ACTIVITY EFFECTS IN SEAWATER ANlD

OTHER SALINE MIXTURES

DONALD RICHARD WHiITE. Jr.

A DISSERTATION PRESENTED TO THE GRALDUATE COUNCIL OF

THE UNIVERSITY OF FLORIDA

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1979

ACKNOWLEDGMENTS

I am forever indebted to my research advisor,

Professor Roger G. Bates, for his patient guidance

throughout the course of my research and the prepara-

tion of this work. His superior knowledge and insight

have greatly contributed to the successful completion

of my formal education.

My utmost gratitude goes to Dr. J. Burns Macaskill

for helpful suggestions in the laboratory and to Dr.

Robert A4. Robinson for stimulating discussions.

Thanks are also expressed to Ms. Diane Keyoth for

typing the final draft of this dissertation.

Finally, I must thank my parents, who are ultimately

responsible for this work, and whose constant encourage-

ment and support have motivated me throughout this

endeavor.

TABLE OF CONTENTS

PAGE

ACKNOWLEDGEMENTS ii

LIST OF TABLES v

LIST OF FIGURES vii

ABSTRACT ix

Chapter

1 INTRODUCTION 1

2 ACTIVITY COEFFICIENTS 7

Theoretical Background 7

Solutions of Single Electrolytes 10

Solutions of Mixed Electrolytes 13

HCI in Seawater 15

3 CONCEPT OF pH 19

Theoretical Background 19

Cells With Liquid Junction 21

pH in Seawater 23

pH in Clinical Media 25

4 OSMOTIC COEFFICIENTS 27

Theoretical Background 27

Solutions of Single Electrolyt;es 29

Solutions of Mixed Electrolytes 32

5 EXPERIMIENTAL 34

Electromotive Force Measurements 34

Materials 34

Preparation of Cell Solutions 37

Preparation of Electrodes 38

Equipment and Procedures 40

Isopiestic Measurements 46

Materials 46

Preparation of Solutions 46

Equipment and Procedures 47

Chapter

Page

6 RESULTS 48

Electromotive Force Measurements 48

Standard Potential of the Silver-

Silver Chloride Electrode 48

Activity Coefficient of HC1 in

Seawater 49

pH Standardization in Seawater 56

pH Standardization in Clinical

Media 56

Isopiestic Measurements 66

NaC1-SrC12 Mixtures 66

NaCl-Na2CO3 Mixtures 67

7 DISCUSSION 76

Electromotive Force Measurements 76

Activity Coefficient of HC1 in

Seawater 76

pH Standardization in Seawater 81

pH Standardization in Clinical

Media 82

Isopiestic Measurements 90

Scatchard Treatment 90

Pitzer Treatment 99

8 CONCLUSIONS 111

APPENDIX 115

REFERENCES 117

BIOGRAPHICAL SKETCH 122

LIST OF TABLES

Table Page

1. Values of E and EO for the Cell:

Pt; H2)HC1(0.01m)lAgC1; Ag 50

2. Electromotive Force of Cells of Type 2.7

Containing HC1-MgCl2 Mixtures and HCl-NaC1

-MgC12 Mixtures From 5 to 450C, in Volts 52

3. Values of -logyO and the Harned Coefficient

(a) for the Sys ems HC1-MgC12 and HC1-NaC1

-MgC1 as a Function of Ionic Strength at 5

to 4520 C 54

4. Comparison of pmH(X) and pHNBS Obtained

by EMIF Measurements of the Cell Hg; Hg2C12'

3.5M KC1 (Soln. S or XIH2(g, latm); Pt at

250C With Corresponding pmHf(S) Values 57

5. Electromotive Force of Cells of Type 2.7:

Pt; H2 (g, latm)lBuffer Soln.lAgC1; Ag,

at 25 and 370C, in Volts 62

6. Electromotive Force of Cells of Type 3.6:

Eg; Eg2C12, 3.5M KC1jIBuffer Soln.lH2 (g, latm);

Pt, at 25 and 379C, in Volts 63

7. Operational pH Values Calculated by

Equation 3.7 from the EMF of Cell 3.6 vs.

Phosphate-Chloride Standard Reference

Solutions at 25 and 370C 64

8. Osmotic Coefficients in Aqueous SrC12

Solutions at 250C; Comparison of Results 69

9. Parameters for Eqs. 4.6 and 4.8 Used in the

Treatment of NaC1-SrC1 -H20 Mixtures 70

10. Compositions and Osmotic Coefficients of

Isopiestic Solutions in the System NaC1(A)

SrC12(B) H20 71

11. Best-Fit Mixing Parameters for the System

NaC1(A) SrC12(B) H20 72

12. Parameters for Eqs. 4.6 and 4.8 Used in the

Treatment of NaC1-Na2CO3-H20 Mixtures 73

13. Compositions and Osmotic Coefficients of

Isopiestic Solutions in the System NaC1(A)

Na2CO3(B) H20 74

14. Best-Fit Mixing Parameters for the System

NaC1(A) Na2CO3(B) H20 75

15. Comparison of the Trace Activity Coefficient

of HC1 in NaC1-MgCl2 Mixtures With That

Determined Experimentally in Synthetic

Seawater 78

16. Mixing Parameters (Pitzer Treatment) for the

System EC1-MgC12-H20 80

17. Excess Free Energy of Mixing (J kg-1~

Comparison of Results 98

LIST OF FIGURES

Figure Pag~e

1. EMF cell without liquid junction 42

2. EMF cell with liquid junction 45

3. Plot of p(a YC1) for the NTBS phosphate

"blood buffer" as a function of molality

of added NaC1 61

4. Variation of the logarithm of the mean

activity coefficient of NaC1 in phosphate-

chloride mixtures of I = 0.16m, as a function

of composition at 25 and 370C 86

5. Effect of the ionic strength and composition

of the reference standard on the operational

pH values of TES, HEPES, and Tris buffer

solutions of ionic strength 0.16m at 370C 89

6. Plot of ~MX as a function of ionic strength

in the system NaC1(A) SrC12(B) H20 for

various ionic strength fractions, yB 94

7. Plot of (MIX as a function of ionic strength

in the system NaC1(A) Na CO3(B) H20 for

various ionic strength fractions, yg 96

8. Mean activity coefficients of NaC1 and SrC1Z

as a funcT~ion of ionic strength in the system

NaC1(A) SrC12(B) H20 for various ionic

strength fractions, yA and yB 104

9. Harned plots for NaC1 and SrCl2, -log y, vs.

YB, in the system NaC1(A) SrC12(B -20 106

10. Mean activity coefficients of NaC1 and

N2CO3 as a function of ionic strength in

the system NaC1(A) Na2CO3(B) H20 for

various ionic strength fractions, yA and yB 108

11. Harned plots for NaC1 and Na2CO3, -log y,

vs. YB, in the system NaC1(A) Na2CO3(B)

H20 110

V111

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

ACTIVITY EFFECTS IN SEAWATER AND

OTHER SALINE MIXTURES

By

DONALD RICHARD WHITE, Jr.

August 1979

Chairman: Roger G. Bates

Major Department: Chemistry

Measurements of electromotive force (EMF) and the iso-

piestic technique were utilized in the determination of

factors which influence the thermodynamic activity and

related properties of individual species in complex saline

mixtures.

EMF measurements in cells without liquid junction were

carried out to determine the mean activity coefficient of

HC1, y,, in electrolyte mixtures resembling seawater. In

mixtures of HC1-MgC12, it was found that y, decreases in a

linear fashion as HC1 is replaced by MlgC12 while maintaining

constant total ionic strength and, in this respect, obeys

Harned's Rule. These measurements were carried out at four

ionic strengths, namely I = 0.1000, 0.3809, 0.6729, and

0.8720 mol kg- at nine temperatures from 5 to 450C. The

three higher ionic strengths correspond to seawater of

salinities 20, 35, and 450/00. In addition, studies were

made on the system HC1-NaC1-MgC12 at I ..= 0.6729, the molal

ratio of NaC1 to MgC12 being maintained at 7.202 as in

natural seawater. The Harned coefficients obtained from

all measurements were found to decrease slowly with tempera-

tr

ture. The trace activity coefficients of HC1, y+ were

calculated from the Harned equation in two ways. First, by

combining Harned coefficients from the ECl-MgC12 study with

those from an earlier HC1-NaC1 study, weighting the two with

respect to their relative ionic strength contributions to

seawater. Secondly, they were calculated using Harned coef-

ficients from the HC1-NaC1-MgCl2 study. All values were

found to be identical with those measured earlier in total

artificial seawater (excluding sulfate) at all ionic strengths

and temperatures included in the experiments.

