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The measurement and validity of ion-selectivity i.e. selective electrode selectivity coefficients under non-Nernstian conditions

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Title:
The measurement and validity of ion-selectivity i.e. selective electrode selectivity coefficients under non-Nernstian conditions
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Dixon, Lois Anna, 1955-
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ix, 114 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Barium ( jstor )
Calcium ( jstor )
Calibration ( jstor )
Chlorides ( jstor )
Constant coefficients ( jstor )
Electrodes ( jstor )
Ions ( jstor )
Ligands ( jstor )
Liquids ( jstor )
Standard deviation ( jstor )
Electrodes, Ion selective ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1986.
Bibliography:
Includes bibliographical references (leaves 109-112).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Lois Anna Dixon.

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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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THE MEASUREMENT AND VALIDITY
OF ION-SELECTIVITY ELECTRODE SELECTIVITY
COEFFICIENTS UNDER NON-NERNSTIAN CONDITIONS








BY

Lois Anna Dixon


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


UNIVERSITY OF FLORIDA


1986













ACKNOWLEDGEMENTS

I would first like to thank all my relatives and

friends who have given me moral support and encouragement

not only during the preparation of this work but throughout

my formal education.

Thanks should also go to the chairman and members of my

supervisory committee for the assistance they have given me

in the preparation of this work. Mere words are an inade-

quate expression of my gratitude to them.

Special thanks go to Dr. Roger G. Bates for providing

me with the opportunity to work at The Technical University

of Budapest, Hungary, where much of the experimental work

reported here was carried out, and for his many helpful

suggestions during the writing of this work.

Most special thanks go to Dr. Erno Pungor, Dr. KlAra

Toth and all the members of their laboratory group at the

Technical University for the help and guidance they gave me

during the experimental work, but especially for the warmth

and friendship which they so freely bestowed on me.

Kdszndim nagyon szepen!







TABLE OF CONTENTS


Page
ACKNOWL EDGEMENTS....... .................. ................ i

LIST OF TABLES ........................................ iv

LIST OF FIGURES ....................................... vi

ABSTRACT ............................................... vii


CHAPTERS

1 INTRODUCTION ................................... 1

2 THE POTENTIAL RESPONSE OF ION-SELECTIVE
ELECTRODES ..................................... 7

3 THE SELECTIVITY OF ION-SELECTIVE ELECTRODES .... 15

4 OBJECTIVES AND OVERVIEW OF THE WORK ............ 26

5 SEPARATE SOLUTION MEASUREMENTS ................. 33

Neutral Carrier Electrode Based on Anal-05 ..... 33
Neutral Carrier Electrode Based on AC-14/81 .... 38
Ion-Exchange Electrode for Calcium Ion ......... 46

6 MIXED SOLUTION MEASUREMENTS .................... 58

Neutral Carrier Electrode Based on Anal-05 ..... 58
Neutral Carrier Electrode Based on AC-14/81..... 77
Ion-Exchange Electrode for Calcium Ion ......... 77

7 DISCUSSION OF RESULTS .......................... 86

8 CONCLUSIONS .................................... 92

9 SUGGESTIONS FOR FURTHER WORK ................... 93

APPENDICES

A MIXED SOLUTION DATA FOR ELECTRODES GI AND G2 ... 97

B MIXED SOLUTION DATA FOR ELECTRODES Q1 AND Q2 ... 106

BIBLIOGRAPHY ........................................... 109

BIOGRAPHICAL SKETCH .................................... 113


iii







LIST OF TABLES


TABLE Page


1 PRESENT CLASSIFICATION OF ION-SELECTIVE
ELECTRODES .................................... 5

2 CONCENTRATIONS OF CaC12 AND BaC12 PURE
SOLUTIONS ..................................... .. 36

3 ACTIVITIES AND CORRECTED POTENTIALS FOR ELECTRODES
G1 AND G2 IN CaC12 AND BaC12 SOLUTIONS ........ 39
pot
4 SEPARATE SOLUTION SELECTIVITY COEFFICIENT kCa,Ba
FOR ELECTRODES Gl AND G2 ............ ......... 42
R
5 SEPARATE SOLUTION SELECTIVITY COEFFICIENT kCa,Ba
FOR ELECTRODES Gl AND G2 ................... .. 43

6 ACTIVITIES AND CORRECTED POTENTIALS FOR ELECTRODE
1Q IN NaCl AND CaC12 SOLUTIONS ................ 47

7 ACTIVITIES AND CORRECTED POTENTIALS FOR ELECTRODE
Q2 IN NaC1 AND CaC12 SOLUTIONS ................ 49
pot
8 SEPARATE SOLUTION SELECTIVITY COEFFICIENT kNa,Ca
FOR ELECTRODES Q1 AND Q2 ........... ......... 51
R
9 SEPARATE SOLUTION SELECTIVITY COEFFICIENT kNaCa
FOR ELECTRODES Q1 AND Q2 ...................... 53

10 ACTIVITIES AND CORRECTED POTENTIALS FOR THE CORNING
ELECTRODE IN CaC12 AND BaC12 SOLUTIONS ........ 56
pot
11 SEPARATE SOLUTION SELECTIVITY COEFFICIENTS kCa,Ba
R
AND kCa,Ba FOR THE CORNING ELECTRODE .......... 57

12 CONCENTRATIONS USED IN CaC12/BaC12 MIXTURES ..... 59

13 ACTIVITIES AND CORRECTED POTENTIALS FOR ELECTRODES
G1 AND G2 IN CaC12/BaC12 MIXTURES ............. 61

14 MIXED SOLUTION CROSS-POINT SELECTIVITY COEFFICIENTS
XP XPR
kCa,Ba AND kCa,Ba FOR ELECTRODES G1 AND G2 .... 67

15 CURVE-FITTING SELECTIVITY COEFFICIENTS FOR
ELECTRODE G .................................... 69







16 COMPARISON OF SEPARATE SOLUTION AND HIGH ACTIVITY
MIXED SOLUTION RESPONSE SLOPES FOR ELECTRODES
Gl AND G2 ....................................... 72

17 COMPARISON OF SEPARATE SOLUTION AND LOW ACTIVITY
MIXED SOLUTION RESPONSE SLOPES FOR ELECTRODES
GI AND G2 ....................................... 74

18 COMPARISON OF CALCULATED AND MEASURED POTENTIALS
FOR ELECTRODES GI AND G2 ...................... 75

19 ACTIVITIES AND CORRECTED POTENTIALS FOR ELECTRODES
Ql AND Q2 IN NaC1/CaC12 MIXTURES .............. 78

20 COMPARISON OF SEPARATE SOLUTION AND HIGH ACTIVITY
MIXED SOLUTION RESPONSE SLOPES FOR ELECTRODES
Ql AND Q2 ... .... .................. .... ........ 80

21 COMPARISON OF CALCULATED AND MEASURED POTENTIALS
FOR ELECTRODES QI AND Q2 ...................... 82

22 ACTIVITIES AND CORRECTED POTENTIALS FOR THE CORNING
ELECTRODE IN CaCl2/BaC12 MIXTURES ............. 84

23 COMPARISON OF CALCULATED AND MEASURED POTENTIALS
FOR THE CORNING ELECTRODE ..................... 85







LIST OF FIGURES


FIGURE Page


1 Ion-Selective Electrode Structure ................ 2

2 The Graphical Cross-point Mixed Solution Method
pot
for Measurement of kA,B ....................... 18

3 Structure of the Ligand Anal-05 .................. 27

4 Structure of the Ligand AC-14/81 ................. 31

5 Apparatus for Potential Measurements Using
Electrodes G1 and G2 ........................... 35

6 Calibration Plot for Electrode G2 ................ 41

7 Apparatus for Potential Measurements Using
Electrodes Ql and Q2 ........................... 45

8 Determination of the Varied-ion Concentration at
the Cross-point ................................ 65

9 Determination of the Fixed-ion Concentration at
the Cross-point ................................ 66













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




THE MEASUREMENT AND VALIDITY
OF ION-SELECTIVE ELECTRODE SELECTIVITY
COEFFICIENTS UNDER NON-NERNSTIAN CONDITIONS


By


Lois Anna Dixon


August 1986



Chairman: Herbert A. Laitinen
Major Department: Chemistry


In this work the activity dependence of ion-selective

electrode selectivity coefficients measured by conventional

methods has been studied, a method for the measurement of

selectivity coefficients which are not activity dependent

has been developed, and selectivity coefficients measured by

this new method have been evaluated with regard to their

ability to describe the behavior of the electrode in mixed

solutions containing both primary and interfering ions.

Three electrode types were used: a neutral carrier

electrode responsive to calcium and barium ions, a neutral


vii







carrier electrode responsive to sodium and calcium ions, and

a liquid ion-exchanger electrode responsive to calcium and

barium ions.

Initially selectivity coefficients were measured over a

wide range of activities by conventional methods, including

the separate solution method at equal activities, the

mixed-solution graphical cross-point method, and curve-

fitting, which are all base on the Nicolsky equation.

These coefficients showed a marked activity dependence.

It was noticed that the response slopes for the

electrodes differed from the Nernstian values, and the ratio

of the response slopes for the primary and interfering ions

did not equal the ratio of the ionic charges, as is assumed

in the Nicolsky equation. The Nicolsky equation was

modified to include the slope ratio rather than the charge

ratio, and selectivity coefficients based on this modified

Nicolsky equation were measured, using separate solutions.

These coefficients showed little or no activity dependence

over the range of activities for which electrode response

was linear.

The modified Nicolsky equation was then used to predict

the potential of the electrodes in mixed solutions. The

predicted potentials agreed fairly well with measured poten-

tials, within the reproducibility of the measurements.

It is concluded that the apparent activity dependence


viii







of selectivity coefficients is a result of assuming

Nernstian electrode behavior. The recommended method for

measuring selectivity coefficients involves measuring

electrode potentials in separate solutions of primary and

interfering ions over a wide range of activities, and using

the modified Nicolsky equation. This produces activity-

independent selectivity coefficients which adequately

describe the electrode behavior in mixed solutions, while

providing a check on linearity and response slope.














CHAPTER 1
INTRODUCTION

The term "ion-selective electrode" refers to a group of

electrodes whose principal component, usually a membrane,

yields a potential in response to the presence of one (or

several) ionic species, in the presence of other ionic spe-

cies. A wide variety of substances can be used in the

membrane, including glasses, charged liquid ion-exchangers,

solid crystals, insoluble precipitates, neutral completing

agents, and enzymes. The structure of a typical ion-

selective electrode is shown in Figure 1.

Although the current interest in ion-selective electro-

des dates from the development in the 1960's of the

precipitate-based heterogeneous membrane electrode by Pungor

and co-workers (1) and the development of the single-crystal

lanthanum fluoride electrode by Frant and Ross (2), the

first ion-selective electrode was actually developed much

earlier. This was the pH glass electrode introduced by

Cremer in 1906 (3), the forerunner of the variety of glass

electrodes, for hydrogen and other cations, which are in

common use today.

In the early thirties studies of the electrochemical

behavior and composition of glass membranes by Lengyel and





































Internal metal .---
contact











Membrane


Inert electrode
body











Internal filling
--- solution


FIGURE 1. Ion-Selective Electrode Structure.


-
* ^^
*** .^






3
Blum (4) resulted in the development of the alkali-sensitive

membranes. The first solid-crystal membrane electrode was

introduced by Kolthoff and Sanders (5) in 1937, and con-

sisted of a fused silver halide melt sealed with wax to a

glass tube; a 0.01 molar halide solution was used as inter-

nal filling solution and a silver/silver halide electrode

was inserted as the internal reference. The electrode was

sensitive to halide ion and was superior to the conventional

Ag/AgCl electrode in that it was insensitive to oxidizing

agents, such as permanganate, and produced a sharper break

in potentiometric titration curves.

The first liquid-membrane electrodes were prepared by

Sollner and Shean in 1964 (6), and consisted of a hydropho-

bic membrane containing a liquid ion-exchanger. The first

neutral carrier liquid-membrane electrodes were developed by

Stefanac and Simon (7), who used the antibiotics monactin,

nonactin and valinomycin to produce electrodes selective for

alkali metal ions. Other neutral carriers, such as cyclic

polyethers (,crowns") and polyesters, have also been

employed as neutral carriers (8-9).

