Equation (77) then reduces to
/o r kb(0)T n
aBaw ka(0)TQhoaw -aB (78
A plot of ( (cJ>/4) ) / ( O (Jo W
ha n (4> '/$') / (' <*) will thus pass through the origin
(that is, the ordinate intercept will be zero). The value
of the intercept, therefore, may be used as a diagnostic
to determine whether or not a given excited-state proton-
transfer reaction attains equilibrium within the lifetime
of the excited state. The closer the reaction is to
equilibrium, the closer to zero will be the intercept of
data plotted according to equation (77) Since the
ordinate intercept of plot D in Figure 4-5 and the
intercepts of plots B and C in Figure 4-10 are not zero,
it may be concluded that the excited-state proton-
transfer reactions of 2-quinolone and 4-quinolone do not
99


CHAPTER VI
NONEQUILIBRIUM EXCITED-STATE PROTON TRANSFER
IN 3-AMINOACRIDINE
Introduction
The molecules considered thus far are all of the H
o
type (that is, they have neutral conjugate bases and
singly charged conjugate acids). The number of fluorescent
Hq type molecules which are appropriate for the study of
excited-state proton-transfer reactions in concentrated
acid is limited by several things. Firstly, the
uncharged conjugate base species are sometimes relatively
insoluble. This is particularly true with molecules that
have three rings. Secondly, those that are soluble may
not exhibit excited-state ionizations in concentrated
acid. Thirdly, those that do exhibit excited-state
ionizations in concentrated acid do not necessarily have
conjugate acids and bases which are possessed of measurable
fluorescence lifetimes. This consideration is, of course,
more of a problem with older fluorescence lifetime
equipment than it is with newer, more sophisticated
equipment (most of which can measure fluorescence lifetimes
shorter than those measurable with the TRW apparatus
described in Chapter II). Finally, even when the first
three considerations present no problems, the compound of
interest may decompose in concentrated acid (the neutral
112


63
Table 3-4
Fluorescence (v ) and longest wavelength absorption (v )
L. cl
maxima of neutral and protonated xanthone.
-1 -1
xanthone species
v cm
d
, cm
neutral
cation
2.91 X 10
2.57 X 10
2.60 X 10
2.25 X 10'


This dissertation was submitted to the Graduate Faculty
of the College of Pharmacy and to the Graduate Council, and
was accepted as partial fulfillment of the requirements
for the degree of Doctor of Philosophy.
August, 1983
Dean, College of Pharmacy
Dean for Graduate Studies and
Research


150
decisions and establish his priorities. He has been
actively involved in church choir and Sunday school
programs.
He went to the College of Pharmacy at the University
of Florida in the fall of 1979. At UF he coauthored eight
publications for scientific journals and coauthored
chapters for two books. He also presented papers at four
meetings on the state and regional levels. At one of these
meetings (American Chemical Society meeting, Florida
section, 1981) he was given first prize for the best
student research presentation in the physical chemistry
division.


Figure 6-2
Plot of absorbance versus H+ for 1.9 X 10
Analytical wavelength = 275 nm.
3-aminoacrid


41
Results and Discussion
The fluorescence lifetimes of neutral and protonated
acridone are presented as a function of the molarity of
Br (derived from NaBr) in Table 3-1. Since t varies
o
with [Br ] but x is invariant, equation (55) should be
applicable to the titration data. Figure 3-2 shows a
quenching curve for protonated acridone (this was used in
the calculation of xQ in the presence of quenchersee note
b of Table 3-1 for details). Figure 3-3 shows fluorimetric
titration curves for acridone in the presence of different
concentrations of Br It is of interest to note that the
titration curve shifts to higher pH as xQ decreases. This
occurs because the rate of the dissociation reaction
decreases when xQ decreases. This shift to higher pH is
predicted by equation (53), which shows that [H+] at the
inflection point (the pH where decrease when m increases (values of m as a function of
[Br ] are also shown in Table 3-1). Figure 3-4 shows a
plot of T^/m versus xQ for acridone. As predicted by
equation (55), the plot is linear. Values of k k, and
a. D
*
pK calculated from the slope and intercept of the line in
cl
*
Figure 3-4 are presented in Table 3-2 along with pK (F.C.)
calculated from the Forster cycle (31). It can be seen
from equation (55) that, for any two different pairs of
values of m, x^, and xQ,


Figure 3-8
Variation of the relative quantum yield of fluorescence (4>1 /cf^)
neutral xanthone with H at various bromide ion concentrations.
- _3 _3 _
(B) [Br ] = 2.5 X 10 M, (C) [Br ] = 5.0 X 10 M, (D) [Br ] =
(E) [Br ] = 2.5 X 10 ^ M. The molecule was titrated with I^SO^
wavelength = 358 nm. Excitation wavelength = 326 nm.
of 2 X 10-6 M
(A) [Br-] = 0,
1.0 X 10-2 M,
Analytical


Figure 3-2
Variation with bromide ion concentration of the relative quantum yield of
fluorescence (4>/4>0) of 5 X 10 ^ M protonated acridone. Analytical
wavelength = 456 nm. Excitation wavelength = 350 nm.


Figure 1-1
* *
The Forster cycle. A, B, A and B refer to the conjugate
acid and base molecules in their ground and excited
A B
states, respectively. E and E are the energies of the
k k k
A+A and B->-B transitions, respectively. AH^ and AH^ are,
respectively, the enthalpies of protolytic dissociation in
the ground and excited states.


2
HC1 (pH = 2) has pH = 0.2 (4), and hence the acidity of the
solution is changed by almost two orders of magnitude by
the addition of the neutral salt. It is conceivable that
the presence of high concentrations of solutes in some body
fluids could lead to unexpectedly high acidities and low
activities of water in those fluids. A study of the
physicochemical properties of molecules in concentrated
electrolytic media could be useful, for such a study could
shed light on whether or not it is legitimate to use
properties measured at infinite dilution in water to
predict the behavior of the molecules in media which
significantly deviate from ideality.
The acid-base properties of functionally substituted
aromatic molecules in electronically excited states are
frequently thermodynamically and kinetically quite different
from these properties in ground electronic states. Because
of this, the ground- and excited-state ionizations may occur
in media which radically differ from each other insofar as
their electrolyte (acidic and/or neutral) compositions are
concerned. When the ionizable group is bonded directly to
an aromatic ring, UV-visible absorption and fluorescence
spectroscopy may be used as tools to study ground- and
excited-state proton-transfer reactions. The author has
used absorption and fluorescence spectroscopy to study
proton-transfer reactions in both dilute, aqueous solutions


Figure 6-5
Plot of ( (4>/0) / (<> ) awr versus h+awn ('/^_otB) for 3-aminoacridine
with n = 1 and r = 1.


1.0
T
T
*/*o
0.8
0.6
0.4
0.2
0.0
1
0
-1


109
(n r) is constant. These plots will be linear, however,
only when the correct (n r) is used in the analysis. The
linearity of the plot shown in Figure 5-4 suggests that the
cofrect value of (n r) for 1-isoquinolone is (n r) = 0.
It is expected, therefore, that the fluorimetric titration
data of 1-isoquinolone plotted according to equation (77)
will yield straight lines with identical slopes and null
intercepts for all combinations of n and r such that
(n r) =0. This expectation is confirmed in Table 5-2,
which presents values of the slopes and intercepts of
these lines with 0 < n ^ 4 and 0 < r < 4 such that n = r.
In all cases the intercept is zero (within experimental
error) and the slopes are identical (within experimental
error). Test values of 5 < n < 8 and 5 < r £ 8 with n = r
yielded the same results. This further confirms that the
excited-state proton transfer of 1-isoquinolone attains
equilibrium within the lifetime of the excited state and
that (n r) =0 for this reaction.
Equation (78) shows that the attainment of
excited-state prototropic equilibrium has several
consequences concerning our knowledge of the reaction. In
the first place, it is not possible to determine the
number of water molecules (n) which enter into the
Hammett indicator reaction or the number of water
molecules (r) which enter into the excited-state
deprctonation reaction of interest. Only the (n r)


17
* *
B A
Customarily, it is assumed that AHte = AHte and
B A
AHte= AHte,so that equations (18) and (19) reduce to
APK = 2
Nhc abs
303RT(VA
v
abs
B
(20)
and
. v Nhc , fl
ApK 2.303RT( A
-
(21) ,
respectively. If pK is known, and fluorescence or
cl
longest wavelength absorption maxima are also known, and if
B* A* A B *
AH, = AH, and AH'" = AHT. then one can estimate pK .
te te te te' c a
When the fluorescence spectrum (as a function of
energy) of a molecule is an approximate mirror image of its
longest wavelength absorption band, then the vibrational
spacings in the ground and excited states are roughly the
same (29) In this case the absorption and fluorescence
spectra will be equally displaced from the 0-0 energy. It
would then be reasonable to estimate and by
VA =
vfbs
A
-fl
+ VA
(22)
and
VB =
abs
VB
-I1
(23) ,
in which case
= Eabs + Efl 4Hte + Aie
(24)
and


J^o
w
O
10
20
30 40 50 60 70 80
h a
'/4>
o w 4>
B
00
o


24
ai a_ + k T
1 B a o
i 1+ Vo + VIH 1
It is thus seen that <¡>/d> + ' = 1. Since
o o
ctg + ctgH+ = 1, equations (41) and (42) can be combined to
give
(42) .
4>/0 1
'/ T Yo B a o
k. t '
b Or.. + n
4> '/4>A
tL
k T 4>' /4>1 ~ a_.
a o r 'Yo B
(43)
A plot of (c¡>/4>_ )/(<()'/<{>' -a ) versus ([H ]

') / (4>'/ U O JD u u o
should, therefore, be a straight line with an ordinate
intercept of l/kaxo and a slope of ^j-)T//,'*caTo w^en T0 an<^ T
*
can be measured or estimated, then k k, and K = k /k,
a. D a. a. D
can be calculated.
Equation (43) was derived assuming that the excited-
state proton-transfer reaction attains steady-state
*
conditions before photophysical deactivation of B or BH
can occur. When this is not true, then equation (43) will
not rigorously describe the chemistry of interest. A more
sophisticated treatment has been derived (58) which
accounts for situations where steady-state conditions are
*
not achieved before photophysical deactivation of B and
+*
BH takes place. Use of that treatment will give more
accurate values of ka and k^ when nonsteady-state
considerations are significant, but equation (43) will
suffice in many situations. It should be noted, however,
that the observable rate constants ka and k^ are subject


Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial
Fulfillment of the Requirements for the
Degree of Doctor of Philosophy
PROTON-TRANSFER KINETICS AND EQUILIBRIA
IN CONCENTRATED MINERAL ACIDS
By
BRIAN STANLEY VOGT
August, 1983
Chairman: Stephen G. Schulman, Ph.D
Major Department: Pharmacy
Ultraviolet-visible absorption and fluorescence
spectroscopy were used to study ground- and excited-state
proton-transfer reactions. A transition-state reaction
scheme was used to propose a model to quantitate the
kinetics of excited-state proton transfer in
concentrated acid. The Hammett acidity function, Hq, was
used as a measure of acidity. The model thus derived
included r, the number of water molecules which enter into
the excited-state deprotonation reaction of the test
compound. Also included was n, the number of water
molecules which enter into the ground-state deprotonation
reaction of the indicator used to define that range of the
H scale over which the excited-state ionization of the
o
test compound occurred. The model successfully described
vi


CHAPTER IV
EXCITED-STATE PROTON TRANSFER IN
2-QUINOLONE AND 4-QUINOLONE
Introduction
Some molecules become so acidic in their excited states
that their excited-state ionizations occur in concentrated
acid. As has already been seen in Chapter I, equation (43)
will not correctly describe the excited-state proton-
transfer reactions of these molecules because k and k, are
a b
usually medium-dependent. Therefore, equation (43) must be
modified to include the medium-independent rate constants
k (0) and k, (0) before the kinetics of excited-state
a o
proton transfer in concentrated acid can be quantitated.
The mechanism of the excited-state proton transfer of
interest can be written as
BH^*(H20)x + rH2Q * B* (IUO) + H+(H20)z (61),
where x, y, and z are the numbers of water molecules
. +* + A
hydrating BH B and H respectively, and X1 is the
transition-state species common to both the protonation and
deprotonation reactions. The coefficient r is the number of
+* A
water molecules which react with hydrated BH to form XT.
By mass balance it is seen that r = y + z x, and it is
assumed that x, y, z, and r remain constant over the
inflection region of a given titration. It is then simpler
67


70
while combination of equations (68) and (72) gives
kb = kb(0)aH+
X
(74)
Equation (8) may be combined with equation (74) to yield
kb V0)Vwn FT^
X o
(75)
The medium-dependent rate constants ka and k^ are thus
related to the medium-independent rate constants k (0) and
cl
k^(0) by equations (73) and (75), respectively.
Substitution of these equations into equation (43) results
m

o r
a =
k, (0) t 4>'/ b ou n T Yo + o
+ h a
'/-b w k (0)T f+ k (0)T w f f
(76)
X o
X
The activity coefficients f+, f'+, and f all correspond to
singly charged species of similar size while fQ and f^
correspond to uncharged species of similar size. These
similarities in size and identities in charge make it
reasonable to assume that f,/f = f!f /f,f' = 1, in which
case equation (76) becomes
<¡>/4>
$w
a o
V0)T, n
+ n a
o w
(77)
a o
4> '/<¡>-cd3


4^
Bromide ion concentration, M


96
would not correctly describe the excited-state chemistry of
interest. Since the plots obtained with equation (77) are
linear, it appears that, at least to a first approximation,
n and r may be considered to be constant.
k
Values of k (0) k, (0), and pK (0) for 4-quinolone
a. D a.
with n = 4 and r = 3 and also with n = 4 and r = 4 are
k
presented in Table 4-4 (pK and pK (F.C.) are also shown in
cl cl
k k
Table 4-4). The agreement between pK (0) and pK (F.C.) for
'cl cl
the excited-state ionizations of 2-quinolone and 4-quinolone
further suggests that the model under consideration is
valid. Furthermore, it suggests that the Forster cycle can
be used with some confidence to relate the acid-base
properties of a molecule in one medium to those properties
in another. In the cases of 2-quinolone and 4-quinolone, at
least two sets of circumstances are consistent with the
latter suggestion. Firstly, it is possible that the
hydrations of the quinolone species do not change with
changing acid concentration (at least not over the
concentration ranges studied in this work). Secondly, it is
possible that their hydrations do change, but that they
change in such a way that the standard free energies of all
the species involved in a given reaction change by the
same amount when going from one medium to another. These
changes would cancel out and would not be apparent in
k
the estimation of pK with the Forster cycle. Once again,
cl


18
,B
= uabs
+ E
B
fl
- H
B
te
H'
B
te
(25)
It may then be assumed that AH* = AH* and
J te te
B* B
= AHfc This is at least safer than assuming that
AH^e = AH^e and AH^e = Aff^e, because any difference
between AH* and AH* will be cut in half in the
te te *
g
denominator of equation (24) (the same is true of AHte and
g
AHte in equation (25)). Thus, it is preferable to estimate
vA and vB from equations (22) and (23).
*
The accuracy of a pK calculated with the Forster
cycle is, of course, dependent upon to what extent the
assumptions inherent in the Forster cycle are adhered to
and upon how accurately pK v and v are known (some of
the inaccuracy in the latter two arises from errors in
positioning the monochromators in the spectrophotometer
and fluorimeter). Many molecules have excited-state
geometries and solvation cages which are similar to their
ground-state geometries and solvation cages. Because of
this, it is reasonable to assume that the ground- and
excited-state entropies of protonation are similar, and
*
then the precision of a pK calculated with the Forster
cl
cycle can be as small as 0.2 (30). This error and the
error in and v"B give typical uncertainties of about
*
0.3 in Forster cycle pK 's (31) When the assumptions in
cl
the Forster cycle are not correct, however, it is not


72
Figure 4-1
Structure of 2-quinolone.


Figure 3-6
Plot of absorbance versus H for 6.5 X 10 6 M xanthone in HSO
o 2
Analytical wavelength = 329 nm.


84
Table 4-2
Ground-state acid-dissociation constant of protonated
*
2-quinolone and rate constants and pK^ for the excited-
state proton transfer between neutral and protonated
2-quinolone.
pKa ka(0)/ S 1 kb(0), M 1s 1 pK*
-0.300.03a 41 X 109 1.00.3 X 108 -1.580.06C
-1.80.3d
aDetermined spectrophotometrically in this work with
^Determined graphically from Figure 4-5 with n = 3 and
r = 4.
c *
pK (0), determined graphically from Figure 4-5 with
n = 3 and r = 4.
d
*
pK (F.C.), estimated with the Forster cycle.
3.


128
resolved) vibrational features in the absorption and
fluorescence spectra of the doubly protonated molecule.
Since these features are not well resolved, the estimation
of the 0-0 energy of the dication is difficult and subject
to inaccuracy. In spite of this, there is reasonable
k k
agreement between pK (0) and pK (F.C.) (see Table 6-2).
cl cl
k k
The small difference between pK (0) and pK (F.C.) is
cl cl
attributed to error in the estimated values of v,.
dication
* k
The agreement between pK (0) and pK (F.C.) further
cl cl
confirms the validity of the model under consideration and
also suggests that equation (60) (modified to include h+
instead of hQ) correctly describes the ground-state
ionization of 3-aminoacridine. Since the ground- and
excited-state ionizations occur in media of radically
different acid composition, we also see that the Forster
cycle may be used with some confidence to relate the
acid-base behavior of 3-aminoacridine in one medium to its
behavior in another medium.
Since both reactions occur in moderately concentrated
acid, it is of interest to compare the values of k (0) and
k^(0) (Table 6-2) for the excited-state ionization of
3-aminoacridine to their values for the excited-state
ionization of 2-quinolone (Table 4-2). Since neither of
these reactions attains prototropic equilibrium, it is not
surprising that the value of k (0) for the 3-aminoacridine
cl
9 -1
excited-state ionization (k (0) = 1.73 X 10 s ) is
cL


CHAPTER I
INTRODUCTION
The physical and chemical properties (solubility, pK ,
Cl
rates of hydrolysis, etc.) of drugs are usually measured in
dilute, aqueous solution. It is frequently assumed that
these measurements reflect the correct values of these same
properties of the drugs when they are found in vivo.
However, the experimental solution media are idealized
compared to the environments found in vivo. For example,
plasma is an approximately 8% solution of proteins,
electrolytes, lipids, sugars, amino acids, hormones, and
metabolic wastes (1), and hence plasma is not a dilute,
aqueous solution. Lymphatic fluid and interstitial fluid
are similar to plasma (except that they contain less
proteins). Cell interiors are another example of media
which do not act as dilute solutions, for somewhere between
10% and 60% of the total volume of cells may be water which
is "bound up" by cell constituents (2). Indeed, it has been
shown that the properties of water in dilute, aqueous
solution are dramatically different from the properties of
water in cells (2) and around hydrophobic solutes (3).
Furthermore, the acidity of aqueous solutions may be
enhanced by the addition of neutral electrolytes. For
example, a 1 M solution of NaCl (approximately 6% NaCl)
made up in 0.01 M
1


65
Table 3-5
Ground-state acid-dissociation constant of protcnated
k
xanthone and rate constants and pK for the excited-state
proton transfer between neutral and protonated xanthone.
PKa ka, s"1 kb, M'V1 PK¡
-4.1710.03a 8.310.6 X 107 5.610.3 X 109 1.8310.02
3.210.3C
aDetermined spectrophotometrically in this work with
(n rg) = 0.
Id
^Determined graphically from Figure 3-9.
c *
pK (F.C.), estimated from the Forster cycle.
3


51
O
Figure 3-5
Structure of xanthone.


86
the ratio of their quantum yields, and the measured value of
tq were used in this calculation. The absorption and
fluorescence spectra of 4-quinolone exhibit a fairly good
mirror-image relationship and a small Stokes shift; hence,
the value of x' estimated with the Strickler-Berg
o
equation is reasonably accurate (82-84) .
Figure 4-7 shows the spectrophotometric titration of
4-quinolone. This ground-state ionization occurs in dilute,
aqueous solution, and hence the titration data were fitted
using equation (60) with a^ = 1, in which equation (60)
reduces to an antilogarithmic form of the Henderson-
Hasselbach equation. This analysis yielded pK = 2.220.01.
Cl
The fluorimetric titration curve of 4-quinolone is
shown in Figure 4-8. The small step in the titration curve
at pH = 2 is probably the result of a vanishingly small rate
of protonation of the excited neutral molecule at that
pH and higher pH (56) The titration data of 4-quinolone
plotted according to equation (77) are shown for n = 3 in
Figure 4-9 and n = 4 in Figure 4-10, with r taking various
values in each figure. The activity of water
significantly deviates from unity only in the most acidic
portion of the fluorimetric titration of 4-quinolone, and
hence it is expected that the inclusion of a in the kinetic
w
treatment will not make as dramatic a difference as it did
with 2-quinclone. This is the case; indeed, plots B
(n = 4, r = 3) and C (n = 4, r = 4) in Figure 4-10 are


92


Table 5-2
Ground- and excited-state acid-dissociation constants for the proton transfer
between neutral and protonated 1-isoquinolone.
n r
intercept
b
slope
b
1.3810.03 0
1
0
1
4.95.5
1.62.7
X
X
10 \
1 o
4.550.06
4.5710.07
X
X
10-3
io i
-2.23l0.03C
-2.2310.03
2
2
0.41.5
X
loi
4.5910.09
X
10-3
-2.2210.03
3
4
3
4
O.lil.l
0.51.5
X
X
10-2
10
4.610.1
4.510.4
X
X
10 ,
10 J
-2.2210.03
-2.2310.04
-2.2310.04
-2.2 i 0.3
Determined spectrophotometrically in this work with (n r ) = 1.
For 1-isoquinolone data plotted according to equation (77).
c *
pK (0), determined graphically from the slope of the line obtained with from
cl
1-isoquinolone data plotted according to equation (77) with the appropriate
values of n and r.
d *
pK (0), the average of the values of pK (0) determined with n = r for
a. a
0 < n < 4 and 0 £ r £ 4.
0 *
pK (F.C.), estimated from the Forster cycle,
a
110


Figure 6-3
-5
Plot of absorbance versus H+ for 1.9 X 10 M 3-aminoacridine in H2S0
Analytical wavelength = 454 nm.


29
using MeOH:CHC1^ (1:19) as the mobile phase, which was
alkalinized by the addition of one drop of NH^OH. The
presence of isosbestic points in the absorption spectra of
these compounds further confirmed their purity.
-4
Stock solutions of the compounds were ==10 M to
-2
=10 M and were made up m either ^0 or MeOH. The stock
solutions were accurately diluted (by a factor of 100) and
the absorbances of the resulting solutions measured at
appropriate analytical wavelengths. These absorbances were
used in conjunction with published molar absorptivities to
calculate the concentrations of the stock solutions. Molar
absorptivities of acridone, 2-quinolone, 4-quinolone, and
1-isoquinolone may be found in reference (61). The molar
absorptivity of 3-aminoacridine may be found in reference
(59) A carefully weighed sample of pure xanthone was
used to prepare the stock solution, and hence its
concentration was calculated.
Absorption and Fluorescence Studies
Absorption spectra were taken on either a Beckman
DB-GT, Beckman Model 25, or Varian Cary 219
spectrophotometer. The Cary 219 was equipped with a cell
compartment thermostatted at 25.00.2C. The cell
compartment in the DB-GT was thermostatted at 25.00.2C
when a constant temperature bath (Brinkmann Lauda K-2/R) was
available. The Model 25 had no provision for temperature
control. All spectra taken in instruments with


85
Table 4-3
Fluorescence (v ) and longest wavelength absorption (v )
£ cl
maxima and fluorescence lifetimes of neutral and
protonated 4-quinolone.
4-quinolone v^, cm ^ v^, cm fluorescence
species lifetime, ns
neutral 3.04 X 104 2.98 X 104 0.790.04a
cation 3.32 X 104 2.76 X 104 21lb
ax^, estimated with the Strickler-Berg equation.
DtQ/ measured in 5.9 M HC1C>4, Hq = -2.8.