The concept of single-ion activity and the problem of

liquid-junction potentials in pH measurement were addressed

in a study of pH in synthetic seawater and saline media simu-

lating serum. Measurements of EMF in a cell with liquid

junction at 250C were carried out in buffered artificial sea-

water at salinities of 30, 35, and 400/00, each containing a

Tris buffer at molalities of 0.02, 0.04, and 0.06.

Comparison of the pmH values calculated by the operational

definition with those determined from measurements in cells

without liquid junction demonstrates that a residual liquid-

junction potential exists which varies with salinity. Within

a given salinity, however, pmH values calculated by the

operational definition are identical regardless of Tris

buffer concentration.

Evidence is presented that pH measurement of blood plasma

and other clinical media at ionic strengths of 0.16m vs. the

NBS standards may involve residual liquid-junction errors

amounting to 0.03 to 0.05 pH unit. EMF measurements of cells

both with and without liquid junction indicated that residual

liquid-junction effects may be nearly eliminated by matching

the ionic strength of the standard to that of the sample. A

phosphate buffer composed of 0.005217m KE2PO 0.018258m

Na2HPO4, and 0.1m NaC1 (buffer ratio 1:3.5 and I = 0.16m) is

to be preferred to the NBS phosphate buffer (I = 0.1m) for

measurements of this sort.

Isopiestic measurements were carried out at 250C on mix-

tures of electrolytes having to do with seawater, NaC1-SrCl2

and NaC1-Na2CO3, and the resulting osmotic coefficients were

determined in the ionic strength range 0.3 to 6.0m. The data

were fitted to the current treatments of Pitzer and Scatchard

for solutions of mixed electrolytes. Activity coefficients

were calculated for the individual solutes in each mixture

using the best-fit ion interaction parameters from the Pitzer

treatment. These are discussed in light of the excess free

energies of mixing calculated from the corresponding

Scatchard parameters.

CHAPTER 1

INTRODUCTION

When a salt such as sodium chloride is dissolved in

water, the resulting solution exhibits a comparatively high.

electrical conductivity showing that charged ions are pres-

ent. The thermodynamic properties of the solution may, in

part, be described by electrostatic interactions of the ions

with each other and by interactions of ions with water mole-

cules. The concentration of the dis-solved species in the

solvent, and thus the magnitude of these effects, will have

a major influence on the thermodynamic activity and related

properties.

Classical thermodynamics1- gives a general formula for

the chemical potential of any solute, i, in an ideal solution

as:

"i = I-? + RT In x [.1

where xi is the mole fraction of the solute and go is its

chemical potential in the standard state, i.e., when xi is

unity. The temperature is given by T, and R is the gas

constant. In an electrolyte solution, however, coulombic

ion-ion forces are present and any attempt to measure the

chemical potential would result in a departure from equation

1.1, the magnitude of which is a measure of the non-ideality

associated with these interactions.

In order to correct equation 1.1, an empirical correc-

tion factor may be applied to modify the concentration term:

S= O + RT In x f. (1.21

This effective concentration term, xi 1 = ai, is termed the

activity of the species i, and fi is the "rational" activity

coefficient. The concentration. may be just as easily ex-

pressed in molality, mi, where the activity coefficient must

take on a different value normally designated by the symbol

Y From equation. 1.2, it can be seen that the activity must

be unity in the standard state. Thus, the standard state on

the morality scale is that of a hypothetical solution where

the mean ionic molality and activity coefficient are unity,

but with the reference state chosen such that a /mi = Yi

when m. approaches zero.8

The change in the Gibbs free energy of any thermodynamic

system as a function of temperature, pressure, and composi-

tion is given as:

dG = -SdT + VdP + Epidn. C1.3)

Therefore, mathematically, the chemical potential of a species

i is the partial derivative of the free energy with respect

to moles of i when temperature, pressure, and moles of other

substances remain constant; it is often written as Gi.

I iT,P,nj

To measure this quantity in an ionic solution, one would

need to measure the change in free energy with change in

concentration of one ionic species only. Obviously, this

would be empirically difficulT; if not impossible. One can

only, therefore, measure the activity coefficient of a net

electrolyte, that is at least two ionic species resulting

from a single neutral electrolyte.

If one considers a symmetrical electrolyte of the 1:1

charge type, such as KC1, the sum of the chemical potentials

of the resulting ions as a function of molality may be given

as:

v+ v- 1/v

GH+ + GC1- = G4+G1) + vRT In (mH~mC1-)

(G+ + vR n y 1-1v 15

where v = v' + v is the number of ions per molecule of elec-

trolyte and in this case is equal to 2. Defining the respec-

tive mean values as:

goGH+ + GCl"

m, = (m l

v' v- 1/v

Y, = (YHYCl-)

an expression can be written for the mean chemical potential

which is, in effect, the average contribution of a mole of

ions to the free energy of the system.

G, = GO + VRT In mi + VRT In y, (1.6)

One now has a relation between the free energy of a state in

which the ions are infinitely far apart and a state corres-

ponding to a given concentration and its mean activity coeffi-

cient, y which is experimentally determinable, To split

this value of r into individual ionic activity coefficients

will require a theoretical and partly arbitrary approach to

be discussed later.

Another way in which the non-ideal behavior of an elec-

trolyte solution may be described is by means of the osmotic

coefficient, which may be regarded as a measure of the non-

ideality of the solvent due to the presence of ion~s. It is

defined in such a way as to become unity in the pure solvent.

A rational activity coefficient for the solvent would fail to

emphasize this adequately; since the mole fraction of the sol-

vent is normally so large, fs would never deviate muck from

unity. For this reason, the "rational" osmotic coefficient,

g, is defined by:

In as g In xs -g In 1 m~ + ii1.7)

where Ws is the molecular weight of the solvent, as is its

activity, and m is molality. The practical osmotic coeffi-

cient, 9, on the molality scale is defined by:

-vmW

Ias 1000 4 (1.8)

Therefore, for an aqueous solution for a single electrolyte,

equation 1.8 becomes:

-55.51 In aw = vm~ (1.9)

In very dilute solutions, the mole fraction of the solute,

x may be described by:

n. n

where ni and nw are the number of moles of solute and water,

respectively. Therefore from equation 1.9 one finds:

-m In a -ln a

W W W

V4 = (1.11)

When xi is very small, the last term may be approximated by:

-In aw -ln aw In a

--- w n X (1 .12 )

From this it can be seen that the osmotic coefficient is approx-

imately proportional to the ratio of the logarithms of activity

to mole fraction and, in this respect, behaves much like the

activity coefficient where fi = ai/x .

The relationship between the rational and the molal activ-

ity coefficient can be shown4 to be:

f, = y,(1 + 0.001vWsm) (1.13)

and that between the rational and molal osmotic coefficient as:

vmW

g In xs Igg 100 (1.14)

In the case of any system at equilibrium and maintained

at constant temperature and pressure, the sum of the chemical

potentials of all species must be zero; as shown by the Gibbs-

Duhem relation,

nAdGA + n"G + ndG + ... = 0 (1.15)

where ni denotes the number of moles of the ith species.

Therefore, for a solution containing only one solute in

water:

n.dG. -n dG (1.16)

1 1W W

The Gibbs-Duhem relation is important in relating the osmotic

and activity coefficients. Recalling that:

G. = Gf + VRT In ai

and G = GO + RT In a

ww Ww

one can express the Gibt~s-Duhem relation as:

vm dln (7 mZ = -55.51 dln a. C1.17)

Combining this result with equation 1.9, the osmotic and

activity coefficients may be related by:

dm

($ 1)q- + d@ = dln y, (1.18)

and upon integration this may be shown to give;

0 = 1 + 1/m I m dln y, C1.19)

Alternatively, activity coefficients can be calculated

from osmotic coefficients by expressing the above relation-

ship in the form:

In Y, = (4 1) + I (4 1) dln m (1.20)

CHAPTER 2

ACTIVITY` COEFFICIENrTS

Theo~retical Backrground

Electromotive force measurements have been useful in

providing a large part of our existing thermodynamic data

for electrolyte solutions. They serve as the most common

and accurate means by which to view ionic activity.

Thse reaction in a galvanic cell is one in which oxida-

tion and reduction occur simultaneously; that is, electrons

are removed from one species which is said to be oxidized

and supplied to another species, said to be reduced. The

reaction may be regarded as the sum of these two half-reactions,

each of which occurs at a respective electrode. If the two

electrodes are connected to a voltmeter with a high input

resistance, such that no reaction is allowed to occur, the

resulting voltage, E, is a measure of the potential for reac-

tion. This potential is related to the molar free energy

change, dG, for the reaction by:

AG = -nE (2.11

where F is the Faraday C96,487 coulombs/moler, a is the num-

ber of moles of electrons exchanged, and E is in volts. The

Gibbs energy change is then in joules and is a measure of the

maximum work that the cell reaction can produce, A nega-

tive AG indicates a spontaneous reaction, while a positive

AG indicates the reaction will not occur spontaneously.

