Proton-transfer kinetics and equilibria in concentrated mineral acids

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Title:
Proton-transfer kinetics and equilibria in concentrated mineral acids
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Equilibria in concentrated mineral acids
Mineral acids
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vii, 150 leaves : ill. ; 29 cm.
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English
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Vogt, Brian Stanley, 1956-
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Acids   ( mesh )
Acridines   ( mesh )
Acid-Base Equilibrium   ( mesh )
Kinetics   ( mesh )
Protons   ( mesh )
Quinolines   ( mesh )
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bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

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

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University of Florida
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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.




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