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39
be a straight line with an ordinate intercept of 1/k^ and
*
a slope of k /k,. Values of k k, and K could thus be
a d a d a
derived from the series of titrations of the molecule of
interest.
Acridone (Figure 3-1) is a molecule in which

pK >> pK (31,74), and hence its fluorimetric titration
cl cl
behavior should be described by equation (53).
Furthermore, since the ground-state ionization occurs in
relatively dilute solution (pK = -0.32) (75), the media
in which the ground- and excited-state ionizations occur
are not appreciably different. Since the assumptions
inherent in the Forster cycle are normally correct for
ionizations which occur in dilute, aqueous solution, the
*
pK of acridone calculated according to equation (55)
ci
*
should agree with the value of its pK calculated with the
Forster cycle. Such a comparison could be used to
determine whether or not equation (55) correctly describes
the excited-state chemistry of interest. If it does, then
equation (55) could be used with confidence to determine the
*
pK of a molecule in which the ground-state ionization
occurs in concentrated acid. The Forster cycle could then
be used to see if the excited-state ionization (which
occurs in dilute, aqueous solution) can be related to the
ground-state ionization (which occurs in concentrated acid).


Absorbance
9 L


23
show that
X = T ^
o 4>1
o
(36) ,
where and ' are the quantum yields of fluorescence of
the conjugate base in the absence and presence of
excited-state proton transfer, respectively, and the relative quantum yield of fluorescence of the conjugate
base. Combination of equation (33) with (35) and of
equation (34) with (36) shows that
/ [B* ] dt = T
o o (37)
and
/[BH+*]dt = t -f-
o o 0
(38)
Therefore, integration of equations (27) and (28) results in
ac+ = T- + kT^ kbx[H+]|t
BH
a o (39)
and
a = t t k, t' [H+]^t k t
B o
(40) .
Equations (39) and (40) can be solved simultaneously for

= ctBH~1' + kbTtH 1
^o 1 + k t + k. T [H+]
a o bo
(41)
and


o
o
Absorbance
o
fo
o
O
cr>
o
00
H-
o
T2T


/o
4>' /<>' ot
o
00
NJ


7
Equations (8) and (10) may be combined and put into the
logarithmic form
f f 1
pKa = Ho" log--6"1-, (n-r ) log a logB (11).
a [BH+] g W fBH+ fo
Lovell and Schulman (10-12) have successfully applied
equation (11) to the prototropic reactions of a series of
unsubstituted and substituted carboxamides and to a series
of tertiary anilines,which all ionized in concentrated acid.
On the basis of similarity in size and charge of the species
involved, they assumed that f_,f'=ft,+f' so that equation
(11) reduces to
pK = H log-^L- (n-r )log a (12).
[BH ] g
It remains to be seen whether or not equation (12) is
generally applicable.
Prototropic Reactivity in Electronically Excited States
The study of the acid-base chemistry of electronically
excited aromatic acids and bases began formally in 1949,
when Forster (13) elaborated upon Weber's earlier
observation (14) that the fluorescence spectrum of
l-naphthylamine-4-sulfonate exhibits pH dependence different
from the pH dependence of its absorption spectrum. Years
of subsequent research have shed much light on this subject.
Electronic excitation of an aromatic molecule results
in a change in electronic distribution in that molecule.
This difference in electronic distribution results in


9
orbitals. This is a consequence of the electronegativity
of the nitrogen being higher than that of the carbons to
which it is bonded, and in the excited state charge is
localized on the nitrogen. The lone pair projects out in
the plane of the ring and is perpendicular to the aromatic
tt system. This perpendicularity prevents the lone pair from
interacting with the aromatic system.
It should be mentioned that excited-state proton
transfer can be either intramolecular or intermolecular.
Intramolecular excited-state proton transfer has been
reviewed (15) and this dissertation is concerned only
with intermolecular proton transfer. Furthermore, the
excited state of interest can be either an electronically
excited singlet or triplet state. The principles of
excited-triplet-state proton transfer are the same as those
for the singlet state (see references (16-26) for examples),
but the research under consideration deals only with proton
transfer in ground and excited singlet states.
The Effects of Protonation on Electronic Spectra
Protonation of a functional group which is intimately
coupled to an aromatic system may have a profound effect
upon the absorption and fluorescence spectra of that
molecule. This is a result of the electronic charge
stabilization incurred by the presence of the proton at the
functional group.


Figure 3-4
Plot of T'/m versus x for acridone.
o o


UNIVERSITY OF FLORIDA
3 1262 08557 0025


127
Hq type molecules. Since the intercept of the line in
Figure 6-5 is not zero, we may conclude that the excited-
state proton transfer between monoprotonated and
diprotonated 3-aminoacridine does not attain equilibrium
within the lifetime of the excited state. When
nonequilibrium conditions prevail for an excited-state
proton transfer in dilute, aqueous solution, there is some
pH range over which there will be a plateau region in the
titration curve. This pH independence is the result of
the rate of the excited-state protonation of the conjugate
base becoming immeasurably small. Equations (77) and (84),
however, predict that both <{>/ and will vary
continuously with acid concentration even when
nonequilibrium conditions prevail. Both the acidity of
the medium and a^ vary with acid concentration, and thus
even if §/§Q and 4> */4> become acidity independent, they
will still vary because they are dependent on a^ This
behavior is observed for both 3-aminoacridine (Figure 6-4)
and 2-quinolone (Figure 4-4). The ability of equations
(77) and (84) to predict titration behavior further
confirms the validity of the model.
*
The value of the pK of 3-aminoacridine estimated
with the Forster cycle is expected to be somewhat
inaccurate because of the difficulty encountered in
estimating the 0-0 energy of the dication. This energy
was estimated from strongly pronounced (but not well


Figure 4-9
Plot of ((4>/_) /(4> '/<¡>'-0) a r versus
O O JD w
hQawn(<|) '/(^-aB) for 4-quinolone with n = 3.
(A) r = 1, (B) r = 2, (C) r = 3, (D) r = 4, (E) r = 5.


PROTON-TRANSFER KINETICS AND EQUILIBRIA
IN CONCENTRATED MINERAL ACIDS
By
BRIAN STANLEY VOGT
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA


VI NONEQUILIBRIUM EXCITED-STATE PROTON
TRANSFER IN 3-AMINOACRIDINE 112
Introduction 112
Results and Discussion 114
VII SUMMARY 131
APPENDICES
A SIMPLE LINEAR LEAST-SQUARES REGRESSION
ANALYSIS 135
B MULTIPLE LINEAR LEAST-SQUARES REGRESSION
ANALYSIS 138
REFERENCES 143
BIOGRAPHICAL SKETCH 149
v


16
*


21
-fa d [ B ] = /(l/T^+kHrH+] ) [B*]dt-/ka [BH+*]dt (28),
B
*
where [B ] and [BH ] are, respectively, the probabilities
*
of finding a [B jor [BH ] molecule in the excited state at
J-* *
time t. Since the fluorescences of BH' and B are being
excited and monitored under steady-state conditions, the
right sides of equations (27) and (28) are to be
integrated over all time (t = 0 to t = ) The lower
limits of integration of [BH ] and [B ] are _+ and
Dll
a respectively, where a + is the fraction of the
ground-state population which is found as the conjugate
acid and a is the fraction found as the conjugate base.
J3
In spectrophotometric terms,
aBH+ =
£bh+[bh ]
eBH+[BH ] + eB[B]
(29)
and
a
£bCb]
B
:bh+[bh+] + £b[b]
(30) ,
where and £+ are the molar absorptivities of the
B bn
conjugate base and acid, respectively, at the wavelength of
excitation. In terms of K ,
ci
aBH+ *
£BK+tH 1
eBH+[H + £BKa
(31)


Figure 4-5
Plot of ( (4>/4>0) / (4> '/^"Ctg) ) aj versus (cf>'/ ( '/^-aB) for 2-quinolone with
n 3. (A) r = 1, (B) r = 2, (C) r = 3, (D) r = 4, (E) r = 5.


74
Table 4-1
Fluorescence (v^) and longest wavelength absorption (v )
L cl
maxima and fluorescence lifetimes of neutral and
protonated 2-quinolone.
2-quinolone
species
fluorescence
lifetime, ns
neutral 3.12 X loj 2.72 X 10? 2.10.2a
cation 3.33 X 10 2.65 X 10 10.40.5D
aT^, measured in water, pH = 2.0.
measured in 7.5 M H2SO^,
H
o
-4.0.


69
where k^ is the rate constant for the dissociation of in
a a
the direction of the conjugate base and k^ is the rate
constant for the rearrangment of in the direction of the
conjugate acid. Equation (64) may be combined with (65) to
yield
+* [BH+*]
rb = k+K+[B*]jV ka[BH' 1 -
X o
(67) ,
which becomes
f +*
r = kb(0) [B*]^aR+ ka[BH+*] ]- (68).
x To
Equations (63) and (66) may be combined to give
ra = kK[BH+*]F:awr kb[H+] tB*] "
a a a r w b t
x o
(69) ,
which becomes
f *
+* + r + fr 1
r = k (0) [BH Irt,- k, [H+] [B ] -
a a r w b t
x o
(70) .
It is seen from reaction (26) that r and r, may also be
given by
*
+* + r b i
r = k [BH+ ] k, [H+] [B ] ^-J-
a a d t
(71)
and
rb = kb[H+] [B*] ka[BH+*] ]-
(72) .
Combination of equation (70) with (71) yields
f+ r
k = k (0) -Ea
a a f w
x
(73) ,


the excited-state ionizations of several aromatic lactams
in ^SO^ or HCIO^. Modification of the model to describe
the excited-state ionization of an H+ type molecule was
successful.
It was found that one of the molecules studied
demonstrated excited-state prototropic equilibrium. While
*
pK could be determined, neither the rate constants for the
cl
reactions steps nor n and r could be determined. The model
predicted that these limitations would apply to all excited-
state prototropic equilibria occurring in concentrated acid.
The other molecules exhibiting excited-state ionizations in
concentrated acid demonstrated nonequilibrium excited-state
k
proton transfer. Values of pK the rate constants for the
reaction steps, and n and r were determined.
Also devised was a general method of determining the
rate constants of the excited-state reaction steps when the
ground-state ionization occurs in concentrated acid but the
excited-state ionization occurs in dilute solution. This
method was successfully applied to several Hq type molecules.
Ground-state ionizations occurring in concentrated acid
were successfully described by a modified Henderson-
Kasselbach equation. This equation accounted for n and also
for r the number of water molecules which enter into the
g
ground-state deprotonation of the test compound.
For all but one of the compounds studied, the Forster

successfully related pK to pK .
3 3
Vll


146
53.Escabi-Perez, J.R., and Fendler, J.H., J. Am. Chem.
Soc., 100 (1978), 2234.
54. Gafni, A., Modlin, R.L., and Brand, L., J. Phys. Chem.,
80 (1976), 898.
55. Ofran, M., and Feitelson, J., Chem. Phys. Letts., 19
(1973), 427.
56. Weller, A., Z. Elektrochem., 56 (1952), 662.
57. Weller, A., Z. Phys. Chem. N. F., 15^ (1958), 438.
58. Weller, A., Z. Elektrochem., 61 (1957), 956.
59. Rosenberg, L.S., A Thermodynamic Evaluation of DNA-
Ligand Interactions, Doctoral dissertation,
University of Florida, 1980.
60. Martin, R.F., and Tong, J.H.Y., Aust. J. Chem., 22
(1969), 487.
61. Weast, R.C., ed., CRC Handbook of Chemistry and Physics,
54th ed., Cleveland, CRC Press, 1973, section C.
62. Dominique, P., and Carpentier, J.M., J. Chem. Res., S
(1979) 58.
63. Paul, M.A., and Long, F.A., Chem. Rev., 57 (1957), 1.
64. Jorgensen, M.J., and Hartter, D.R., J. Am. Chem. Soc.,
85. (1963) 878.
65. Giaque, W.F., Hornung, E.M., Kunzler, J.E., and Rubin,
T.R., J. Am, Chem. Soc., 82 (1960), 62.
66. Robinson, R.A., and Stokes, R.H., Electrolyte
Solutions, London, Butterworths, 1955.
67. Long, F.A., and Purchase, M., J. Am. Chem. Soc.,
72 (1950), 3267.
68. Rosenthal, D., and Dwyer, J.S., Can. J. Chem., 41
(1963), 80.
69. O'Conner, C.J., J. Chem. Ed., 46 (1969), 686.
70. Kokobun, H., Z. Elektrochem., 62 (1958), 559.
71. Watkins, A.R., Z. Phys. Chem. N. F., 75 (1971), 327.


102
Table 5-1
Fluorescence (v_) and longest wavelength absorption (v )
u- cl
maxima and fluorescence lifetimes of neutral and protonated
1-isoquinolone.
1-isoquinolone
species
fluorescence
lifetime, ns
neutral 3.10 X 10* 2.73 X 10* 2.00.1?
cation 3.21 X 10 2.77 X 10 2.610.1
ax^, measured in water, pH = 1.7.
tq, measured in 8.4 M H2S04' Hq = -4.1.




66
to the thermodynamics of proton transfer in concentrated
acid. If this is a consequence of changes in hydration of
a given reactant, then the standard state of that reactant
is different in the ground- and excited-state reactions.
If this is the case, then it may not even be
*
thermodynamically correct to predict the value of pK (or
pK if the Forster cycle is used in reverse) in one
medium based upon measurements in another. However, it will
be seen from other data presented in this dissertation
that the Forster cycle is generally quite successful in
*
predicting pK even when the ground- and excited-state
ionizations occur in media of substantially different
acid composition. The behavior of xanthone does, however,
suggest that the prediction of the behavior of a molecule
in one medium based upon measurements in a different
medium should be done only with caution.


3
and in concentrated electrolytic media. Before discussing
the author's research, however, a review of ground- and
excited-state acid-base chemistry is in order.
Br^nsted-Lowry Acid-Base Chemistry in Ground Electronic States
We shall restrict ourselves to the Br0nsted-Lowry
definitions (5,6) of acid and base (an acid is a species
which can donate a proton and a base is a species which can
accept a proton). The acid-base properties of a given
organic molecule are a consequence of the presence of one
or more electronegative atoms (usually nitrogen, oxygen,
or sulfur) in that molecule. In a Br0nsted-Lowry acid, at
least one of these atoms is present and has covalently
bonded to it a hydrogen atom. Sufficiently strong
interaction between the solvent and the hydrogen atom results
in the loss of the hydrogen atom from the molecule to form
a solvated proton and the conjugate base of the organic
acid. Br^nsted-Lowry bases contain at least one
electronegative atom with at least one pair of unshared
electrons (lone pair). Protonation (ionization) is the
formation of a coordinate-covalent bond between the lone
pair on the base and a proton (which may come from the
solvent, if it is sufficiently acidic, or from some other
source of protons). The conjugate acid of the organic base
and the solvent lyate anion (when the solvent is the proton
donor) are formed when protonation of the base occurs. The


83
relationship 4' /<> = 1

spectra of the protonated species overlap and eclipse those
of the neutral species. It can be seen that most
combinations of n and r result in curved plots. The best
fit to a straight line (chosen on the basis of the highest
linear least-squares correlation coefficientsee Appendix
A) was obtained with n = 3 and r = 4 (plot D in Figure 4-5).
The linearity of plot D in Figure 4-5 suggests several
things. In the first place, the titration data of
2-quinolone in concentrated acid are fitted well with equation
(77), which suggests that the model is valid. Secondly,
the assumption that f+/f = f_J_f /f f = 1 is probably a
good assumption. Thirdly, the value of n in reaction (7)
for this region of acidity is n = 3 and the value of r in
reaction (62) is r = 4 for 2-quinolone. These observations
are consistent with the values of n = 3 and n = 4 proposed
by Teng and Lenzi (79) and by Bascombe and Bell (80) for
solutions in which Hq > -3.5. Values of ka(0), k^tO), and
rk
pK (0) = -log(k (0)/k, (0)) are presented in Table 4-2,
3 3D

along with pK (F.C.) and pK .
The fluorescence lifetimes and spectral maxima of
neutral and protonated 4-quinolone are presented in Table
4-3. The fluorescence lifetime, t^, of neutral 4-quinolone
was estimated with the Strickler-Berg equation (81). The
ratio of the radiative lifetimes of protonated and neutral
4-quinolone (estimated with the Strickler-Berg equation),


'/<>
h+awcJ)' /4)aB
125


73
Figure 4-2
Structure of 4-quinolone.


25
to medium effects, and hence equation (43) will not be
applicable to an excited-state proton-transfer reaction which
occurs in concentrated acid, where the medium is
different from one part of the titration inflection region
to another. The hypothetical, medium-independent rate
constants for the reaction in concentrated acid are k (0)
u
and k^iO), which correspond to the deprotonation and
protonation steps, respectively, for the reaction as it
would occur in infinitely dilute, aqueous solution. The
author's research represents the first attempt to
quantitate k (0) and k, (0).
cl O
Summary
Proton transfer in both ground and excited states has
been thoroughly studied and quantitated for those acid-base
reactions which occur at or close to infinite dilution and
where 1 < pH < 13. However, up to the time when the
author began his research, no attempts had been made to
quantitate the kinetics and equilibria of excited-state
proton-transfer reactions in concentrated electrolytic media.
It was the goal of the author to develop a successful model
for these reactions in concentrated acidic media (pH < 1).
The author also wished to see if equation (12) has more
general application than it has had to date. Finally, the
author desired to see if there exists a fundamental
relationship between the thermodynamics and kinetics of


o


Figure 1-2
*
Modified Forster cycle. A. B, A. and B, refer to
-1 te te te te
the thermally equilibrated conjugate acid and base
molecules in their ground and excited states, respectively.
* ic
Ajc, B£c, A^ and B^c refer to the conjugate acid and base
in their Franck-Condon ground and excited states,
respectively. AH^e an ^Hte are t^e ent^alpies f
equilibration from the Franck-Condon ground states to the
thermally equilibrated ground states of the conjugate acid
A* B*
and base, respectively. AHte and AHte are the enthalpies
of equilibrium from the Franck-Condon excited states to
the thermally equilibrated excited states of the conjugate
A A. B B
acid and base, respectively. Ea^ Efl' Eabs' an<^ Efl
refer to the energies of absorption and fluorescence of the

conjugate acid and base, respectively. AH^ and AH^ are,
respectively, the enthalpies of protolytic dissociation
in the ground and excited states.


130
moderately concentrated acid but neither attains
prototropic equilibrium within the lifetime of the excited
state).


126
Table 6-2
Ground-state acid-dissociation constant of diprotonated
*
3-aminoacridine and rate constants and pK for the excited-
state proton transfer between monoprotonated and
diprotonated 3-aminoacridine.
pKa ka()/ s-1 kb(0), M-1s 1 pK*
-1.760.02a
1.730.08 X 10
3.80.2 X 10
-4.660.01
-5.1 0.3
c
d
determined spectrophotometrically in this work with
(n r ) =0.
determined graphically from Figure 6-5.
c *
pK (0), determined graphically from Figure 6-5.
3
d .
pK (F.C.), estimated with the Forster cycle.
3


113
conjugate bases are sometimes more susceptible to this
degradation than are the conjugate acid species).
Degradation of an aromatic compound in concentrated acid
is usually indicated by a time-dependent change in
wavelength and/or intensity in the spectrum of either the
conjugate acid or base (or both).
These difficulties are lessened with H+ type
molecules, which have monocationic conjugate bases and
dicationic conjugate acids. The use of H+ type compounds
requires the use of the H+ scale (87) to quantitate the
acidity of the medium. Indicators of this type react
according to the mechanism
H2In++ + nH20 < . > HIn+ + H+ (79) ,
where H2In and HIn are the indicator conjugate acid and
base species, respectively. In analogy to equation (8),
a^t is related to h+ by
aH+ = MW" ff <80) '
where f_J_ and f^_+ are the activity coefficients of HIn+ and
H2In++, respectively, and h+ = antilog(-H ). The excited-
state reaction of interest is then
BH
++
BH,
++*.
+ + *
H + BH :
k-'
Kf
BH
(81)
k '
Kd
The modification of equation (43) for H+ type compounds
parallels that for Hq type compounds, and, in analogy to


49
Table 3-2
k
Rate constants and pK& for the excited-state proton
transfer between neutral and protonated acridone.
2.7 X 108 1.4 X 1010 1.71a
2.90.3 X 10 1.50.1 X 10 U 1.710.04D
1.60.3C
aDetermined graphically from Figure 3-3.
^Calculated from the data in Table 3-1.
c *
pK (F.C.), taken from the Forster cycle calculation in
cl
reference (31).


140
where
a
i
i
i =
xn
X,
X.
-1 XN Yl^
(109)
.t .
and I is the transpose of matrix I. Matrix D is then
given by the product
D = IfcP
(110)
where
P =
(111)
JN
The matrix of fitted values of the dependent variable is
given by
F = IA (112)
and the matrix of residuals is given by
R = P F
th
where the residual of the i point is
(113)
R. = Z F.
ill
(114)


22
and
a
B
(32) .
If the rate of attainment of steady-state conditions for the
excited-state proton-transfer reaction is much higher than
the rates of photophysical deactivation of B and BH ,
then [B*] = e~t/T' and [BH+*] = et/x (57). The
fluorescence lifetimes x and x' are the lifetimes of the
conjugate acid and base, respectively, in the presence of
excited-state proton transfer, where x = l/(k^ + k^ + k^)
and x' = l/(k£ + k^ + k^tH+]). The expressions for [B ]
+*
and [BH ] may be integrated from t = 0 to t = 00, and
then
(33)
o
o
and
(34) .
o
o
The quantum yields of fluorescence of the conjugate acid in
the absence and presence of excited-state proton transfer
are, respectively, $ = k^x and 4>= k,x. The relative
quantum yield of fluorescence of the conjugate acid, §/§Q,
is thus related to x and x^ by
o
o
(35) .
Analogous reasoning for the conjugate base may be used to


129
similar to that for the 2-quinolone excited-state
ionization (k (0) = 4 X 10^ s ^). The value of k, (0) for
a- D
the 3-aminoacridine reaction (k^(0) = 3.8 X lo"* M-1s1) is,
however, substantially lower than it is for the 2-quinolone
8 11
reaction (k^(0) = 1.0 X 10 M s ). This observation is
not surprising if one considers the charge types of the
reactants. The conjugate base of 2-quinolone is a neutral
molecule, whereas the conjugate base of 3-aminoacridine is
a cation. Because of the electrostatic repulsion between
species of like charge, it is expected that the rate
constant for the combination of two cations (the proton
and monoprotonated 3-aminoacridine) will be lower than that
for the combination of a cation (the proton) with a neutral
species (the conjugate base of 2-quinolone). Whether or
not this comparison is legitimate, of course, depends upon
whether or not the conjugate bases in the two reactions
are in the same standard state. As has already been
discussed in Chapters III and IV, differences in standard
state could result from changes in hydration, and these
changes would not necessarily be detectable with the
Forster cycle. It is not possible, therefore, to state at
this time whether or not the above comparison of rate
constants is legitimate. The comparison does seem
qualitatively justified because of the electrostatic
considerations already given and because of the
similarity between the reactions (both occur in


97
Table 4-4
Ground-state acid-dissociation constant of protonated
k
4-quinolone and rate constants and pKa for the excited-
state proton transfer between neutral and protonated
4-quinolone.
pKa ka(0)' s 1 kb(0), M-1s1 pK*
2.00.6
X
8b
io8
1.310.5
X
10b
10 u
1.8010.08
1.710.5
X
8d
io8
1.010.3
X
iod
10U
1.7710.05s
1.7l0.3f
aDetermined spectrophotometrically in this work. The value
of (n r ) could not be determined since a =1 over the
g w
inflection region of the titration.
^Determined graphically from Figure 4-10 with n = 4 and
r = 3.
c *
pKa(0), determined graphically from Figure 4-10 with
n = 4 and r = 3.
^Determined graphically from Figure 4-10 with n = 4 and
r = 4.
e *
pK (0), determined graphically from Figure 4-10 with
cl
n = 4 and r = 4.
f *
pK (F.C.), estimated with the Forster cycle.
a.