Considering the following general chemical reaction:

aA + bB + .,, = uU + vV + ... C2.2)

then the change in free energy which accompanies the reaction

is the sum of all the chemical potentials of the products

times their respective number of moles minus the same quan-

tities for the reactants:

dG = uGU + vGV + ... aGA bIGB ... (2.3)

If one writes for nGo:

AGO = uGo + vGo + ,.. aGA bG~ .,, C2.4)

and recalls equation 1,1, then:

AG = AGO + RT a -a~b~j- C2.5)_

aAaB

which is the general form for the free energy of a reaction.

Combining relation 2.1 with the above gives the Nernst equa-

tion:

u v

RT aU V '

E= EO In (2.6)

nF ab

a~aB

which relates EMT to the activities of the various ions.

This equation will be used extensively in this work. The

term EO is the standard potential; it is equal to E when all

ions are in their standard states.

Considering the following galvanic cell9,10 containing

aqueous HC1:

Pt; H2(g, latm) KC1(m) AgC1; A4g(s) (2.7)

the cell reaction may be regarded as a combination of two

half reactions:

}H2 = K' + e (2.8)

and AgC1 + e = A4g + Cl (2.9)

which, when combined, give the total cell reaction:

:H2(g, latm) + AgC1(s) = Ag~s)+ H m) +C1(m) (2.10)

The cell 2.7 is written such that oxidation is taking place

at the left electrode, the anode, and reduction takes place

at the right, the cathode. A positive EMF, or negative AG,

indicates that the reaction will occur spontaneously as

written. The EMF of the cell is given as:

RT

E = E* In a 4aC1' C2.11)

since hydrogen, silver, and silver chloride are all in their

standard states. This may be expanded to give E in terms of

the molalities and mean activity coefficients of the respec-

tive species as follows:

R.T RT 2

E = EO F In m 4mCl- F In Y, (2.12)

Therefore, it can be seen that EMF measurements are useful in

that they easily yield the mean activity coefficient or log 7 :

logy~ = -fl(E EO)/k + logmK~mC1~] (2.13)

where k = 2.303RT/nF.

Solutions of' Single Electrolytes

A theoretical treatment of the thermodynamic properties

of electrolyte solutions must deal with both long-range inter-

ionic forces and short-range ion-solvent interactions. The

former net effect of attractions and repulsions will tend to

decrease the free energy of any particular charged species,

manifested in a decrease in the activity coefficient. Also

stabilization of ions by solvent molecules tend to lower

their free energies. On the other hand, at higher concentra-

tion ion-solvent interactions tend to lower the vapor pressure

of the solvent, and thus its activity, appearing to increase

the activity coefficient of the solute species. There is

normally a concentration where these two phenomena are in

balance, resulting in an activity coefficient minimum. K~ow-

ever, in dilute solutions, interionic forces may be assumed

to dominate.

The contribution of electrical interactions with other

ions to the free energy of a specified mole of j-ions is

shown to be:

AU.(el) = -L_- ---- 2.14)

2c 1 + ra

This arises from the well-known Debye-Hiickel formula for the

time average potential for an ion of diameter, a, with a

charge zje, in the absence of other external forces. The

term, C, is the dielectric constant of the medium in which

the ions are immersed, N is A4vogadro's number; K is defined

by

1008 Nek2 \1/2/7(.5

and is obviously a function of concentration, ionic charge,

temperature, and dielectric constant. It is often called

the Debye-Hiickel reciprocal length since it is this distance,

Kat which all of the charge of the ionic atmosphere sur-

rounding a central ion may be considered to be concentrated.

The Boltzmann constant, k, arises from the assumed distribu-

tion function.

Assuming that an ionic solution would behave ideally in

the absence of these interionic forces, then the partial free

energy of a mole of j-ions may be split into,

G. = G.(ideal) + aG.(el) (2.16)

The term AG.(el) is essentially the non-ideal contribution

containing the activity coefficient, hence:

2 2

di.(el) -z.e

In f. J 3L -- --- (2.17)

RT 2EkT 1+K

For the mean activity coefficient, f which is experimentally

determinable:

2 2 2

-e

In f, = -- - - 2.18)

2ckT 1 +

The condition of electroneutrality, "lzl '2z2, allows the

following transformation:

In f, = ----(2.19)

2ckT 1 +

Substituting for <, equation 2.19 can be written in decadic

logarithmic form as:

-Ajzl212 T

logf, = (2.20)

1 +B /TJ

where A and B are constants dependent on T and c. The ion-

size, a, is given in angstroms for numerical convenience.

A=1.8246 x 10 (.1

()3/2

Bx18 5.029 x 10 (.2

(T1/2

At very low concentrations of electrolytes, that is at low /Y,

the term Bill becomes negligible compared to unity and equa-

tion 2.20 will take the form:

logfi = -Ar zlz2 7 1f (2.23)

which is known as the Debye-Hiickel limiting law. This form

is useful in predicting activity coefficient behavior in very

dilute solutions. Therefore one could say, with reasonable

justification, that the numerator in equation 2.20 is the

effect due to long-range coulombic forces, while the denomi-

nator brings in modifications for short-range interactions.

By choosing 3.04 A as a reasonable value of 1 for all elec-

trolytes at 250C, Giintelbergl2 expressed equation 2.20

simply as:

-ABzl21 'f

logf, = (2.24)

which is superior to the limiting law, but not adequate above

I = 0.1m. Guggenheim,13 by adding an adjustable parameter

linear in concentration, improved the equation still further:

-A112 zlz2

logf, = + bl (2.25)

Solutions of Mixed Electrolytes

Studies of mixed electrolytes are importantl41 from

the standpoint that they provide an experimental criterion

for judging theoretical predictions. From the bodies of

water in the oceans to the biological fluids in the body,

solutions of mixed electrolytes are of great importance.

In 1922, Br~nstedl9 proposed his theory of specific

interaction which states that, "in a dilute solution of con-

stant total concentration, ions will be uniformly influenced

by ions of their own sign and specific effects are to be

sought in interactions between oppositely charged ions."

Employing a modification of the Debye-Hiickel expression

(equation 2.25) with a term, b, linear in concentration,

Guggenheim continued to build a theory of mixed electrolyte

solutions. He introduced specific interaction coefficients,

b, into equations for the activity coefficient of an elec-

trolyte, B, in the presence of another electrolyte, C:

n B 1 + [ 2xbMX + (bNX + bMY)(1 x)]m [2.26)

Here, MC and X- are the ions from B and N+ and Y- are the

ions of C, both being 1:1 electrolytes in aqueous solution

at 250C. The total molality is m, while xm and (1 x)m are

the molalities of B and C respectively. This form, taken

from Robinson and Stokes,4 describes the activity coefficient

and concentration on the molal scale. A similar equation may

be written for the electrolyte C:

In YC =+ [2(1 x)bNY + (bN + b d)xlm (2.27)

Now, letting y' refer to the term in brackets on the right of

equations 2.26 and 2.27, then when x = 0 and only component C

is in solution one can define:

In YCO)B = (bMY + bNX)m (2.28)

In TC(0) = 2bN m (2.29)

In contrast, when x = 1:

In YB(0) = 2bMXm (2.30)

In y(0)C = (bNX + b n)m (2.31)

Now it can be seen that:

In yB = In Y(0)B + (ln YBC0) In Y(0)Brx (2.32)

and similarly for C:

In vC = In Y(0)C + (In YC(0) In Y(0)C)(1 x) (2.33)

Thus, the logarithm of the activity coefficient of either

component in a mixture maintained at constant total morality

varies linearly with composition.

Harned and co-workers202 have made numerous EMF

measurements in solutions of two components at constant

ionic strength, and from their results has emerged Harned's

Rule:

logyB = logy~ "B C (2.34)

which states that the change in-logyB rmisvlei a pure

solution of B is linear in molality of the other component.

The Harned slope, aB, is itself a function of ionic strength.

This rule has also been found to be valid for mixtures of

non-symmetrical electrolytes as long as the total ionic

strength is maintained constant. In this case, the decrease

in logy of one component is a function of the ionic strength

fraction, y, of the other component.

HC1 in Seawater

In a mixture such as seawater, composed of many dissolved

electrolytes, one could imagine the decrease in logy of any

single electrolyte to be a function of the respective contri-

butions of the other electrolytes to the total ionic strength.