In 1969 Guilbault and co-workers introduced the enzyme

electrode, in which an ion-selective electrode is covered by

a polymeric matrix containing the enzyme (10-11). The

enzyme (urease, for example) reacts with the analyte (urea)

to produce an ion (ammonium ion) which is sensed by the ion-

selective electrode. A similar principle is involved in the





4

gas-sensing electrode (12), in which the gas passes through

a gas-permeable membrane and reacts with an internal solu-

tion to produce an ion, which is then detected by an ion-

selective electrode.

The newest type of ion-selective electrode is the Ion

Sensitive Field Effect Transistor (ISFET). The ISFET (13)

is a conventional Field Effect Transistor on which a layer

of ion-sensitive material, such as silicon dioxide, silicon

nitride, or a valinomycin/plasticizer/polyvinyl chloride

mixture, has been deposited.

As can be seen from the above, a wide variety of ion-

selective electrodes is now available. Several classifica-

tion schemes have been proposed for these electrodes

(14-16), but perhaps the best is a classification, given in

Table 1 (17), based on the type of material used in the

construction of the electrodes.






5

TABLE 1
PRESENT CLASSIFICATION OF ION-SELECTIVE ELECTRODES

A. MONOMEMBRANE ELECTRODES

1. Homogeneous, fixed-site, ion-exchange membranes--e.g.,

ion-exchange cellulose paper and polyquinhydrone-HCOH

membranes (for pH measurements).

2. Homogeneous, fixed-site, non-glass solid-state crystal,

or pressed pellet membranes--e.g., Ag2S, AgCl and LaF3

membranes.

3. Homogeneous, fixed-site, glass membranes--e.g., pH sen-

sitive glass membrane and cation sensitive glass

membranes.

4. Homogeneous, mobile-site, liquid ion-exchange

membranes--e.g., long-chain ion-exchange materials,

such as the alkyl phosphate salts and the tetraalkyl

ammonium salts.

5. Homogeneous, site-free, electroneutral macrocyclic ion

carriers--e.g., valinomycin, nonactin, monactin and

synthetic crown ethers.

6. Immobilized liquid membranes--e.g., liquid ion-exchangers

or neutral carriers immobilized in PVC (polyvinyl

chloride) matrices.

7. Homogeneous, semiconductor membranes--e.g., Ge, InSb,

Si, Pb02 and MnO2 membranes.

8. Heterogeneous, fixed-site, solid-state crystal

membranes--e.g., electroactive materials such as silver

halide crystals imbedded in supporting matrices

(silicone rubber or ceramics).








B. MULTIMEMBRANE ELECTRODES

1. Immobilized enzyme electrodes--e.g., urease enzyme

electrode (an immobilized enzyme matrix coated on an

ion-selective electrode).

2. Gas sensing electrodes--e.g., CO2 electrode and S02

electrode (a hydrophobic membrane such as Teflon

placed over an ion-selective electrode (usually a pH

electrode) with a solution between the membrane and pH

sensing glass).













CHAPTER 2
THE POTENTIAL RESPONSE OF ION-SELECTIVE ELECTRODES

The attractiveness of ion-selective electrodes lies in

their ability to produce a potential which is dependent on

the activity of a given ion in solution, and which is either

independent of or considerably less dependent on the acti-

vity of any other ions which may also be present. The

source of this potential has been the subject of a number of

theories.

The earliest theories, not surprisingly, were developed

for the glass electrodes (18-22). Of these theories the

ion-exchange theory developed by Eisenman (23), a refinement

of the theory introduced by Nicolsky, has gained general

acceptance.

In the Eisenman theory it is assumed that the principal

potential-determining reaction is the exchange of ions in

the glass with ions in the external solution:

I+ (glass) + J+(aqueous) J+(glass) + (1)

I+(aqueous); AGij

where I+ and J+ are ionic species and AGj is the standard

free energy change for the reaction. At equilibrium the

ionic electrochemical potentials, (5i), in the glass must be
equal to those (5i) in the solution, and can be expressed

in terms of the chemical potential pi and the electrostatic

potential V:








pi = Ui + ziFV (2)

where zi is the charge on ion I and F is Faraday's constant.

The chemical potential can be expressed in terms of the

standard chemical potential, ,j, and the activity, ai or aj,

of the ion:

Pi = Mi + RT ln(ai) (3)

where R is the Universal Gas Constant and T is the Kelvin

temperature. Adding the assumption that the activity of the

ion in the glass is proportional to the nth power of its

mole fraction, where n is a whole number, one obtains an

expression for the electrode potential, E:


E = E + RT n(al/n + Kl/nal/n)n (4)
F_ I n i
where Eo is the standard potential and Kn is a selectivity

parameter given by


Kn = a [(-Xi) /Xi n (5)


where Xi is the mole fraction of the ion in the glass.

The Eisenman theory developed for glass electrodes is

also applicable, with some modifications, to liquid-membrane

electrodes based on liquid ion-exchangers (24). In a

liquid-membrane electrode based on a liquid ion-exchanger, a

membrane containing the ion-exchanger separates two aqueous

solutions. One of the solutions is maintained at a constant

concentration and is considered to be the internal filling








solution. The other (external) solution is the test solu-

tion.

In the case of liquid ion-exchange membranes the

exchange sites are not fixed rigidly in place, as they are

in glass, but are charged species free to move throughout

the membrane. The membrane is assumed to be ideally perm-

selective, permitting only ions opposite in charge to the

exchanger to enter the membrane from the aqueous solutions.

The neutral species formed by the association of exchange

site and counter-ion is assumed to be in equilibrium with

the free sites and counter-ions throughout the membrane, and

the mobilities of all species within the membrane are

assumed to be constant.

Under these conditions it is possible to obtain an

expression for E, the electrode potential:


,, 7 Uis
Luikiai L --ci
RT i d i Ki
S Fzi n to In
Luikiai
i Luici
i i (6)
Lc (6)
usjs dx
RT
fo
( Uis i uis
us+LK-ci uici+uscs -Kci
i i 1


where the subscript "i" refers to the counter-ion, the

subscript "s" refers to the exchange site, and the subscript

"is" refers to the associated species. The symbols u, a, z

and c represent the mobility, activity, charge and








concentration of the species indicated by subscript. Ki is

the equilibrium constant for the dissociation of the complex,

Js is the total flux of all site species, d is the thickness

of the membrane, and the 'and" refer to the two solutions in

contact with the membrane. The symbols R, F and T have

their usual meanings. The parameter ki is essentially a

thermodynamic equilibrium constant for the distribution of

the ion between the solution and the membrane. The value of

ki is given by


ki = exp(hi0 io(m)) (7)
RT
0
where ui is the standard chemical potential of species i,

and m refers to the membrane.

The parameter t in Eqn. 6 is merely a collection of

mathematical terms inserted for convenience. It is equal

to


t = c (8)
( uscs + 1) Zuici+uscs
luiscis i


For the special case of a steady state (Js equal to

zero) in which two counter-ions are present and the asso-

ciation of counter-ions and sites is strong, it is possible

to solve Eqn. 6 explicitly:

2
L Cui+us)kiai L ikia
RT i=l i=lKi
E (1 T) In 2 + T In 2 (9)
7 (ui+us)kiai ikiai
i=l i=lKi







where T is given by

U2s Uls
us(K2 K1
(ul + U2s (u2 + Us) Uls (10)
K2 K1
When the internal filling solution (kept at constant con-

centration) is the one designated with the ', Eqn. 9 can be

written as



E = RT/Fzi[C + (I T) in (1 + ul + Us kl lIX ) (ll)
u2 + Us k2

+ T In ( 1 + [uls K2 k1 -lX
u2s K1 k2

Where X1 is the mole fraction of species i in the solution

on the side of the membrane designated (the external

solution).

Buck and others have treated the response of an ion-

exchange membrane electrode using the Teorell-Meyer-Sievers

model (25-26). In this approach the electrode potential is

taken to be the sum of three potentials: a Donnan potential

established at the interface between the test solution and

the membrane, a potential resulting from diffusion and

migration within the membrane, and a second Donnan potential

established at the interface between the membrane and the

internal solution.

The diffusion-migration potential (pII VI) for a

negatively charged mobile site membrane is given by

pII PI = (URT/F)ln(m+I/m+II) (12)

where I and II refer to the boundaries of the membrane, m is







the molal concentration and U is dependent upon the ionic

mobilities:

U = (u+ u_)/(u+ + u_) (13)
The electrode potential E is then

II_ I II I I II
E = RT r+ Y+ Y+ URT lr+ a+ Y+
i- n ( ) +-F-- In t ) (14)
I- II I II- II- I
r+ Y+ y+ r+ a+ y+
where y is the single ion activity coefficient in the

membrane, y is the single ion-activity coefficient in the

solution, r+ is the ratio of the molal concentration of the

cation in the membrane to that in the solution, and

a+ is the mean molal ion activity in the solution.

This model predicts that as the activity in the exter-

nal test solution is increased, keeping the activity in the

internal solution constant, a region will be reached in

which Donnan Exclusion fails and co-ions enter the membrane.

The magnitude and sign of the slope of the response are then

dependent on the value of U, and are equal to 2U/(1 + U).

At very high activities, for membranes with large negative

values of U this model predicts a third linear region, with

a slope equal to URT/F. Using the liquid ion-exchanger

Aliquat 336S, Buck and co-workers were able to demonstrate

experimentally the validity of this approach (27-32).

For liquid-membrane electrodes containing a neutral

ligand (carrier) rather than a charged exchanger, Morf has

proposed a model similar to the Eisenman model (33). For







the case in which two cations of equal charge are present,

the membrane potential is given by


Luis,nKi,nai + L ujs,nKj,naj
RT n n
Em = -- in { } (15)

ZUis,nKi,nai + ujs,nKj,naj
n n

where n is the number of neutral ligands (s) present in the

metal-ligand complex, i and j are the two cations, the' and

"denote the two membrane surfaces, and K is the distribu-

tion parameter, given by

ams,n(x)
Km,n = km am(x) = 8ms,n kmas (16)


where m refers to the cation, km is the distribution coef-

ficient for the cation distributing between the membrane

phase and the external solution, ams,n (x) is the activity
z+
of the complex MSn in the membrane, am(x) is the activity of
the cation in the membrane, 6ms,n is the stability constant

for the complex in the membrane, and as is the activity of

the ligand S in the membrane phase.

Regardless of whether the electrode membrane is treated

as a solid ion-exchanger, a liquid ion-exchanger or a semi-

permeable membrane at which Donnan equilibrium is

established, the electrode potential is found to be depen-

dent on ion activity in a logarithmic fashion. It has been






14


generally assumed in practice that the behavior of any ion-

selective electrode can be described by the Nernst

equation (34):

RT
E = EO + nT in aA (17)
nF













CHAPTER 3
THE SELECTIVITY OF ION-SELECTIVE ELECTRODES


The oldest, and still the most widely used, parameter

for the quantitative description of the selectivity of an
pot
ion-selective electrode is the Nicolsky parameter, kA,B, as

it appears in the well-known Nicolsky equation (35):



E = constant + 2.303RT log (aA + k A/B (18)
ZAF lgaA+aB

where A and B are species to which the electrode responds, z

represents the charge on the species and a is the activity.

Based upon this equation a number of methods for the

experimental determination of kot have been developed

(36). These can be grouped into two main categories, the

separate solution and the mixed solution methods. Separate

solution methods use pure solutions of the ion to which the

electrode gives the maximum response (the primary ion A) and

of another ion (the secondary or interfering ion B) to which

the electrode also responds. Mixed solution methods use

solutions containing both the primary and the interfering

ions.

When separate solutions are used, two approaches may be

taken. The potential of the electrode may be measured in

pure solutions containing identical activities, usually





16

0.1 M, of the primary or interfering ion; in this case k ,B

is given by
(1-zA/ZB)
log ot EB-EA
log kO = 2.303RT/F + log aA (19)

On the other hand, the activities of the ions may be

adjusted so that the two potentials, EA and Eg are equal.