141
The sum of the squares of the residuals is
N
S = SR.'
r i=l 1
(115) .
The estimated standard deviations of aQ, a^, and a2 are
given by (92)
and
= ((S /(N-3))C71,)1/2
ao r 1,1
sax ((s/w-snc^)172
(116),
(117),
Sa2 = ((Sr/(N-3)Jc"^)1/2 (118),
th
respectively, and C. is the (i,i) element of
1/1
matrix C The coefficient of multiple determination (90),
2
R is given by
R2 = 1 r-: (119),
2 (Z. Z)
i=l 1
where
N
E Z.
' =1 1
Z = (120) .
N
2 2
The value of R may range from zero to one, and when R 1
the data are well described by equation (96).
The rapid calculation of the regression coefficients
and their estimated standard deviations for a data set of


48


2.0
T
t/l'o
W
1.5
1.0
0.5
0.0
0
100
T
T
T
200 300 400
h a
o w
/4>'
500
108


139
N
SYZ = E Y.Z. (102),
i=l 1 1
respectively. Equations (97-99) can be put into matrix
form:
where
and
D = CA
E Z
D
=
EXZ
_EYZ_
N
EX
EY
s
EX
2
EX
EXY
EY
EXY
EY2
(103),
(104),
(105),
(106).
Simple matrix arithmetic shows that
A = C_1D (107) ,
where C ^ is the inverse matrix of matrix of C. Therefore,
the regression coefficients may be estimated from N (X,Y,Z)
points by calculating matrix elements and subsequently
performing matrix inversion and matrix multiplication.
The elements of matrix C may be calculated by multiplication
C = ItI (108) ,


10
As we have seen, there is a greater degree of charge
localization at an excited-state charge accepting group in
the excited state than there is at that group in the ground
state. Consequently, there will be a greater amount of
electrostatic attraction between the proton and the
functional group in the excited-state molecule than in the
ground-state molecule. Protonation of the excited-state
group, therefore, stabilizes the excited state more than
protonation of the ground-state group stabilizes the ground
state. Since protonation stabilizes the excited state
relative to the ground state, the fluorescence and longest
wavelength absorption bands shift to longer wavelength
(redshift) when the ionizable group is protonated.
Excited-state electronic charge donating groups,
however, are possessed of a greater degree of charge
localization in the ground state than they are in the
excited state. Protonation of these groups, therefore,
stabilizes the ground state relative to the excited state,
and hence the fluorescence and longest wavelength absorption
bands will shift to shorter wavelength (blueshift) when the
functional group is protonated.
The Forster Cycle
In 1950, Forster (27) proposed that the energies of
the spectral shifts incurred by protonation of an aromatic
base could be quantitatively related to the difference


Figure 4-4
Plot of the relative quantum yield of fluorescence (4>/<¡> )
-5
of 3 X 10 M protonated 2-quinolone in HCIO^ versus H .
Analytical wavelength = 370 nm. Excitation wavelength =
280 nm (isosbestic point).


90
H
o


REFERENCES
1. Tortora, G.J., and Anagnostakos, N.P., Principles of
Anatomy and Physiology, San Francisco, Canfield
Press, 1975, chapter 16.
2. Beall, P.T., The Sciences, January (1981), 6.
3. Hallenga, K., Grigera, J.R., and Berendsen, H.J.C.,
J. Phvs. Chem., 84 (1980), 2381.
4. Paul, M.A., J. Am. Chem. Soc., 76 (1954), 3236.
5. Br^nsted, J.N., Reel. Trav. Chim. Pays-Bas, 42 (1953),
718.
6. Lowry, T.M., Chem. Ind. (London), 42 (1923), 43.
7. Henderson, L.J., J. Am. Chem. Soc., 30 (1908), 954.
8. Hasselbach, K.A., Biochem. Bull., 2 (1913), 367.
9. Hammett, L.P., and Deyrup, A.J., J. Am. Chem. Soc.,
54 (1932), 2721.
10.Lovell, M.W., and Schulman, S.G., Anal. Chim. Acta,
127 (1981), 203.
11. Lovell, M.W., and Schulman, S.G., Int. J. Pharm., 11
(1982), 345.
12. Lovell, M.W., The Influence of Hydration on Prototropic
Equilibria in Acidic Aqueous Media, Doctoral
dissertation, University of Florida, 1982.
13. Forster, T., Naturwiss., 36 (1949), 186.
14.
Weber, K., Z.
Phys. Chem. B, 15 (1931), 18.
15.
Klopffer, W.,
Adv. Photochem., 10 (1977), 311.
16.
Schulman, S.G
., and Winefordner, J.D., Talanta,
(1970), 607.
17. Vander Donckt, E., Prog. React. Kinetics, 5^ (1970), 273.
143


28
Acridcne (9-(10H)-acridanone) and 1-isoquinolone
(isocarbostyril) were purchased from Aldrich Chemical
Company (Milwaukee, WI). Both 2-quinolone and 4-quinolone
were purchased from K&K Labs (Plainview, NY). Xanthone
(xanthen-9-one) was purchased from Eastman Organic
Chemicals (Rochester, NY). The sample of 3-aminoacridine
that was used was synthesized and identified by L.S.
Rosenberg (59) after the method of Martin and Tong (60).
Acridone was recrystallized three times from
EtOHii^O (1:1). Xanthone was purified with column
chromatography on silica gel using CHCl^ as the mobile
phase. Purity was confirmed with TLC on silica gel using
CHCl^ as the mobile phase and UV light from a handheld UV
lamp as the method of spot visualization (short wavelength
UV light excited the fluorescent indicator in the silica,
revealing both fluorescent and nonfluorescent spots, while
long wavelength UV light visualized only fluorescent spots).
Both 2-quinolone and 4-quinolone were recrystallized three
times from Et0H:Ko0 (1:3). Crystalline 1-isoquinolone was
used as received from Aldrich. Purity was confirmed by
TLC on silica gel using three different mobile phases (CHCl^z
1:9 MeOH: CHC1-,, and 1:4 MeOH : CHC1,) Impure
3-aminoacridine was purified with column chromatography on
silica gel. Pure 3-aminoacridine was gradient eluted with
MeOH^HCl^ (the composition of which varied from 1:19 to
2:3) as the mobile phase. Purity was confirmed with TLC


Figure 6-4
Plot of the relative quantum yield of fluorescence ($/<|>o)
_ g
of 1.9 X 10 M doubly prctonated 3-aminoacridine in
t^SO^ versus H+. Analytical wavelength = 470 nm.
Excitation wavelength = 358 nm (isosbestic point.


101
Figure 5-1
Structure of 1-isoquinolone.


134
a general method for predicting the thermodynamics of
proton transfer in dilute, aqueous solution based on
measurements made in nonaqueous or mixed-aqueous solvents.
This would greatly simplify the determination of the
pKa's of many water-insoluble pharmaceuticals, for then
the thermodynamic pK 's of relatively water-insoluble
species could be calculated from measurements made in
nonaqueous or mixed-aqueous solvents in which the species
are soluble. A study of acid-base thermodynamics in
methanolic sulfuric acid could not be performed, however,
until an acidity scale for the medium is determined.
Values of aw in the solvent, and perhaps of the activity
of methanol in the solvent, would also have to be measured.




o
o
o
o
Absorbance
o

i-1
O O C 00 o
611


42
Table 3-1
Variation with bromide ion concentration of i', x and
m for acridone.
[Br'
"]
, M
x', nsa
b
x ns
m
o
o
0
-3
14.80.5
26.010.4
1311'
5.0
1.0
X
X
10_3
10 J
14.80.5
14.810.5
18.7
15.6
3318
4013
3.0
X
10-2
14.810.5
9.7
5913
5.0
X
10-1
14.810.5
6.7
7115
1.0
4.0
5.0
X
X
X
10-1
10-1
10 x
14.810.5
14.810.5
14.810.5
3.7
0.59
0.45
10419
16916
17519
aThe lifetime of neutral acridone was measured in water
at pH = 7.0.
^The lifetime of protonated acridone was calculated as
T0 = (<>/cf)o) x t/, where <{>/<}>o is the relative quantum
yield of fluorescence at the bromide ion concentration
of interest (values of §/§Q are shown in Figure 3-2)
and xoa is the fluorescence lifetime of protonated
acridone in the absence of quencher (measured in 2.3
M HC104, Hq = -1.0).
Q
Taken from reference (31).


147
72.
Watkins,
A.R., Z. Phys.
Chem. N. F.,
78 (1972), 103
73.
Watkins,
A.R., J. Chem.
Soc. Faraday
Trans. I., 68
(1972) ,
28.
74. Schulman, S.G., Vogt, B.S., and Lovell, M.W., Chem.
Phys. Letts., 75 (1980), 224.
75. Albert, A., and Phillips, J.N., J. Chem. Soc., Pt. 2
(1956), 1294.
76. Ireland, J.F., and Wyatt, P.A.H., J. Chem. Soc.
Faraday Trans. I, 68 (1972), 1053.
77. Vogt, B.S., and Schulman, S.G., Chem. Phys. Letts.,
in press (1983).
78. Schulman, S.G., and Vogt, B.S., J. Phys. Chem., 85
(1981), 2074.
79. Teng, T.T., and Lenzi, F., Can. J. Chem., 50 (1972),
3283.
80. Bascombe, K.N., and Bell, R.P., Discuss. Faraday Soc.,
2_4 (1957),158.
81. Strickler, S.J., and Berg, R.A., J. Chem. Phys., 37
(1962), 814.
82. El-Bayoumi, M.A., Dalle, J.P, and O'Dwyer, M.F.,
J. Am. Chem. Soc., 92 (1970), 3494.
83. Ross, R.T., Photochem. Photobiol., 21 (1975), 401.
84. Werner, T.C., in Modern Fluorescence Spectroscopy,
v. 2, ed. E.L. Wehry, New York, Plenum, 1976, p. 277.
85. Schulman, S.G., Rosenberg, L.S., and Vincent, W.R.,
J. Am. Chem. Soc., 101 (1979), 139.
86. Vogt, B.S., and Schulman, S.G., Chem. Phys. Letts., 95
(1983), 159.
87. Vetesnik, P., Bielavsky, J., and Vecera, M., Coll.
Czech. Chem. Comm., 33 (1968), 1687.
88. Vogt, B.S., and Schulman, S.G., submitted to Chem.
Phys. Letts. (1983).
89. Lovell, M.W., and Schulman, S.G., Anal. Chem.,
(1983) .
in press


APPENDIX B
MULTIPLE LINEAR LEAST-SQUARES
REGRESSION ANALYSIS
In some cases it is postulated that experimental
data will fit an equation of the form
Z = a + a^X + a2Y (96) ,
where Z is the dependent variable, X and Y are the
independent variables, and aQ, a^, and a2 are the
regression coefficients (unknowns). The regression
coefficients may be estimated by the simultaneous solution
of the three normal equations (90)
EZ = aQN + a,ZX + a2EY (97),
EXZ = aQIX + a1EX2 + a2ZXY (98),
and
EYZ = aQZY + a1EXY + a2ZY2 (99),
where all of the symbols are the same as defined in
equations (88-91) and EZ, EXZ, and EYZ are given by
N
EZ = E Z. (100),
i=l 1
N
EXZ = E X.Z. (101),
i=l 1 X
and
138


14
equilibrated. While both fluorescence and absorption
originate from vibrationally relaxed and thermally
equilibrated electronic states, they frequently terminate
in Franck-Condon electronic states (28). Figure 1-1,
therefore, is not an accurate representation of the
transitions of interest. Figure 1-2 shows a modified
Forster cycle which includes Franck-Condon ground and
excited states. It can be seen from Figure 1-2 that
absorption may occur at higher energy than the 0-0 energy,
and fluorescence may occur at energy lower than the 0-0
energy. Both and \>B, therefore, may be estimated from
the fluorescence and longest wavelength absorption maxima
of the conjugate pair, but they will not necessarily
reflect the true 0-0 energies.
From Figure 1-2 we see that
(16)
and
(17)
Still assuming that the entropies of protonation in the
ground and excited states are identical, equations (16) and
(17) may be transformed into equations (18) and (19),
respectively.
* *
A pK
(18)
(19)


8
differences between ground- and excited-state prototropic
reactivities. Those functional groups which have lone pairs
from which electronic charge is donated to the aromatic
system upon molecular excitation become more acidic in the
excited state. In the excited state, electronic charge is
delocalized from the functional group to the aromatic tt
system, and hence the electrostatic attraction between the
functional group and the proton is lower in the excited
state than it is in the ground state. The proton may thus
be lost more easily in the excited state, and hence
k k
pK^ < pK^ (where pKa is the negative logarithm of the
acid-dissociation equilibrium constant for the reaction as
it occurs in the excited state). Examples of excited-state
electronic charge donating groups include -OH, -O -OH*,
-SH, -s-, -SH*, -NH0, -NH~, -NH*, and pyrrolic nitrogens.
Functional groups that have vacant low-lying it
orbitals can accept electronic charge upon molecular
excitation. These groups include -COOH, -COO -COOH*,
-CONH2, -CONH-, -CONH*, -COSH, -COS", and -COSH*. In the
excited state, electronic charge is delocalized from the
aromatic it system to the vacant orbital of the functional
group, and the resulting increase in electrostatic
attraction between the functional group and the proton
k
results in pK > pK Pyridinic nitrogens are
excited-state electronic charge acceptors even though they
possess a lone pair but not any vacant low-lying tt


95
identically straight lines. It is not possible, therefore,
to discern whether it is three or four water molecules which
react with the hydrated, protonated 4-quinolone in the
deprotonation step of the excited-state reaction. The
value of n = 4, however, is still in keeping with the
values of n previously proposed (79,80) for the region of
acidity in which the excited-state proton transfer of
4-quinolone occurs. It is not surprising that n was found
to be three in the case of 2-quinolone but four in the case
of 4-quinolone because the Hammett indicators (9) which
were used to define the Hammett acidity function in these
respective regions of acidity are different and their
deprotonation reactions may have different hydration
requirements. This is reasonable not only because of
structural differences between the indicators, but also
because the activity of water at the inflection point of
the fluorimetric titration of 4-quinolone (a^ = 0.98) is
quite different from that at the inflection point of the
fluorimetric titration of 2-quinolone (a = 0.66). These
differences in the availability of water could result in
different numbers of water molecules entering into reactions
which occur in solutions of significantly different acid
composition.
If the various indicator and quinolone species each
have several different hydrates, then it is possible that
n and r are not constant, in which case equation (77)


Figure 3-9
Plot of T'/m versus x for xanthone.
o o


30
unthermostatted cell compartments were taken at room
temperature, which was found to be 242C.
All fluorescence spectra were uncorrected for
instrumental response and were taken on a Perkin-Elmer
MPF-2A steady-state fluorescence spectrophotometer. This
fluorimeter was equipped with a thermostatted cell
compartment, which, when a constant temperature bath was
available, was kept thermostatted at 25.00.2C. When the
ground- and excited-state proton-transfer reactions
overlapped, fluorescence was excited at an isosbestic
point (at which en = £_+), and hence equations (31) and
o on
(32) reduced to
and
aBH+
[H+]
[H+] + K.
(44)
K
a
B
.+
(45) ,
[H ] + K.
respectively. The quantities 4>/4>0 and were
calculated in terms of fluorescence intensities. The
fluorescence intensity, F, at any point on the titration
inflection region is, for a given analytical wavelength,
given by
F=2.3IoeBH+[BH+]l + 2.3<|>I0eB[B]l +
2.3,I0£B[B]l + 2.3 (46) ,


Figure 3-3
Variation of the relative quantum yield of fluorescence (<1>' /$'Q) of 5 X 10~
neutral acridone with pH at various bromide ion concentrations. (A) [Br-]
(B) [Br~] = 5.0 X 10"3 M, (C) [Br] = 5.0 X 10_2 M, (D) [Br] = 1.0 X 10"
(E) [Br ] = 5.0 X 10 1 M. Analytical wavelength = 440 nm. Excitation
wavelength = 350 nm.


35
the analyte in a solution of different acid concentration
was then added to the 2 mis of solution already in the
cuvette. The solution was then stirred with a fine glass
rod. The resulting acid concentration was calculated, and
then the spectrum of the analyte and the acid molarity
were recorded. The acid solutions which were mixed were
prepared so as to differ by two or fewer molar units in
order to minimize partial molar volume effects and
temperature changes due to heat of mixing and heat of
dilution. This procedure was repeated with different
initial and final concentrations of acid until no further
significant changes in the spectrum were observed.
Solutions for all titrations were prepared immediately prior
to their being used to minimize the possibility of
degradation of the test compound.
Analytical wavelengths were chosen to be at or as close
to a peak maximum as possible while still yielding the
greatest difference between the spectra of the conjugate
acid and base. This was done to maximize analytical
sensitivity, accuracy, and precision.
Computation
Routine calculations (and sometimes simple linear
regression analysissee Appendix A) were performed on a
card-programmable calculator (Texas Instruments TI-59).
Complex calculations (simple and multiple linear regression
analysessee Appendices A and B) were performed on either


Figure 4-7
-4
Plot of absorbance versus pH for 1 X 10 M 4-quinolone in
water. Analytical wavelength = 327 nm.


137
The sign of r simply indicates whether the slope is positive
(r > 0) or negative (r < 0). When r 0, then Y is not
linearly dependent on X.
The equations in this appendix are short-form
computational formulae which are particularly useful when
computation is limited to devices with small amounts of
RAM (random access memory). Because of this, equations
(86-95) are well suited for the estimation of r, a S ,
ao
a., and S with handheld programmable calculators. Simple
I ax
linear regression, analysis may also be performed with matrix
operations (92), but this method is beyond the
capabilities of most of the currently available handheld
computing devices.


TABLE OF CONTENTS
ACKNOWLEDGEMENTS iii
ABSTRACT vi
CHAPTER PAGE
I INTRODUCTION 1
BrgSnsted-Lowry Acid-Base Chemistry in
Ground Electronic States 3
Prototropic Reactivity in Electronically
Excited States 7
The Effects of Protonation on
Electronic Spectra 9
The Forster Cycle 10
Steady-State Kinetics of Excited-State
Proton-Transfer Reactions 20
Summary 25
II EXPERIMENTAL 27
Reagents and Chemicals 27
Absorption and Fluorescence Studies 29
Measurements of Acidity 33
Titration Methods 33
Computation 35
III GROUND- AND EXCITED-STATE PROTON TRANSFER
IN ACRIDONE AND XANTHONE 37
Introduction 37
Results and Discussion 41
IV EXCITED-STATE PROTON TRANSFER IN
2-QUINOLONE AND 4-QUINOLONE 67
Introduction 67
Results and Discussion 71
V EQUILIBRIUM EXCITED-STATE PROTON TRANSFER
IN 1-ISOQUINOLONE 99
Introduction 99
Results and Discussion 100
iv


PROTON-TRANSFER KINETICS AND EQUILIBRIA
IN CONCENTRATED MINERAL ACIDS
By
BRIAN STANLEY VOGT
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA

This dissertation is lovingly dedicated to my dear
wife, Carla,
encouragement
Her continual love, patience, and
were instrumental in the completion of this
work.

ACKNOWLEDGEMENTS
I would first like to thank Dr. S.G. Schulman,
chairman of my supervisory committee, for his patient
guidance throughout my graduate career. His perception,
experience, and advice were indispensable in the completion
of the research which culminated in this dissertation. I
would also like to thank the other members of my supervisory
committee, Dr. F.A. Vilallonga, Dr. K.B. Sloan, Dr. J.H.
Perrin, and Dr. J. D. Winefordner, for their suggestions
and support.
I would also like to thank the other members of the
research group not only for their friendship, but also for
the many thought-provoking discussions and heated
arguments which helped all those involved to gain a clearer
perspective on the strengths and weaknesses of their
scientific understandings. Michael Lovell was
particularly helpful in these regards.
Finally, I would like to thank my parents, Stanley and
Blanche Vogt, for the understanding and wisdom with which
they have encouraged me. They have played an important role
in the years of success that I have been privileged to.
iii

TABLE OF CONTENTS
ACKNOWLEDGEMENTS iii
ABSTRACT vi
CHAPTER PAGE
I INTRODUCTION 1
BrgSnsted-Lowry Acid-Base Chemistry in
Ground Electronic States 3
Prototropic Reactivity in Electronically
Excited States 7
The Effects of Protonation on
Electronic Spectra 9
The Forster Cycle 10
Steady-State Kinetics of Excited-State
Proton-Transfer Reactions 20
Summary ' 25
II EXPERIMENTAL 27
Reagents and Chemicals 27
Absorption and Fluorescence Studies 29
Measurements of Acidity 33
Titration Methods 33
Computation 35
III GROUND- AND EXCITED-STATE PROTON TRANSFER
IN ACRIDONE AND XANTHONE 37
Introduction 37
Results and Discussion 41
IV EXCITED-STATE PROTON TRANSFER IN
2-QUINOLONE AND 4-QUINOLONE 67
Introduction 67
Results and Discussion 71
V EQUILIBRIUM EXCITED-STATE PROTON TRANSFER
IN 1-ISOQUINOLONE 99
Introduction 99
Results and Discussion 100
iv

VI NONEQUILIBRIUM EXCITED-STATE PROTON
TRANSFER IN 3-AMINOACRIDINE 112
Introduction 112
Results and Discussion 114
VII SUMMARY 131
APPENDICES
A SIMPLE LINEAR LEAST-SQUARES REGRESSION
ANALYSIS 135
B MULTIPLE LINEAR LEAST-SQUARES REGRESSION
ANALYSIS 138
REFERENCES 143
BIOGRAPHICAL SKETCH 149
v

Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial
Fulfillment of the Requirements for the
Degree of Doctor of Philosophy
PROTON-TRANSFER KINETICS AND EQUILIBRIA
IN CONCENTRATED MINERAL ACIDS
By
BRIAN STANLEY VOGT
August, 1983
Chairman: Stephen G. Schulman, Ph.D
Major Department: Pharmacy
Ultraviolet-visible absorption and fluorescence
spectroscopy were used to study ground- and excited-state
proton-transfer reactions. A transition-state reaction
scheme was used to propose a model to quantitate the
kinetics of excited-state proton transfer in
concentrated acid. The Hammett acidity function, Hq, was
used as a measure of acidity. The model thus derived
included r, the number of water molecules which enter into
the excited-state deprotonation reaction of the test
compound. Also included was n, the number of water
molecules which enter into the ground-state deprotonation
reaction of the indicator used to define that range of the
H scale over which the excited-state ionization of the
o
test compound occurred. The model successfully described
vi

the excited-state ionizations of several aromatic lactams
in í^SO^ or HCIO^. Modification of the model to describe
the excited-state ionization of an H+ type molecule was
successful.
It was found that one of the molecules studied
demonstrated excited-state prototropic equilibrium. While
*
pK could be determined, neither the rate constants for the
cl
reactions steps nor n and r could be determined. The model
predicted that these limitations would apply to all excited-
state prototropic equilibria occurring in concentrated acid.
The other molecules exhibiting excited-state ionizations in
concentrated acid demonstrated nonequilibrium excited-state
•k
proton transfer. Values of pK , the rate constants for the
reaction steps, and n and r were determined.
Also devised was a general method of determining the
rate constants of the excited-state reaction steps when the
ground-state ionization occurs in concentrated acid but the
excited-state ionization occurs in dilute solution. This
method was successfully applied to several Hq type molecules.
Ground-state ionizations occurring in concentrated acid
were successfully described by a modified Henderson-
Kasselbach equation. This equation accounted for n and also
for r , the number of water molecules which enter into the
g
ground-state deprotonation of the test compound.
For all but one of the compounds studied, the Forster
★
successfully related pK to pK .
3 3
Vll

CHAPTER I
INTRODUCTION
The physical and chemical properties (solubility, pK ,
Cl
rates of hydrolysis, etc.) of drugs are usually measured in
dilute, aqueous solution. It is frequently assumed that
these measurements reflect the correct values of these same
properties of the drugs when they are found in vivo.
However, the experimental solution media are idealized
compared to the environments found in vivo. For example,
plasma is an approximately 8% solution of proteins,
electrolytes, lipids, sugars, amino acids, hormones, and
metabolic wastes (1), and hence plasma is not a dilute,
aqueous solution. Lymphatic fluid and interstitial fluid
are similar to plasma (except that they contain less
proteins). Cell interiors are another example of media
which do not act as dilute solutions, for somewhere between
10% and 60% of the total volume of cells may be water which
is "bound up" by cell constituents (2). Indeed, it has been
shown that the properties of water in dilute, aqueous
solution are dramatically different from the properties of
water in cells (2) and around hydrophobic solutes (3).
Furthermore, the acidity of aqueous solutions may be
enhanced by the addition of neutral electrolytes. For
example, a 1 M solution of NaCl (approximately 6% NaCl)
made up in 0.01 M
1

2
HC1 (pH - 2) has pH = 0.2 (4), and hence the acidity of the
solution is changed by almost two orders of magnitude by
the addition of the neutral salt. It is conceivable that
the presence of high concentrations of solutes in some body
fluids could lead to unexpectedly high acidities and low
activities of water in those fluids. A study of the
physicochemical properties of molecules in concentrated
electrolytic media could be useful, for such a study could
shed light on whether or not it is legitimate to use
properties measured at infinite dilution in water to
predict the behavior of the molecules in media which
significantly deviate from ideality.
The acid-base properties of functionally substituted
aromatic molecules in electronically excited states are
frequently thermodynamically and kinetically quite different
from these properties in ground electronic states. Because
of this, the ground- and excited-state ionizations may occur
in media which radically differ from each other insofar as
their electrolyte (acidic and/or neutral) compositions are
concerned. When the ionizable group is bonded directly to
an aromatic ring, UV-visible absorption and fluorescence
spectroscopy may be used as tools to study ground- and
excited-state proton-transfer reactions. The author has
used absorption and fluorescence spectroscopy to study
proton-transfer reactions in both dilute, aqueous solutions