Macaskill et al.2 have made measurements of the cell:

Pt; H2(g, latm)lHC1(mA), NaC1(mB)]AgC1; Ag (2.35)

where the molalities of the two components were varied while

maintaining a constant total ionic strength. The activity

coefficient of HC1 can be calculated from:

logyHiC1 =-}[E EO/k + logmHC1 Hm~C1 + NaC1)] (2.36)

where Eo is the standard EMF of the cell and k is again writ-

ten for (RT In 10)/F. The study included three ionic strengths,

namely 0.3809, 0.6729, and 0.8720 mol kg-1 of water, corres-

ponding to seawater with salinities of 20, 35, and 450/00

respectively. It was found that Harned's Rule is indeed

valid for these mixtures in the temperature range 5 to 500C.

By casting the Nernst equation in the following form:

E + klogyHC =E 2logHC + 2key aCI (2.37)

= 4+3NaC1

the Harned slope, a, may be evaluated by the method of least-

squares. It is then possible to calculate the trace activity

coefficient of KCl using Harned's Rule:

logyHC = logyHC (ay aC)I (2.38)

The trace activity coefficient, @Cl, can be calculated in

this manner for rKCl when yNaC1 = 1, that is, when NaC1 is the

only solute; it should approximate the yHC which would actu-

ally be measured in a solution of pure NaC1 at ionic strength,

I, containing only a trace of HC1. These calculated values

tr

of YHC1 at the various temperatures and ionic strength agree

closely with the "trace" activity coefficients actually

measured by Khoo et al.2 with 0.01m HC1 in artificial seawater

without sulfate, although they are somewhat higher. From this

it may be deduced that the decrease in YHC1 from YHC1 is

nearly accounted for, in seawater, by the effects of NaC1

alone.

A recipe for "sulfate free" seawater suggested by Khoo

is as follows:

NaC1 = 0.46444m

KC1 = 0.01058m

CaCl2 = 0.01077m

MgC12 = 0.05518m

where m is molality and the ionic strength contribution of

Na2SO4 has been replaced by NaC1. Since KCl and CaC12 are

rather minor components, a simpler recipe could be followed

in which KC1 and CaC12 are replaced by NaC1 and MgC12 respec-

tively such that:

NaC1 = 0.47502m

MgC12 = 0.06595m

The total ionic strength of such a mixture would be 0.67287m

(salinity = 350/00) and the corresponding ionic strength

fractions are yaC 0.706 and y~g1 0.294 such that

Na1 MgC12 = 1. Now for a three component system such as

HC1-NaC1-MgC12 in water, a logical extension of Karned's Rule

might be:

logyHC1 = 10gy Cl "1 NaCll O2 MgC12I (2.39)

where a1 is the Harned slope determined by the Macaskill

study and a2 is that to be determined from a similar study of

the HC1-MgC12 system in a cell identical to 2.35. Equation

2.39 assumes a linear dependence of logyHC on the ionic

tr

strength fractions of either component. Thus (yHCNC/g1

can be calculated for the case where y~laC1 "'MgC12 = 1, that

18.

log~yEC1) = logyO [al(0.706) + a2(0.294)]I (2.40)

These calculated values should agree closely with the values

of (yHCs measured by Khoo if our assumptions are correct

and if NaC1 and MgC12 are the major influence on the decrease

o HC1'

It might also be fruitful to make measurements in a cell

of type 2.35 actually containing all three components in

water, keeping the ratio NaC1/MgC12 constant as it is in our

recipe, and varying only (mNaC1 f MgC1 ) with mHC1 at con-

stant ionic strength. In this case, measurements should yield

values of ar that, when put in equation 2.38 with y = 1, give

tr

values of YHC1 identical to those calculated by 2.40. This

was investigated in the present study.26

CHAPTER 3

CONCEPT OF pH

Theoretical Background

In the preceding chapter we have seen how thermodyn~a-

mics coupled with experimental practice can provide informa-

tion concerning mean activities and activity coefficients of

electrolytes. However, when it becomes necessary to assign

the corresponding values for individual ions one faces a

problem for which there is no direct solution.272 This

problem manifests itself very clearly in the determination

of paH or hydrogen ion activity.92

Recalling cell 2.7, electromotive force measurements

would yield E in terms of the following:

E = EO k log aH C1 Cl (3.1)

It is then possible to write an expression for paH = -log aH

in the following manner:

E EO

paH~ =- + log mCl + log yC1 C3.2)

In order to obtain a thermodynamically sound value for pa ,

a knowledge of yCl would be needed. For a conventional rep-

resentation of this quantity, the Bates-Guggenheim conven-

.30

tion was proposed.

Because of the success of th~e Debye-Kiiekel equation in

fitting activity coefficient data at low ionic strengths,

Bates and Guggenheim proposed that the activity coefficient

of chloride ion be expressed in the following form at ionic

strengths up to 0.1m:

log YC1= 33

The choice of the coefficient 1.5 in the denominator is rea-

sonable in that it assigns yC1 nearly the same value as the

mean activity coefficient, y for NaC1 up to 0.1m. This

"convention" has been instrumental in providing a basis for

the NBS standard scale for the paHl = pH(S) of various dilute

buffer substances. If equation 3.2 is cast as follows:

E -EO

p~HYC1) = + log mCl C3.4)

then a plot of this acidity function, p~affC1), as a function

of mC1 should be approximately linear. This has been carried

out313 for a variety of buffer substances to which chloride

has been added, and at the point of intercept, p~a TC1)o,

equation 3.3 was applied to obtain values of pH(S):

pH(S) = paH = p~aH C1). + log yC1 C3.5)

The need for a pH(S) scale is apparent from the stand-

point that it is often desirable to evaluate pH changes with

precision greater than 0.1 unit. An internally consistent

scale of this sort enables the experimenter to calibrate his

pH measuring equipment at pH values both above and below that

of the sample by proper choice of NBS standards.

Cells With Liquid-Junction

In practice, most pH determinations are made using cells

of the type:

Reference electrodes KCl(M) ISoln XjPt; H2 or glass (3.6)

where the most common reference electrode is the calomel

electrode in either 3.5M or saturated KC1. The double ver-

tical lines indicate a liquid junction between solution X

and the KC1 solution. The cell is first calibrated by employ-

ing a pH standard buffer, S, in place of solution X. For

this solution, pH(S) is known and the potential, Es, between

the hydrogen sensing and the reference electrode is recorded.

A sample solution of unknown pH is introduced into the cell

replacing the standard and a new potential, Ex, is measured.

Ideally, the pH(X) is related to pH(S) and the measured

quantities by:

(Ex E)F

pH(X) = pH(S) RTI s 3.7)

This is the operational definition of pH and provides a

simple way in which to relate the pH of an unknown solution

to the NBS standard scale. Unfortunately, pH(X) values

determined in this manner never fall exactly on the conven-

tional scale because of a residual potential, E., across the

liquid junction (vertical lines in 3.6). This potential is

a complicated function of the activities and transference

numbers of the several ionic species, i, in the boundary

layers of the junction and may be represented by:9

2 .t

-RT i

E = q- E -- dln miY (3.8)

where ti is the transference number for species i and zi is

its charge. An exact evaluation of Ej is not possible with-

out a knowledge of aII which, in turn, is the object of the

calculation. This is a dilemma which can only be resolved

from "outside the realm of thermodynamics."16

The Kenderson method33 of integration of equation 3.8

has been moderately successful in the estimation of the

liquid-junction potential. Henderson assumed that the

junction consists of a continuous series of mixtures of

solutions 1 and 2. The activity of each ion is assumed to

be equal to its concentration, and its mobility is constant

throughout the junction. The concentration of each species

is then given as a function of the concentration in the end

solution and the mixing fraction, a. The transference num-

ber is given in terms of concentrations, c., and mobilities,

q,' as:

ti = n ii 3.9)

al c Cp + (1 ") C ci~i

1 li1

Substitution of 3.9 into 3.8 and integration give:

RT Ciz )(ci ) Z Ci4

E =- In (3.10)

If the ionic mobilities in the two end solutions are taken

equal to the mobilities at infinite dilution then one can

write:

RT CU1 V1) CU2 2) Ul + V1

E. In (3.11)

(U 1) (U2 2) U2 2

In this equation, U is C c 10 and V is E c 10 for the

cations and anions in the end solutions 1 or 2, U and V

are C c I~z [ and C c_A"(z respectively. The term hO is

the limiting ionic conductivity. The concentrations are in

molarity. Equation 3.11 often yields useful estimates of

the magnitude and sign of the liquid-junction potentials and

is used in this work.

ph in Seawater

Seawater is a special type of solvent medium in that

its pH is regulated within narrow limits. Due to the complete

dissociation of the primary electrolyte, NaC1, the ionic

strength is high and seawater possesses the favorable charac-

terstcsofa "constant ionic medium.345 Media of ti

sort can be expected to demonstrate minimal changes in yH

as small changes in chemical composition occur. Furthermore,

if pE standards were available which match the ionic strength

of seawater, residual liquid-junction potentials would be

expected to be minimized. Thus, an experimental scale of pmH

could be set up rendering the possibility of measuring hydro-

gen ion concentration in addition to activity. Bates and

Ma~caskill6 have shown the minor variation in log yHC when

NaCl in sulfate-free seawater is replaced by small quantities

of HCI at constant ionic strength. In addition, it appears

that seawater of 350/00 salinity indeed effectively nulli-

fies the residual liquid-junction potential.