In this case

pt aA
kAB = (ZA/ZB) (20)
aB
A number of approaches are possible also when using

mixed solution data. Light and Swartz (37) have used a com-

parison of the potential measured in a solution of pure pri-

mary ion (EA) and that measured in a solution containing the

same concentration of the primary ion in addition to some

amount of the interfering ion (EAB). The selectivity coef-

ficient is then given by


pot EA-EAB)A aA (21)
log kA, RT/F
A,B dBg

A graphical approach has also been used with mixed

solution data, requiring potential measurements in a number

of mixed solutions of varying concentrations (36,38). A

series of solutions are prepared, all containing one of the

ions at a fixed concentration and the other ion at varied

concentrations. The potentials measured in these solutions

are then plotted as a function of the concentration of the

ion which is varied. If one is careful to use ions for








which the selectivity coefficient is roughly 0.01 to 1, a

curve similar to that shown in Figure 2 is obtained. At the

low concentration end the electrode is assumed to be

responding only to the ion whose concentration is fixed, and

the potential does not change. At the high concentration

end the electrode is presumed to be responding only to the

ion whose concentration is being varied. Thus two linear

equations can be written:


E = Eo RT In(a) (22)
=A ZAF

o RT o RT n pot ZA/ZB
E B ZgF lnCag) = EA ZA n (kA,8 aB (23)

The activity at which the two linear portions intersect can
pot
then be used to calculate kA,B:


kOB = aAZ/) (24)
aB
Computer curvefitting has also been used with the mixed

solution method (39). Potentials are measured in a number

of solutions containing various concentrations of both of

the ions. The data are then fitted to the Nicolsky equation
pot
by varying the parameters kA,B RT/zF and the constant (Eo)

to achieve the minimum difference between the measured

potentials and those calculated from the Nicolsky equation.

In addition to the methods based on the Nicolsky

equation, several other methods have been suggested for the

measurement of the selectivity coefficient. Buck (40) has

suggested that in fact two types of selectivity behavior may






18





























P*
*e







0
T
E
N
T
I .
A
L /
/

/




Log Activity




FIGURE 2. The Graphical Cross-point Mixed Solution
Method for Measurement of kpo,
A,B'






19
be exhibited by an electrode, in view of the Teorell-Meyer-

Sievers model. If the interfacial processes are rapid and

reversible and the integrals in the diffusion potential

equation can be exactly solved, then the behavior is in

accord with the Nicolsky equation. If the interfacial pro-

cesses are not at equilibrium, however, or the diffusion

potential depends on the path of integration (as would be

the case if co-ions are present or if other complexes or ion

pairs can form), the apparent selectivity coefficient, k

(app), depends not only on the activities of the two ions

but also on their relative activities:
pot aB
In kA,B (app) = In {exp(EAB EA)/S-l} In(--) (25)
aA
where S is the calibration slope for the primary ion A, EA

is the potential measured in a pure solution of A and EAB is

that measured in mixed solution. Buck advocates using three

or four different concentrations of pure primary ion in

addition to about fifteen mixtures of primary and inter-
pot
fearing ions. The selectivity coefficient kA,B (app) is then

calculated according to Eqn. 25, and its logarithm plotted

as function of the logarithm of aB/aA. If a horizontal line
pot pot
results, then kA,B (app) is equal to kA,B, the Nicolsky

selectivity coefficient.

Mohan and Rechnitz (41) and Hakoila and co-workers (42)

have presented an empirical equation for the calculation of

the selectivity coefficient, KS, for electrodes which do not

exhibit Nernstian slopes:

EB-EA (SB/SA-1)
KS E-A log a (26)
SA






20
where SB and SA are the measured calibration slopes for the

two ions, and EB and EA are the measured potentials when the

ions are present in pure solution at an activity equal to a.

The values of KS calculated in this manner are far less

dependent on activity than those calculated using the

Nicolsky equation.

Liteanu and co-workers (43) have applied statistical

analysis, taking into account fluctuations in the signal, to

the measurement of selectivity. They obtain an expression

for a selectivity coefficient'6:


S(CA ) (27)
P1O,PII
where cA and cB are the concentrations of the interfering

and primary ion respectively for which there is a probabi-

lity of Pll that the interfering ion affects the primary

ion signal and a probability of P10 that it does not. On

the basis of statistical calculations of 8 for both separate

solutions and mixed solutions, they have concluded that the

values of B obtained from separate solution data will be

different from those obtained from mixed solution data, and

that only mixed solution data should be used.

In addition to devising these various methods for the

measurement of selectivity, a considerable amount of work,

both theoretical and experimental, has been done to identify

the parameters (such as ionic mobilities, partition coef-

ficients and equilibrium constants) which contribute to the





21

value of the selectivity coefficient. Bagg and co-workers

(44,45) have used the Eisenman model to calculate an

expression for the response of a liquid membrane electrode,

based on the calcium salt of dodecylphosphoric acid (ddp),

to a monovalent cation M+. The final expression is of the

same form as the Nicolsky equation, with a selectivity para-

meter Km equal to

2
K12s(K2s) YCa 1/2
Km = {(Kls)4/3 (2)1/3y 2 2

where y refers to a single ion activity coefficient in the

membrane, E is the concentration of the Ca(ddp)2 salt in the

membrane, and KlS, K2S and K12S are the equilibrium

constants for the following reactions:

Ca(ddp)2 + Ca2+ + 2 ddp -; Kls (29)

M(ddp) $ M+ + ddp-; K2s (30)

Ca(ddp)2 + 2 M+ 2 M(ddp) + Ca2+; Kl2s (31)

Danesi and co-workers (46) have shown that the selec-

tivity of an organic cationic exchanger for one anion over

another is given by

pot
kA,B = KAuA/KBUB (32)

where K is the distribution constant and u is mobility.

They point out that both the ratio uA/uB and the values of

KA and KB may be dependent upon the concentration of the

exchanger, as a result of its effect on the dielectric

constant.

Fujinaga, Okazaki and Hara (47, 48) have shown that






22
the selectivity of a liquid ion-exchanger electrode based on

an organic sulfonate or benzoate can be improved drastically

by the addition of an alkylphenol to the membrane. They

assume a case of strong association, using the Eisenman

model, so that the selectivity coefficient is given by

pot
A,B = SBKSBkB/USAKSAkA (33)
where uSB and uSA are mobilities of the exchanger-ion pairs

in the membrane, KSA and KSB are the ion pair dissociation

constants, and kB and kA are the single ion partition coef-

ficients. The single ion partition coefficients can be

correlated with the free energy of transfer of the ion from

water to the membrane, which is dependent upon the energy of

hydration of the ion in water and its energy of solvation in

the membrane. The presence of the alkylphenol apparently

increases the solvation energy as a result of hydrogen

bonding between the alkylphenol and the ion; the size of the

increase depends upon the strength of the conjugate acid of

the ion.

Back and Sandblom (49) and James, Carmack and Freiser

(50) have examined the effect of solvent extraction parame-

ters on the selectivity of ion-exchange type electrodes.

Using the Eisenman model, Back and Sandblom obtained an

expression for the selectivity coefficient in terms of the

extraction constants, EQXA and EQXB, for the two ions A and

B:
POt 1/2
AB = (EQXA/EQXB)1 (343






23

The extraction constants are equal to the concentration of

the ion pair QX in the organic phase (the membrane) divided

by the concentration of the extractant Q and ion X in the

aqueous phase. James et al. (50) have shown that the

extraction constants do indeed correlate with measured

selectivity constants.

Eyal and Rechnitz (51,52) have studied the selectivity

of valinomycin-based and cyclic polyether-based neutral

carrier electrodes. They measured the formation constants

for several valinomycin/monovalent cation complexes in

water/methanol mixtures, and compared the ratio of the for-

mation constants for the cation complexes to the measured

selectivity coefficient, finding reasonably good agreement.

They concluded that the selectivity of the valinomycin-based

electrode depended only on the formation constants in the

aqueous phase and not on any membrane phase characteristics.

They repeated these experiments using cyclic polyethers, in

a 50% tetrahydrofuran/50% water mixture, and again found

good agreement between the formation constants and the

selectivity coefficients.

Yasaka and co-workers (53) have also studied the cyclic

polyethers, in particular those which are chiral and show

enantiomer selectivity, and have concluded that the selec-

tivity depends primarily on the selectivity of the complex

formation, which in turn appears to be dependent on the pre-

sence of bulky chiral side chains on the cyclic polyether.








The Morf model for neutral carriers predicts that

selectivity is dependent on the partition coefficient for

the complex. The partition coefficient is in turn a func-

tion of the charge on the ion and of the dielectric constant
pot
of the membrane. The selectivity coefficient kA,B is then

given by

pot 2a 1
log kA,B = constant + 2r -C) (35)

where 2r is the overall diameter of the complex, a is a

constant for a given complex and e is the dielectric

constant. Fiedler (54) has studied the effect of the

dielectric constant on the selectivity of neutral carrier-

type electrodes selective for sodium and calcium. The

dielectric constant was varied by varying the relative

amounts of two solvents used as the plasticizer in a PVC

membrane containing the neutral carrier. The selectivity

coefficients were found to vary in the manner predicted by

theory, with selectivity for monovalent cations over diva-

lent cations, and for large cations over smaller ones of the

same charge, being favored by decreasing dielectric

constants.

Morf and co-workers (55) have tabulated the theoretical

expressions for the selectivity factor. In general the

selectivity of a liquid membrane electrode is predicted from

theory to depend upon the mobilities of the ions in the

membrane and the partition coefficient of the ions between

the external solution and the membrane. For liquid ion-






25


exchangers where there is a high degree of association, and

for neutral carriers where there is in addition a dependence

on the equilibrium constant for the displacement of the pri-

mary ion by the interfering ion in a complex, any factor,

such as dielectric constant or solvation energy, which can

alter the mobility, partition coefficient or equilibrium

constant, can also be expected to affect selectivity.













CHAPTER 4
OBJECTIVES AND OVERVIEW OF THE WORK

It has been noted by several researchers (40-42, 56,

57) that the values of the selectivity coefficient deter-

mined using the Nicolsky equation may vary considerably as

the activity of the test solutions is varied. It was

decided to explore this activity dependence in more depth in

this present work with the goal of characterizing the pat-

tern of the activity dependence, attempting to identify the

cause, and determining which of the various measurement

methods produces the least activity dependence.

For this work a neutral carrier-type electrode based on

the ligand Anal-05, whose structure is shown in Figure 3,

was chosen. This ligand had previously been used by

Pungor's group in Budapest, and was known to be responsive

to calcium in preference to the other alkaline earth or

alkali metals, but also to give activity-dependent selec-

tivity coefficients by both the separate solution and mixed

solution methods. It was also known from Fiedler's work

(54) that the selectivity of electrodes of this type could

be varied by changing the composition of the plasticizer.

This is important since it is necessary that the selectivity

coefficient be in the range of 0.01 to 1, so that two good





27


N v*
0






N o


FIGURE 3. Structure of the Ligand Anal-05.






28
linear portions can be obtained in the graphical mixed solu-

tion method. A placticizer composition of 0.8 mole fraction

dibutyl sebacate and 0.2 mole fraction o-nitrophenyl-n-octyl

ether was chosen, which gave an acceptable selectivity for

calcium over barium.
pot
The selectivity coefficient, kCa,Ba, was then measured

by both the separate solution and mixed solution methods,

over a wide range of activities. It became apparent early

on that the response of the electrode was not Nernstian, in

that the slope of the response to either calcium or barium

was lower than the Nernstian value of 29.5 mV per decade

activity change, and in addition the response of the

electrode to barium deviated somewhat from linearity. The

linearity problem was handled by simply using only those

data points which approximated linearity, as judged both

visually and by the value of the correlation coefficient

obtained from linear regression analysis. An attempt was

made to correct, or modify, the Nicolsky equation to include

the measured slopes; this yielded an equation similar to

that previously reported by Mohan and Rechnitz (41) and

Hakoila and co-workers (42). The derivation of this

equation is as follows:

1. The two ions, A and B with charges zA and zB

respectively, exhibit linear calibration curves with slopes
o o
of SA and SB and intercepts of EA and EB. The following







two equations are then valid.
0
EA = EA + SA log aA (36)
0
EB = EB + SB log aB (37)

2. The response to ion B may be expressed in terms of

the slope and intercept for ion A, using a selectivity para-
R
meter kA,B which is defined as follows:

R o o
log KA,B = (EB EA)/SA (38)

Eqn. 37 then becomes

o R (SB/SA)
EB = EA + SA log (kA,B aB ) (39)

3. In the separate solution method using approximately

equal activities it is the two potentials, EA and EB, that

are compared. Subtracting Eqn. 36 from Eqn. 39 one

obtains
R (SB/SA)
EB EA = SA log (kA,BaB /aA) (40)

4. The corresponding Nicolsky equation for the

situation in which the experimental slope is used for ion A

but it is assumed that the ratio of slopes is equal to the

ratio of the charges on the ions is as follows:

pot (ZA/ZB)
EB EA = SA log (kA,B aB /aA) (41)

Comparing this to Eqn. 40 it can be shown that the
R
selectivity coefficient kA,B calculated using experimental
pot
slopes bears the following relationship to kA,B:

R pot
log kA,B = log kA,B + (ZA/ZB SB/SA) log aB (42)

5. In the mixed solution graphical cross-point method

it is the potentials which are equal, at the cross-point.