3
and in concentrated electrolytic media. Before discussing
the author's research, however, a review of ground- and
excited-state acid-base chemistry is in order.
Br^nsted-Lowry Acid-Base Chemistry in Ground Electronic States
We shall restrict ourselves to the Br0nsted-Lowry
definitions (5,6) of acid and base (an acid is a species
which can donate a proton and a base is a species which can
accept a proton). The acid-base properties of a given
organic molecule are a consequence of the presence of one
or more electronegative atoms (usually nitrogen, oxygen,
or sulfur) in that molecule. In a Br0nsted-Lowry acid, at
least one of these atoms is present and has covalently
bonded to it a hydrogen atom. Sufficiently strong
interaction between the solvent and the hydrogen atom results
in the loss of the hydrogen atom from the molecule to form
a solvated proton and the conjugate base of the organic
acid. Br^nsted-Lowry bases contain at least one
electronegative atom with at least one pair of unshared
electrons (lone pair). Protonation (ionization) is the
formation of a coordinate-covalent bond between the lone
pair on the base and a proton (which may come from the
solvent, if it is sufficiently acidic, or from some other
source of protons). The conjugate acid of the organic base
and the solvent lyate anion (when the solvent is the proton
donor) are formed when protonation of the base occurs. The

4
molecules which we shall consider have conjugate acids and
bases which react according to the mechanism
BH + SH
B + SH,
(1) ,
+ .
where B is the conjugate base, BH is the conjugate acid,
,+ .
SH is the solvent, and SH2 is the solvent lyonium ion.
rate constants ka and k^ are, respectively, the pseudo-
The
first-order rate constant for deprotonation of BH and the
second-order rate constant for bimolecular protonation of B.
In aqueous solution, SH is water and SH* is the hydronium
ion, and then reaction (1) becomes
k
BH + H20
—> B + H30+
(2)
It is also possible to have a conjugate acid that is so
weakly acidic that solvent lyate anions must be present for
the deprotonation reaction to occur, in which case the
reaction will be described by
BH+ + S
B + SH
(3) ,
where S is the solvent lyate anion ( in water this is the
hydroxide ion) and k' and k¿ are, respectively, the
second-order rate constant for bimolecular deprotonation of
BH+ and the pseudo-first-order rate constant for protonation
of B. The research presented in this dissertation, however,

5
deals only with molecules which react according to mechanism
(2), and hence we shall restrict ourselves to a discussion
of that mechanism.
The acid-dissociation equilibrium constant, K , for
reaction (2) is defined as
K = ^
a k,
a3aH+
aBH+ aw
(4) ,
where a0 and aT,„+ are the activities of the conjugate base
and acid, respectively, and aH+ and a^ are the activities
of proton and water, respectively. In dilute, aqueous
solution a - 1, and then
w
_ aBaH+ _ fe]fBaH+
K — ;—
a a^TT+
BH
[BH+]fBH+
(5) ,
where [B] and f are, respectively, the equilibrium molar
concentration and activity coefficient of B, and [BH+] and
f + are, respectively, the equilibrium molar concentration
BH
and activity coefficient of BH+. At infinite dilution,
f_= 1 and f_„+ = 1, and then equation (5) may be
B BH
transformed into the familiar Henderson-Hasselbach
equation (7,8) :
PK = pH - log [B]r~
a [ BH+ ]
(6) .
In concentrated acidic solutions equation (6) cannot
be used. The acidity of the medium (pH < 1) cannot be
measured with a pH meter, but it can be measured with the
Hammett acidity function (9). This acidity scale is based

6
upon the spectrophotometrically measured conjugate base/acid
ratios of a series of primary nitroaniline indicators which
behave according to the reaction
HIn+ + nH20 , In + H+ (7) ,
where In and HIn+ are, respectively, the conjugate base and
acid of the indicator, and n is the number of water molecules
which react with the hydrated conjugate acid to form the
hydrated conjugate base and hydrated proton. The activity
of proton is related to the Hammett acidity, Hq (where
Ho = “log hQ)' by
a„+ = ha
H o w
n
f;
(8)
o
where f_J_ and f^ are the activity coefficients of HIn+ and
In, respectively. In concentrated acid aw < 1, and hence
a cannot be eliminated from equation (8). The acid-base
w
reaction of the test compound of interest is then
BH+ + r H^O * B + H+ (9)
g 2 •*
/
/
where r is the number of water molecules which react with
g
hydrated, ground-state BH+ to form hydrated, ground-state B
and the hydrated proton. The equilibrium constant for this
reaction is defined as
K
a
^ fBaH+
‘BH+1 fBH+ ^9
(10) .

7
Equations (8) and (10) may be combined and put into the
logarithmic form
f f'
pKa = Ho~ log--6"1-, - (n-r ) log a - log,,6 * (11).
a ° [BH+] g W fBH+ fo
Lovell and Schulman (10-12) have successfully applied
equation (11) to the prototropic reactions of a series of
unsubstituted and substituted carboxamides and to a series
of tertiary anilines,which all ionized in concentrated acid.
On the basis of similarity in size and charge of the species
involved, they assumed that f„f ' =füt,+f ' , so that equation
(11) reduces to
pK = H - log-^L- (n-r )log a (12).
a ° [BH ] g
It remains to be seen whether or not equation (12) is
generally applicable.
Prototropic Reactivity in Electronically Excited States
The study of the acid-base chemistry of electronically
excited aromatic acids and bases began formally in 1949,
when Forster (13) elaborated upon Weber's earlier
observation (14) that the fluorescence spectrum of
l-naphthylamine-4-sulfonate exhibits pH dependence different
from the pH dependence of its absorption spectrum. Years
of subsequent research have shed much light on this subject.
Electronic excitation of an aromatic molecule results
in a change in electronic distribution in that molecule.
This difference in electronic distribution results in

8
differences between ground- and excited-state prototropic
reactivities. Those functional groups which have lone pairs
from which electronic charge is donated to the aromatic
system upon molecular excitation become more acidic in the
excited state. In the excited state, electronic charge is
delocalized from the functional group to the aromatic tt
system, and hence the electrostatic attraction between the
functional group and the proton is lower in the excited
state than it is in the ground state. The proton may thus
be lost more easily in the excited state, and hence
•k k
pK^ < pK^ (where pKa is the negative logarithm of the
acid-dissociation equilibrium constant for the reaction as
it occurs in the excited state). Examples of excited-state
electronic charge donating groups include -OH, -O , -OH*,
-SH, -s-, -SH*, -NH0, -NH~, -NH*, and pyrrolic nitrogens.
Functional groups that have vacant low-lying it
orbitals can accept electronic charge upon molecular
excitation. These groups include -COOH, -COO , -COOH*,
-CONH2, -CONH~, -CONH*, -COSH, -COS_, and -COSH*. In the
excited state, electronic charge is delocalized from the
aromatic it system to the vacant orbital of the functional
group, and the resulting increase in electrostatic
attraction between the functional group and the proton
k
results in pK > pK . Pyridinic nitrogens are
excited-state electronic charge acceptors even though they
possess a lone pair but not any vacant low-lying tt

9
orbitals. This is a consequence of the electronegativity
of the nitrogen being higher than that of the carbons to
which it is bonded, and in the excited state charge is
localized on the nitrogen. The lone pair projects out in
the plane of the ring and is perpendicular to the aromatic
tt system. This perpendicularity prevents the lone pair from
interacting with the aromatic system.
It should be mentioned that excited-state proton
transfer can be either intramolecular or intermolecular.
Intramolecular excited-state proton transfer has been
reviewed (15) , and this dissertation is concerned only
with intermolecular proton transfer. Furthermore, the
excited state of interest can be either an electronically
excited singlet or triplet state. The principles of
excited-triplet-state proton transfer are the same as those
for the singlet state (see references (16-26) for examples),
but the research under consideration deals only with proton
transfer in ground and excited singlet states.
The Effects of Protonation on Electronic Spectra
Protonation of a functional group which is intimately
coupled to an aromatic system may have a profound effect
upon the absorption and fluorescence spectra of that
molecule. This is a result of the electronic charge
stabilization incurred by the presence of the proton at the
functional group.

10
As we have seen, there is a greater degree of charge
localization at an excited-state charge accepting group in
the excited state than there is at that group in the ground
state. Consequently, there will be a greater amount of
electrostatic attraction between the proton and the
functional group in the excited-state molecule than in the
ground-state molecule. Protonation of the excited-state
group, therefore, stabilizes the excited state more than
protonation of the ground-state group stabilizes the ground
state. Since protonation stabilizes the excited state
relative to the ground state, the fluorescence and longest
wavelength absorption bands shift to longer wavelength
(redshift) when the ionizable group is protonated.
Excited-state electronic charge donating groups,
however, are possessed of a greater degree of charge
localization in the ground state than they are in the
excited state. Protonation of these groups, therefore,
stabilizes the ground state relative to the excited state,
and hence the fluorescence and longest wavelength absorption
bands will shift to shorter wavelength (blueshift) when the
functional group is protonated.
The Forster Cycle
In 1950, Forster (27) proposed that the energies of
the spectral shifts incurred by protonation of an aromatic
base could be quantitatively related to the difference

11
k
between pK and pK . This relationship has come to be
known as the Forster cycle, a schematic diagram of which is
shown in Figure 1-1.
Since the energy terms in Figure 1-1 correspond to
thermodynamic state functions, it is correct to write
EA + AH* = EB + AHd (13) .
Forster (27) assumed that the entropies of the ground- and
excited-state proton-transfer reactions are identical, in
which case equation (13) can be changed to
AG - AG* = EA - EB (14) ,
k
where AG and AG are the Gibbs free energies of
protonation in the ground and excited states, respectively.
A n
Furthermore, E and E can be given by E = Nhcv^ and
D
E = Nhcv_,, respectively, where N is Avagadro' s number, h
is Planck's constant, c is the speed of light, and vA and
v_ are, respectively, the frequencies (in wavenumbers) of
B
★ *
the A->-A and B->-B transitions. It is also true that
k k
pK =AG/2.303RT and pK =AG /2.303 RT, where R is the universal
a a
gas constant and T is the absolute temperature. Equation
(14) can then be transformed into
k MV» C —
ApK = pKa - pKa = 2.303RT(VA “ VB) (15)*
In principle, the Forster cycle can be used only when
the 0-0 energies (v,. and v_) are known. These energies
correspond to transitions between ground and excited states
which are both vibrationally relaxed and thermally

Figure 1-1
* *
The Forster cycle. A, B, A , and B refer to the conjugate
acid and base molecules in their ground and excited
A B
states, respectively. E and E are the energies of the
k k k
A+A and B->-B transitions, respectively. AH^ and AH^ are,
respectively, the enthalpies of protolytic dissociation in
the ground and excited states.

13

14
equilibrated. While both fluorescence and absorption
originate from vibrationally relaxed and thermally
equilibrated electronic states, they frequently terminate
in Franck-Condon electronic states (28). Figure 1-1,
therefore, is not an accurate representation of the
transitions of interest. Figure 1-2 shows a modified
Forster cycle which includes Franck-Condon ground and
excited states. It can be seen from Figure 1-2 that
absorption may occur at higher energy than the 0-0 energy,
and fluorescence may occur at energy lower than the 0-0
energy. Both and \>B, therefore, may be estimated from
the fluorescence and longest wavelength absorption maxima
of the conjugate pair, but they will not necessarily
reflect the true 0-0 energies.
From Figure 1-2 we see that
(16)
and
(17)
Still assuming that the entropies of protonation in the
ground and excited states are identical, equations (16) and
(17) may be transformed into equations (18) and (19),
respectively.
* *
A pK
(18)
(19)

Figure 1-2
* ★
Modified Forster cycle. A. , B, , A. , and B, refer to
-1 te te te te
the thermally equilibrated conjugate acid and base
molecules in their ground and excited states, respectively.
* ic
A£C, B^, A^ , and B^c refer to the conjugate acid and base
in their Franck-Condon ground and excited states,
respectively. AH^e an¿ ^Hte are t^e ent^alpies °f
equilibration from the Franck-Condon ground states to the
thermally equilibrated ground states of the conjugate acid
A* B*
and base, respectively. AHte and AHte are the enthalpies
of equilibrium from the Franck-Condon excited states to
the thermally equilibrated excited states of the conjugate
A A. B B
acid and base, respectively. , Efi' Eabs' an<^ Efl
refer to the energies of absorption and fluorescence of the
★
conjugate acid and base, respectively. AH^ and AH^ are,
respectively, the enthalpies of protolytic dissociation
in the ground and excited states.

16
*

17
* -k
B A
Customarily, it is assumed that AHte = AHte and
B A
AHte= AHte,so that equations (18) and (19) reduce to
APK = 2
Nhc abs
303RT(VA
v
—abs
B
(20)
and
A v _ Nhc ,— fl
ApK 2.303RT( A
-
(21) ,
respectively. If pK is known, and fluorescence or
cl
longest wavelength absorption maxima are also known, and if
B* A* A B *
AH, = AH, and AH'" = AHT. , then one can estimate pK .
te te te te' c a
When the fluorescence spectrum (as a function of
energy) of a molecule is an approximate mirror image of its
longest wavelength absorption band, then the vibrational
spacings in the ground and excited states are roughly the
same (29) . In this case the absorption and fluorescence
spectra will be equally displaced from the 0-0 energy. It
would then be reasonable to estimate and by
VA =
A
-fl
+ VA
(22)
and
VB =
—abs
VB
-I1
(23) ,
in which case
= Eabs + Efl - 4Hte + Aiíe
(24)
and

18
,B
= uabs
+ E
B
fl
- H
B
te
H'
B
te
(25)
It may then be assumed that AH^ = AHÍ and
J te te
B* B
= AHfc . This is at least safer than assuming that
AH^e = AH^e and AH^e = AH‘^e, because any difference
between AH* and AH* will be cut in half in the
te te *
g
denominator of equation (24) (the same is true of AHte and
g
AHte in equation (25)). Thus, it is preferable to estimate
vA and vB from equations (22) and (23).
* .
The accuracy of a pK calculated with the Forster
cycle is, of course, dependent upon to what extent the
assumptions inherent in the Forster cycle are adhered to
and upon how accurately pK , v , and v are known (some of
the inaccuracy in the latter two arises from errors in
positioning the monochromators in the spectrophotometer
and fluorimeter). Many molecules have excited-state
geometries and solvation cages which are similar to their
ground-state geometries and solvation cages. Because of
this, it is reasonable to assume that the ground- and
excited-state entropies of protonation are similar, and
*
then the precision of a pK calculated with the Forster
cl
cycle can be as small as ±0.2 (30). This error and the
error in and give typical uncertainties of about
*
±0.3 in Forster cycle pK 's (31). When the assumptions in
B.
the Forster cycle are not correct, however, it is not

19
possible to determine how much uncertainty will be present
*
in a pK calculated with the Forster cycle. These
cL
assumptions have been reviewed in depth (17,26,30,32-39),
and any further elaboration upon them here would serve no
useful purpose.
*
The Forster cycle has been used to calculate PKa's
more than any other method (15,17,26,40-44). These
calculations have been performed for excited-state
ionizations which occur in dilute, aqueous solution and also
for some which occur in concentrated acid. Unfortunately,
the Forster cycle gives no information concerning the rates
of excited-state proton transfer. A method that could give
k
such information could be used to determine not only K ,
cl
k
but also k and k, . The resulting value of pK could be
cl D cl
compared to that calculated with the Forster cycle, and
hence the results of each method could be used to confirm
or challenge the results of the other. While fluorescence
spectroscopy which is time-resolved on the nanosecond and
picosecond time scale has been used to determine the rate
constants for some excited-state protonation and
deprotonation reactions, this technique requires
instrumentation that is both very sophisticated and very
expensive, and also requires the extensive use of computers
for the complicated data reduction that is necessary. We
shall restrict ourselves to a discussion of

20
steady-state kinetics. Representative examples of
time-resolved studies of excited-state proton-transfer
kinetics may be found in references (45-55) .
Steady-State Kinetics of Excited-State Proton-
Transfer Reactions
The kinetic equations for excited-state proton-
transfer reactions in dilute, aqueous solution were first
derived by Weller (56). The excited-state reaction which
we are concerned with is
+ kf +* k * k'
BH i BH >H + B -■■■■ »B (26) ,
where k^ and k^ are the rate constants for the fluorescences
of BH and B , respectively, and k^ and k^ are the sums of
the rate constants for all nonradiative processes
+ * *
deactivating BH and B , respectively. The fluorescence
*
lifetime of the conjugate acid (present when pH << pK&) in
the absence of excited-state proton transfer is
tq = 1/(k^ + k^), and that of the conjugate base (present
*
when pH >> pK ) in the absence of excited-state proton
0.
transfer is = l/(k£ + k¿) . Prior to integration, the
+* *
rate expressions for the disappearance of BH and B from
the excited state may be put into the forms
-/ d[BH+*] =-/®(l/T'+k. [H+] ) [B*] dt+/°°k [3H+*]dt (27)
a_„+ L J o obLJLJ o
and

21
-f°a d [ B * ] = /°°(l/T^+kHrH+] ) [B*]dt-/°X [BH+*]dt (28),
B
* .).*
where [B ] and [BH ] are, respectively, the probabilities
*
of finding a [B ]or [BH ] molecule in the excited state at
J-* *
time t. Since the fluorescences of BH' and B are being
excited and monitored under steady-state conditions, the
right sides of equations (27) and (28) are to be
integrated over all time (t = 0 to t = °°) . The lower
limits of integration of [BH ] and [B ] are «_„+ and
Dll
a , respectively, where a + is the fraction of the
b bn
ground-state population which is found as the conjugate
acid and a is the fraction found as the conjugate base,
b
In spectrophotometric terms,
aBH+ =
£bh+[bh ]
eBH+[BH ] + eB[B]
(29)
and
a
£bCb]
B
;bh+[bh+] + £b[b]
(30) ,
where and £„„+ are the molar absorptivities of the
b bn
conjugate base and acid, respectively, at the wavelength of
excitation. In terms of K ,
Cl
aBH+ *
£BK+tH 1
eBH+[H ! + £BKa
(31)

22
and
a
B
(32) .
If the rate of attainment of steady-state conditions for the
excited-state proton-transfer reaction is much higher than
the rates of photophysical deactivation of B and BH ,
then [B*] = e~t/T' and [BH+*] = e“t/x (57). The
fluorescence lifetimes x and x' are the lifetimes of the
conjugate acid and base, respectively, in the presence of
excited-state proton transfer, where x = l/(k^ + k^ + k^)
and x' = l/(k^ + k^ + k^[H+]). The expressions for [B ]
+*
and [BH ] may be integrated from t = 0 to t = 00, and
then
(33)
o
o
and
(34) .
o
o
The quantum yields of fluorescence of the conjugate acid in
the absence and presence of excited-state proton transfer
are, respectively, <|>o = and <í)= k^x. The relative
quantum yield of fluorescence of the conjugate acid, §/§0,
is thus related to x and x^ by
o
o
(35) .
Analogous reasoning for the conjugate base may be used to

23
show that
X ' = T ' ^—
o 4>1
o
(36) ,
where and the conjugate base in the absence and presence of
excited-state proton transfer, respectively, and the relative quantum yield of fluorescence of the conjugate
base. Combination of equation (33) with (35) and of
equation (34) with (36) shows that
f°° [B* ] dt = t •
0 O o
(37)
and
/“[ BH+*]dt = i $-
o o 4>o
(38)
Therefore, integration of equations (27) and (28) results in
<*„„+ = T- + k„T^ - kfcTo [H+] |t
BH
a o (39)
and
a = t— t k, t' [H+]^t - k t
B 4>q b o <()¿ a oo
(40) .
Equations (39) and (40) can be solved simultaneously for
and to yield
= ctBH~1' + kbT¿tH 1
^o 1 + k t + k. T ' [H+]
a o bo
(41)
and

24
ai a_ + k T
1 _ B a o
♦i 1+ Vo + V¿[H 1
It is thus seen that + o o
ag + ctgH+ = I# equations (41) and (42) can be combined to
give
(42) .
4>/4>0 1
' / T Yo B a o
k.x' i 4> '/<}>'
+ ^[h+1xt °
k x J d>' /4>1 - a_,
a o r 'Yo B
(43)
A plot of (<4>/4>) / ( '/4>' -a ) versus ([H ]

'/ should, therefore, be a straight line with an ordinate
intercept of l/kaxo and a slope of k^T^/k^i^. When tq and
*
can be measured or estimated, then k , k, , and K = k /k,
a. D 3. a. D
can be calculated.
Equation (43) was derived assuming that the excited-
state proton-transfer reaction attains steady-state
*
conditions before photophysical deactivation of B or BH
can occur. When this is not true, then equation (43) will
not rigorously describe the chemistry of interest. A more
sophisticated treatment has been derived (58) which
accounts for situations where steady-state conditions are
*
not achieved before photophysical deactivation of B and
+*
BH takes place. Use of that treatment will give more
accurate values of ka and k^ when nonsteady-state
considerations are significant, but equation (43) will
suffice in many situations. It should be noted, however,
that the observable rate constants ka and are subject

25
to medium effects, and hence equation (43) will not be
applicable to an excited-state proton-transfer reaction which
occurs in concentrated acid, where the medium is
different from one part of the titration inflection region
to another. The hypothetical, medium-independent rate
constants for the reaction in concentrated acid are k (0)
cl
and k^iO), which correspond to the deprotonation and
protonation steps, respectively, for the reaction as it
would occur in infinitely dilute, aqueous solution. The
author's research represents the first attempt to
quantitate k (0) and k, (0).
cl O
Summary
Proton transfer in both ground and excited states has
been thoroughly studied and quantitated for those acid-base
reactions which occur at or close to infinite dilution and
where 1 < pH < 13. However, up to the time when the
author began his research, no attempts had been made to
quantitate the kinetics and equilibria of excited-state
proton-transfer reactions in concentrated electrolytic media.
It was the goal of the author to develop a successful model
for these reactions in concentrated acidic media (pH < 1).
The author also wished to see if equation (12) has more
general application than it has had to date. Finally, the
author desired to see if there exists a fundamental
relationship between the thermodynamics and kinetics of

26
proton transfer in dilute, aqueous solution and the
thermodynamics and kinetics of proton transfer in
concentrated acid.