From the Nernst equation one can derive the following

for a cell of type 2.7:

E = EO k log mH Cl 2k log TEC1 (.3.12)

It is useful to alter the standard state such that the

activity coefficient becomes unity at zero molality of KC1

in seawater solvent rather than in pure water.373 This

is accomplished through.the following substitutions in

equation 3.12:

Ea* E. 2k log YHC1; KC1 = HC1 HCI [.3

tr

where YHC1 is the transfer activity coefficient or medium

effect in going from water to seawater and is actually

the trace activity coefficient of HC1 in seawater. This

yields:

E + k log mH Cl = EO* 2k log YKHC1 (3.141

The quantity Ea* may be determined by plotting the left side

of equation 3.14 as a function of mHC1 when small quantities

of HC1 replace NaC1 and extrapolating to m = 0. These types

of plots have been found to be straight lines with the slope

amounting to only 0.04mV at 0.01 mol kg- of added KC1. In

view of this, EO* can be determined routinely with 0.01m HCI

with a reasonable estimate of yHC at this concentration.

By assuming that YHC1 is virtually constant in the seawater

medium when small quantities of buffer substances are added

in place of NaC1, as is the case with the addition of HC1,

one can determine pmH = -log (mH) from dilute buffer solu-

tions in seawater by measurements of cell 2.7 and the

relation:

E Eas

pmH = k + log mCl (3.15)

Measurements of this sort have been carried out2 under these

conditions and point to the practicality of a standard pmH(S)

scale in seawat~er from which values of pmH(X) could be ob-

tained through use of the operational definition:

(Ex -E )F

90H(X) = pmH(S) RT In sO (3.16)

Since nullification of the residual liquid-junction potential

requires a constant ionic medium and matched ionic strength

between the standard buffered seawater and sample, it is of

interest to determine the magnitude of liquid-junction errors

due to salinity variations. This is investigated in the

present study by calibrating a cell of type 3.6 with a buff-

ere sewatr a 30/00 salinity where the value pmHCS) has

been determined.34 Values of pmH(X) can be calculated by

the operational definition from similar measurements above

and below 350/00. These results can be compared with pre-

determined values from cells without liquid junction.

pH in Clinical Media

Measurement of pH in biological fluids is an important

part of clinical diagnosis39,40 and is normally carried out

with a glass electrode assembly in a cell such as 3.6.

Standardization of the cell at a point close to the pH of

the sample is possible by means of the NBS scale. It is

also desirable to match the ionic strength of the standard

buffer to that of the sample to minimize residual liquid-

junction effects. As was previously shown, the NBS standard

buffers are the result of a convention proposed for use at

ionic strengths of 0.1m or below and for that reason are more

dilute than is desirable for clinical work where the ionic

strength is about 0.16m. Attempts41 have been made to es-

tablish primary reference standards at this ionic strength

using a solution of Tris-HC1 (0.05m), Tris (0.01667m), and

NaCl (0.11m); however pH(S) values assigned to this buffer

in the usual manner were found to be inconsistent with. the

NBS scale when compared in cells of type 3.6. Vega and

Bates4 have proposed the use of two substituted ethanesul-

fonic acids for pH control in the physiological range of pH

and at I = 0.16m which are investigated for their usefulness

43

in the present work.

CHAPTER 4

OSMIOTIC COEPTICIENTS

Theoretical Background

The isopiestic method is an important tool for studies

of electrolytes in solution in that it gives a direct meas-

ure of the osmotic coefficient. In making a measurement, a

series of solutions containing the salts of interest are

allowed to equilibrate with a series of solutions of known

vapor pressure at the vapor pressure of water through the

vapor phase. The activity of the solvent is related to the

vapor pressure, p, by the following:

a~~ = p/pa C4.11

where pO is the partial pressure of pure solvent, in this

case, water. Strictly speaking, this relation should be a

ratio of fugacities; however, the correction is nearly iden-

tical for the numerator and denominator and therefore, effec-

tively cancels. When isopiestic vapor equilibrium is at-

tained, aw is the same for all solutions. Recalling equation

1.9, the criterion for isopiestic equilibrium is:

(ummtes = [vm@) (4.2)

This allows one to calculate $ts directly if #re is

known. For this reason, a reference solution for which 4

27

is known is always equilibrated with the test solutions.

For a mixture of two salts, equation 4.2 is simply:

C 1mi + 2m2 ~test = v~ref (4.3)

The success of this method depends on three essential factors

outlined by Sinclair44 and mentioned briefly here:

1) Good thermal conduction between solutions should

be provided in order to ensure solvent transfer

rather than a temperature gradient.

2) Small quantities of solution nearly at isopiestic

equilibrium should be used so that little solvent

need actually distill.

3) Stirring should be sufficient to allow for maximum

diffusion of solute and good heat conduction.

As mentioned in Chapter 1, the osmotic coefficient des-

cribes the non-ideal behavior of the solvent. This non-

ideality is largely due to the interaction of the electrostat-

ic forces of the ions. Therefore, as a first approximation

one can say that # is proportional to the charge density of

the solution. This would imply that two solutions, one of

NaC1 and one of KC1, at the same ionic strength, would have

similar osmotic coefficients, This is not the case, however,

as a 1 molal solution of NaC1 has a (P value of 0.967 while

at the same concentration of KC1, 4 = 0.897. In this sense,

the solvent activity must be controlled by other more specif-

ic forces dependent on the nature of the ions. In general,

one might say that two salts of the same charge type generate

different osmotic coefficients as a consequence of specific-

ities in cation-anion interactions and/or different hydration

characteristics.

Solutions of Single E~lectrolytes

Since the work of Debye and Hiickel1 there have been-

several advances in explaining theoretically the behavior

of electrolytes at appreciable concentrations. However,

only in the last two decades has extensive correlation of

experimental data with theory resulted in useful semi-

empirical treatments.1465

From equation 2.20 for the logarithm of the activity co-

efficient according to Debye and Hiickel, we have, on changing

the symbolism slightly,47,51

S z z |/1

In r, = (4.4)

1 + A/1

where now S = -1.17202 is the Debye limiting slope at 250C,

/z z_/ = Z is the charge factor, and A is the adjustable term

Ba. If this relationship is differentiated, substituted into

equation 1,19, and integrated analytically, the following ex-

pression for the osmotic coefficient, 4, is obtained:

vm@ SZ 1

3 [(1 + A/T) 2 In (1 + A/Y)] C4.5)

I A3I (1 + A/T)

For higher concentrations, where this equation would normally

fail, additional arbitrary terms may be added in higher pow-

ers of ionic strength, such that:

=1+SZ [( /)- 1 -2In1+A/)

I A3I (1 + A/T

+ BI + CI2 + DI3 + EI4 (4.6)

The corresponding equation for the activity coefficient can

be written:

In'y, = +Z (2CB)I + C3/2C)I2 + (4/3D)I3 + (5/4E)I4 (4.7)

1 + A/Y

Equation 4.6 can be applied to osmotic coefficient data for

solutions of single electrolytes and the parameters A through

E evaluated by the method of least-squares. The parameters

are chosen such that the sum squared of $ observed minus O

calculated or ($obs calc)2 is minimized over the ionic

strength range. The parameters can then be tabulated for a

variety of electrolytes. It is possible to employ these data

in Scatchard's neutral-electrolyte treatment for electrolyte

mixtures.50,52 Although this method represents the osmotic

and activity coefficients accurately for many pure electro-

lyte systems, there is little promise of a simple physical

interpretation of the parameters obtained in this way.