Thus:

o o XPR (SB/SA)
EA + SA log aA = EA + SA log (kA,B aB (43)
XPR (S/SA)
kAPB = aA/aSB/SA) (44)

The corresponding form of the Nicolsky equation is

o o XP (ZA/ZB)
EA + SA log aA = EA + SA log (kA,B aB ) (45)

By comparison of Eqns. 43 and 45 it can be shown that

Eqn. 42 holds in this case also.
R
Values of kA,B were computed for the Anal-05

electrode, and were found to be virtually independent of

activity in the region of linear response.

Having shown that, through use of measured slopes

rather than Nernstian slopes, a selectivity parameter could

be obtained which was independent of activity, attention was

turned to determining which of the methods--separate or

mixed solution, Nernstian or real slope--gave the most

accurate description of the electrode response. For this

part of the study two additional electrodes were selected.

In view of Morf's contention (55) that the response of an

electrode to a mixture of monovalent and divalent cations

does not obey the simple Nicolsky equation, it was decided

to examine an electrode based on a ligand responsive to both

a monovalent and a divalent cation. An electrode based on

the ligand AC-14/81, whose structure is shown in Figure 4,

was chosen. This ligand responds primarily to sodium ion,

but also responds to calcium ion. In addition, in view of




31


0


FIGURE 4. Structure of the Ligand AC-14/81.


G






32
Buck's suggestion that non-Nernstian behavior is a result of

Donnan Exclusion failure (26-32), it was decided to examine

an electrode based on a charged liquid ion-exchanger, rather

than a neutral carrier, since in this type of electrode the

presence of a charged ion-exchanger in the membrane would be

expected to affect the ability of co-ions to penetrate the

membrane. A commercially available electrode, the Corning

calcium-selective electrode, was chosen. Selectivity coef-

ficients were measured by both the separate and the mixed

solution methods, using both measured and Nernstian slopes.

These selectivity coefficients were then used to predict the

potentials that would be exhibited by the electrode in

various mixed solutions, and these were compared to the

actual measured potentials. The results of these experi-

ments are given in the next chapters.













CHAPTER 5
SEPARATE SOLUTION MEASUREMENTS

Neutral Carrier Electrode Based on Anal-05

Experimental System

As mentioned earlier, the first set of experiments

involved a neutral carrier electrode based on the ligand

Anal-05, or N,N' di [(ll-ethoxycarbonyl) undecyl]-N,N', 4,5-

tetramethyl-3,6-dioxaoctane amide. The Anal-05 was incor-

porated in a membrane prepared by dissolving approximately 5

mg of Anal-05, 45 mg of polyvinyl chloride (PVC) powder and

about 100 mg of plasticizer (a mixture of dibutyl sebacate

and o-nitrophenyl-n-octyl ether, with a mole fraction of

dibutyl sebacate of 0.8) in two to three ml of tetrahydro-

furan. This solution was poured into a 28-mm diameter glass

ring and allowed to evaporate at room temperature to produce

a membrane of about 0.5 mm thickness, which was then cut

into 7-mm diameter circles using a cork borer. Two of these

7-mm diameter circles were incorporated into NV Philips ion-

selective electrode bodies, using a 0.01 M CaCl2 internal

filling solution, to produce two electrodes given the code

names G1 and G2. These electrodes were soaked in 0.001 M

CaCl2 for several days before use.

The potentials of these electrodes in test solutions

containing CaC12 and/or BaC12 were measured relative to a








Radelkis OP-0820P Ag/AgCl electrode with a 1 M KC1 filling

solution; the cell short-hand notation is given below.

Ag/AgC1, 1M KCl//test solution/PVC membrane/0.01 M

CaCl2/internal metal contact

All potential measurements were made using a Radiometer

PHM 64 Research pH Meter. The electrodes and test solution

were placed in a water-jacketed cell, and the temperature

was kept at 25.0+0.10C using a circulating constant-

temperature bath. During measurements the test solution was

stirred using a magnetic stirrer. A diagram of the appara-

tus is shown in Figure 5.

In this portion of the work ten different con-

centrations of pure solutions of CaCl2 and of BaCl2 were

used; these are given in Table 2. The solutions were pre-

pared by consecutively adding small amounts of 0.1 M and 1 M

solutions of either BaCl2 or CaCl2 to a known volume of an

initially 10-5 M solution of the same salt. The volumes

added were measured using either a Radelkis OP-930 Automatic

Burette or a Dispensette bottle buret, both of which had

been previously calibrated. In this way a large number of

concentrations could be prepared in a single container and

the electrode potentials measured in them, in a relatively

short period of time. The entire set of measurements was

repeated on six successive days.



















fl


Electrode
G1


Reference
Electrode


Magnetic
Stirring
Bar


Electrode G2






-" Water Inlet


FIGURE 5. Apparatus for Potential Measurements Using
Electrodes Gl and G2.
















TABLE 2
CONCENTRATIONS OF CaC12 AND BaCl2 PURE SOLUTIONS

1.000 x 10-5 M

1.083 x 10-4 M

2.896 x 10-4 M

4.702 x 10-4 M

8.294 x 10-4 M

1.891 x 10-3 M

3.613 x 10-3 M

6.878 x 10-3 M

2.493 x 10-2 M

4.234 x 10-2 M








Data Treatment

For each of the solutions used, mean activity coef-

ficients were calculated for the calcium or barium salt, as

appropriate, using a two parameter Debye-Huckel equation

(58):

-0.509 I Z+ZlIvI
log y+ = -0509 Z+ cI (46)
1 + 0.328A -I

where z+ is the charge on the cation, z_ is the charge on

the anion, I is the ionic strength, and A and c are parame-

ters which are experimentally determined to give the closest

fit to measured mean activity coefficients. Individual ion

activity coefficients for Ca2+ and Ba2+ were calculated

using the convention (59)


log y+ = Iz+ I log y, (47)
-

The concentrations of the salt solutions were then converted

to activities of calcium or barium ion using these single-

ion activity coefficients.

The measured potentials include a contribution due to

the liquid-junction potential at the reference electrode (1M

KC1)/test solution interface. This liquid-junction, or dif-

fusion potential, Ed, was calculated using a form of the

Henderson equation, given below, and subtracted from each

measured potential to obtain the corrected potential needed

for the calculation of the selectivity coefficient.









L ZnUn(cn-cn) / Znuncn (48)
n RT n
E j = 2-- ,--- ,,-- -F"- ln --- 5 ----
dE 2 n F 2 in
znun(cn-cn) L znuncn
n n

Here n refers to any ion, positive or negative, present in

the solution; z, u and c refer to the charge, mobility and

concentration of the ion, and the 'and" refer to the

reference electrode and test solution respectively. The

activities and corrected potentials for electrodes G1 and G2

are given in Table 3 for the six days on which measurements

were made.

Calibration plots were prepared using these data; a

typical plot is shown in Figure 6. As can be seen, the data

at the low and high concentration ends vary somewhat from

linearity; these points were omitted from all further calcu-

lations. Using the data in the linear region, response

slopes and y-intercepts were calculated using the linear

regression program "CURVE" supplied with the Hewlett-Packard

HP-85 Computer.

The slope and intercept calculated for calcium on each

day were used in the calculation of the Nicolsky selectivity
pot
coefficient, kCa,Ba, using Eqn. 41. The results are given

in Table 4, along with the standard deviation over both the

time and the activity ranges involved. These values of
pot R
kCa,Ba were then converted to values of kCa,Ba using Eqn.

42. The results are given in Table 5.








TABLE 3
ACTIVITIES AND CORRECTED POTENTIALS FOR ELECTRODES G1 AND G2
IN CaC12 AND BaC12 SOLUTIONS

Electrode GI

Activity EMF-1 EMF-2 EMF-3 EMF-4

9.75 x 10-6 M CaC12 23.6mV 35.3mV 31.9mV 37.2mV

1.00 x 10-4 45.4 53.1 51.0 55.6

2.54 x 10-4 57.2 62.8 60.9 65.6

3.99 x 10-4 63.9 67.4 66.0 70.2

6.70 x 10-4 71.1 73.5 72.1 75.8

1.38 x 10-3 80.5 82.4 80.7 84.1

2.39 x 10-3 89.5 89.5 87.4 90.5

4.02 x 10-3 96.7 96.1 94.0 96.6

1.05 x 10-2 110.1 108.2 106.5 108.2

1.51 x 10-2 115.4 116.7 111.6 113.0


9.75 x 10-6 M BaC12 30.6mV 36.2mV 35.1mV 23.1mV

9.96 x 10-5 36.8 42.3 41.7 31.2

2.54 x 10-4 43.4 48.6 47.5 38.1

3.98 x 10-4 46.1 51.6 50.3 41.9

6.67 x 10-4 50.9 55.8 54.6 46.5

1.38 x 10-3 58.2 62.4 60.6 53.6

2.36 x 10-3 63.9 67.7 65.5 59.0

3.98 x 10-3 70.1 73.0 70.5 64.5

1.00 x 10-2 81.1 82.6 79.5 75.7

1.44 x 10-2 85.9 87.1 83.7 80.8












Electrode G2


EMF-5 EMF-6 EMF-1


32.9mV

52.9

62.5

67.2

72.9

80.9

87.2

93.2

104.5

109.2


22.0mV

30.1

37.1

40.5

45.3

51.7

57.2

62.7

74.4

79.6


34.2mV

49.4

59.0

63.3

69.2

77.3

83.9

89.8

102.0

107.0


26.2mV

31.4

37.1

39.7

44.2

50.4

55.9

61.3

73.4

78.4


19.5mV

40.6

51.9

57.9

64.7

73.7

81.4

88.4

100.5

105.5


17.6

25.6

32.4

36.3

41.5

49.4

55.7

61.9

74.1

79.3


EMF-2 EMF-3 EMF-4

27.5mV 26.7mV 25.5mV

46.0 45.7 45.0

55.8 55.5 55.3

60.6 60.4 60.3

66.5 66.0 66.0

75.4 74.5 74.2

82.2 81.0 80.6

88.7 87.5 86.9

106.5 99.0 98.4

112.6 103.9 103.5


22.7

30.4

36.9

40.5

45.4

52.6

58.3

64.1

75.4

80.5


22.0

30.6

36.6

40.2

44.7

51.8

57.3

63.0

73.8

78.9


19.2

27.8

34.9

38.7

43.4

50.7

56.4

62.1

73.3

78.4


EMF-5

23.9mV

45.7

55.9

60.8

66.7

75.0

81.2

87.5

98.9

103.9


18.7

27.9

34.7

38.4

43.1

50.3

55.9

61.7

73.5

78.7


EMF-6

27.6mV

44.2

54.0

58.7

64.6

72.7

79.1

85.5

97.5

102.4


21.7

27.3

32.6

36.0

40.5

47.4

53.0

58.7

70.4

75.6





























80 '4
P 80
0
T 60 /
E
N
40 *
I
A
L 20 --
L
(mV) 20

-5.0 -4.0 -3.0 -2.0

Log activity barium


FIGURE 6. Calibration Plot for Electrode G2.