CHAPTER II
EXPERIMENTAL
Reagents and Chemicals
The water that was used was either deionized, distilled
water or doubly deionized water. Sulfuric acid, perchloric
acid, chloroform, methanol, ammonium hydroxide, sodium
hydroxide, sodium bromide, and potassium hydrogen phthalate
were all ACS reagent grade and were purchased from either
Fisher Scientific Company (Fair Lawn, NJ) or Scientific
Products (McGaw Park, IL). Ethanol was 95% and was
purchased locally from hospital stores (J. Hillis Miller
Health Center, Gainesville, FL). Thin-layer
chromatography plates were fluorescent-indicator
impregnated, 250 micron thick silica gel plates and were
purchased from Analabs (North Haven, CT). Dry silica gel
(100-200 mesh) for atmospheric pressure column
chromatography was purchased from Fisher Scientific
Company. All acid solutions were standardized against
standard NaOH (the NaOH was standardized against potassium
acid phthalate). All reagents were checked for spurious
absorption and emission prior to their being used for
spectroscopic studies.
All weighings were performed on a Mettler Type B6
electronic analytical balance.
27

28
Acridcne (9-(10H)-acridanone) and 1-isoquinolone
(isocarbostyril) were purchased from Aldrich Chemical
Company (Milwaukee, WI). Both 2-quinolone and 4-quinolone
were purchased from K&K Labs (Plainview, NY). Xanthone
(xanthen-9-one) was purchased from Eastman Organic
Chemicals (Rochester, NY). The sample of 3-aminoacridine
that was used was synthesized and identified by L.S.
Rosenberg (59) after the method of Martin and Tong (60).
Acridone was recrystallized three times from
EtOHii^O (1:1). Xanthone was purified with column
chromatography on silica gel using CHCl^ as the mobile
phase. Purity was confirmed with TLC on silica gel using
CHCl^ as the mobile phase and UV light from a handheld UV
lamp as the method of spot visualization (short wavelength
UV light excited the fluorescent indicator in the silica,
revealing both fluorescent and nonfluorescent spots, while
long wavelength UV light visualized only fluorescent spots).
Both 2-quinolone and 4-quinolone were recrystallized three
times from Et0H:Ko0 (1:3). Crystalline 1-isoquinolone was
used as received from Aldrich. Purity was confirmed by
TLC on silica gel using three different mobile phases (CHCl^z
1:9 MeOH: CHC1-,, and 1:4 MeOH : CHC1,) . Impure
â– J -5
3-aminoacridine was purified with column chromatography on
silica gel. Pure 3-aminoacridine was gradient eluted with
MeOH^HCl^ (the composition of which varied from 1:19 to
2:3) as the mobile phase. Purity was confirmed with TLC

29
using MeOH:CHC1^ (1:19) as the mobile phase, which was
alkalinized by the addition of one drop of NH^OH. The
presence of isosbestic points in the absorption spectra of
these compounds further confirmed their purity.
-4
Stock solutions of the compounds were ==10 M to
-2
=10 M and were made up in either ^0 or MeOH. The stock
solutions were accurately diluted (by a factor of 100) and
the absorbances of the resulting solutions measured at
appropriate analytical wavelengths. These absorbances were
used in conjunction with published molar absorptivities to
calculate the concentrations of the stock solutions. Molar
absorptivities of acridone, 2-quinolone, 4-quinolone, and
1-isoquinolone may be found in reference (61). The molar
absorptivity of 3-aminoacridine may be found in reference
(59) . A carefully weighed sample of pure xanthone was
used to prepare the stock solution, and hence its
concentration was calculated.
Absorption and Fluorescence Studies
Absorption spectra were taken on either a Beckman
DB-GT, Beckman Model 25, or Varian Cary 219
spectrophotometer. The Cary 219 was equipped with a cell
compartment thermostatted at 25.0±0.2°C. The cell
compartment in the DB-GT was thermostatted at 25.0±0.2°C
when a constant temperature bath (Brinkmann Lauda K-2/R) was
available. The Model 25 had no provision for temperature
control. All spectra taken in instruments with

30
unthermostatted cell compartments were taken at room
temperature, which was found to be 24±2°C.
All fluorescence spectra were uncorrected for
instrumental response and were taken on a Perkin-Elmer
MPF-2A steady-state fluorescence spectrophotometer. This
fluorimeter was equipped with a thermostatted cell
compartment, which, when a constant temperature bath was
available, was kept thermostatted at 25.0±0.2°C. When the
ground- and excited-state proton-transfer reactions
overlapped, fluorescence was excited at an isosbestic
point (at which = £_„+), and hence equations (31) and
o on
(32) reduced to
and
aBH+
[H+]
[H+] + K.
(44)
K
a
B
.+
(45) ,
[H ] + K.
respectively. The quantities 4>/4>0 and were
calculated in terms of fluorescence intensities. The
fluorescence intensity, F, at any point on the titration
inflection region is, for a given analytical wavelength,
given by
F=2.3IoeBH+[BH+]l + 2.3<|>I0eB[B]l +
2.3 (46) ,

31
where 1 is the optical depth of the sample and I is the
o
intensity of the exciting light. The first and second
terms on the right side of equation (46) correspond to the
fluorescence from directly excited conjugate acid and that
from the conjugate acid formed by excited-state protonation
of the conjugate base, respectively. The third and fourth
terms on the right side of equation (46) correspond to the
fluorescence from directly excited conjugate base and that
from the conjugate base formed by excited-state deprotonation
of the conjugate acid, respectively. When pH >> pK and
cl
*
pH >> pK , then F = F_ = 2.3' I e^C-l, from which it is
a. b O O tí D
seen that
2.31 £_1 =
B
O B ' Ca
O B
(47) ,
where CL, = [B] + [BH ] and Fn is the fluorescence intensity
b b
of the isolated conjugate base. When pH << pK and
3.
k
pH << pK , then F = FotJ+ = 2.3$ I £_,„+(:„ 1, and then
cl tín O O Dll b
0 e 11 FBK+
o£bh - (48) ,
where Fot,+ is the fluorescence intensity of the isolated
bn
conjugate acid. Combination of equations (47) and (48)
with (46) yields
, CBH+] (j> [B] tj>' [B] [BH+]
BH^o C3 BH+(!)oCb B^¿Cb ' Bcp¿ C3
F
(49) .

32
When fluorescence is excited at an isosbestic point, then
equations (29) and
(30) reduce to
aBH+ = [BH+]/Cb and
a_, = [B]/C_, respectively.
Equation (49) then becomes
F = F cl 4*
BH 4> BH
+ F +—
BH
~°tB +
F ——a + F a +
B4>^B B<í>¿ BH
(50) .
Since + aBH+ = 1
and o + $
= 1, equation
(50)
can be reduced to
4>
F
- fb
(51) ,
4>
o
fbh+
- fb
and it then follows
that
'
fbh+
- F
(52) .
4>'
o
fbh+
- fb
When the ground- and excited-state proton-transfer reactions
do not overlap, then a ->-1 and aBH+->-0 or an(^ aBH+"^' anc^
in either case equations (51) and (52) still follow from (50).
Fluorescence lifetimes were measured at room
temperature with a TRW model 75A decay-time flúorimeter
without excitation or emission filters. This instrument
was equipped with a TRW model 31B nanosecond spectral
source and was used with an 18 watt deuterium lamp, which
was thyratron-pulsed at 5kHz. A TRW model 32A analog decay
computer was used to deconvolute the fluorescence decay time
of the analyte from the experimentally measured fluorescence
decay, which was actually an instrumentally distorted
convolution of the lamp pulse and the analyte fluorescence.
The TRW instruments were interfaced to a Tektronix model 556

33
dual-beam oscilloscope, on which the convoluted fluorescence
decay from the sample was displayed. Lifetimes >1.7 ns were
measurable with this apparatus.
Measurements of Acidity
All pH measurements were made at room temperature with
a Markson ElektroMark pH meter equipped with a silver/silver-
chloride combination glass electrode. The pH meter was
standardized against Fisher Scientific Company pH buffers
or Markson Scientific Inc. (Del Mar, CA) pH buffers at
room temperature. These buffers were accurate to ±0.02
pH unit and were of pH 1.00, 4.00, 7.00, and 10.00. The
precision of the pH meter was estimated to be ±0.01 pH
unit, and it was used for the measurement of pH > 1.
The Hammett acidity function was used as a measure of
the acidity of solutions in which pH < 1. This acidity
scale may be used to quantitate the acidity of media when
the species involved have neutral conjugate bases and
singly charged conjugate acids. Values of Hq in HClO^ and
H2SO4 may be found in references (62-64). Values of a^ in
the same media may be found in references (65-69).
Titration Methods
Solutions for absorption and fluorescence studies were
put into UV-visible quartz cuvettes with pathlengths of
10 mm and volume capacities of =4 mis. Absorption spectra
were taken against a reference solution of composition

34
identical to that which the sample was put in (that is,
the reference solution was either water or acid).
Aliquots of stock solution (^200yl) were injected
into a series of 10 ml volumetric flasks and the flasks
filled to the lines with either water or acid (the stock
solution solvent was first evaporated under dry nitrogen
when the stock solution was methanolic) and the concentration
of acid corrected for any dilution. For titrations where
pH > 1, 2 mis of the aqueous solution were placed in the
sample cuvette, the spectrum recorded, and the pH
measured and recorded immediately after recording the
spectrum. An aliquot of an acidic solution of the analyte
was then added to the cuvette with a micropipette, the
spectrum recorded, and the pH again measured and recorded.
Very small changes in pH (==0.1 unit) were effected by
dipping the end of a heat-fused Pasteur pipette into an
acidic solution of the analyte and then into the aqueous
solution in the cuvette (submicroliter volumes of titrant
were added in this way). The formal concentration of the
analyte was, therefore, constant throughout the titration.
The pH was varied until no further significant changes in
the spectrum were observed.
For titrations where pH < 1, 2.000 mis of an acid
solution of the analyte were put into a cuvette. The
spectrum of the analyte and the molarity of the acid were
recorded. An accurately known volume of a solution of

35
the analyte in a solution of different acid concentration
was then added to the 2 mis of solution already in the
cuvette. The solution was then stirred with a fine glass
rod. The resulting acid concentration was calculated, and
then the spectrum of the analyte and the acid molarity
were recorded. The acid solutions which were mixed were
prepared so as to differ by two or fewer molar units in
order to minimize partial molar volume effects and
temperature changes due to heat of mixing and heat of
dilution. This procedure was repeated with different
initial and final concentrations of acid until no further
significant changes in the spectrum were observed.
Solutions for all titrations were prepared immediately prior
to their being used to minimize the possibility of
degradation of the test compound.
Analytical wavelengths were chosen to be at or as close
to a peak maximum as possible while still yielding the
greatest difference between the spectra of the conjugate
acid and base. This was done to maximize analytical
sensitivity, accuracy, and precision.
Computation
Routine calculations (and sometimes simple linear
regression analysis—see Appendix A) were performed on a
card-programmable calculator (Texas Instruments TI-59).
Complex calculations (simple and multiple linear regression
analyses—see Appendices A and B) were performed on either

36
an International Business Machines IBM 4341 or on a
Digital Equipment Corporation DEC VAX 11/780. All
computer programs were written in BASIC (beginners
all-purpose symbolic instruction code) by the author. The
BASIC language on the IBM 4341 was used through MUSIC
(McGill University system for interactive computing), while
BASIC on the VAX 11/780 was used through DEC VMS (DEC
virtual memory system).

CHAPTER III
GROUND- AND EXCITED-STATE PROTON-TRANSFER
IN ACRIDONE AND XANTHONE
Introduction
The titration behavior of melecules which become much
more basic (or much less acidic) in the excited state than
they are in the ground state will be described by a
★
simplified form of equation (43) . Since pK >> pK , aD->l,
a a a
and then equation (43) can be reduced and rearranged (70) to
k,x'
b ° [H+]
♦ i + Vo
Even if i and x' are known, there is no linear form
o o
(53)
equation (53) can be put into such that k^, k^, and can
be extracted from the data of a single fluorimetric
titration. A method (71-73) of titration involving the use
of HCl has been developed which, in favorable
circumstances, does permit the used of a linear plot to
extract k and k, from a single titration. In this
method, the fluorescence of the conjugate acid is quenched
by Cl while the proton transfer is effected by H+, where
both the Cl and H+ come from the HCl. However, this
method is limited in its application to those molecules
which ionize at pH such that the rate of proton transfer is
approximately the same as the rate of quenching of the
37

38
conjugate acid fluorescence. Furthermore, <£/<£> q and /§'Q
must be calculated independently of each other, and hence
the fluorescence spectra of the conjugate acid and base
must be well resolved from each other. These conditions
must all be met before the HCl method can be used. It was
desirable, therefore, to devise a more generally applicable
method of determing ka and .
It can be seen from equation (53) that the slope, m,
of a plot of () / (<{>'/$'0) versus [H+] will be
m =
k,x'
b o
1 + k x
a o
(54) ,
which can be rearranged to
x' 1 k
o a
^ + \ T°
(55) .
If a quencher can be added to the titration medium that
will quench the fluorescence of the conjugate acid so that
(1 + k x ) will vary with quencher concentration relative to
k^x^, then m will be a function of quencher concentration.
A series of titrations, each with a different constant
concentration of quencher in the titration medium, should
then yield a different value of m and xq for each
titration (if the fluorescence of the conjugate base is also
quenched, then different values of x^ will also be obtained).
According to equation (55) , a plot of x^/m versus xq should

39
be a straight line with an ordinate intercept of 1/k^ and
*
a slope of k /k,. Values of k , k, , and K could thus be
a d a d a
derived from the series of titrations of the molecule of
interest.
Acridone (Figure 3-1) is a molecule in which
k
pK >> pK (31,74), and hence its fluorimetric titration
cl cl
behavior should be described by equation (53).
Furthermore, since the ground-state ionization occurs in
relatively dilute solution (pK = -0.32) (75), the media
in which the ground- and excited-state ionizations occur
are not appreciably different. Since the assumptions
inherent in the Forster cycle are normally correct for
ionizations which occur in dilute, aqueous solution, the
*
pK of acridone calculated according to equation (55)
*
should agree with the value of its pK calculated with the
Forster cycle. Such a comparison could be used to
determine whether or not equation (55) correctly describes
the excited-state chemistry of interest. If it does, then
equation (55) could be used with confidence to determine the
k
pK of a molecule in which the ground-state ionization
occurs in concentrated acid. The Forster cycle could then
be used to see if the excited-state ionization (which
occurs in dilute, aqueous solution) can be related to the
ground-state ionization (which occurs in concentrated acid).

40
0
Figure 3-1
Structure of acridone.

41
Results and Discussion
The fluorescence lifetimes of neutral and protonated
acridone are presented as a function of the molarity of
Br (derived from NaBr) in Table 3-1. Since t varies
o
with [Br ] but x¿ is invariant, equation (55) should be
applicable to the titration data. Figure 3-2 shows a
quenching curve for protonated acridone (this was used in
the calculation of xQ in the presence of quencher—see note
b of Table 3-1 for details). Figure 3-3 shows fluorimetric
titration curves for acridone in the presence of different
concentrations of Br . It is of interest to note that the
titration curve shifts to higher pH as xQ decreases. This
occurs because the rate of the dissociation reaction
decreases when xQ decreases. This shift to higher pH is
predicted by equation (53), which shows that [H+] at the
inflection point (the pH where decrease when m increases (values of m as a function of
[Br ] are also shown in Table 3-1). Figure 3-4 shows a
plot of T^/m versus xQ for acridone. As predicted by
equation (55), the plot is linear. Values of k , k, and
a. D
*
pK calculated from the slope and intercept of the line in
cl
*
Figure 3-4 are presented in Table 3-2 along with pK (F.C.)
calculated from the Forster cycle (31). It can be seen
from equation (55) that, for any two different pairs of
values of m, x^, and xQ,

42
Table 3-1
Variation with bromide ion concentration of x', x , and
m for acridone.
[Br'
"]
, M
x' nsa
b
x , ns
m
o
o
0
-3
14.8±0.5
26.010.4
1311'
5.0
1.0
X
X
10_3
10-2
14.8±0.5
14.810.5
18.7
15.6
3318
4013
3.0
X
10-2
14.810.5
9.7
5913
5.0
X
10-1
14.810.5
6.7
7115
1.0
4.0
X
X
10-1
10-1
14.810.5
14.810.5
3.7
0.59
10419
16916
5.0
X
10 1
14.810.5
0.45
17519
aThe lifetime of neutral acridone was measured in water
at pH = 7.0.
^The lifetime of protonated acridone was calculated as
T0 = (cí>/cf)o) x x a, where <{>/<}>o is the relative quantum
yield of fluorescence at the bromide ion concentration
of interest (values of 4>/4>o are shown in Figure 3-2)
and xoa is the fluorescence lifetime of protonated
acridone in the absence of quencher (measured in 2.3
M HC104, Hq = -1.0).
Q
Taken from reference (31).

Figure 3-2
Variation with bromide ion concentration of the relative quantum yield of
fluorescence (4>/4>0) of 5 X 10 ^ M protonated acridone. Analytical
wavelength = 456 nm. Excitation wavelength = 350 nm.

4^
Bromide ion concentration, M

Figure 3-3
Variation of the relative quantum yield of fluorescence (<|>' /$'0) of 5 X 10~
neutral acridone with pH at various bromide ion concentrations. (A) [Br-]
(B) [Br~] = 5.0 X 10"3 M, (C) [Br“] = 5.0 X 10_2 M, (D) [Br“] = 1.0 X 10"
(E) [Br ] = 5.0 X 10 1 M. Analytical wavelength = 440 nm. Excitation
wavelength = 350 nm.


Figure 3-4
Plot of T'/m versus x for acridone.
o o

48

49
Table 3-2
k
Rate constants and pK& for the excited-state proton
transfer between neutral and protonated acridone.
2.7 X 108 1.4 X 1010 1.71a
2.9±0.3 X 10° 1.5±0.1 X 10 U 1.71±0.04D
1.6±0.3C
aDetermined graphically from Figure 3-3.
^Calculated from the data in Table 3-1.
c *
pK (F.C.), taken from the Forster cycle calculation in
cl
reference (31).

50
1
T
k.
(56)
b
and
1
T
k.
(57) .
’b
Equations (56) and (57) may be combined to yield
(58) ,
so that only two titrations are needed to estimate K . This
3
*
value of K can then be used in conjunction with equation
cl
(55) to determine k, , and then k can be calculated.
¿D cl
*
Values of ka, k^, and pK^ calculated in this way are also
presented in Table 3-2. The excellent agreement between
•k *
pK and pK (F.C.) suggests that equations (55-58) may be
3. 3.
used with confidence to determine pK when the excited-
3
state reaction occurs according to mechanism (26) and
*
when pK >> pK .
Xanthone (Figure 3-5) has a ground-state ionization in
concentrated acid (76,77) and an excited-state ionization
in dilute, aqueous solution (76,77). While pK has been
estimated using the Hammett acidity function without
including atrf (76), it has not been seen whether equation
*
(12) is applicable or not. Furthermore, pK^ has been

51
O
Figure 3-5
Structure of xanthone.

52
estimated (76) , but it was assumed that pK^ = pH at the
inflection point. Equation (53) shows that this
assumption is incorrect.
In terms of absorbances, equation (12) is
A ~
pKa = Ho * lo9 Ag - A where A is the absorbance anywhere on the inflection region
of the titration, and Ag^+ and Ag are, respectively, the
absorbances of the isolated conjugate acid and base at the
analytical wavelength of interest. Equation (59) may be
put into antilogarithmic form and rearranged to
A =
+ +
K A
a
- n-r,,
ha 9
o w
, n-r,,
ha 9
o w
(60) ,
from which it is seen that a multiple linear regression (see
Appendix B) may be used to fit for AgH+, KaAg, and K^, and
then Ag may also be calculated. A computer program to
perform this type of fit was written by the author. The
program was constructed to vary integral values of (n-r )
g
until a good fit was obtained. The fit was judged to be
good when the fitted Agg+ and Ag agreed with the
measured AgH+ and Ag and when the coefficient of multiple
determination approximated unity. Figure 3-6 shows a
spectrophotcmetric titration curve of xanthone. The
titration was fitted using equation (60), and the best fit
was obtained with (n-r^) = 0, which yielded pK^
-4.17±0.03.

Figure 3-6
Plot of absorbance versus H for 6.5 X 10 6 M xanthone in H„SO
o — 2
Analytical wavelength = 329 nm.

Absorbance

55
This value of pK agrees with the value of pK = -4.1
cl 3.
published in reference (76). When (n-r ) = 0, the fit
amounts to fitting the data with the Hammett acidity
function without including a because then a n r<3 = 1.
It is not surprising, therefore, that the pK determined
in this work agrees with that already published. This does
not say that the data should not be fitted with equation
(60): it only means that, in this case, n = r .
9
Figure 3-7 shows the variation of x and x' with
o o
[Br ]. Since xq significantly varies while x^ remains
constant, the titration behavior of xanthone should be
similar to that of acridone. Figure 3-8 shows that this is
the case, for the titration curve of xanthone shifts to
higher pH with increasing Br concentration. Table 3-3
presents m (as well as x and x') for xanthone as a
o o
function of (Br ], and Figure 3-9 shows a plot of x'/m
o
versus xq for xanthone. Once again, the plot is linear,
which indicates that equation (55) is being obeyed. It is
possible, therefore, that equation (55) will find general
application to molecules of the type under consideration.
This method is limited to molecules where xq can be varied,
but no limitations concerning pH or spectral overlap are
apparent at this time.
Table 3-4 presents the absorption and fluorescence
maxima of neutral and protonated xanthone. The value of
*
pK (F.C.) calculated with the value of pK = -4.17 is
a cl

Figure 3-7
_ r
Plot of the fluorescence lifetime of 2 X 10 M xanthone
versus bromide ion concentration. (A) tq (protonated
xanthone), (B) (neutral xanthone).

30
25
20
15
10
5
0
57
B
-L
-L
0.02 0.03 0.04
Bromide ion concentration, M
00
0.01
0.05

Figure 3-8
Variation of the relative quantum yield of fluorescence (4>1 /(f»^)
neutral xanthone with H at various bromide ion concentrations.
- _3 ° _ _3 _
(B) [Br ] = 2.5 X 10 M, (C) [Br ] = 5.0 X 10 M, (D) [Br ] =
(E) [Br ] = 2.5 X 10 ^ M. The molecule was titrated with I^SO^
wavelength = 358 nm. Excitation wavelength = 326 nm.
of 2 X 10-6 M
(A) [Br-] = 0,
1.0 X 10-2 M,
Analytical

o

60
Table 3-3
Variation with bromide ion concentration of t1, x , and m
for xanthone.
[Br
"] ,
M
. a
ns
b
V ns
m
0
2.5
X
10-3
3.4±0.1
3.4C
31.810.8
23.3C
5.310.2
6.510.1
5.0
X
10-2
3.4±0.1
18.210.4
7.410.1
1.0
X
10-2
3.4±0.2
11.810.3
9.6910.08
2.5
X
10 ^
3.510.2
6.510.4
12.810.1
Determined in water, pH = 5.5.
T_
determined in 4.0 M H~S0., H = -1.7.
— 2 4 o
Q
Estimated from Figure 3-7.

Figure 3-9
Plot of x'/n» versus x for xanthone.
o o


63
Table 3-4
Fluorescence (v ) and longest wavelength absorption (v )
L. cl
maxima of neutral and protonated xanthone.
-1 - -1
xanthone species
v , cm
d
, cm
neutral
cation
2.91 X 10
2.57 X 10‘
2.60 X 10
2.25 X 10'

64
*
presented in Table 3-5 along with ka, k^, and pK^
. *
estimated graphically from Figure 3-9. This value of pK
3
*
does not agree with pK (F.C.). It was observed that the
absorption spectrum of isolated neutral xanthone shifts to
shorter wavelength (by -3 nm) as the medium (I^SO^) was
changed to more dilute H^SO^. This solvent effect on the
spectrum of neutral xanthone introduces significant error
ic
into the estimation of its 0-0 energy, and hence pK (F.C.)
will also be inaccurate. It thus seems likely that a
*
substantial amount of the discrepancy between pK^ and
*
pK (F.C.) in Table 3-5 is due to the solvent-effect-
3
induced failure of the Forster cycle. The nature of the
solvent effect is not known. Since the activity of water in
the sulfuric acid in which the solvent effect occurs
deviates significantly from unity (65,66), it is possible
that the state of hydration of neutral xanthone changes
when the medium changes. If a hydration change of this
type affects the absorption spectrum, then this explains
the solvent effect. If the hydration change is occurring
but does not affect the spectrum, then the solvent effect
remains unexplained. To date, no experiment has been done
which could confirm or disprove the change-in-hydration
hypothesis.
It is not possible, therefore, at least in the case of
xanthone, to use the Forster cycle to relate the
thermodynamics of proton transfer in dilute, aqueous solution

65
Table 3-5
Ground-state acid-dissociation constant of protcnated
•k
xanthone and rate constants and pK for the excited-state
3.
proton transfer between neutral and protonated xanthone.
-1 -1 -1 *
pK k , s k, , M s pK
3 3 b ~ 3
-4.17±0.03a 8.3±0.6 X 107 5.6±0.3 X 109 1.83±0.02
3.2±0.3C
aDetermined spectrophotometrically in this work with
(n - r ) = 0.
b
^Determined graphically from Figure 3-9.
c * ,
pK (F.C.), estimated from the Forster cycle.
3

66
to the thermodynamics of proton transfer in concentrated
acid. If this is a consequence of changes in hydration of
a given reactant, then the standard state of that reactant
is different in the ground- and excited-state reactions.
If this is the case, then it may not even be
*
thermodynamically correct to predict the value of pK (or
pK , if the Forster cycle is used in reverse) in one
medium based upon measurements in another. However, it will
be seen from other data presented in this dissertation
that the Forster cycle is generally quite successful in
★
predicting pK , even when the ground- and excited-state
ionizations occur in media of substantially different
acid composition. The behavior of xanthone does, however,
suggest that the prediction of the behavior of a molecule
in one medium based upon measurements in a different
medium should be done only with caution.