Pitzer, on the other hand, has taken a somewhat differ-

ent approach in seeking to use fewer parameters, each of

which retains as much physical meaning as possible. By mod-

ification of the Debye-H~ckel equation in the manner of

Rasaiah and Friedman53,54 and using a three-term power series

expansion, he derives a rigorous expression which relates

the osmotic coefficient to an "electrostatic" term plus a

series of virial coefficients, each of which is a peculiar

and purely theoretical function of ionic strength.46

In these terms, the properties of single electrolyte

solutions take the following forms for an electrolyte hlX:

+ 2 2 X3/2/] C4.8)

where # I A =-0.392

BMX aMX +6 d exp(2

It can be seen that f' is the electrostatic term coming di-

rectly from the Debye-H~ekel theory; it reduces to the limit-

ing slope for osmotic coefficients (-0.392) at low concentra-

tin.The parameter B X represents interactions between

ions of like charge and may be represented by a linear term,

B plus a second term, 8Xep-/) hsfnto a

the property of a rapid change with /Y~ at low ionic strengths

and a smooth approach to a constant value at high ionic

strngts.The third parameter, C X, presents triplet in-

teractions involving two ions of like charge and one of oppo-

site charge and is certain to be small in magnitude. An ex-

pression analogous to equation 4.8 may be written for the

activity coefficient, with appropriate changes in these virial

coefficients:

In yq = z z_ fY + m(2vM YX/v)BhfX 2 m[2(vau )2/V] ChX C4.9)

where

f' = A [/C1/1+ 1.2/71 + (2/1.21~ In (1 +1.2/-1)

B=Bg + 1/I i B (xC)dx

C~ = 3/2CM1X

Thus, osmotic coefficient data fitted to equation 4.8 may be

converted readily into activity coefficient data for the sol-

ute.

Solutions of Mixed E~lectrolytes

In seeking to describe the variation of osmotic coeffi-

cients of mixtures of electrolytes, two noteworthy treat-

ments have been used extensively, namely Scatchard's neutral-

electrolyte505,55 treatment and the equations of

Pitzer.46,58-60

As mentioned above, Scatchard's equations for mixtures

of electrolytes result directly from single electrolyte equa-

tions 4.6 and 4.7 where the Debye-H~ckel theory was extended

using power-series terms in ionic strength. Rearrangement of

Scatchard's general equation for the osmotic coefficient of a

mixture of two 1:1 electrolytes in water yields the following:

29 = 2 AgA + 2m4B B A BI~(b01 + bO2I + b03 2)

+ YA B A BI(bl21 + bl3 2) (4.10)

where 4~ is the osmotic coefficient in the pure single elec-

trolyte solution derived from equation 4.6, y. is the ionic

strength fraction of component j and the terms b.. are

various mixing parameters. Osmotic coefficients obtained

from such mixtures in conjunction with the best-fit param-

et~ers from equation 4.6 may be used to evaluate the mixing

parameters, b.. by the method of least-squares. Correspon-

13

ding equations can also be written for the activity coeffi-

cients of the individual species, which may be calculated

from the appropriate forms when these mixing parameters are

available. Similarly, one can express the osmotic coefficient

for a mixture of 1:1 and 1:2 electrolytes in water by:

(1 + yA)$ = 24~A A BB~ + mixing terms (4.11)

Pitzer's general equation for electrolyte mixtures is

not readily reduced to terms in to and y for the single

electrolytes. For a solution composed of two electrolytes

MX and rMX with a common ion X, with no restriction on charge,

his equation rather takes the form:

4 1 =[2/CmM N m+X) Mm, .CB X + mNm BNX

+ EgmT( IN+ MN MN)+ + z/zM 1/2p~im mCI

+ [zX/zN m11 mXCNx M m~iNm QMNX} (4.12)

where eMN and (IMNX arise from a consideration of additional

interactions among combinations of ions. The term QM

arises from the dependence of 9MN on ionic strength and is

expected to be small. The other terms are identical to those

in equation 4.8 and are determined from data on the single

electrolyte solutions, MX and fJX.

CHABPTER. 5

EXPERIMENTAL

Electromotive Force Measurements

Materials

Purified hydrochloric acid for the EMF measurements was

obtained by distilling reagent grade (FisherZ HC1, retaining

the middle fraction from each of two distillations. The

product was analyzed gravimetrically for chloride by precip-

itation of AgC1 using a standard procedure.6 Results of

analysis indicated 5.63600 mol chloride per kg Cair weight)

of stock solution. A secondary stock (0.186625 mol kg- sol-

ution) was prepared by dilution and this was used in prepara-

tion of the mixtures.

A solution of magnesium chloride was prepared by dissolv-

ing reagent grade (Mallinckrodt) MgC12 61120 in water to

make a solution approximately 1.5 molal. The resulting solu-

tion was analyzed gravimetrically to yield a stock solution

3.04958 mol kg in chloride.

Sodium chloride was purified by twice recrystallizing

reagent grade (MYallinckdrodt) NaC1 from water and drying the

product at 3000C prior to use. Stock solutions were prepared

by weighing the dried solid.

Phosphate buffer solutions for the pH measurements were

prepared from the NBS Standard Reference Materials: KH2PO4,

SRMLI186Ic, and Na2KPO4, SRM1186IIc, The solids were dried

overnight at 1100C prior to use and the solutions prepared

by weighing the dried solids and adding degassed water

according to standard procedure.9

Buffers of N-tris~bydroxymethyl)methyl-2-amincethane

sulfonic acid (TES) and a N-2-hydroxyethylpiperazine-N'-2-

ethanesulfonic acid CKEPES) were prepared from the commercial

solids (Sigma) which had been recrystallized twice from 80%

ethanol-water and dried at 800C in a vacuum desiccator, Each

was then weighed accurately into a glass-stoppered flask to

which was added an appropriate amount of standardized NaOK

solution. Dried NaC1 was then added as necessary to achieve

the desired ionic strength.

Standard carbonate-free sodium hydroxide solution was

prepared by dilution of a 50%6 (wt/wt) NaoH solution with de-

gassed water. It was standardized by titrating with primary

standard grade (NBS SRM84h) potassium acid phthalate.

A buffer solution of tris(hydroxymethyl)aminomethane

(Tris) was prepared from a solution of the primary standard

grade (Sigma) base to which was added standard HC1 solution

and the appropriate amount of NaC1.

Potassium chloride for the synthetic seawater solutions

was reagent grade (Mallinckrodt) which had been recrystal-

lized twice from water and dried overnight at 1200C. Solu-

tions were prepared by weighing the dried solid.

A stock solution of calcium chloride was prepared from

reagent grade (Matheson, Coleman, and Bell) CaC12 2H20 by

dissolving the salt in water to make a solution approximately

2.0m. The solution was analyzed gravimetrically, and the

results indicated 2.73604 mol kg solution.

Sodium sulfate was reagent grade CFisher) anhydrous

Na2SO4 dried at 1200C in vacuo for at least 6 hours. A

stock solution was prepared by weighing the dried solid.

Water used in the preparation of all solutions was de-

ionized in a central building source and redistilled in our

laboratory from an all-glass still, For buffer solutions

the water was degassed either by boiling or bubbling N2.

Hydrogen gas was obtained in a commercial cylinder and

purified by passage over a platinum "De~xo" catalyst prior

to introduction into the cells.

Silver oxide for the preparation of the silver-silver

chloride electrodes was prepared by addition of a solution of

sodium hydroxide to silver nitrate solution as described by

Bates.' The precipitate was washed 30 times with distilled

water,

Platinizing solution for the hydrogen electrodes was

prepared by dissolving 2 grams of hexachloroplatinic acid in

100ml of 2M HC1.

Mercury for the calomel electrode was commercial in-

strument mercury (Bethlehem) triply distilled in continuous

vacuum. The calomel was reagent grade (Fisher) Hg C12.

Preparation of Cell Solutions

All solution mixtures were prepared by weighing and

combining stock solutions containing a known amount of each

substance such that the desired mole ratios were achieved.

The stock solutions were made sufficiently concentrated so

that water was always added as a last step to reach the

desired ionic strength, Weighings were performed on a

Sartorius 5-decimal or a Mettler 3- or 4-decimal balance as

appropriate such that accuracy was always better than 1 part

in ten thousand. Vacuum corrections were made in all weigh-

ings.

For the EC1-MgC12 mixtures, KC1 was weighed into a tared

glass-stoppered erlenmeyer flask and the amount of MgC12

needed to achieve approximate mole fractions of 0.9, 0.7,

0.5, 0.3, and 0,1 in MgC12 was added. One solution of pure

HC1 was prepared at each of the ionic strengths. The quanti-

ties of HC1 stock weighed out initially were such that the

final solutions would weigh about 100 grams. This procedure

was carried out to give solutions at four ionic strengths,

namely 0.1000, 0.3809, 0.6729, and 0,8720 mol kg-1

Three-component mixtures of HC17NaC1-MgC12 were prepared

similarly from HC1 stock and a solution of NaCl and MgC12 of

a fixed molal ratio, NaC1/MgC12 =722 orsltoswr

prepared in which NaCl and MgC12 together contributed frac-

tions of approximately 0.5, 0.3, 0.1, and 0.0 to the total

ionic strength, I = 0.6729 mol kg-

The compositions of th~e buffer solutions used for pK

measurements are given in Table 5. In cases where buffer

and/or the NaCl concentration was varied, the buffer was

appropriately diluted and NaC1 added by weighing the dried

solid.