TABLE 4 pot
pot
SEPARATE SOLUTION SELECTIVITY COEFFICIENT kCa,Ba
FOR ELECTRODES GI AND G2


Concentration


Electrode Gl


4.702 x 10-4

8.294 x 10-4

1.891 x 10-3

3.613 x 10-3

6.878 x 10-3


Standardb
Deviation


Electrode G2


4.702 x 10-4

8.294 x 10-4

1.891 x 10-3

3.613 x 10-3

6.878 x 10-3


Standard
Deviation


DAY1 DAY2 DAY3 DAY4

M .284 .269 .277 .0887

.240 .229 .239 .0815

.206 .188 .192 .0731

.163 .162 .166 .0673

.153 .147 .146 .0643



.054 .050 .054 .010


M .194 .189 .184 .153

.172 .174 .167 .141

.157 .150 .148 .129

.142 .137 .136 .122

.134 .130 .128 .117



.024 .025 .022 .014


pot
a Standard deviation of kCaBa (measured at the indicated
concentration) over the six days.
Spot
b Standard deviation of kCa,Ba on the day indicated over the
concentration range.


DAY6

.136

.121

.102

.0933

.0899


S.D.a

.094

.077

.062

.048

.041


DAY5

.0975

.0902

.0779

.0729

.0701



.012


.020


.149

.135

.122

.116

.112



.015


.149

.132

.119

.111

.106


.022

.020

.016

.013

.011


.017








TABLE 5
SEPARATE SOLUTION SELECTIVITY COEFFICIENT kCa,Ba FOR
ELECTRODES G1 AND G2

Concentration

Electrode GI


4.702 x 10-4 M

8.294 x 10-4

1.891 x 10-3

3.613 x 10-3

6.878 x 10-3

Standardb
Deviation


DAY1

.0432

.0413

.0422

.0380

.0404


DAY2

.0581

.0547

.0514

.0496

.0498


DAY3 DAY4

.0366 .0415

.0359 .0401

.0349 .0386

.0347 .0374

.0349 .0376


DAY5 DAY6 S.D.a

.0506 .0511 .0078

.0489 .0485 .0070

.0449 .0448 .0057

.0440 .0438 .0055

.0442 .0450 .0054


.0020 .0036 .0095 .0017 .0030 .0029


Electrode G2

4.702 x 10-4

8.294 x 10-4

1.891 x 10-3

3.613 x 10-3

6.878 x 10-3

Standard
Deviation


.0826

.0776

.0766

.0734

.0734


.0879

.0851

.0788

.0758

.0757


.0038 .0056


.0736

.0710

.0685

.0670

.0671


.0952

.0905

.0866

.0845

.0837


.0028 .0048


.0429

.0423

.0428

.0443

.0465


.0316 .026

.0310 .026

.0322 .022

.0335 .020

.0355 .019


.0017 .0018


R
a Standard deviation of kCa Ba (measured at the indicated
concentration) over the six days.
R
bStandard deviation of kCa,Ba on the day indicated over the
concentration range.








Neutral Carrier Electrode Based on AC-14/81

Experimental System

In the second set of experiments a neutral carrier

electrode using the ligand AC-14/81, which is selective for

sodium but also responds to calcium, was used. The membrane

was prepared in the same manner as that using Anal-05; the

membrane composition was approximately 2 mg of AC-14/81, 48

mg of PVC powder and 100 mg of o-nitrophenyl-n-octyl ether.

Two electrodes, Ql qnd Q2, were prepared, with 0.01 M NaCl

as the internal filling solution. The electrodes were

soaked in 0.01 M NaC1 prior to use.

The reference electrode was again a Radelkis Ag/AgCl

electrode, but with a 0.1 M lithium acetate filling solu-

tion. The short-hand cell notation is

Ag/AgCl,O.1M LiC2H302//test solution/PVC membrane/

0.01 M NaCl/ internal contact

A Radiometer PHM 84 Research pH Meter was used for the

potential measurements. The electrodes and test solution

were placed in a measuring cell which consisted of a beaker

cut flat at the top and a plastic cap with holes drilled to

accommodate the electrodes and a paddle-type mechanical

stirrer. The entire cell was placed in a constant-

temperature bath, and the temperature was maintained at

25.00.10C. A diagram of the apparatus is shown in Figure 7.

Eight concentrations of sodium chloride and of calcium

chloride were used, ranging from 9 x 10-5 to 7 x 10-2 M.















Stirrer
J


Electrode Q1


''- ':':^-^ '~ Constant
............ ........... Temperature
Bath









Shelf


















FIGURE 7. Apparatus for Potential Measurements Using
Electrodes Q01 and Q2.








These solutions were prepared in the same manner as those

used in the first set of experiments. Measurements were

repeated on 12 days.

Single-ion activity coefficients were calculated for

sodium or calcium in each solution using Eqns. 46 and 47,

and diffusion potentials using Eqn. 48. Activities and

corrected potentials were then calculated; these are given

in Tables 6 and 7 for the twelve days on which measurements

were made.

Once again some non-linearity was observed, especially

for the interfering ion, calcium. As in the first set of

experiments points deviating from linearity were deleted

before calculation of the linear regression line. The
pot R
values of kNa,Ca and kNa,Ca were calculated from Eqns. 41

and 42; these are shown in Tables 8 and 9.

Ion-Exchange Electrode for Calcium Ion

Experimental System

In the third set of measurements a Corning ion-exchange

type electrode, selective for calcium but also responsive to

barium, was used. A Fisher Ag/AgCl Inverted Sleeve Junction

reference electrode was used, with 1 M KC1 as the filling

solution. The short-hand cell notation is

Ag/AgC1, 1 M KCl//test solution/Corning electrode

The calcium electrode was soaked in 0.01 M calcium chloride

before use.

The apparatus used was similar to that used in the














TABLE 6
ACTIVITIES AND CORRECTED POTENTIALS FOR
ELECTRODE QI IN NaC1 AND CaC12 SOLUTIONS


Activity EMF-1

2.771 x 10-4 M NaC1 -42.3mV

4.585 x 10-4 -32.7

8.157 x 10-4 -20.9

1.853 x 10-3 -3.0

3.630 x 10-3 10.8


2.296

3.691

6.299

1.319

2.366


10-4 M CaC12

10-4

10-4

10-3

10-3


-65.6

-61.9

-57.7

-50.5

-44.6


EMF-2

-42.7mV

-33.1

-22.6

-4.7

7.6


-66.4

-62.4

-58.0

-51.2

-46.0


EMF-3

-44.0mV

-33.8

-22.2

- 3.6

10.5


-60.8

-57.1

-53.3

-45.9

-40.1


EMF-4

-44.5mV

-34.4

-23.4

- 4.6

9.1


-61.8

-57.9

-54.7

-47.6

-41.7


EMF-5

-44.5mV

-34.7

-23.6

- 4.9

9.0


-64.5

-60.7

-57.2

-50.0

-44.3



















EMF-6

-43.8mV

-34.3

-23.0

-4.8

8.0


-64.6

-61.0

-57.4

-49.8

-44.0


EMF-7

-44.5mV

-35.7

-24.7

-7.2

5.7


-64.2

-60.6

-56.8

-49.4

-43.6


EMF-8

-47.4mV

-37.3

-25.7

-7.4

6.8


-67.8

-64.4

-60.2

-53.4

-47.7


EMF-9

-48.8mV

-38.8

-26.9

-8.6

5.4


-70.6

-67.0

-62.9

-55.7

-50.7


EMF-10

-47. mV

-37.3

-26.1

-7.8

6.3


-71.3

-68.4

-66.2

-59.2

-54.0


EMF-11

-48.8mV

-39.5

-29.0

-10.8

2.4


-73.2

-69.3

-65.8

-58.4

-52.5


EMF-12

-51.7mV

-41.7

-29.5

-11.1

3.4


-74.6

-72.9

-70.2

-63.6

-57.2















ACTIVITIES


TABLE 7
AND CORRECTED POTENTIALS FOR ELECTRODE Q2
IN NaC1 AND CaC12 SOLUTIONS


Activity

2.771 x

4.585 x

8.157 x

1.853 x

3.630 x


2.296

3.691

6.299

1.319

2.366


10-4 M

10-4

10-4

10-3

10-3


x 10-4 M

x 10-4

x 10-4

x 10-3

x 10-3


NaC1


EMF-1

-40.3mV

-30.8

-18.6

-1.2

13.2


CaC12 -59.5

-56.0

-51.2

-44.3

-37.3


EMF-2

-41.7mV

-32.4

-20.7

-3.5

10.7


-58.6

-54.7

-49.7

-43.4

-37.6


EMF-3

-33.3mV

-23.5

-11.8

5.9

19.8


-50.2

-47.4

-42.9

-36.1

-30.2


EMF-4

-34.5mV

-25.2

-14.7

2.8

16.2


-53.1

-49.8

-45.3

-39.4

-32.7


EMF-5

-38.8mV

-30.1

-18.2

-0.1

14.3


-54.4

-51.4

-46.4

-40.3

-33.5


















EMF-6

-39.0mV

-29.2

-17.1

0.9

14.3


-51.9

-49.2

-44.7

-38.1

-31.3


EMF-7

-39.0 mV

-30.5

-18.6

-1.3

12.9


-53.4

-50.6

-45.6

-38.7

-32.0


EMF-8

-39.3mV

-28.9

-16.7

1.8

16.4


-52.7

-49.9

-45.0

-38.4

-31.9


EMF-9

-40.4mV

-30.6

-18.0

0.2

15.1


-55.8

-52.4

-47.5

-40.4

-34.1


EMF-10

-39.6mV

-29.6

-17.4

0.7

15.1


-56.5

-55.4

-50.8

-44.7

-37.9


EMF-11

-47.8mV

-38.0

-26.4

-8.4

6.1


-60.1

-55.0

-50.9

-44.0

-37.7


1












TABLE 8
pot
SEPARATE SOLUTION SELECTIVITY COEFFICIENTS kNa,Ca
FOR ELECTRODES Q1 AND Q2


Concentration

Electrode Ql

2.825 x 10-4 M

4.700 x 10-4

8.428 x 10-4

1.945 x 10-3

3.882 x 10-3

Standard Deviation

Relative Std. Dev.


Electrode Q2

2.825 x 10-4 M

4.700 x 10-4

8.428 x 10-4

1.945 x 10-3

3.882 x 10-3

Standard Deviation

Relative Std. Dev.