CHAPTER IV
EXCITED-STATE PROTON TRANSFER IN
2-QUINOLONE AND 4-QUINOLONE
Introduction
Some molecules become so acidic in their excited states
that their excited-state ionizations occur in concentrated
acid. As has already been seen in Chapter I, equation (43)
will not correctly describe the excited-state proton-
transfer reactions of these molecules because k and k, are
a b
usually medium-dependent. Therefore, equation (43) must be
modified to include the medium-independent rate constants
k (0) and k, (0) before the kinetics of excited-state
a a
proton transfer in concentrated acid can be quantitated.
The mechanism of the excited-state proton transfer of
interest can be written as
BH^*(H20)x + rH2Q , » X^~ *■ B* (IUO) + H+(H20)z (61),
where x, y, and z are the numbers of water molecules
. +* * + i
hydrating BH , B , and H , respectively, and X1 is the
transition-state species common to both the protonation and
deprotonation reactions. The coefficient r is the number of
+* 4=
water molecules which react with hydrated BH to form XT.
By mass balance it is seen that r = y + z - x, and it is
assumed that x, y, z, and r remain constant over the
inflection region of a given titration. It is then simpler
67

68
to write equation (61) as
.+*
BH
+ rn2o <-
:x
t
â–º * +
-B + H
(62) .
If X+ is the transition-state subspecies formed by the
combination of BH
+*
with r water molecules and xí is the
b
transition-state subspecies formed by the combination of B
and H , then the equilibrium constants for the formation of
4
X' and xj are, respectively, defined as
K
+ =
[XT] f
a x
+ * r
[BH ]fa
+ w
(63)
and
4-
i4]fx
(64) ,
4= +* ± *
where [XJ] , [BH ], [X¿], and [B ] are the equilibrium
a. D
concentrations of X', BH
a'
+* ± *
, Xj, and B , respectively. The
*
activity coefficients f+ and f correspond to BH and B ,
respectively. It is assumed that the activity coefficients
of xj and xj are identical. These coefficients are both
designated as f . The rate of production of BH
X
*
the rate of production of B , r , are given by
3.
, rb, and
*-+i -
rb = k¿txS]
k [BH+*] - t-B.H-1
(65)
and
= k+[XT] -
a L a
[H+] £B*J -
(66) ,

69
where k^ is the rate constant for the dissociation of X^ in
a a
the direction of the conjugate base and k^ is the rate
constant for the rearrangment of in the direction of the
conjugate acid. Equation (64) may be combined with (65) to
yield
+* [BH+*]
rb = ^K+tB'lrV - ka[BH' ] -
X o
(67) ,
which becomes
f +*
r = kb(0) [B*]^aR+ - ka[BH+*] - ]- (68).
x To
Equations (63) and (66) may be combined to give
ra = kíKÍ[BH+*]F:awr " kbtH+] tB*] "
a a a r w b t
x o
(69) ,
which becomes
f *
+* + r + * fr 1
r = k (0) [BH Irt,- k, [H+] [B ] -
a a r w b t
x o
(70) .
It is seen from reaction (26) that r and r, may also be
given by
*
+* + * r b i
ra = ka[BH+ ] - kb[H+] [B ] -
(71)
and
rb = kb[H+] [B*] - ka[BH+*] - i-
(72) .
Combination of equation (70) with (71) yields
f+ r
k = k (0) -E—a
a a f w
x
(73) ,

70
while combination of equations (68) and (72) gives
kb = V0)aH+r
x
(74)
Equation (8) may be combined with equation (74) to yield
kb â–  V0)Vwn
X o
(75)
The medium-dependent rate constants ka and are thus
related to the medium-independent rate constants k (0) and
cl
k^(0) by equations (73) and (75), respectively.
Substitution of these equations into equation (43) results
m

o r
â– a =
k, (0) t ' <¡>'/' f ’ f
b ou „ n T ' Yo + o
+ h a
♦'/♦¿-“b w k (0)T f+ k (0)T ° w f f
(76)
X o
X
The activity coefficients f+, f'+, and f all correspond to
singly charged species of similar size while fQ and f^
correspond to uncharged species of similar size. These
similarities in size and identities in charge make it
reasonable to assume that f,/f = f!f /f,f' = 1, in which
case equation (76) becomes
<¡>/<¡>
a o
V0)T¿, n ♦'/♦i
+ n a
o w
(77)
a o
4> '/<¡>¿-cd3

71
which should correctly describe the excited-state proton-
transfer kinetics of reactions which occur in
concentrated acid. A plot of ( (/0) / ) aw
versus hQawn (<{>' /§'Q) / (4>' /<{>¿”ciB) should be a straight line
with an ordinate intercept of 1/k (0)t and a slope of
a. O
kb(0)T¿Aa(°)To.
Several molecules (78) which have excited ionizations
which occur in acid such that the inflection points are
found at pH < 1 are 2-quinolone (Figure 4-1) and
4-quinolone (Figure 4-2). It is of interest to see
whether or not these ionizations are described by
equation (77).
Results and Discussion
The absorption and fluorescence maxima of neutral and
protonated 2-quinolone, as well as their fluorescence
lifetimes, are presented in Table 4-1. The
spectrophotometric titration of 2-quinolone is shown in
Figure 4-3. These titration data were best fitted
according to equation (60) with (n-r ) =4, which yielded
9
pK = -0.30±0.03.
Cl
Figure 4-4 shows the fluorimetric titration curve of
2-quinolone. Figures 4-5 and 4-6 show plots of
((/ '/<¡>¿-aB) )awr versus h^11 (4,'/$'Q) / (<¡> '/4>¿-oib) for
2-quinolone with various values of r and n = 3 (Figure 4-5)
or n = 4 (Figure 4-6) . Values of §'/§'Q f°r both 2-quinolone
and 4-quinolone were calculated according to the

72
Figure 4-1
Structure of 2-quinolone.

73
Figure 4-2
Structure of 4-quinolone.

74
Table 4-1
Fluorescence (v^) and longest wavelength absorption (v )
L cl
maxima and fluorescence lifetimes of neutral and
protonated 2-quinolone.
2-quinolone
species
fluorescence
lifetime, ns
neutral 3.12 X loj 2.72 X 10? 2.1±0.2a
cation 3.33 X 10 2.65 X 10 10.4±0.5D
aT^, measured in water, pH = 2.0.
T , measured in 7.5 M H-SO,, H = -4.0.
o — 2 4 o

Figure 4-3
-4
Plot of absorbance versus H for 1 X 10 M 2-quinolone in H„S04.
wavelength = 269 nm. °
Analytical

Absorbance
9 L

Figure 4-4
Plot of the relative quantum yield of fluorescence (4>/(¡> )
-5 °
of 3 X 10 M protonated 2-quinolone in HCIO^ versus H .
Analytical wavelength = 370 nm. Excitation wavelength =
280 nm (isosbestic point).

78
4>/
-5 -4 -3 -2-1 O 1

Figure 4-5
Plot of ( (4>/4>0) / (4> '/^¿“Ctg) ) aj° versus (cf>'/ ( '/^¿-aB) for 2-quinolone with
n - 3. (A) r = 1, (B) r = 2, (C) r = 3, (D) r = 4, (E) r = 5.

J^o
w
O
10
20
^oaw (J) '/(J)1 -an
Y ' To B
00
o

Figure 4-6
Plot of ((4>/ ) / (4)'/

O O ti w
= 4. (A) r = 1, (B) r = 2, (C) r =
hoawn(f/^)/(^/^B) for
3, (D) r = 4, (E) r = 5, (F)
2-quinolone
r =
with
n
6.

♦/♦o
4>'/4>'-aR
o ü
00
NJ

83
relationship 4»' /<í>¿ = 1 -

spectra of the protonated species overlap and eclipse those
of the neutral species. It can be seen that most
combinations of n and r result in curved plots. The best
fit to a straight line (chosen on the basis of the highest
linear least-squares correlation coefficient—see Appendix
A) was obtained with n = 3 and r = 4 (plot D in Figure 4-5).
The linearity of plot D in Figure 4-5 suggests several
things. In the first place, the titration data of
2-quinolone in concentrated acid are fitted well with equation
(77), which suggests that the model is valid. Secondly,
the assumption that f+/f = f_J_f /f f^ = 1 is probably a
good assumption. Thirdly, the value of n in reaction (7)
for this region of acidity is n = 3 and the value of r in
reaction (62) is r = 4 for 2-quinolone. These observations
are consistent with the values of n = 3 and n = 4 proposed
by Teng and Lenzi (79) and by Bascombe and Bell (80) for
solutions in which Hq > -3.5. Values of ka(0), k^tO), and
rk
pK (0) = -log(k (0)/k, (0)) are presented in Table 4-2,
3 3D
★
along with pK (F.C.) and pK .
The fluorescence lifetimes and spectral maxima of
neutral and protonated 4-quinolone are presented in Table
4-3. The fluorescence lifetime, t^, of neutral 4-quinolone
was estimated with the Strickler-Berg equation (81). The
ratio of the radiative lifetimes of protonated and neutral
4-quinolone (estimated with the Strickler-Berg equation),

84
Table 4-2
Ground-state acid-dissociation constant of protonated
*
2-quinolone and rate constants and pK^ for the excited-
state proton transfer between neutral and protonated
2-quinolone.
PK.
ka(0), s 1 kb(0), M-1s 1
PK.
-0.30±0.03 4±1 X 10* 1.0±0.3 X 10 -1.58±0.06
-1.8±0.3d
Determined spectrophotometrically in this work with
(n - r ) =4.
y
^Determined graphically from Figure 4-5 with n = 3 and
r = 4.
'pK (0), determined graphically from Figure 4-5 with
n = 3 and r = 4.
d *
pK (F.C.), estimated with the Forster cycle.
8.

85
Table 4-3
Fluorescence (v ) and longest wavelength absorption (v )
£ cl
maxima and fluorescence lifetimes of neutral and
protonated 4-quinolone.
4-quinolone v^, cm ^ v^, cm fluorescence
species lifetime, ns
neutral 3.04 X 104 2.98 X 104 0.79±0.04a
cation 3.32 X 104 2.76 X 104 21±lb
ax^, estimated with the Strickler-Berg equation.
tq/ measured in 5.9 M HC1C>4, Hq = -2.8.

86
the ratio of their quantum yields, and the measured value of
tq were used in this calculation. The absorption and
fluorescence spectra of 4-quinolone exhibit a fairly good
mirror-image relationship and a small Stokes shift; hence,
the value of x' estimated with the Strickler-Berg
o
equation is reasonably accurate (82-84) .
Figure 4-7 shows the spectrophotometric titration of
4-quinolone. This ground-state ionization occurs in dilute,
aqueous solution, and hence the titration data were fitted
using equation (60) with a^ = 1, in which equation (60)
reduces to an antilogarithmic form of the Henderson-
Hasselbach equation. This analysis yielded pK = 2.22±0.01.
Cl
The fluorimetric titration curve of 4-quinolone is
shown in Figure 4-8. The small step in the titration curve
at pH = 2 is probably the result of a vanishingly small rate
of protonation of the excited neutral molecule at that
pH and higher pH (56) . The titration data of 4-quinolone
plotted according to equation (77) are shown for n = 3 in
Figure 4-9 and n = 4 in Figure 4-10, with r taking various
values in each figure. The activity of water
significantly deviates from unity only in the most acidic
portion of the fluorimetric titration of 4-quinolone, and
hence it is expected that the inclusion of a in the kinetic
w
treatment will not make as dramatic a difference as it did
with 2-quinclone. This is the case; indeed, plots B
(n = 4, r = 3) and C (n = 4, r = 4) in Figure 4-10 are

Figure 4-7
-4
Plot of absorbance versus pH for 1 X 10 M 4-quinolone in
water. Analytical wavelength = 327 nm.

Absorbance
o o o o o o o o o
•• • •• • • • »
Oh-1 K) U> 4^ (J1 CT\ 00
03
co

Figure 4-8
Plot of the relative quantum yield of fluorescence (d>/4>0)
of 3 X 10 5 M protonated 4-quinolone versus H . The
molecule was titrated with HCIO^. Analytical wavelength =
360 nm. Excitation wavelength = 302 nm (isosbestic point) .

90
H
o

Figure 4-9
Plot of ((4>/$_)/($ '/$'-a_)) a,,r versus
O O JD w
hQawn(<|) '/(^¿-aB) for 4-quinolone with n = 3.
(A) r = 1, (B) r = 2, (C) r = 3, (D) r = 4, (E) r = 5.

92

Figure 4-10
Plot of ( (4>/ )/($'/4>'-a )) a r versus
O O D W
h.a„n ('/4>') / (4>'/4> '-<*„) for 4-quinolone with
W O O O
(A) r = 2, (B) r = 3, (C) r = 4, (D) r = 5,
n = 4 .
(E) r = 6.

94

95
identically straight lines. It is not possible, therefore,
to discern whether it is three or four water molecules which
react with the hydrated, protonated 4-quinolone in the
deprotonation step of the excited-state reaction. The
value of n = 4, however, is still in keeping with the
values of n previously proposed (79,80) for the region of
acidity in which the excited-state proton transfer of
4-quinolone occurs. It is not surprising that n was found
to be three in the case of 2-quinolone but four in the case
of 4-quinolone because the Hammett indicators (9) which
were used to define the Hammett acidity function in these
respective regions of acidity are different and their
deprotonation reactions may have different hydration
requirements. This is reasonable not only because of
structural differences between the indicators, but also
because the activity of water at the inflection point of
the fluorimetric titration of 4-quinolone (a^ = 0.98) is
quite different from that at the inflection point of the
fluorimetric titration of 2-quinolone (a = 0.66). These
differences in the availability of water could result in
different numbers of water molecules entering into reactions
which occur in solutions of significantly different acid
composition.
If the various indicator and quinolone species each
have several different hydrates, then it is possible that
n and r are not constant, in which case equation (77)

96
would not correctly describe the excited-state chemistry of
interest. Since the plots obtained with equation (77) are
linear, it appears that, at least to a first approximation,
n and r may be considered to be constant.
•k
Values of k (0) , k,(0) , and pK (0) for 4-quinolone
a. D a.
with n = 4 and r = 3 and also with n = 4 and r = 4 are
k
presented in Table 4-4 (pK and pK (F.C.) are also shown in
cl cl
k k
Table 4-4). The agreement between pK (0) and pK (F.C.) for
'“cl cl
the excited-state ionizations of 2-quinolone and 4-quinolone
further suggests that the model under consideration is
valid. Furthermore, it suggests that the Forster cycle can
be used with some confidence to relate the acid-base
properties of a molecule in one medium to those properties
in another. In the cases of 2-quinolone and 4-quinolone, at
least two sets of circumstances are consistent with the
latter suggestion. Firstly, it is possible that the
hydrations of the quinolone species do not change with
changing acid concentration (at least not over the
concentration ranges studied in this work). Secondly, it is
possible that their hydrations do change, but that they
change in such a way that the standard free energies of all
the species involved in a given reaction change by the
same amount when going from one medium to another. These
changes would cancel out and would not be apparent in
k
the estimation of pK with the Forster cycle. Once again,
cl

97
Table 4-4
Ground-state acid-dissociation constant of protonated
ic
4-quinolone and rate constants and pKa for the excited-
state proton transfer between neutral and protonated
4-quinolone.
pKa ka(0)' s 1 kb(0), M-1s“1 pK*
2.0±0.6
X
8b
io8
1.310.5
X
i-1
o
M
O
tr
1.8010.08C
1.710.5
X
8d
io8
1.010.3
X
10d
10±u
1.7710.05s
1.7l0.3f
aDeterrained spectrophotometrically in this work. The value
of (n - r ) could not be determined since a =1 over the
g w
inflection region of the titration.
^Determined graphically from Figure 4-10 with n = 4 and
r = 3.
c *
pKa(0), determined graphically from Figure 4-10 with
n = 4 and r = 3.
^Determined graphically from Figure 4-10 with n = 4 and
r = 4.
e *
pK (0), determined graphically from Figure 4-10 with
cl
n = 4 and r = 4.
f *
pK (F.C.), estimated with the Forster cycle.
a.

98
it has not yet been determined if the actual circumstance
is the first, second, or some other yet unconsidered
possibility.
Finally, the excited-state proton-transfer reactions
of both 2-quinolone and 4-quinolone do not attain
equilibrium within the lifetimes of their lowest excited
singlet states. This is intuitively obvious from the fact
that the rate constants for the protonation and
deprotonation steps were measurable. A quantitative
explanation of this conclusion is found in the next
chapter, where the criteria for and the implications of the
establishment of equilibrium within the lifetime of the
excited state will be discussed.

CHAPTER V
EQUILIBRIUM EXCITED-STATE PROTON TRANSFER
IN 1-ISOQUINOLONE
Introduction
When the rates of the excited-state protonation and
deprotonation reactions are equal, the excited-state
reaction is at prototropic equilibrium. It has been
shown (85) that 1/k (0)t ->-0 when this condition is met.
ci O
Equation (77) then reduces to
♦/♦o r kb(0)T¿ n
ccBaw “ ka(0)TQhoaw ¿-aB (78
A plot of ((4>/ )/ ( O (Jo W
ha n (<¡> ’/(p ") / (4>'/4> * -ct_) will thus pass through the origin
(that is, the ordinate intercept will be zero). The value
of the intercept, therefore, may be used as a diagnostic
to determine whether or not a given excited-state proton-
transfer reaction attains equilibrium within the lifetime
of the excited state. The closer the reaction is to
equilibrium, the closer to zero will be the intercept of
data plotted according to equation (77) . Since the
ordinate intercept of plot D in Figure 4-5 and the
intercepts of plots B and C in Figure 4-10 are not zero,
it may be concluded that the excited-state proton-
transfer reactions of 2-quinolone and 4-quinolone do not
99

100
attain equilibrium within the lifetimes of their excited
states. A molecule which demonstrates excited-state
prototropic equilibrium is 1-isoquinolone (Figure 5-1) (86).
Results and Discussion
The fluorescence lifetimes and absorption and
fluorescence maxima of neutral and protonated 1-isoquinolone
are presented in Table 5-1. Figure 5-2 shows the
absorptiometric titration of 1-isoquinolone. These data
were best fitted according to equation (60) with
(n - r ) = 1, which gave a value of pK = -1.38±0.03.
g a
The fluorimetric titration of 1-isoquinolone is
shown in Figure 5-3. The fluorescence spectra of neutral
and protonated 1-isoquinolone show considerable overlap,
and thus $'/<}> was calculated according to the
relationship = 1 - cj>/0. Figure 5-4 shows the
fluorimetric titration data of 1-isoquinolone plotted
according to equation (77) with n = 2 and r = 2. The plot
is a straight line which passes through the origin, and
it is concluded that the excited-state proton-transfer
reaction of 1-isoquinolone attains equilibrium within the
lifetime of the excited state.
Examination of equation (78) shows that, when a
given excited-state proton transfer attains equilibrium,
then all plots of ( (_) / (4> '/ ' -an)) a. r versus
O O íj W
hoawn(f/tf/(^/^aB) will have the same slope and
intercept regardless of the values of n and r as long as

101
Figure 5-1
Structure of 1-isoquinolone.

102
Table 5-1
Fluorescence (v_) and longest wavelength absorption (v )
u- cl
maxima and fluorescence lifetimes of neutral and protonated
1-isoquinolone.
1-isoquinolone
species
fluorescence
lifetime, ns
neutral 3.10 X 10* 2.73 X 10* 2.0±0.1?
cation 3.21 X 10 2.77 X 10 2.610.1°
ax^, measured in water, pH = 1.7.
measured in 8.4 M H2S04' Hq = -4.1.

Figure 5-2
-4
Plot of absorbance versus Hq for 1 X 10 M 1-isoquinolone in I^SO^.
wavelength = 275 nm.
Analytical

Absorbance
o
O
O
O
o
o
o
•
•
•
•
•
•
•
N3
u>
JS-
U1
O'!
—1
00
frOT

Figure 5-3
_5
Plot of the relative quantum yield of fluorescence of 2.5 X 10 M
protonated 1-isoquinolone in I^SO^ versus Hq. Analytical wavelength = 360 nm.
Excitation wavelength = 252 nm (isosbestic point).

1.0
0.8
0.6
0.4
0.2
0.0
1
0
-1

Figure 5-4
Plot of ( (4>/ '/4>¿“«b) ) ^wr versus hQawn ('/4>¿) / (<í> '/4>¿-aB) for
1-isoquinolone with n = 2 and r = 2.

t/l'o
w
0 100 200 300 400 500
h a ¿ o
o w 4> '/<|)¿-aB
108

109
(n - r) is constant. These plots will be linear, however,
only when the correct (n - r) is used in the analysis. The
linearity of the plot shown in Figure 5-4 suggests that the
cofrect value of (n - r) for 1-isoquinolone is (n - r) = 0.
It is expected, therefore, that the fluorimetric titration
data of 1-isoquinolone plotted according to equation (77)
will yield straight lines with identical slopes and null
intercepts for all combinations of n and r such that
(n - r) =0. This expectation is confirmed in Table 5-2,
which presents values of the slopes and intercepts of
these lines with 0 < n < 4 and 0 < r < 4 such that n = r.
In all cases the intercept is zero (within experimental
error) and the slopes are identical (within experimental
error). Test values of 5 < n < 8 and 5 < r £ 8 with n = r
yielded the same results. This further confirms that the
excited-state proton transfer of 1-isoquinolone attains
equilibrium within the lifetime of the excited state and
that (n - r) =0 for this reaction.
Equation (78) shows that the attainment of
excited-state prototropic equilibrium has several
consequences concerning our knowledge of the reaction. In
the first place, it is not possible to determine the
number of water molecules (n) which enter into the
Hammett indicator reaction or the number of water
molecules (r) which enter into the excited-state
deprctonation reaction of interest. Only the (n - r)

Table 5-2
Ground- and excited-state acid-dissociation constants for the proton transfer
between neutral and protonated 1-isoquinolone.
n r
intercept
b
slope
b
1.3810.03 0
1
0
1
4.9±5.5
1.6±2.7
X
X
10 ^
1° o
4.55±0.06
4.5710.07
X
X
10-3
io i
-2.2310.03
-2.2310.03°
2
2
0.4±1.5
X
loi
4.5910.09
X
10-3
-2.2210.03°
3
4
3
4
O.lil.l
0.5±1.5
X
X
10-2
10
4.610.1
4.510.4
X
X
10 ,
10 J
-2.2210.03°
-2.2310.04°
-2.2310.04°
-2.2 i 0.3°
Determined spectrophotometrically in this work with (n - r ) = 1.
For 1-isoquinolone data plotted according to equation (77).
c *
pK (0), determined graphically from the slope of the line obtained with from
cl
1-isoquinolone data plotted according to equation (77) with the appropriate
values of n and r.
d * *
pK (0), the average of the values of pK (0) determined with n = r for
ci a
0 < n < 4 and 0 £ r £ 4.
0 *
pK (F.C.), estimated from the Forster cycle,
a
110

Ill
difference can be determined. Secondly, it is not
possible to estimate k (0) and k, (0). When t and t'
a d o o
*
are known, pK (0) may be calculated because the slopes (in
cl
Table 5-2) all represent values of k^(0)T^/ka(0)x .
*
Values of pK (0) calculated in this manner, as well as
cL
•k
the values of pK and pK (F.C.), are also presented in
3. cl
Table 5-2. Even though k (0) is not known, we may still
conclude that the rate of the dissociation reaction is
high (85). It is seen that pK^ÍF.C.) = -2.2±0.3 is
*
identical to pK (0) = -2.23±0.04. This agreement not only
further confirms the validity of equation (77) , but also
suggests that equation (60) correctly describes the
ground-state ionization of 1-isoquinolone.