Synthetic seawater solutions buffered with an equimolal

Tris buffer were prepared at salinities of 40, 35, and 300/0

with three buffer concentrations, 0.06, 0.04, and G.02m, at

each salinity. This was achieved by combination of a concen-

trated seawater stock solution containing less than the de-

sired amount of NaC1, a stock solution of NaC1, and an equi-

molal Tris:Tris-HC1 buffer. The synthetic seawater stock

solution was prepared according to the recipe given by Khoo

et al., such that if all of the required NaC1 had been added

the salinity would have been greater than 450/00. The solu-

tions were prepared by weighing out an aliquot of this sea-

water stock and calculating the amount of water necessary to

dilute it to the desired salinity. Appropriate quantities

of Tris:Tris-HC1 and NaC1 solutions were then added by weight

and finally the mixture diluted with water. It should be

noted that Tris:Tris-HC1 was added at the expense of NaCI to

maintain the proper chloride content.

Preparation of Electrodes

The hydrogen electrodes were made from platinum foil

approximately 1cm2 in area, spot-welded to a platinum wire

sealed in glass tubing. The foil was platinized in a

solution of 2%0 (wt/vol) chloroplatinic acid in 2M1 KCl by

electrolyzing at about 30mA for 5 minutes. Care was taken

such that no bubbles formed at the electrode surface during

electrolysis. The electrodes were stored in distilled water

and cleaned after use by boiling in "aqua regia."

The silver-silver chloride electrodes were of the

thermal-electrolytic type9 and were prepared by thermal

decomposition of a paste of silver oxide and water formed

at the base of the electrode. The base was a helix of No, 26

platinum wire about 2mm in diameter sealed in glass tubing,

The surface of the silver formed was then converted to silver

chloride by electrolysis in 1M HC1. Th.e electrodes were

stored in dilute (0.1m.) NaC1 and, after use, were cleaned by

boiling in concentrated nitric acid. Following preparation,

the electrodes were checked for bias by measuring the EMF of

each electrode versus an arbitrary reference electrode, Any

bias was taken into account in the measurements.

The calomel electrode in the cell with liquid junction

was prepared with 3.5M KC1, A mercury pool about 1cm deep

was formed in the right-hand half cell and was covered with

a 2mm layer of calomel which had been wetted with the KCl

solution. The cell compartment was carefully filled to the

14/20 ground glass joint at the top and a platinum wire

sealed in glass tubing with a 14/20 adaptor was carefully

lowered through the KC1 solution and calomel into the mer-

cury to avoid mixing of the layers. The cell compartment

was completely filled with KC1 solution prior to this step

to exclude all air and create an airtight seal at the joint.

Equipment and Procedures

The cell without liquid junction is shown in Figure Il

and is described by Gary, Bates, and Robinson.6 It is an

all-pyrex cell except for teflon stopcocks. A three-stage

saturation process takes place in the compartments to the

right of the electrodes and insures that no change in solu-

tion composition will occur in the electrode compartments

due to the passage of hydrogen gas.

The cells were first flushed with hydrogen to remove

any traces of oxygen. The solutions, also deaerated and

saturated with hydrogen, were then introduced into the cell

via the y-tube, care taken so as not to introduce oxygen.

The electrodes were then placed into their respective com-

partments. The cells were supported in brass frames and

placed in a water bath; temperature control to +0.(loC in

the range 5 500C was provided. Purified K2 was allowed

to bubble constantly through the saturator over the hydro-

gen electrode and out of the gas trap. The measurements

were shown to be consistent after 2 hours at 250C, at which

time the temperature was lowered. Equilibrium was reattained

rapidly, within 30 minutes, and the next measurement re-

corded. This procedure was followed at 50 intervals to 50C,

and then the temperature was cycled upward to 250C where

Figure 1. EMF cell without liquid junction

the original measurement was checked for reproducibility.

Measurements were then made at 50 intervals to 500C and

back to 250C for a final reading. Cell measurements ob-

tained in this manner demonstrated excellent reproducibility,

within 0.04mV, when EMF's were corrected to standard

1 atmosphere pressure.

The cell with liquid junction is shown in Figure 2. A

calomel electrode was prepared in the right-hand compartment,

and the KC1 solution was constantly renewed. Thse left-hand

compartment was equipped with a gas tube through which pre-

saturated H2 was bubbled over the electrode. The electrode

was seated in a 14/20 ground-glass joint. Gas was allowed

to escape through the gas trap. Solutions that had been

deaerated and saturated with H2 were introduced into the

left-hand compartment followed by the electrode, care being

taken to avoid air. The KC1 solution being the heavier,

formation of the liquid-junction above the 3-way stopcock

was permitted. A water jacket completely surrounded the

cell compartments, and each solution was allowed to ther-

mally equilibrate for 1 to 2 hours. After formation of the

junction, the calomel and hydrogen electrodes were connected

to a digital voltmeter and the EMF recorded when it appeared

stable, usually within 5 minutes. Inasmuch as the EMF was

not always reproducible from day to day, all measurements

were normalized to a fixed value for a phosphate reference

buffer, measurements of which were constantly repeated through-

out the course of the experiments.

Figure 2. EMF cell with liquid junction

L~

I'sopiestic Measulrementss

;Materials

Strontium chloride was purified by twice recrystalliz-

ing reagent grade (Mallinckdrodt) SrC12 from slightly

acidified water. A stock solution was prepared and analyzed

gravimetrically for chloride. The results indicated 1.63068

mol SrC12 per kg solution.

Sodium carbonate CFisherr was heated at 3000C for 24

hours to drive off H20 and was then dissolved in degassed

water to yield 1.65165 mol kg-1 solution.

Sodium chloride for use as the isopiestic reference

was recrystallized twice from water and dried at 300aC.

Solutions were made by weighing the dried solid.

Preparation of Solutions

All solution mixtures were prepared by combining stock

solutions by weight to achieve the desired mole ratios.

The water was previously degassed to minimize sputtering of

the solutions when they were subjected to vacuum. The

NaC1-SrC12 and the NaC1-Na2CO3 mixtures were prepared by

identical methods, with the ionic strength fraction of the

second component, yB, varying from 0.17 to 0.85. The solu-

tion with the highest yB also necessarily had the highest

ionic strength. The exact compositions of the solutions

are given in Tables 10 and 13.

Equipment and Procedures

The apparatus for the isopiestic measurements consists

of a vacuum desiccator containing up to 12 gold-plated sil-

ver cups. The cups, containing 2 to 3 grams of solution,

were seated on a copper block 2.5cm thick to ensure thermal

equilibration. The desiccator was slowly evacuated to a

pressure of about 25 torr, carefully avoiding sputtering of

the solutions. The entire desiccator was then immersed in

a water bath maintained at 25 0.010C and was rocked gently

by mechanical means. Stirring was accomplished by the use

of either glass beads or platinum gause in each cup. Con-

centrated solutions C>lm) required only 3 days to a week to

reach equilibrium, while more dilute solutions would require

up to 2 weeks. Duplicate cups were run, that is, 2 cups for

each solution. At the end of the equilibrating period, the

cups were weighed on a microbalance. Knowing the weight of

the solid in each cup and the weight of the cup, the initial

calculation was a measure of wt. solid/wt. solution from

which the molality of each solution was determined. Equilib-

rium was assumed complete when this result agreed within

0.1% between 2 cups containing identical solutions. Follow-

ing the weighing, the cups were returned to the desiccator

and the amount of water necessary to dilute the solutions

to a lower ionic strength was calculated and added dropwise

with a graduated syringe. The system was then re-evacuated

and the procedure repeated until the desired ionic strength

range.was covered.

CHAPTER. 6

RESULTS

Electromotive Force Measurements

Standard Potential of the Silver-Silver Chloride Electrode

Before analyzing results from EMF Measurements in a

cell of type 2.7, one needs to evaluate the quantity E. in

the Nernst equation, that is, the standard potential of the

silver-silver chloride electrode. It has been discovered

that values of E"gAC determined in different laboratories

lead to varying results, presumably due to variations in

preparative techniques.6 For this reason, routine standard-

ization should be continued, and such determinations have

been made in the present work.