DAY1 DAY2 DAY3 DAY4 DAY5


.00597

.00586

.00555

.00520

.00521

.00036

6.4%




.00731

.00716

.00686

.00651

.00669

.00033

4.8%


.00552

.00541

.00543

.00485

.00495

.00031

5.9%




.00801

.00802

.00788

.00726

.00704

.00046

6.0%


.00832

.00800

.00757

.00702

.00696

.00060

7.9%




.00811

.00754

.00728

.00675

.00671

.00058

8.0%


.00803

.00778

.00732

.00657

.00663

.00066

9.1%




.00717

.00691

.00696

.00609

.00635

.00045

6.8%


.00705

.00691

.00656

.00595

.00588

.00054

8.3%




.00867

.00860

.00844

.00745

.00757

.00059

7.2%


DAY6



.00659

.00643

.00768

.00560

.00581

.00082

12.7%




.00988

.00917

.00871

.00792

.00845

.00074

8.4%
















DAY7 DAY8 DAY9 DAY10 DAY11 DAY12



.00675 .00699 .00656 .00575 .00544 .00632

.00676 .00664 .00632 .00538 .00542 .00560

.00641 .00639 .00597 .00477 .00522 .00492

.00603 .00583 .00556 .00436 .00479 .00446

.00616 .00570 .00532 .00416 .00487 .00448

.00033 .00054 .00051 .00067 .00030 .00080

5.2% 8.6% 8.7% 13.8% 5.9% 15.5%




.00903 .00989 .00901 .00830 .0102

.00889 .00909 .00874 .00713 .0106

.00865 .00886 .00837 .00682 .0102

.00814 .00805 .00787 .00610 .00942

.00823 .00811 .00774 .00625 .00933

.00039 .00076 .00055 .00088 .00055

4.6% 8.6% 6.5% 12.7% 5.5%








TABLE 9 R
SEPARATE SOLUTION SELECTIVITY COEFFICIENTS kNa,Ca
FOR ELECTRODES QI AND Q2


Concentration DAY1 DAY2 DAY3 DAY4 DAY5 DAY6

2.825 x 10-4 M .00344 .00345 .00417 .00371 .00337 .000382

4.700 x 10-4 .00348 .00347 .00417 .00376 .00345 .000385

8.428 x 10-4 .00342 .00359 .00412 .00371 .00343 .000476

1.945 x 10-3 .00336 .00334 .00406 .00357 .00332 .000364

3.882 x 10-3 .00350 .00353 .00423 .00380 .00345 .000392

Standard Deviation .00005 .00009 .00006 .00009 .00006 .000038

Relative Std. Dev. 1.6% 2.7% 1.5% 2.3% 1.7% 11.0%


Electrode Q2

2.825 x 10-4 M .00490 .00482 .00409 .00417 .00475 .00519

4.700 x 10-4 .00491 .00497 .00396 .00415 .00488 .00500

8.428 x 10-4 .00483 .00504 .00399 .00432 .00497 .00495

1.945 x 10-3 .00474 .00486 .00393 .00397 .00463 .00476

3.882 x 10-3 .00501 .00488 .00410 .00430 .00491 .00531

Standard Deviation .00010 .00009 .00008 .00014 .00014 .00021

Relative Std. Dev. 2.1% 1.8% 1.7% 3.4% 2.8% 4.2%














DAY7

.00438

.00449

.00438

.00428

.00451

.00009

2.1%



.00615

.00619

.00617

.00601

.00624

.00009

1.4%


DAY8

.00323

.00320

.00324

.00316

.00326

.00004

1.2%



.00478

.00458

.00467

.00453

.00480

.00012

2.5%


DAY9

.00301

.00303

.00301

.00300

.00303

.00001

0.4%



.00510

.00511

.00507

.00501

.00513

.00005

0.9%


DAY10

.00171

.00172

.00164

.00167

.00174

.00004

2.4%



.00309

.00281

.00286

.00279

.00306

.00014

4.9%


DAY11

.00331

.00339

.00337

.00323

.00340

.00007

2.1%


DAY12

.00178

.00169

.00161

.00164

.00180

.00008

4.9%


.00645

.00688

.00682

.00656

.00671

.00018

2.7%








second set of experiments and consisted of a beaker with a

plastic cap designed to accommodate the electrodes and a

paddle-type stirrer. It was observed that the stirrer

caused noise in the potential response; as a result the

stirrer was turned off during measurements. The beaker was

placed in a constant-temperature bath maintained at

25.0+0.10C. A Corning Model 190 pH Meter was used for all

potential measurements, and a Sargent-Welch Model SRG

Recorder was used to record the response of the electrodes,

which was rather slow and often required ten minutes or

longer to reach a stable potential.

Seven concentrations of calcium chloride and of barium

chloride were used, ranging from 10-5 M to 0.01 M. These

were prepared in a manner analogous to that previously used.

The measurements were repeated on five days.

Data Treatment

Once again non-linearity was observed at the low and

high concentrations ends, and these data points were omitted

from the calculations. Activity coefficients and diffusion

potentials were again calculated using Eqns. 46-48; activi-

ties and corrected potentials are given in Table 10. Values
pot R
of kCa,Ba and kCa,Ba were calculated; these are given in

Table 11.













TABLE 10
ACTIVITIES AND CORRECTED POTENTIALS FOR THE CORNING
ELECTRODE IN CaC12 AND BaC12 SOLUTIONS


Activity EMF-1 EMF-2 EMF-3 EMF-4 EMF-5

9.96xlO-5M CaC12 56.7mV 57.1mV 56.2mV 55.6mV 55.2mV

4.95x10-4M 77.7 77.5 76.4 76.1 75.4

8.46x10-4 85.0 84.8 83.8 83.0 82.9

3.54x10-3 104.4 102.4 102.9 102.6 101.9


9.96x10-5M BaC12 27.3 23.4 24.0 23.2 27.4

4.94x10-4 34.2 30.4 30.7 29.3 31.9

8.43x10-4 34.1 31.9 31.3 29.8 34.0

3.50x10-3 41.5 38.3 39.8 35.6 40.2









TABLE 11
pot
SEPARATE SOLUTION SELECTIVITY COEFFICIENTS kCa,Ba
R
AND kCa,Ba FOR THE CORNING ELECTRODE


Concentration

1.08 x 10-4 M

5.95 x 10-4

1.08 x 10-3

5.90 x 10-3

Standard Deviation

Relative Std. Dev.





1.08 x 10-4 M

5.95 x 10-4

1.08 x 10-4

5.90 x 10-3

Standard Deviation

Relative Std. Dev.


Day 1

.110

.0384

.0220

.00904

.0451

100%





.000158

.000172

.000144

.000163

.000012

7.35%


Day 2

.0701

.0244

.0155

.00645

.0283

97.2%





.000144

.000147

.000134

.000145

.000006

4.07%


pot
kCa,Ba

Day 3

.0852

.0304

.0181

.00810

.0344

97.0%


R
kCa,Ba

.000181

.000188

.000160

.000186

.000013

7.18%


Day 4 Day 5

.0852 .119

.0286 .0360

.0176 .0238

.00622 .00902

.0351 .0493

102% 105%





.000094 .000150

.000103 .000145

.000094 .000141

.000095 .000150

.000004 .000004

4.52% 2.98%













CHAPTER 6
MIXED SOLUTION MEASUREMENTS


Neutral Carrier Electrode Based on Anal-05

Experimental System

The experimental apparatus has already been described.

The mixtures of calcium chloride and barium chloride were

prepared in a manner analogous to that used in the prepara-

tion of the pure solutions. Initially a solution was pre-

pared containing one salt at 10-5 M and the other salt at a

higher concentration. The concentration of the first salt

was then increased by adding small volumes of 0.1 M or 1 M

solutions of that salt. For example, a solution containing

10-5 M calcium chloride was prepared, 50 ml of this trans-

ferred into the cell by pipette, and the concentration of

barium chloride varied by adding 0.1 M or 1 M barium

chloride to the cell. On days 1-3 the concentration of

barium was varied, leaving the calcium concentration fixed

at one of seven levels, while on days 4-6 the calcium con-

centration was varied, with the barium concentration fixed

at one of the five levels. The concentrations used are

given in Table 12.







TABLE 12
CONCENTRATIONS USED IN CaC12/BaCl2 MIXTURES



Fixed-ion Concentrations Varied-ion concentrations

9.10 x 10-5 M CaC12 1.000 x 10-5 M

2.73 x 10-4 1.083 x 10-4

4.55 x 10-4 2.064 x 10-4

6.37 x 10-4 3.043 x 10-4

9.10 x 10-4 4.020 x 10-4

2.73 x 10-3 7.616 x 10-4

4.55 x 10-3 1.296 x 10-3

2.001 x 10-3

9.10 x 10-4 M BaC12 2.694 x 10-3

2.73 x 10-3 3.378 x 10-3

4.55 x 10-3 4.387 x 10-3

6.37 x 10-3 6.117 x 10-3

9.10 x 10-3 7.840 x 10-3

9.558 x 10-3

1.297 x 10-2

1.805 x 10-2

2.641 x 10-2

3.462 x 10-2

4.270 x 10-2

5.064 x 10-2








Data Treatment

Activity coefficients and diffusion potentials were

calculated as for the separate solution measurements; acti-

vities and corrected potentials are given in Table 13 and

Appendix A.

The data for the mixed solutions were plotted and the

activity of the ion whose concentration was varied was

determined at the cross-point, as shown in Figure 8. The

activity of the ion whose concentration was fixed was deter-

mined by interpolation, as shown in Figure 9. The values of
pot
the selectivity coefficient, kCa,Ba, were then calculated

using Eqn. 45; they are shown in Table 14 along with the
pot
standard deviations. The values of kCa,Ba were converted
R
to values of kCa,Ba using Eqn. 42; these are also given in

Table 14.

The mixed solution data were also treated using a

multi-parametric curve-fitting program, "SELECT", available

at the Technical University of Budapest. This program
pot
varies the values of S, K (kA,B) and the constant (Eo) in

the Nicolsky equation by user-specified increments, and

calculates the sum of the squares of the difference between

calculated and measured potentials. The results are shown

in Table 15.

As mentioned earlier, it is assumed in the graphical

cross-point method that the electrode is responding only to

one ion at the extreme ends of the concentration range.







61



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t
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aXP



Log activity varied-ion


FIGURE 8. Determination of the Varied-ion Concentration
at the Cross-point.






















Activity of I
fixed-ion :




\


aXP
Log activity varied-ion


FIGURE 9. Determination of the Fixed-ion Concentration
at the Cross-point.








TABLE 14
XP
MIXED SOLUTION CROSS-POINT SELECTIVITY COEFFICIENTS kCa,Ba
XPR
AND kCa,8a FOR ELECTRODES G1 AND G2


Electrode G1


Concentration

4.55 x 10-4 M CaC12

6.37 x 10-4

9.10 x 10-4

2.73 x 10-3

4.55 x 10-3

Standard Deviation

Relative Std. Dev.


2.73 x 10-3 M BaC12

4.55 x 10-3

6.37 x 10-3

Standard Deviation

Relative Std. Dev.


XP-1
kCa,Ba

.0890

.0629

.122

.163



.043

40%

XP-4
kCa,Ba

.190

.125



.046

29%


XP-2
kCa,Ba

.0798

.0760

.109

.150

.198

.052

42%

XP-5
kCa,Ba

.122

.131

.110

.015

8.7%


XP-3
kCa,Ba

.0708

.0851

.0952

.159

.228

.065

51%

XP-6
kCa,Ba

.187

.124


XPR-1
kCa ,Ba

.0220

.0176

.0322

.0496



.0142

47%

XPR-4
kCa,Ba

.103

.0796


.106

.043 0.023

31% 26%


XPR-2
kCa,Ba

.0260

.0262

.0375

.0576

.0796

.0231

51%

XPR-5
kCa,Ba

.0720

.0800

.0688

.0058

7.8%












Electrode G2
xP-3X-4 XP-5 XP-6
KCa,8a kCa,Ba kca,Ba kCa,3a kCa,8a kCa,3a kCa,Ba
.0165 .0887 .0736 .0905 .0471 .0423 .0458
.0165 .058 .0975 .0911 .0302 .0563 .0475
.02049 .136 .16 .116 .0737 .0679 .0611
.023945 .136 .193 .172 .105 .118 .0962
.0445 .181 .228 .266 .142 .0149
o228 .266
.0205 .056 .066 .074 .0327 .0427 .0436
.0205 .0566% 50% 51.1 50% 54.6%
60% 49% pR-5 XPR-6

XPR-6 P-5 XP-6 XPR-4 XPR-5 XpR-6
kCa,Ba kca,Ba kaB Caa kCa,Ba kCa,8a kCaBa
.0849 .181 .173 .182 0.123 .0635 .0522
.059 .18 .142 .167 .0966 .0557 .0519
.0594 .138 .101 .105 .0413 .0345
.i01 .105
.0525 -- 0 .0113 .0101
.0171 .030 .036 .041 0.019 11
.01726 19 26 27% 17% 21.1% 21.9%
26% 19% 26








TABLE 15
CURVE-FITTING SELECTIVITY COEFFICIENTS FOR ELECTRODES
GI AND G2

Electrode G1


Concentration
9.10xlO-5M Ca
EO
S
K
r


2.73x10-4M


4.55x10-4M


6.37x10-4M


9.10x10-4M





2.73xlO-3M


DAY 1

153.0
24.14
.0805
16.2


154.6
24.83
.0900
6.9


157.4
25.90
.137
4.2


156.3
24.98
.120
10.0


156.6
25.12
.120
5.6


156.9
24.60
.140
0.3


4.55xlO-3M


DAY 2

145.1
21.46
.111
10.1


147.9
22.27
.116
3.8


157.8
24.79
.0959
0.8


149.0
22.28
.120
1.1


148.9
22.32
.120
0.8


149.6
21.77
.120
0.9


150.1
21.49
.120
0.4


DAY 3 DAY 4 DAY 5
9.10xlO-4M Ba


140.8
20.89
.105
5.2


140.2
20.92
.120
5.0


146.5
22.52
.102
1.2


140.9
20.95
.100
1.4


140.7
21.10
.100
2.1


141.0
20.71
.120
1.7


146.1
20.73
.140
4.9


175.8
28.33
.200
3.1


167.0
27.06
.140
0.7


2.73x10-3M Ba
171.3 158.5
29.28 24.42
.180 .120
4.4 35.8

4.55x10-3M Ba
171.0 167.5
29.37 29.35
.160 .150
3.7 3.1


DAY 6

160.4
29.43
.180
7.1


162.0
30.98
.200
4.1


163.8
31.58
.160
5.7


6.37x10-3M Ba
166.8 163.5
29.22 31.78
.160 .160
15.9 4.1


9.10x10-3M Ba
177.7
29.50
0.130
9.9


168.0
32.09
0.142
2.0


a E0 is the standard potential for the electrode in mV, S is the
response slope in mV, K is the selectivity coefficient obtained
by curve fitting, and r is the correlation coefficient for the
curve-fitting.