CHAPTER VI
NONEQUILIBRIUM EXCITED-STATE PROTON TRANSFER
IN 3-AMINOACRIDINE
Introduction
The molecules considered thus far are all of the H
o
type (that is, they have neutral conjugate bases and
singly charged conjugate acids). The number of fluorescent
Hq type molecules which are appropriate for the study of
excited-state proton-transfer reactions in concentrated
acid is limited by several things. Firstly, the
uncharged conjugate base species are sometimes relatively
insoluble. This is particularly true with molecules that
have three rings. Secondly, those that are soluble may
not exhibit excited-state ionizations in concentrated
acid. Thirdly, those that do exhibit excited-state
ionizations in concentrated acid do not necessarily have
conjugate acids and bases which are possessed of measurable
fluorescence lifetimes. This consideration is, of course,
more of a problem with older fluorescence lifetime
equipment than it is with newer, more sophisticated
equipment (most of which can measure fluorescence lifetimes
shorter than those measurable with the TRW apparatus
described in Chapter II). Finally, even when the first
three considerations present no problems, the compound of
interest may decompose in concentrated acid (the neutral
112

113
conjugate bases are sometimes more susceptible to this
degradation than are the conjugate acid species).
Degradation of an aromatic compound in concentrated acid
is usually indicated by a time-dependent change in
wavelength and/or intensity in the spectrum of either the
conjugate acid or base (or both).
These difficulties are lessened with H+ type
molecules, which have monocationic conjugate bases and
dicationic conjugate acids. The use of H+ type compounds
requires the use of the H+ scale (87) to quantitate the
acidity of the medium. Indicators of this type react
according to the mechanism
H2In++ + nH20 < —. > HIn+ + H+ (79) ,
where H2In and HIn are the indicator conjugate acid and
base species, respectively. In analogy to equation (8),
a^t is related to h+ by
aH+ = Vwn rp <80) -
where f_J_ and f^_+ are the activity coefficients of HIn+ and
H2In++, respectively, and h+ = antilog(-H ). The excited-
state reaction of interest is then
BH
++
BH,
++*.
H“ 4“ *
H + BH :
k-'
Kf
BH
(81)
k '
Kd
The modification of equation (43) for H+ type compounds
parallels that for Hq type compounds, and, in analogy to

114
equation (76), culminates in
4>/4>,
r
a =
w
kb(0)T¿,
+ — —h
4) ' / n y ' yo
ka(0)V
+ +
k (0)T + w
cl O
f;+f+
f f
X o
(82)
x
where f+ and f++ are the activity coefficients for the H+
+* -*-+*
type conjugate base (BH ) and conjugate acid (BH2' ),
respectively, and f is the activity coefficient of the
transition-state species in the excited-state reaction
BH2 + rH20 ► XT- ■» BH , + H (83)
Because of similarities in charge and size, it is now
reasonable to assume that f,,/f = f'f./f f) = 1, in
which case equation (82) reduces to
*'*o r _ 1 + kb(0)T¿. „ n
w ka(0)To ka(0)To + “ ♦‘/♦¿'“b
and a plot of ( U/O / (4 ' /'-an) ) atrr versus
h+awn (tp '/ k, (0)x'/k (0)t and an ordinate intercept of 1/k (0)t .
b o a o r a o
An H+ type molecule which is amenable to study in
concentrated acid is 3-aminoacridine (88) , the structure
of which is shown in Figure 6-1.
Results and Discussion
The fluorescence and absorption maxima and the
fluorescence lifetimes of monoprotonated and diprotonated
3-aminoacridine are presented in Table 6-1. Values of H+
in H2SO^ may be found in reference (87). A recent

115
Figure 6-1
Structure of 3-aminoacridine.

116
Table 6-1
Fluorescence (vf) and longest wavelength absorption (v )
H cl
maxima and fluorescence lifetimes of monoprotonated and
diprotonated 3-aminoacridine.
3-aminoacridine v , cm ^ v^, cm ^ fluorescence
species lifetime, ns
monocation 2.20 X 104 1.91 X 104 4.12±0.08b
. a .a
dication 2.32 X 10 2.13 X 10 26.0 ± 0.3C
These energies were estimated from strongly pronounced
(but not well resolved) vibrational features in the
spectra.
bT^, measured in 3.1 M H2SC>4, H+ = -1.6.
ctq, measured in 16.3 M H2S04, H+ = -8.7.

117
study (89) showed that the values of H+ in reference (87)
for I^SO^ :> 7 M are inaccurate due to poor choices of
indicators. Correct values of H+ for this concentration
range may be found in reference (89). It was also shown
that H = H for HoS0. > 7 M, and values of H in
references (63,64) could be used as H+ for >_ 7 M.
Spectrophotometric titration curves for 3-aminoacridine
are shown in Figures 6-2 and 6-3. These titration data
were best fitted according to equation (60) using h+ in
place of h , which resulted in a value of pK = -1.76±0.02
O cl
with (n - r ) =0.
9
The fluorimetric titration curve of 3-aminoacridine is
shown in Figure 6-4. The fluorescence spectrum of the
dication overlaps and eclipses that of the monocation, and
hence (¡> * /¿ was calculated according to the
relationship */4>¿ = 1 - Figure 6-5 shows the
3-aminoacridine titration data plotted according to
equation (84) with n = 1 and r = 1 (other values of n and
r did not fit the data) . Values of k (0) , k, (0) , and
a d
*
pK (0) determined from this plot, as well as the values of
cl
★
pK and pK (F.C.), are presented in Table 6-2.
The linearity of the plot shown in Figure 6-5 suggests
that the model under consideration is valid for H+ type
molecules. The criteria for the establishment of
prototropic equilibrium within the lifetime of the excited
state are the same for H+ type molecules as they are for

Figure 6-2
Plot of absorbance versus H+ for 1.9 X 10
Analytical wavelength = 275 nm.
3-aminoacrid

o
o
o
o
Absorbance
o
• • • •
i-1
O ÍO ifc» oí 00 o
611

Figure 6-3
-5
Plot of absorbance versus H+ for 1.9 X 10 M 3-aminoacridine in H2S0
Analytical wavelength = 454 nm.

o
o
Absorbance
o
ho
o
o
cr>
o
00
o

Figure 6-4
Plot of the relative quantum yield of fluorescence ($/<|>o)
_ g
of 1.9 X 10 M doubly prctonated 3-aminoacridine in
t^SO^ versus H+. Analytical wavelength = 470 nra.
Excitation wavelength = 358 nm (isosbestic point.

123
4>/tj)
-9 -8 -7 -6 -5 -4 -3 -2 -1
H
+

Figure 6-5
Plot of ((^/^0)/(f/^-aB))awr versus h+awn ('for 3-aminoacridine
with n = 1 and r = 1.

*/4>¿
h+awcJ>
125

126
Table 6-2
Ground-state acid-dissociation constant of diprotonated
*
3-aminoacridine and rate constants and pK for the excited-
state proton transfer between monoprotonated and
diprotonated 3-aminoacridine.
pKa ka(°)/ s-1 kb(0), M-1s 1 pK*
-1.76±0.02a
1.73±0.08 X 10
3.8±0.2 X 10
-4.66±0.01
-5.1 ± 0.3
c
d
determined spectrophotometrically in this work with
(n - r ) =0.
determined graphically from Figure 6-5.
c *
pK (0), determined graphically from Figure 6-5.
3
d * .
pK (F.C.), estimated with the Forster cycle.
3

127
Hq type molecules. Since the intercept of the line in
Figure 6-5 is not zero, we may conclude that the excited-
state proton transfer between monoprotonated and
diprotonated 3-aminoacridine does not attain equilibrium
within the lifetime of the excited state. When
nonequilibrium conditions prevail for an excited-state
proton transfer in dilute, aqueous solution, there is some
pH range over which there will be a plateau region in the
titration curve. This pH independence is the result of
the rate of the excited-state protonation of the conjugate
base becoming immeasurably small. Equations (77) and (84),
however, predict that both <{>/ and will vary
continuously with acid concentration even when
nonequilibrium conditions prevail. Both the acidity of
the medium and a^ vary with acid concentration, and thus
even if §/§Q and become acidity independent, they
will still vary because they are dependent on a^ . This
behavior is observed for both 3-aminoacridine (Figure 6-4)
and 2-quinolone (Figure 4-4). The ability of equations
(77) and (84) to predict titration behavior further
confirms the validity of the model.
*
The value of the pK of 3-aminoacridine estimated
with the Forster cycle is expected to be somewhat
inaccurate because of the difficulty encountered in
estimating the 0-0 energy of the dication. This energy
was estimated from strongly pronounced (but not well

128
resolved) vibrational features in the absorption and
fluorescence spectra of the doubly protonated molecule.
Since these features are not well resolved, the estimation
of the 0-0 energy of the dication is difficult and subject
to inaccuracy. In spite of this, there is reasonable
k â– k
agreement between pK (0) and pK (F.C.) (see Table 6-2).
cl cl
k k
The small difference between pK (0) and pK (F.C.) is
cl cl
attributed to error in the estimated values of v,.
dication
* k
The agreement between pK (0) and pK (F.C.) further
cl cl
confirms the validity of the model under consideration and
also suggests that equation (60) (modified to include h+
instead of hQ) correctly describes the ground-state
ionization of 3-aminoacridine. Since the ground- and
excited-state ionizations occur in media of radically
different acid composition, we also see that the Forster
cycle may be used with some confidence to relate the
acid-base behavior of 3-aminoacridine in one medium to its
behavior in another medium.
Since both reactions occur in moderately concentrated
acid, it is of interest to compare the values of k (0) and
k^(0) (Table 6-2) for the excited-state ionization of
3-aminoacridine to their values for the excited-state
ionization of 2-quinolone (Table 4-2). Since neither of
these reactions attains prototropic equilibrium, it is not
surprising that the value of k (0) for the 3-aminoacridine
cl
9 -1
excited-state ionization (k (0) = 1.73 X 10 s ) is
cL

129
similar to that for the 2-quinolone excited-state
ionization (k (0) = 4 X 10^ s ^). The value of k, (0) for
a- D
the 3-aminoacridine reaction (k^(0) = 3.8 X lo"* M^s”1) is,
however, substantially lower than it is for the 2-quinolone
8 —1—1
reaction (k^(0) = 1.0 X 10 M s ). This observation is
not surprising if one considers the charge types of the
reactants. The conjugate base of 2-quinolone is a neutral
molecule, whereas the conjugate base of 3-aminoacridine is
a cation. Because of the electrostatic repulsion between
species of like charge, it is expected that the rate
constant for the combination of two cations (the proton
and monoprotonated 3-aminoacridine) will be lower than that
for the combination of a cation (the proton) with a neutral
species (the conjugate base of 2-quinolone). Whether or
not this comparison is legitimate, of course, depends upon
whether or not the conjugate bases in the two reactions
are in the same standard state. As has already been
discussed in Chapters III and IV, differences in standard
state could result from changes in hydration, and these
changes would not necessarily be detectable with the
Forster cycle. It is not possible, therefore, to state at
this time whether or not the above comparison of rate
constants is legitimate. The comparison does seem
qualitatively justified because of the electrostatic
considerations already given and because of the
similarity between the reactions (both occur in

130
moderately concentrated acid but neither attains
prototropic equilibrium within the lifetime of the excited
state).

CHAPTER VII
SUMMARY
Many questions were raised before and during the
research carried out for this dissertation. While this
work has not definitively answered all of these questions,
it has certainly contributed to the understanding of the
fundamental process of proton transfer in concentrated
electrolytes. It was found that the model supported by
the data of Lovell and Schulman (10-12) for ground-state
ionizations occurring in concentrated acid was applicable
to the compounds examined in this dissertation. This
model has now been successfully applied to unsubstituted
and substituted carboxamides, tertiary anilines, aromatic
lactams, and several other heterocylic bases (including
those with oxygen or nitrogen as the heteroatom). This
broad application to molecules of dissimilar structure
suggests that equation (12) will find wide application
to ground-state ionizations occurring in concentrated acid.
The model proposed to quantitate the kinetics of
excited-state proton transfer in concentrated acid
appears to be valid. This conclusion is supported by
several observations. In the first place, equations (77)
and (84) correctly predicted the shapes of the fluoimetric
titration curves both in the cases where excited-state
131

132
nonequilibrium conditions prevailed and in the case where
excited-state prototropic equilibrium was observed.
Secondly, the model predicted that the fluorimetric
titration data of the molecules exhibiting excited-state
ionizations in concentrated acid should result in linear
plots when plotted according to equation (77) or (84)
(depending upon the charge types of the species involved).
Linearity was observed in these plots when the appropriate
combinations of n and r were used. Thirdly, the Forster
cycle, which is independent of the titration curves
themselves and of kinetic considerations, was, in most
*
cases, successful in relating pK and pK to each other.
This not only confirms the validity of the model for
excited-state ionizations which occur in concentrated acid,
but also further confirms the applicability of the ground-
state model as well.
That both the models for ground- and excited-state
ionizations were successful in predicting the acid-base
titration behavior of both H and H, type molecules
suggests that these models may be applicable to species of
other charge types as well. Further research should show
whether or not this is true. It would also be interesting
to see if these models apply to ionizations which occur in
concentrated base (NaOH or KOH).
Further research also needs to be done in order to
clarify the question of whether or not the standard states

133
of the reactants change when the composition of the medium
is changed. The success of the Forster cycle in the
research presented in this dissertation suggests that
either the standard states do not change with a change in
acid composition or that they do change but in such a way
that the standard free energies of all the species
involved in a given reaction change by the same amount. It
was not possible, however, to discern which one of these
circumstances was responsible for the success of the
Forster cycle. Furthermore, it appears that acid-base
chemistry in concentrated acid may be simply and
fundamentally related to acid-base chemistry in dilute,
aqueous solution by the inclusion of water as a reactant
in the equilibrium expressions of interest.
Finally, a look at the possible utility of the methods
developed in this dissertation is in order. The
application of these methods to the investigation of
acid-base chemistry in a mixed solvent system such as
methanol:sulfuric acid could be of great benefit. The
addition of methanol would greatly increase the number of
aromatic acids and bases that could be studied because
more of these compounds are soluble in methanolic sulfuric
acid than are soluble in nonmethanolic sulfuric acid. If
the acid-base properties of molecules in dilute, aqueous
solution could be related to those same properties in
methanolic sulfuric acid, then it may be possible to devise

134
a general method for predicting the thermodynamics of
proton transfer in dilute, aqueous solution based on
measurements made in nonaqueous or mixed-aqueous solvents.
This would greatly simplify the determination of the
pKa's of many water-insoluble pharmaceuticals, for then
the thermodynamic pK 's of relatively water-insoluble
species could be calculated from measurements made in
nonaqueous or mixed-aqueous solvents in which the species
are soluble. A study of acid-base thermodynamics in
methanolic sulfuric acid could not be performed, however,
until an acidity scale for the medium is determined.
Values of aTrf in the solvent, and perhaps of the activity
of methanol in the solvent, would also have to be measured.

APPENDIX A
SIMPLE LINEAR LEAST-SQUARES
REGRESSION ANALYSIS
The statistics of the straight line are well
understood and may be found in many basic and advanced
statistics books (90-93) . The derivation of these equations
is not relevant here. Their importance to this dissertation
lies in how the slope and intercept of a given line may be
statistically estimated.
The equation of a straight line is given by
Y = a0 + axX (85),
where Y is the dependent variable, X is the independent
variable, aQ is the ordinate intercept, and a^ is the slope.
The values of the intercept and slope may be calculated
(90) as
= (ZY)(EX2) - (EX)(EXY)
° NZX2 - (EX)2
and
(86)
_ _ NEXY - (EX)(EY)
al 9 2 '
NEX^ - (EX)
where N is the number of (X,Y) data points. The various
sums in equations (86) and (87) are short-form notation
for the following:
135

136
N
ZY = Z Y. (88)
i=l 1
N
ZX = Z X. (89)
i=l 1
N
ZXY = Z X.Y. (90)
i=l 1 1
and
ZX2 = Z X.2 (91)
i=l 1
The standard deviation of the slope (91) , S , is given by
al
Sa = (S2/(ZX2-NX2))1/2 (92)
al
where X = ZX/N. The term S in equation (92) is calculated
as
S=((ZY2-(ZY)2/N-(ZXY-ZXZY/N)2/(ZX2-(ZX)2/N))/(N-2))1/2 (93)
The standard deviation of the intercept (91), S /is
ao
calculated as
S= =(S(ZX2/(NZX2-(ZX)2)))1/2 (94)
cl
The cofficient of correlation (90) , r, is given by
r=(NZXY-(ZX)(ZY))/((NZX2-(ZX)2)(NZY2-(ZY)2))1/2 (95)
The value of r will fall into the range -1 £ r ^ 1, and
the data are best fitted to a straight line when |r| = 1.

137
The sign of r simply indicates whether the slope is positive
(r > 0) or negative (r < 0). When r - 0, then Y is not
linearly dependent on X.
The equations in this appendix are short-form
computational formulae which are particularly useful when
computation is limited to devices with small amounts of
RAM (random access memory). Because of this, equations
(86-95) are well suited for the estimation of r, a , S ,
° ao
a., and S with handheld programmable calculators. Simple
I ax
linear regression, analysis may also be performed with matrix
operations (92), but this method is beyond the
capabilities of most of the currently available handheld
computing devices.

APPENDIX B
MULTIPLE LINEAR LEAST-SQUARES
REGRESSION ANALYSIS
In some cases it is postulated that experimental
data will fit an equation of the form
Z = a© + a^X + a2Y (96) ,
where Z is the dependent variable, X and Y are the
independent variables, and aQ, a^, and a2 are the
regression coefficients (unknowns). The regression
coefficients may be estimated by the simultaneous solution
of the three normal equations (90)
£Z = aQN + a±ZX + a2EY (97),
IXZ = aQlX + a1IX2 + a2IXY (98),
and
EYZ = aQIY + a1EXY + a2ZY2 (99),
where all of the symbols are the same as defined in
equations (88-91) and EZ, EXZ, and EYZ are given by
N
ZZ = Z Z. (100) ,
i=l 1
N
EXZ = Z X.Z. (101),
i=l 1 X
and
138

139
N
ZYZ = Z Y.Z. (102),
i=l 1 1
respectively. Equations (97-99) can be put into matrix
form:
where
and
D = CA
Z Z
D
=
EXZ
_EYZ_
” N
EX
EY "
s
EX
2
EX
EXY
EY
EXY
EY2
(103),
(104),
(105),
(106).
Simple matrix arithmetic shows that
A = C_1D (107) ,
where C ^ is the inverse matrix of matrix of C. Therefore,
the regression coefficients may be estimated from N (X,Y,Z)
points by calculating matrix elements and subsequently
performing matrix inversion and matrix multiplication.
The elements of matrix C may be calculated by multiplication
C = ItI (108) ,

140
where
II
1
1
I =
Xn
X,
X.
-1 XN Yl^
(109)
.t .
and I is the transpose of matrix I. Matrix D is then
given by the product
D = IfcP
(110)
where
P =
(111)
JN
The matrix of fitted values of the dependent variable is
given by
F = IA (112)
and the matrix of residuals is given by
R = P - F
th
where the residual of the i point is
(113)
R. = Z . - F.
ill
(114)

141
The sum of the squares of the residuals is
N
S = SR.'
r i=l 1
(115) .
The estimated standard deviations of aQ, a^, and a3 are
given by (92)
and
= ((S /(N-3))CT1,)1/2
ao r 1,1
% - ((s/m-snc^)172
(116),
(117),
sa2 = ( (Sr/(N-3) )C^3) 1/2 (118),
th
respectively, and C. . is the (i,i) element of
1/1
matrix C The coefficient of multiple determination (90),
2
R , is given by
R2 = 1 - r-: (119),
2 (z. - zr
i=l 1
where
N
S Z.
' =1 1
Z = —— (120) .
N
2 2
The value of R may range from zero to one, and when R ^1
the data are well described by equation (96).
The rapid calculation of the regression coefficients
and their estimated standard deviations for a data set of

142
even modest size (ten points) requires many calculations
and the storage of many numbers. The computation and
storage requirements of this statistical analysis are
not found in any currently available handheld computing
devices, and hence digital computers are used for this
type of curve fitting.

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BIOGRAPHICAL SKETCH
Brian Stanley Vogt was born on April 29, 1956, in the
Clover Hill Hospital in Lawrence, Massachusetts,to Stanley
and Blanche Vogt. He is their second son and has one
brother and one sister.
He attended kindergarten, elementary school, junior
high school, and high school in the Andover, Massachusetts,
public system between the years of 1961 and 1974. He
became a member of the National Honor Society in the
1973-1974 school year.
Subsequent to graduation from high school in 1974,
he attended Bob Jones University in Greenville, South
Carolina. He had a double major (biology/chemistry), and
graduated cum laude with a Bachelor of Science in 1979.
The science faculty at Bob Jones University selected him as
the outstanding biology graduate in the 1979 graduating
class.
He participated in the sports of fencing, soccer, and
table tennis while in undergraduate school. He also
enjoys fishing, bicycling, photography, birdwatching,
classical music, and woodworking.
When he was young, he made a personal committment to
the Lord Jesus Christ. He has read and studied the Bible,
and has used the principles found therein to guide his
149

150
decisions and establish his priorities. He has been
actively involved in church choir and Sunday school
programs.
He went to the College of Pharmacy at the University
of Florida in the fall of 1979. At UF he coauthored eight
publications for scientific journals and coauthored
chapters for two books. He also presented papers at four
meetings on the state and regional levels. At one of these
meetings (American Chemical Society meeting, Florida
section, 1981) he was given first prize for the best
student research presentation in the physical chemistry
division.

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Stephen G. Schulman, Chairman
Professor of Pharmacy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Frederico A. Vilallonga
Professor of Pharmacy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Kenneth E. Sloan
Assistant Professor of Medicinal
Chemistry
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
John H. Perrin
Professor of Pharmacy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
James D. Winefordner
Graduate Research Professor
of Chemistry

This dissertation was submitted to the Graduate Faculty
of the College of Pharmacy and to the Graduate Council, and
was accepted as partial fulfillment of the requirements
for the degree of Doctor of Philosophy.
August, 1983
Dean, College of Pharmacy
Dean for Graduate Studies and
Research

UNIVERSITY OF FLORIDA
3 1262 08557 0025



5
deals only with molecules which react according to mechanism
(2), and hence we shall restrict ourselves to a discussion
of that mechanism.
The acid-dissociation equilibrium constant, K for
reaction (2) is defined as
K = ^
a k,
a3aH+
aBH+ aw
(4) ,
where a0 and aT,+ are the activities of the conjugate base
and acid, respectively, and aH+ and a^ are the activities
of proton and water, respectively. In dilute, aqueous
solution a =1, and then
w
_ aBaH+ [Bl fBaH+
K ;
a a^TT+
BH
[BH+]fBH+
(5) ,
where [B] and f are, respectively, the equilibrium molar
concentration and activity coefficient of B, and [BH+] and
f + are, respectively, the equilibrium molar concentration
BH
and activity coefficient of BH+. At infinite dilution,
f 1 and f_+ = 1, and then equation (5) may be
transformed into the familiar Henderson-Hasselbach
equation (7,8) :
PK = pH log [B]r~
a [ BH+ ]
(6) .
In concentrated acidic solutions equation (6) cannot
be used. The acidity of the medium (pH < 1) cannot be
measured with a pH meter, but it can be measured with the
Hammett acidity function (9). This acidity scale is based


13


132
nonequilibrium conditions prevailed and in the case where
excited-state prototropic equilibrium was observed.
Secondly, the model predicted that the fluorimetric
titration data of the molecules exhibiting excited-state
ionizations in concentrated acid should result in linear
plots when plotted according to equation (77) or (84)
(depending upon the charge types of the species involved).
Linearity was observed in these plots when the appropriate
combinations of n and r were used. Thirdly, the Forster
cycle, which is independent of the titration curves
themselves and of kinetic considerations, was, in most
*
cases, successful in relating pK and pK to each other.
This not only confirms the validity of the model for
excited-state ionizations which occur in concentrated acid,
but also further confirms the applicability of the ground-
state model as well.
That both the models for ground- and excited-state
ionizations were successful in predicting the acid-base
titration behavior of both H and H, type molecules
suggests that these models may be applicable to species of
other charge types as well. Further research should show
whether or not this is true. It would also be interesting
to see if these models apply to ionizations which occur in
concentrated base (NaOH or KOH).
Further research also needs to be done in order to
clarify the question of whether or not the standard states


APPENDIX A
SIMPLE LINEAR LEAST-SQUARES
REGRESSION ANALYSIS
The statistics of the straight line are well
understood and may be found in many basic and advanced
statistics books (90-93) The derivation of these equations
is not relevant here. Their importance to this dissertation
lies in how the slope and intercept of a given line may be
statistically estimated.
The equation of a straight line is given by
Y = a0 + axX (85),
where Y is the dependent variable, X is the independent
variable, aQ is the ordinate intercept, and a^ is the slope.
The values of the intercept and slope may be calculated
(90) as
= (ZY)(EX2) (EX)(EXY)
NZX2 (EX)2
and
(86)
_ NEXY (EX)(EY)
al 9 9 '
NEX^ (EX)
where N is the number of (X,Y) data points. The various
sums in equations (86) and (87) are short-form notation
for the following:
135


33
dual-beam oscilloscope, on which the convoluted fluorescence
decay from the sample was displayed. Lifetimes >1.7 ns were
measurable with this apparatus.
Measurements of Acidity
All pH measurements were made at room temperature with
a Markson ElektroMark pH meter equipped with a silver/silver-
chloride combination glass electrode. The pH meter was
standardized against Fisher Scientific Company pH buffers
or Markson Scientific Inc. (Del Mar, CA) pH buffers at
room temperature. These buffers were accurate to 0.02
pH unit and were of pH 1.00, 4.00, 7.00, and 10.00. The
precision of the pH meter was estimated to be 0.01 pH
unit, and it was used for the measurement of pH > 1.
The Hammett acidity function was used as a measure of
the acidity of solutions in which pH < 1. This acidity
scale may be used to quantitate the acidity of media when
the species involved have neutral conjugate bases and
singly charged conjugate acids. Values of Hq in HClO^ and
HoS0. may be found in references (62-64) Values of a in
the same media may be found in references (65-69).
Titration Methods
Solutions for absorption and fluorescence studies were
put into UV-visible quartz cuvettes with pathlengths of
10 mm and volume capacities of =4 mis. Absorption spectra
were taken against a reference solution of composition


71
which should correctly describe the excited-state proton-
transfer kinetics of reactions which occur in
concentrated acid. A plot of ( ($/0) / ) aw
versus h^a^11 (<{>' /$'Q) / (4>' /^ctg) should be a straight line
with an ordinate intercept of 1/k (0)t and a slope of
cl O
kb(0)T/ka(0)To.
Several molecules (78) which have excited ionizations
which occur in acid such that the inflection points are
found at pH < 1 are 2-quinolone (Figure 4-1) and
4-quinolone (Figure 4-2). It is of interest to see
whether or not these ionizations are described by
equation (77).
Results and Discussion
The absorption and fluorescence maxima of neutral and
protonated 2-quinolone, as well as their fluorescence
lifetimes, are presented in Table 4-1. The
spectrophotometric titration of 2-quinolone is shown in
Figure 4-3. These titration data were best fitted
according to equation (60) with (n-r ) =4, which yielded
9
pK = -0.300.03.
cl
Figure 4-4 shows the fluorimetric titration curve of
2-quinolone. Figures 4-5 and 4-6 show plots of
((/ '/<¡>-aB) )awr versus h^11 (<|,'/$'Q) / (<¡> '/4>-oib) for
2-quinolone with various values of r and n = 3 (Figure 4-5)
or n = 4 (Figure 4-6) Values of §'/§'Q fr both 2-quinolone
and 4-quinolone were calculated according to the


Figure 4-10
Plot of ( (4>/ )/($'/4>'-a )) a r versus
O O D W
h.a" ('/4>') / (4>'/4> '-<*) for 4-quinolone with
W O O O
(A) r = 2, (B) r = 3, (C) r = 4, (D) r = 5,
n = 4 .
(E) r = 6.