TABLE 15 -


Electrode G2


Concentration
9.10xlO-5M Ca
EO
S
K
r

2.73x10-4M Ca
EO
S
K
r

4.55x10-4M Ca
EO
S
K
r

6.37x10-4M Ca
EO
S
K
r


9.10x10-4M Ca
EO
S
K
r

2.73xlO-3M Ca
EO


DAY 1

146.5
25.48
.126
11.8


152.7
27.08
.125
9.0


145.7
25.01
.160
14.5


148.3
25.68
.181
97.6


152.6
26.70
.140
23.4


153.7


S 27.02
K .180
r 0.9


4.55x10-3M Ca
EO
S
K


DAY 2

147.8
25.13
.133
18.7


148.3
25.40
.145
9.7


148.9
25.11
.130
12.1


149.8
25.50
.140
4.8


149.5
25.29
.140
5.6


149.1
25.21
.180
1.5


149.6
24.93
.140
5.9


DAY 3

155.1
26.93
.107
5.9


156.7
27.46
.108
5.0


147.7
24.74
.121
14.8


148.3
24.95
.141
3.9


147.1
24.56
.140
6.9


147.0
24.34
.180
1.7


152.1
25.65
.155
2.2


DAY 4 DAY 5
9.10x10-4M Ba
161.4 157.4
29.18 28.46
.230 .199
6.3 3.0

2.73xlO-3M Ba
160.2 157.4
28.85 28.20
.160 .160
1.8 4.4

4.55x10-3M Ba
160.1 156.8
29.01 27.97
.160 .140
2.6 4.5

6.37xlO-3M Ca
160.6
29.28
.139
1.0

9.10x10-3M Ca
161.4
29.58
.139
1.0


a EO is the standard potential for the electrode in mV, S is
the response slope in mV, K is the selectivity coefficient
obtained by curve fitting, and r is the correlation coefficient
for the curve-fitting.


DAY 6

152.8
27.90
.165
12.8


156.7
29.72
.180
5.7


159.8
30.66
.150
1.4


159.2
30.45
.159
6.1


157.0
28.21
.0901
8.3


Continued








This means that the potential of the electrode at the

lowest activity of the varied-ion should be the same as that

observed for the other (fixed activity) ion in pure solu-

tion, and that the potentials observed at the highest acti-

vities of the varied-ion should display the same slope as is

observed in pure solutions of that ion. The slopes of the

linear portion obtained at the high activity end for the

twelve fixed-ion concentrations have been calculated; they

are shown in Table 16 along with the separate solution

calibration slopes. The potentials at the lower varied-ion

concentrations were considered as a function of the fixed-

ion concentration, and a slope and y-intercept calculated.

These results are compared in Table 17 to the separate solu-

tion values.

The mixed solution measurements were also used as a

check on the ability of the selectivity coefficients

measured in separate solution to describe the response of

the electrode in mixed solutions. For this purpose a selec-

tivity coefficient was calculated from Eqn. 38 using the

slopes and y-intercepts calculated from separate solution

measurements. This selectivity coefficient was then used to

calculate the potential according to the modified Nicolsky

equation:

o R SB/SA
E = EA + SA log (aA + kA,B aB (49)

A representative sample of these results is given in Table

18.














r r' oo o%



_- --4



xO CO 0 CM
N4 N N N



n N N N








- .
0 \0 \0 \0


N N- N ^




-4 -4 -4
NO Pl rn
* "0
-4 -4 -
- r \N
N N- N
V) Ch CM
* *-
oo oo r^

CM JCMCM


Z
0
C2
I-1

-J




0

C)

C-Z
Q




IO


)O-
CL



c- CD
ZLJ
M 0
-y






-i4

I- C 0





.J
r) 0





:wz
I CI
no






Z

o
1-
I




0
o


0
>.


























CD

>-














CD




O
>..




























0 c



C
0 0
o C
u 9c
-4 0



ul C
ot> (
U 0


0o -n

cO04
CM


-4 0

N 0


\V -;* (~- 0 0M

14 CN io L 0%
CN N -





-4 04 -4 -4



N 0 -4 -4


1 4 4 N N


n n N 4 0

-f C "0 0
N N N N -4





C4 -14 -4 -4


0 '-4 N M










o N Uo m c
-C\ 0 n \



















n PC) r-4 r- 4 n
~ CI I I
o CCD CD CD C

-4 4 4 -
)( x )(
It' N ~CD r I t
u- r" N I
'O "0 % N -


CO (0 (0 (.



rC n U' r-
0 0 0 0

-4 -4 -4 -


0 0 0 0
o M r TT


,-
-4


1-4


0 0



o0 C


0. O
OL 0




0C >
t0 0
Co0


> 4-)
er V/)














(.
I PN \0 N C 0
U)

L- I- in n CD

\O > .* .. .. .. 3
-4 -. ON \O N-44
.

>-C



S C4 04 -4 (,4 04 N


0 NU


N N 0\ L0 N 0 4
-a
c





0






44 0 0 a)
., o.




CO N O' L
S .






4- O 4 \ 4



O* E

MO N N N N N c







-0
"0 1 0 0 (





1 0 \"0 7 N -04 U)





C

0 N LC (7N ON n (
C \o Nr A pa
N> .. .. .a












0 C 3 OO M 0 N N O C >
0 .- U





N 4 0 0 0- 4 04 -




0 4M N N4 N* -M
oi oo









-I .' I I I I I- I *C










S* *

S 0 0 n CN C o (C

-4 -4 N ,-4 ,-4 IC .-H

ON :: \ -- NT C-- 0
'3 \ CO N N N (



CM C-- CO CM.
c c co CL



















C 0 0 Co Co co Co Co Co Co Co CDC > CD
N 0 -4 CH Cu C u C C C C 0.0 0
C_ -4 4- 4.J 0-4 4-)
4-I Co C 4 I oc






a) Co p- pM ': Z -- K n nn Uicc o 41MJ
.00 0 I I I I I I I I I H .- C

,-4 ..-4 ,--4 -4 -4 .-4 --1 -4 .-4 ,-4 --4 0) I)
C Co x x x x x x x X cO C
S-4 C Co > 4 I Z"
C c O C O -(O O O CO O NO -0 (O N O C > -U


























z
0







0
HO
















0
I--













CLU




0 CL
J

















0


<-i












-0
I-


0-
V-)
ao
O-




Z--J




LU d CL
















0
C--
I-



a.o



a:
I--



WQ-








C)


>-
cr













0-4


o







O -
C
4-)
a) Ca



o o
4-0 a)
C, Ci


-4 0
ild 0


'0 '0
() a)
x x
--I -4


C C



ct Ca
o c
,,, -


x x
.-4 *.-4
4- 4-

C C
0 0
,-q .,-I

Ca CO
L_) C


cU




,-4







0
C)

V)
r-(












a)
o-














Ca

C-0
cn















C:
4a)
.c

a)









o
CL









I0
..
o


a)

c
4-'-











(U




Ca
0
1-1



C.,




ca





0)
a)





c




4-' 4-


cna
(0
ca.







TABLE 18
COMPARISON OF CALCULATED AND MEASURED POTENTIALS
FOR ELECTRODES G1 AND G2


E-measured


Electrode Gl, Day 1
4.55x10-4M CaC12




















Electrode G2, Day 1
4.55x10-4M CaCl2


69.7 mV
69.6
69.6
69.7
69.8
70.4
71.0
71.8
72.7
73.4
74.3
75.7
77.0
78.1
80.2
82.1
84.7
87.3
88.8
90.3

60.0mV
60.3
60.5
60.8
60.8
61.6
62.3
63.5
64.4
65.4
66.3
68.3
69.8
71.1
72.9
75.5
78.2
80.7
84.4
84.6


E-calculated


63.7 mV
64.6
65.2
65.6
66.0
67.1
68.5
69.9
71.0
71.9
74.6
73.0
75.9
76.9
78.6
80.5
82.7
84.4
85.7
86.8

57.4mV
57.8
58.1
58.4
58.6
59.4
60.6
61.8
62.9
63.8
64.9
66.6
68.0
69.1
70.9
73.0
75.5
77.4
78.9
80.0


Error

6.0 mV
5.0
4.4
4.1
3.8
3.3
2.5
1.9
1.7
1.5
1.1
1.3
1.1
1.2
1.6
1.6
2.0
2.9
3.1
3.5

2.6mV
2.5
2.4
2.4
2.2
2.2
1.7
1.7
1.5
1.6
1.4
1.7
1.8
2.0
2.0
2.5
2.7
3.3
5.5
4.6











TABLE 18 Continued


E-measured


Electrode Gl, Day 6
4.55x10-3M BaCl2




















Electrode G2, Day 6
4.55xlO-3M BaCl2


58.2mV
60.5
61.9
63.3
64.4
68.5
72.6
76.3
79.0
81.0
83.7
86.8
89.1
90.0
93.9
97.2
100.8
103.5
105.5
107.1

56.5mV
58.7
60.0
61.4
62.5
66.5
70.4
74.1
76.7
78.9
81.4
84.7
86.9
88.9
91.9
95.3
98.9
101.8
103.9
105.8


E-calculateo


59.7mV
62.0
63.8
65.4
66.8
70.8
74.8
78.4
81.2
83.2
86.7
88.8
91.0
92.9
95.7
98.6
102.0
104.2
105.9
107.3

55.2mV
57.4
59.2
60.8
62.2
66.1
70.1
73.8
76.5
78.5
81.0
84.1
86.4
88.3
91.0
94.0
97.4
99.6
101.3
102.8


Error

-1. 5mV
-1.5
-1.9
-2.1
-2.4
-2.3
-2.2
-2.1
-2.2
-2.2
-2.0
-2.0
-1.9
-2.0
-1.8
-1.4
-1.2
-0.7
-0.4
-0.2

1.3mV
1.3
0.8
0.6
0.3
0.4
0.3
0.3
0.2
0.4
0.4
0.6
0.5
0.6
1.3
1.3
1.5
2.2
2.6
3.1








Neutral Carrier Electrode base on AC-14/81

Experimental System

The experimental apparatus has already been described.

The calcium ion activity was fixed at one of four levels--

2 x 10-3, 3 x 10-3, 4 x 10-3 and 8 x lO-3--and the sodium

ion concentration was varied from 9 x 10-5 M to 2 x 10-5 M.

Data Treatment

Activity coefficients and diffusion potentials were

calculated as before; activities and corrected potentials

are shown in Table 19 and in Appendix B.

It was not possible to use the graphical cross-point

approach, since a horizontal initial line was not observed

for any of the fixed-ion concentrations.

A comparison of the slopes of the linear portion at the

high activity end and the separate solution calibration slo-

pes was made; the results are shown in Table 20.

Expected potentials were again calculated according to

the modified Nicolsky equation using the separate solution

selectivity coefficient given by Eqn. 38. A representative

sample of the results is given in Table 21.

Ion-Exchange Electrode for Calcium Ion

Experimental System

The experimental apparatus has already been described.