Absorbance
o o o o o o o o o

OH1 K) U> £* U1 cr 00
03
00


4
molecules which we shall consider have conjugate acids and
bases which react according to the mechanism
BH + SH
B + SH,
(1) ,
+ .
where B is the conjugate base, BH is the conjugate acid,
,+ .
SH is the solvent, and SH2 is the solvent lyonium ion.
rate constants ka and k^ are, respectively, the pseudo-
The
first-order rate constant for deprotonation of BH and the
second-order rate constant for bimolecular protonation of B.
In aqueous solution, SH is water and SH* is the hydronium
ion, and then reaction (1) becomes
k
BH + H20
> B + H30+
(2)
It is also possible to have a conjugate acid that is so
weakly acidic that solvent lyate anions must be present for
the deprotonation reaction to occur, in which case the
reaction will be described by
BH+ + S
B + SH
(3) ,
where S is the solvent lyate anion ( in water this is the
hydroxide ion) and k' and k are, respectively, the
second-order rate constant for bimolecular deprotonation of
BH+ and the pseudo-first-order rate constant for protonation
of B. The research presented in this dissertation, however,


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Stephen G. Schulman, Chairman
Professor of Pharmacy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Frederico A. Vilallonga
Professor of Pharmacy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Kenneth E. Sloan
Assistant Professor of Medicinal
Chemistry
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
John H. Perrin
Professor of Pharmacy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
James D. Winefordner
Graduate Research Professor
of Chemistry


50
1
T
k.
(56)
b
and
1
T
k.
(57) .
b
Equations (56) and (57) may be combined to yield
(58) ,
so that only two titrations are needed to estimate K This
cl
*
value of K can then be used in conjunction with equation
cl
(55) to determine k, and then k can be calculated.
D cl
*
Values of k^, k^, and pK^ calculated in this way are also
presented in Table 3-2. The excellent agreement between
k *
pK and pK (F.C.) suggests that equations (55-58) may be
3. 3.
used with confidence to determine pK when the excited-
3
state reaction occurs according to mechanism (26) and
*
when pK >> pK .
Xanthone (Figure 3-5) has a ground-state ionization in
concentrated acid (76,77) and an excited-state ionization
in dilute, aqueous solution (76,77). While pK has been
estimated using the Hammett acidity function without
including atrf (76), it has not been seen whether equation
*
(12) is applicable or not. Furthermore, pK^ has been


36
an International Business Machines IBM 4341 or on a
Digital Equipment Corporation DEC VAX 11/780. All
computer programs were written in BASIC (beginners
all-purpose symbolic instruction code) by the author. The
BASIC language on the IBM 4341 was used through MUSIC
(McGill University system for interactive computing), while
BASIC on the VAX 11/780 was used through DEC VMS (DEC
virtual memory system).


CHAPTER III
GROUND- AND EXCITED-STATE PROTON-TRANSFER
IN ACRIDONE AND XANTHONE
Introduction
The titration behavior of melecules which become much
more basic (or much less acidic) in the excited state than
they are in the ground state will be described by a

simplified form of equation (43) Since pK >> pK aD->l,
a a a
and then equation (43) can be reduced and rearranged (70) to
k,x'
b [H+]
i + Vo
Even if i and x' are known, there is no linear form
o o
(53)
equation (53) can be put into such that k^, k^, and can
be extracted from the data of a single fluorimetric
titration. A method (71-73) of titration involving the use
of HCl has been developed which, in favorable
circumstances, does permit the used of a linear plot to
extract k and k, from a single titration. In this
method, the fluorescence of the conjugate acid is quenched
by Cl while the proton transfer is effected by H+, where
both the Cl and H+ come from the HCl. However, this
method is limited in its application to those molecules
which ionize at pH such that the rate of proton transfer is
approximately the same as the rate of quenching of the
37


145
35. Schulman, S.G., Capomacchia, A.C., and Rietta, M.S.,
Anal. Chim. Acta, 56 (1971), 91.
36. Schulman, S.G., Tidwell, P.T., Cetorelli, J.J., and
Winefordner, J.D., J. Am. Chem. Soc., 93 (1971), 3179.
37. Schulman, S.G., Capomacchia, A.C., and Tussey, B.,
Photochem. Photobiol., 14 (1971), 733.
38. Wehry, E.L., and Rogers, L.B., Spectrochim. Acta,
21 (1965), 1976.
39. Jaffe, H.H., and Jones, H.L., J. Org. Chem., 30
(1965), 964.
40. Weller, A., Prog. React. Kinetics, 1 (1961), 187.
41. Schulman, S.G., Rev. Anal. Chem., 1 (1971), 85.
42. Parker, C.A., Photoluminescence of Solutions,
Amsterdam, Elsevier, 1968, pp. 333-343.
43. Martynov, I., Demyashkevitch, A., Uzhinov, B., and
Kuzmin, M., Usp. Chem. (Akad. Nauk USSR), 47 (1977), 3.
44. Shim, S.C., Hwahak Kwa Kongop Ui Chinbo, 20 (1980), 81.
45. Harris, C.M., and Selinger, B.K., J. Phys. Chem., 84
(1980), 891.
46. Hafner, F., Worner, J., Steiner, U., and Hauser, M.,
Chem. Phys. Letts., 73 (1980), 139.
47. Campillo, A.J., Clark, J.H., Shapiro, S.L., Winn,
K.R., and Woodbridge, P.K., Chem. Phys. Letts., 67
(1979), 218.
48. Kobayashi, T., and Rentzepis, P.M., J. Chem. Phys., 70
(1979), 886.
49. Shizuka, H., Tsutsumi, K., Takeuchi, H., and Tanaka,
I., Chem. Phys. Letts., 62 (1979), 408.
50. Smith, K.K., Kaufmann, K.J., Huppert, D., and Gutman,
M., Chem. Phys. Letts., 64 (1979), 522.
51. Gafni, A., and Brand, L., Chem. Phvs. Letts., 58
(1978), 346.
52. Demjaschkewitch, A.B., Zaitsev, N.K., and Kuzmin, M.
G., Chem. Phys. Letts., 55 (1978), 80.


133
of the reactants change when the composition of the medium
is changed. The success of the Forster cycle in the
research presented in this dissertation suggests that
either the standard states do not change with a change in
acid composition or that they do change but in such a way
that the standard free energies of all the species
involved in a given reaction change by the same amount. It
was not possible, however, to discern which one of these
circumstances was responsible for the success of the
Forster cycle. Furthermore, it appears that acid-base
chemistry in concentrated acid may be simply and
fundamentally related to acid-base chemistry in dilute,
aqueous solution by the inclusion of water as a reactant
in the equilibrium expressions of interest.
Finally, a look at the possible utility of the methods
developed in this dissertation is in order. The
application of these methods to the investigation of
acid-base chemistry in a mixed solvent system such as
methanol:sulfuric acid could be of great benefit. The
addition of methanol would greatly increase the number of
aromatic acids and bases that could be studied because
more of these compounds are soluble in methanolic sulfuric
acid than are soluble in nonmethanolic sulfuric acid. If
the acid-base properties of molecules in dilute, aqueous
solution could be related to those same properties in
methanolic sulfuric acid, then it may be possible to devise


114
equation (76), culminates in
4>/4>,
r
a =
w
kb(0)T,
+ h
4) / n y yo
ka(0)V
+ +
k (0)T + w
3. O
f;+f+
f f
X o
(82)
x
where f+ and f++ are the activity coefficients for the H+
+* -*-+*
type conjugate base (BH ) and conjugate acid (BH2' ),
respectively, and f is the activity coefficient of the
transition-state species in the excited-state reaction
-f- -f-
BH2 + rH20 XT- BH + H (83)
Because of similarities in charge and size, it is now
reasonable to assume that f,,/f = f'f./f f' = 1, in
which case equation (82) reduces to
/o r 1 + kb(0)T. n
W ka(0)To ka(0)To + w
and a plot of ( U/O / (4 /cji'-O ) atrr versus
o u o w
h+awn (

k, (0)x'/k (0)t and an ordinate intercept of 1/k (0)t .
b o' a o r a o
An H+ type molecule which is amenable to study in
concentrated acid is 3-aminoacridine (88), the structure
of which is shown in Figure 6-1.
Results and Discussion
The fluorescence and absorption maxima and the
fluorescence lifetimes of monoprotonated and diprotonated
3-aminoacridine are presented in Table 6-1. Values of H+
in H2SO^ may be found in reference (87). A recent


117
study (89) showed that the values of H+ in reference (87)
for I^SO^ j> 7 M are inaccurate due to poor choices of
indicators. Correct values of H+ for this concentration
range may be found in reference (89). It was also shown
that H = H for HoS0. > 7 M, and values of H in
references (63,64) could be used as H+ for i^SO^ >_ 7 M.
Spectrophotometric titration curves for 3-aminoacridine
are shown in Figures 6-2 and 6-3. These titration data
were best fitted according to equation (60) using h+ in
place of h which resulted in a value of pK = -1.760.02
O cl
with (n r ) =0.
9
The fluorimetric titration curve of 3-aminoacridine is
shown in Figure 6-4. The fluorescence spectrum of the
dication overlaps and eclipses that of the monocation, and
hence <¡> / was calculated according to the
relationship = 1 tj>/0. Figure 6-5 shows the
3-aminoacridine titration data plotted according to
equation (84) with n = 1 and r = 1 (other values of n and
r did not fit the data) Values of k (0) k, (0) and
a d
*
pK (0) determined from this plot, as well as the values of
cl

pK and pK (F.C.), are presented in Table 6-2.
The linearity of the plot shown in Figure 6-5 suggests
that the model under consideration is valid for H+ type
molecules. The criteria for the establishment of
prototropic equilibrium within the lifetime of the excited
state are the same for H+ type molecules as they are for


20
steady-state kinetics. Representative examples of
time-resolved studies of excited-state proton-transfer
kinetics may be found in references (45-55) .
Steady-State Kinetics of Excited-State Proton-
Transfer Reactions
The kinetic equations for excited-state proton-
transfer reactions in dilute, aqueous solution were first
derived by Weller (56). The excited-state reaction which
we are concerned with is
, kf +* K k'
BH i 1 BH + B - B (26) ,
where k^ and k^ are the rate constants for the fluorescences
of BH and B respectively, and k^ and k^ are the sums of
the rate constants for all nonradiative processes
*
deactivating BH and B respectively. The fluorescence
:k
lifetime of the conjugate acid (present when pH << pK&) in
the absence of excited-state proton transfer is
tq = 1/(kf + k^), and that of the conjugate base (present
*
when pH >> pK ) in the absence of excited-state proton
d.
transfer is = l/(k£ + k^). Prior to integration, the
+* *
rate expressions for the disappearance of BH and B from
the excited state may be put into the forms
-/ d[ BH+*] = -/ (1/T'+k, [ H+] ) [ B*] dt+/k [ 3H+*]dt (27)
a + L J 0 obLJLJ o
and


38
conjugate acid fluorescence. Furthermore, /<>0 and /§'Q
must be calculated independently of each other, and hence
the fluorescence spectra of the conjugate acid and base
must be well resolved from each other. These conditions
must all be met before the HCl method can be used. It was
desirable, therefore, to devise a more generally applicable
method of determing and k^.
It can be seen from equation (53) that the slope, m,
of a plot of (4>/Q) / (<> versus [H+] will be
m =
k,x'
b o
1 + k x
a o
(54) ,
which can be rearranged to
x' 1 k
o a
^ + \ T
(55) .
If a quencher can be added to the titration medium that
will quench the fluorescence of the conjugate acid so that
(1 + k x ) will vary with quencher concentration relative to
k^x^, then m will be a function of quencher concentration.
A series of titrations, each with a different constant
concentration of quencher in the titration medium, should
then yield a different value of m and xq for each
titration (if the fluorescence of the conjugate base is also
quenched, then different values of x^ will also be obtained).
According to equation (55) a plot of x^/m versus xq should


123
4>/4>


ACKNOWLEDGEMENTS
I would first like to thank Dr. S.G. Schulman,
chairman of my supervisory committee, for his patient
guidance throughout my graduate career. His perception,
experience, and advice were indispensable in the completion
of the research which culminated in this dissertation. I
would also like to thank the other members of my supervisory
committee, Dr. F.A. Vilallonga, Dr. K.B. Sloan, Dr. J.H.
Perrin, and Dr. J. D. Winefordner, for their suggestions
and support.
I would also like to thank the other members of the
research group not only for their friendship, but also for
the many thought-provoking discussions and heated
arguments which helped all those involved to gain a clearer
perspective on the strengths and weaknesses of their
scientific understandings. Michael Lovell was
particularly helpful in these regards.
Finally, I would like to thank my parents, Stanley and
Blanche Vogt, for the understanding and wisdom with which
they have encouraged me. They have played an important role
in the years of success that I have been privileged to.
iii


This dissertation is lovingly dedicated to my dear
wife, Carla,
encouragement
Her continual love, patience, and
were instrumental in the completion of this
work.


Figure 3-7
_ r
Plot of the fluorescence lifetime of 2 X 10 M xanthone
versus bromide ion concentration. (A) tq (protonated
xanthone), (B) (neutral xanthone).


64
*
presented in Table 3-5 along with ka, k^, and pK^
. *
estimated graphically from Figure 3-9. This value of pK
cl
*
does not agree with pK (F.C.). It was observed that the
cl
absorption spectrum of isolated neutral xanthone shifts to
shorter wavelength (by -3 nm) as the medium (I^SO^) was
changed to more dilute H^SO^. This solvent effect on the
spectrum of neutral xanthone introduces significant error
ic
into the estimation of its 0-0 energy, and hence pK (F.C.)
^ <3.
will also be inaccurate. It thus seems likely that a
1c
substantial amount of the discrepancy between pK^ and
*
pK (F.C.) in Table 3-5 is due to the solvent-effect-
3
induced failure of the Forster cycle. The nature of the
solvent effect is not known. Since the activity of water in
the sulfuric acid in which the solvent effect occurs
deviates significantly from unity (65,66), it is possible
that the state of hydration of neutral xanthone changes
when the medium changes. If a hydration change of this
type affects the absorption spectrum, then this explains
the solvent effect. If the hydration change is occurring
but does not affect the spectrum, then the solvent effect
remains unexplained. To date, no experiment has been done
which could confirm or disprove the change-in-hydration
hypothesis.
It is not possible, therefore, at least in the case of
xanthone, to use the Forster cycle to relate the
thermodynamics of proton transfer in dilute, aqueous solution


Figure 5-2
-4
Plot of absorbance versus Hq for 1 X 10 M 1-isoquinolone in I^SO^.
wavelength = 275 nm.
Analytical


32
When fluorescence is excited at an isosbestic point, then
equations (29) and
(30) reduce to
aBH+ = [BH+]/Cb and
a_, = [B]/C_, respectively.
Equation (49) then becomes
F = F cl 4*
rBH <|> BH
+ F +
BH
~aB +
F a + F a +
BiJ^B B<> BH
(50) .
Since + aBH+ = 1
and <{)/(j)o + $
= 1, equation
(50)
can be reduced to
4>
F
- fb
(51) ,
4>
o
fbh+
- fb
and it then follows
that
4'
fbh+
- F
(52) .
4>'
o
fbh+
- fb
When the ground- and excited-state proton-transfer reactions
do not overlap, then a ->-1 and aBH+->-0 or an(^ aBH+"^' anc^
in either case equations (51) and (52) still follow from (50).
Fluorescence lifetimes were measured at room
temperature with a TRW model 75A decay-time florimeter
without excitation or emission filters. This instrument
was equipped with a TRW model 31B nanosecond spectral
source and was used with an 18 watt deuterium lamp, which
was thyratron-pulsed at 5kHz. A TRW model 32A analog decay
computer was used to deconvolute the fluorescence decay time
of the analyte from the experimentally measured fluorescence
decay, which was actually an instrumentally distorted
convolution of the lamp pulse and the analyte fluorescence.
The TRW instruments were interfaced to a Tektronix model 556


60
Table 3-3
Variation with bromide ion concentration of t1, t and m
for xanthone.
[Br
"] ,
M
. a
ns
b
V ns
m
0
2.5
X
10-3
3.40.1
3.4C
31.810.8
23.3C
5.310.2
6.510.1
5.0
X
10-2
3.40.1
18.210.4
7.410.1
1.0
X
10-2
3.40.2
11.810.3
9.6910.08
2.5
X
10 ^
3.510.2
6.510.4
12.810.1
Determined in water, pH = 5.5.
T_
determined in 4.0 M HoS0., H = -1.7.
2 4 o
Q
Estimated from Figure 3-7.


78
4>/
-5 -4 -3 -2-1 O 1


100
attain equilibrium within the lifetimes of their excited
states. A molecule which demonstrates excited-state
prototropic equilibrium is 1-isoquinolone (Figure 5-1) (86).
Results and Discussion
The fluorescence lifetimes and absorption and
fluorescence maxima of neutral and protonated 1-isoquinolone
are presented in Table 5-1. Figure 5-2 shows the
absorptiometric titration of 1-isoquinolone. These data
were best fitted according to equation (60) with
(n r ) = 1, which gave a value of pK = -1.380.03.
g a
The fluorimetric titration of 1-isoquinolone is
shown in Figure 5-3. The fluorescence spectra of neutral
and protonated 1-isoquinolone show considerable overlap,
and thus was calculated according to the
relationship = 1 cj>/0. Figure 5-4 shows the
fluorimetric titration data of 1-isoquinolone plotted
according to equation (77) with n = 2 and r = 2. The plot
is a straight line which passes through the origin, and
it is concluded that the excited-state proton-transfer
reaction of 1-isoquinolone attains equilibrium within the
lifetime of the excited state.
Examination of equation (78) shows that, when a
given excited-state proton transfer attains equilibrium,
then all plots of ( (_) / (4> '/ -a)) a r versus
O O n> W
hoawn^^)/(i'/^B) will have the same slope and
intercept regardless of the values of n and r as long as


94


115
Figure 6-1
Structure of 3-aminoacridine.


CHAPTER VII
SUMMARY
Many questions were raised before and during the
research carried out for this dissertation. While this
work has not definitively answered all of these questions,
it has certainly contributed to the understanding of the
fundamental process of proton transfer in concentrated
electrolytes. It was found that the model supported by
the data of Lovell and Schulman (10-12) for ground-state
ionizations occurring in concentrated acid was applicable
to the compounds examined in this dissertation. This
model has now been successfully applied to unsubstituted
and substituted carboxamides, tertiary anilines, aromatic
lactams, and several other heterocylic bases (including
those with oxygen or nitrogen as the heteroatom). This
broad application to molecules of dissimilar structure
suggests that equation (12) will find wide application
to ground-state ionizations occurring in concentrated acid.
The model proposed to quantitate the kinetics of
excited-state proton transfer in concentrated acid
appears to be valid. This conclusion is supported by
several observations. In the first place, equations (77)
and (84) correctly predicted the shapes of the fluoimetric
titration curves both in the cases where excited-state
131


Figure 4-8
Plot of the relative quantum yield of fluorescence (d>/4>0)
of 3 X 10 5 M protonated 4-quinolone versus H The
molecule was titrated with HCIO^. Analytical wavelength =
360 nm. Excitation wavelength = 302 nm (isosbestic point) .


136
N
ZY = Z Y. (88)
i=l 1
N
ZX = Z X. (89)
i=l 1
N
ZXY = Z X.Y. (90)
i=l 1 1
and
ZX2 = Z X.2 (91)
i=l 1
The standard deviation of the slope (91) S is given by
al
Sa = (S2/(ZX2-NX2))1/2 (92)
al
where X = ZX/N. The term S in equation (92) is calculated
as
S=((ZY2-(ZY)2/N-(ZXY-ZXZY/N)2/(ZX2-(ZX)2/N))/(N-2))1/2 (93)
The standard deviation of the intercept (91), S /is
ao
calculated as
S= =(S(ZX2/(NZX2-(ZX)2)))1/2 (94)
cl
The cofficient of correlation (90) r, is given by
r=(NZXY-(ZX)(ZY))/((NZX2-(ZX)2)(NZY2-(ZY)2))1/2 (95)
The value of r will fall into the range -1 £ r ^ 1, and
the data are best fitted to a straight line when |r| = 1.


98
it has not yet been determined if the actual circumstance
is the first, second, or some other yet unconsidered
possibility.
Finally, the excited-state proton-transfer reactions
of both 2-quinolone and 4-quinolone do not attain
equilibrium within the lifetimes of their lowest excited
singlet states. This is intuitively obvious from the fact
that the rate constants for the protonation and
deprotonation steps were measurable. A quantitative
explanation of this conclusion is found in the next
chapter, where the criteria for and the implications of the
establishment of equilibrium within the lifetime of the
excited state will be discussed.


Ill
difference can be determined. Secondly, it is not
possible to estimate k (0) and k, (0). When x and x'
a o o o
*
are known, pK (0) may be calculated because the slopes (in
cl
Table 5-2) all represent values of k^(0)x^/ka(0)x .
*
Values of pK (0) calculated in this manner, as well as
cL
k
the values of pK and pK (F.C.), are also presented in
cl cl
Table 5-2. Even though k (0) is not known, we may still
conclude that the rate of the dissociation reaction is
high (85). It is seen that pK^(F.C.) = -2.20.3 is
*
identical to pK (0) = -2.230.04. This agreement not only
further confirms the validity of equation (77), but also
suggests that equation (60) correctly describes the
ground-state ionization of 1-isoquinolone.


142
even modest size (ten points) requires many calculations
and the storage of many numbers. The computation and
storage requirements of this statistical analysis are
not found in any currently available handheld computing
devices, and hence digital computers are used for this
type of curve fitting.


CHAPTER II
EXPERIMENTAL
Reagents and Chemicals
The water that was used was either deionized, distilled
water or doubly deionized water. Sulfuric acid, perchloric
acid, chloroform, methanol, ammonium hydroxide, sodium
hydroxide, sodium bromide, and potassium hydrogen phthalate
were all ACS reagent grade and were purchased from either
Fisher Scientific Company (Fair Lawn, NJ) or Scientific
Products (McGaw Park, IL). Ethanol was 95% and was
purchased locally from hospital stores (J. Hillis Miller
Health Center, Gainesville, FL). Thin-layer
chromatography plates were fluorescent-indicator
impregnated, 250 micron thick silica gel plates and were
purchased from Analabs (North Haven, CT). Dry silica gel
(100-200 mesh) for atmospheric pressure column
chromatography was purchased from Fisher Scientific
Company. All acid solutions were standardized against
standard NaOH (the NaOH was standardized against potassium
acid phthalate). All reagents were checked for spurious
absorption and emission prior to their being used for
spectroscopic studies.
All weighings were performed on a Mettler Type B6
electronic analytical balance.
27