Since the response of the electrode was rather slow it was

only possible to obtain data for one fixed concentration on

each of five days. The fixed concentration was 4.903 x 10-3








TABLE 19
ACTIVITIES AND CORRECTED POTENTIALS FOR ELECTRODES Ql
AND Q2 IN NaC1/CaC12 MIXTURES


Activity Na

Electrode Ql

8.56x10-5M
1.71xl0-4
3.41xl0-4
5.94x10-4
9.28x10-4
1.26xl0-3
1.59x10-3
2.07xl0-3
2.93xl0-3
4.61x10-3
6.27xl0-3
8.72xl0-3
1.27x10-2
2.03x10-2

Electrode Q2

8.56x10-5M
1.71xl0-4
3.41x10-4
5.94x10-4
9.28x10-4
1.26x10-3
1.59xl0-3
2.07xl0-3
2.93x10-3
4.61x10-3
6.27x10-3
8.72x10-3
1.27x10-2
2.03x10-2


Activity Ca EMF-1


1.89x10-3
1.88xi0-3
1.87xl0-3
1.86x10-3
1.84xl0-3
1.82x10-3
1.80x10-3
1.77x10-3
1.74x10-3
1.69xl0-3
1.65xi0-3
1.58x10-3
1.50xl0-3
1.37x10-2


1.89xl0-3
1.88x10-3
1.87x10-3
1.86x10-3
1.84xl0-3
1.82xl0-3
1.80x10-3
1.77x10-3
1.74xl0-3
1.69xl0-3
1.65xl0-3
1.58x10-3
1.50x10-3
1.37x10-2


EMF-2 EMF-3 EMF-4 EMF-5


-41.3mV
-38.0
-32.5
-25.1
-18.3
-12.5
- 8.3
- 2.8
3.5
13.3
19.5
27.0
34.5
45.5


-32.5mV
-30.1
-24.7
-18.0
-11.5
- 7.1
- 2.8
1.5
8.0
16.8
23.3
30.2
38.3
47.6


-37.4mV
-34.4
-29.6
-22.9
-16.4
-11.1
- 6.8
- 1.2
5.4
15.4
21.8
29.7
37.5
48.8


-23.6mV
-21.4
-16.4
-10.0
- 3.6
2.1
6.4
11.1
17.6
26.5
32.9
35.9
43.6
53.2


-39.4mV
-36.2
-31.0
-24.2
-17.6
-12.1
- 7.5
- 2.2
4.5

20.8
28.0
36.6
47.0


-27.4mV
-25.2
-19.7
-13.4
- 6.9
- 1.7
2.5
7.6
14.4

30.0
37.3
45.2
55.7


-40.5mV
-37.1
-32.4
-25.1
-18.3
-12.7
- 8.5
- 3.0
3.5
13.6
19.2
27.0
34.5
45.5


-26.5mV
-23.9
-18.7
-12.7
- 6.4
- 1.5
2.6
7.6
14.1
23.4
28.1
34.2
42.5
51.3


""'





""'














EMF-6


-41.7mV
-38.5
-33.2
-26.1
-19.1
-13.5
- 9.2
- 3.6
3.2
12.9
19.6
27.0
35.4
46.4



-28.8mV
-26.2
-20.8
-14.2
- 7.6
- 2.2
2.0
7.4
14.1
23.0
29.5
36.0
44.4
52.2


EMF-7


-41.0mV
-37.9
-32.6
-26.9
-20.5
-15.2
-10.7
- 5.4
1.4
11.3
18.0
25.4
34.0
44.9



-29.1mV
-26.8
-22.0
-16.3
-10.1
- 5.0
- 0.9
4.0
10.6
20.3
26.8
33.9
42.4
53.1


EMF-8


-43.3mV
-40.5
-35.3
-28.6
-21.5
-16.0
-11.4
- 6.0
0.9
10.5
17.2
24.7
33.3
44.2



-28.4mV
-26.3
-21.2
-15.1
- 8.7
- 3.8
0.4
5.5
12.3
21.5
28.2
35.4
43.7
53.5


EMF-9


-47.8mV
-44.3
-38.3
-31.0
-23.2
-17.7
-13.1
- 7.6
- 0.5
9.6
16.4
24.0
32.6
43.5



-32.4mV
-29.3
-24.0
-17.5
-11.0
- 5.7
- 1.3
4.4
10.8
20.2
26.9
34.5
43.0
53.7


EMF-10


-50.4mV
-46.9
-41.0
-33.4
-25.6
-20.0
-15.2
- 9.8
- 2.8
7.3
14.6
23.1
32.1
42.9



-34.0mV
-31.4
-26.5
-20.6
-13.5
- 8.2
- 3.8
0.5
7.6
17.6
24.6
32.4
41.2
51.9


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-48.2mV
-44.8
-39.2
-31.7
-24.4
-18.7
-14.2
- 8.4
- 2.1
8.6
15.2
22.9
31.0
42.6


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-50.8mV
-47.1
-40.8
-32.9
-25.3
-19.4
-14.7
- 9.1
- 1.8
8.1
15.1
22.6
31.2
42.1


-34.4mV
-31.1
-26.7
-19.8
-14.3
- 8.1
- 4.9
0.3
6.0
16.5
22.7
30.2
37.8
47.2








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M barium chloride. The calcium chloride concentration was

varied between 10-5 M and 10-2 M.

Data Treatment

Activity coefficients and diffusion potentials were

again calculated; activities and corrected potentials are

given in Table 22.

The measured potentials have again been compared to

those calculated using a separate solution selectivity coef-

ficient; these are shown in Table 23.















ACTIVITIES



Log Act Ca

-5.212

-5.038

-4.914

-4.373

-4.141

-3.438

-3.191

-2.513

-2.298


TABLE 22
AND CORRECTED POTENTIALS FOR THE CORNING ELECTRODE
IN CaC12/BaCl2 MIXTURES


Log Act

-2.516

-2.519

-2.520

-2.523

-2.526

-2.536

-2.545

-2.609

-2.654


EMF-1

40.4mV

39.1

39.5

45.3

51.9

74.4

82.1

102.9

109.9


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37.4mV

36.4

36.4

44.3

52.5

73.9

81.5

102.4

108.9


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37.1mV

35.6

36.5

44.9

51.6

73.8

81.7

102.1


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30.7 38.1

40.7 45.2

47.8 50.9

71.4 70.9

80.2 79.7

100.9 100.6

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CHAPTER 7
DISCUSSION OF RESULTS

The interpretation of the results of these experiments

is hindered somewhat by the lack of reproducibility of the

measured data. Comparison of the potentials observed for a

particular concentration over several days (Tables 3, 6, 7,

10, 13, 19, 22 and Appendices A and B) shows that the poten-

tial often changes as much as 4 mV. Despite this dif-

ficulty, however, several trends can be seen.

First, it is clear from the results shown in Tables 4,

5, 8, 9 and 11 for the separate solution method that the
R
selectivity coefficient kA,B (calculated using measured

slopes) is much less activity dependent than the Nicolsky
pot
selectivity coefficient kA,B. For example, the results for

electrode Gl for day 1 of the measurements show a relative
pot
standard deviation of about 26% in kCa,Ba over the activity
R
range, while the relative standard deviation for kCa,Ba over

the same activity range is only about 5%. For electrode Q1

on day 1 the improvement is less dramatic, with a relative
pot
standard deviation of about 6.4% for kNa,Ca and 1.6% for
R
kNa,Ca. The largest improvement is seen with the Corning

electrode, from a relative standard deviation of 100% for
pot R
kCa,Ba to only 7% for kCa,Ba on day 1. This variation in

improvement among the three electrodes is easily explained







when one considers the degree to which they deviate from

Nernstian behavior. Electrode Q1, which showed the least

improvement, exhibited an average slope of 19.7 mV per

decade for calcium and 47.8 mV for sodium over the twelve

days on which measurements were made. This is a ratio of

2.4:1, not very different from the Nernstian prediction of

2:1 for a divalent/monovalent cation mixture. Electrode Gl

exhibited an average slope of 28.0 mV for calcium and 23.2

mV for barium over the six days of use. This gives a ratio

of 1.3:1 rather than the Nernstian 1:1, a somewhat larger

deviation than that for Electrode Ql. The Corning

electrode, however, exhibited an average calcium response

slope of 30.1 mV, but only 8.9 mV for barium. This gives a

slope ratio of 3.4:1, far different from the Nernstian value

of 1:1. Thus it can be seen that the degree to which the

activity dependence is decreased on using measured, rather

than theoretical slope ratios, depends upon the degree to

which the observed slope ratios deviate from the Nernstian

ones.

It is equally clear from the results shown in Table 14

that the use of measured slope ratios rather than Nernstian

ratios does not significantly affect the activity dependence

of selectivity coefficients obtained using the mixed solu-

tion method with the graphical cross-point approach. The
XP
selectivity parameter kCa,Ba, although different in magnitude,

exhibits an activity dependence similar to that of the
XPR
selectivity parameter kCa,Ba. In fact, for about half of







XP
the data sets, the parameter kCa,Ba is slightly less activity
XPR
dependent than is kCa,Ba. A possible explanation centers on

the fact that the cross-point is determined by drawing the

two best lines through the data points, and thus the cross-

point in effect is obtained using measured rather than

theoretical slopes. There is, then, in effect a slope

correction inherent in the graphical approach. When Eqn. 42
XP
is used to correct the values of kCa,Ba for the non-
XPR
Nernstian slope ratio, the values of kCa,Ba obtained have

in effect been over-corrected. It is important to note,

however, that the activity dependence of the values of
XP XPR
either kCa,Ba or kCa,Ba obtained by the graphical method is
R
much greater than that of the values of kCa,Ba obtained by

the separate solution method.

The mixed solution data can be used to check the

validity of the assumption (made in the separate solution

method) that the electrode responds in the same manner to a

one-component solution as it does to a multi-component solu-

tion. If this were true, then the slope of the line

obtained at the high activity end of a plot of mixed solu-

tion data should be identical to the calibration slope

observed for the ion whose activity was varied to obtain the

set of mixed solution data. A comparison of these slopes

(Tables 16, 17 and 20) clearly shows that this is not the

case. For electrodes Gl and G2 in almost every instance the

average of the slopes observed in mixed solution is higher





89

than that observed in pure solution. In addition the slopes

observed in mixed solution when the activity of barium (the

interfering ion) was varied decrease considerably as the

activity of the fixed-concentration calcium ion is

increased, although there is little activity dependence when

the barium ion is the fixed-concentration ion. For electro-

des Ql and Q2 the slopes in mixed solutions, with very few

exceptions, also are higher than those observed in pure

solutions; again there is very little activity dependence of

the slope when the interfering ion (calcium in this case) is

the fixed-concentration ion. Thus, it appears that the pre-

sence of a second ion, even at very low activity, always

affects the response of the electrode, but the effect is

more pronounced when the second ion (the one present at

lower activity) is the ion to which the electrode preferen-

tially responds.

While it is clear that the slopes observed in separate

and in mixed solution differ, it can be inferred from the

results in Tables 18, 21, and 23 that this change in slope

does not seriously affect the potential observed. These

tables show a comparison of potentials measured in two-

component mixed solutions with those calculated according to
R
Eqn. 49 using selectivity coefficients (kA,B) measured by

the separate solution method using measured slopes. It can

be seen that the difference between the measured and calcu-

lated potentials for electrodes GI and G2 is usually 2 mV







or less. While this is a rather large difference on an

absolute scale, especially when one considers that an error

of only 0.1 mV in potential represents a 4% error in acti-

vity, it must be remembered that the potentials observed for

Gl and G2 often varied by as much as 4 mV from day to day,

and in addition that there was a problem with non-linearity

which could not be totally overcome by restricting the acti-

vity range over which measurements were made. In view of

these difficulties, then, a difference of only 2 mV between

measured and calculated potentials is not excessive. The

differences for electrodes Qi and Q2 and for the Corning

electrode are somewhat higher, averaging about 4 mV, but

again this is within the reproducibility of the measure-

ments.

Finally, while it can be seen that the selectivity

coefficients measured using the separate solution method

with measured slopes do an acceptable job of describing the

behavior of the electrode in mixed solutions, it is clear

from the results shown in Table 15 that a better fit can be

obtained by using the curve-fitting approach. For electrode

Gl, for example, the average difference between measured and

calculated potentials is about 0.5 mV. However, it must be

remembered that the curve-fitting program obtains this low

difference by varying the values of Eo, S and K to obtain

the best fit for a particular set of points--if a different

set of points is used a good fit can also be obtained, but






91

the values of Eo, S and K needed to obtain it may well be

different from those which gave the best fit for the first

set of points. This can be seen in the results shown in

Table 15. The values of K calculated for electrodes G1 and

G2 on days 1-3, when the calcium ion concentration was kept

constant, have a relative standard deviation of 14% and 16%

respectively. On days 4-6, when the barium concentration

was kept constant, the relative standard deviations are

15% and 21% respectively. Thus, while it is possible

to obtain a good fit for a particular set of data using the

curve-fitting approach, the values of Eo, S and K thus

obtained will not give a good fit when used with a different

set of data.




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