From the Nernst equation describing the EMF of cell

2.7, one can write:

4.605RT

E = EO_ nF (log mHC1 log YHC1) (6.1)

As pointed out in Chapter 2, log YHC1 can be accurately rep-

resented at low concentrations by an equation of the form:

Aml/2

-log YHC1 = 1/2 m (6.2)

where A is the constant of the Debye-Hiickel limiting law for

a particular temperature. Thus, from equation 6.1, one has:

48

E + 2k lg m KC1 ,/A1/2 =EO Sm (6.3)

A plot of the left side of equation 6.3 as a function of m

should give a straight line with an intercept of E*, Bates

64

and Bower h ave tabulated values of Eo at various tempera-

tures based on extrapolations of this sort, only with the in-

clusion of the ion-size parameter which can be varied to give

the best fit of the data. K-aving obtained the best values

for ED, one can then return to equation 6.1 and calculate

values of log yH1 Cons-idering cell 2,7 containing 0.01

mol kg-1 HC1, one may express the standard potential as:

EO = E + 2k log (0.01)yE~ C6.4)

Thus, ED may be calculated over a range of temperatures from

one measurement only at each temperature, with a knowledge

of YKCl at that concentration, Table 1 gives the values of

E and ED obtained from measurements of this sort in the

temperature range 5 to 450C. Values of EO from Bates and

Bower's extrapolations are given for comparison.

Activity C~oefficient of HCI in Seawater

In an attempt to elucidate activity coefficient behavior

of HC1 in saline mixtures aprxmtn ewtr65,66EM

measurements have been carried out in mixtures of HC1-MgCl2

and EC1-NaCl-MgCl2. The sodium and magnesium chlorides, the

major salt components of seawater,6 exert a substantial

influence on the observed behavior.

for the Cell:

Ag

EO (7)

+0,23410

0.23141

0.22857

0.22556

0.22238

0.21907

0,21566

0.21208

0.20836

Table 1. Values of E and EO

Pt; HZIHCICO.01m)lAgC1;

E* (Vr64

+0,23413

0.23142

0,22857

0.22557

0.22234

0.21904

0.21565

0.21208

0.20835

t(oC)

5

10

15

20

25

30

35

40

45

E (7)

+0.45951

0.46091

0.46216

0.46325

0.46417

0.46498

0,46565

0.46615

0.46665

The measurements were made in cells of the type:

Pt; H2Cg, latm) KC1(mA) + MgC12 B)|lAgC1; Ag (6.51

and

Pt; H2(~g, latm) IHC10mA1 + [NaC1/MdgC12](ImB) AgC1; Ag (6 .6)

where mA and mB are respectively the molality of HC1 and the

molality of added MgC12 or the mixture NaC1/MigC12. In the

first case, the ratio of acid to salt was varied while the

total ionic strength was kept constant. The measurements

were carried out in this manner at four ionic strengths,

namely 0.1, 0.3809, 0.6729, and 0.8720 mol kg-1 The three

higher ionic strengths correspond to seawater of salinities

20, 35, and 400/00. In the second series of measurements,

the ternary mixture EC1-NaC1-MgC12 was investigated, where

the ratio of HC1 to total salt was varied at an ionic

strength of I = 0.6729 mol kg-1 (S = 350/00). The molal

ratio of NaC1/MgC12 was always kept constant at 7.202, which

would be the same ratio as in seawater consisting of only

those two salts, All measurements were made at nine temper-

atures, 5 to 45 C. The results of all of the EMT measure-

ments are given in Table 2.

The EC1-MgC12 mixtures have a total ionic strength

given by I = mA + 3mg The ionic strength fraction, yB, of

MgC12 is:

YB = 3mB/1

C6.7)

Table 2. Electromotive Force of Cells of Type 2.7 Containing IICl-MgCl2 Mixtures

and HC1-NaCl-MgCl2 Mixtures From 5 to 450C, in Volts

y9 5"C 10'C 150C 20"C 25"C 30*C 35"C

8 DCI-MgCI2; lonic jLtrengthI 0.1U000 mol kg-1

0.9000 0.41)29 0).42001 0.42063 0.42106 0.42133 0.42140 0.4215)

0.7001 0.39060 0.39082 0.39000 0.39083 0.39060 0.39025 0.38977

0.5000 0.37622 0.37618 0.37600 0.37569 0.37520 0.37459 0.37384

0.3001 0.36618 0.36508 0.36562 0.36512 0.36~44 0.36367 0.36277

0.60931 O,35831 0.35789 0.35747 0.35684 0.35605 0.35511 0.35407

0 0.35499 0.35458 0.35403 0.35334 0.35248 0.35151 0.35040

IlC]-MgCl2: 10nic strength = 0.38109 mol kg

O,9000 0.35856 0.35H33 0.35791 0.35735 0.35664 0.35580 01.35487

0.6999 0.32955 0.32881 0.32787 0.32679 0.32558 0,32426 0.32282

0.a999 0.31486 0.31386 0.31267 O,31133 0.30987 0.80830 0,30660

0.3001 0.30457 0.30339 0.30202 0.30052 0.29889 0.29712 0.29525

0.09983 0.29643 0.29512 0.29361 0.29197 0.20021 0.28833 0.28632

O 0.29289 0.20153 O,28996 0.38826 0.28644 0.28449 0.28242

IlCL-M gC l2: Ilrloo strengthl O,6729 uslul kg-1

0.9000 0.33135 0.93066 0.32'983 0.32t88: 0.32771 0.32650 0.93515

1. 7000 0.30205 0. 300841 01.29049 0.29797 0.29636 0.293464 0,29278

0.4999 0.28702 0.28554 0.283941 0.28213 0.280311 0.27833 0.27622

0.3001 0.27636 0.27472 0.27294 0.27100 0.26897 O,26680 0.26452

0.1001 O,26789 0.26611 O,26420 0.26213 0.25997 0.25767 0.25526

O 0.26122 0.26239 0.260142 0.25826 0. 256038 0.25372 0.25126

HICl-MgCl2: I~loni r;lstrengt 0.720 mol kg~~

0.9000 0.31837 0.:117415 0.316410 0.315~2 0.31393 0.31''35 0.31097

0.7000 0.28884 0.287111 0.28586 0.28410 0.28236 0.28029 0.27840

0.5000 0.27358 0.27190 0.2700 0 O26815 0.26610 0.26376 0.26163

0.2099 0.2G270 0.26086 0.25888 0.25676 0.25451 0.25200 0.24970

0.1001 0.25404 0.25206 0.24094 0.24770 0.24533 0.24269 0.24026

0 0.25027 0.24823 0.24606 0.24375 0.24133 0.23880 0.23616

lICl-NnCl-MlgCl2; lonic atrengthl = 0.6729 mlol kl-1

1. 5000 0.28369 0.28212 0.Z8042 0.27858 0.27(iO0 0.27450 0.27232

0.3000 0.27443 0.27274 0.27089 0.26802 0.26680 0.26458 0.26227

0.09998 0.26734 0.26554 0.20359 0.26140 0.25927 0.25696 0.254154

O O,26427 0.262414 0.20040 0.25834 0.25606 0.25371 0.25125

40*C 45oC

0.42132

0.38918

0.37300

0.36174

0.35291

0.34918

0.35380

0.32124

0.30478

0.29325

0.28420

0.2802

0.32370

0.29)082

0.27400

0.26213

0.25274

0.24869

0.30932

0.27625

0.25922

0."4713

0.23754

0.23340

0.27004

0.25084

0.25200

0.24867

0.42113

0.38844

0.37201

0.36057

0.35161

0.34785

0.35263

0.319541

0.30283

0.29113

0.28195

0.27792

0.32211

0.288741

0.27168

0.25964

0.25012

0.246i02

0.30756i

0.293397

O,25670

0.24444

0.23472

0.23055

0.2676i3

0.25727

0.24934

0.24596

Thus, both mA and mg can be calculated from the values of

I and yg given in Table 2. For the ternary mixtures where

mNaC1 = 7,202mMgC12, the total ionic strength is given by:

I = mA + 1.2348mB C6.8)

where yA = 1.2348mB/I (6.9)

Mean ionic activity coefficients of HC1, yA, in the pres-

ence of MgC12 are easily calculated from the Nernst equation

expressed in terms of y :

log yA YE--k 0.5 log (1 YB)(1 B/3)I2 (6.10)

and for the ternary mixtures:

log yA YE - 0.5 log (1 yB)(1 0.09802yB)I2 (6.11)

Just as in equation 2.37, the Harned slope may be calculated

by the method of least-squares for any given values of I and

YB. With modification for HC1-MgC12, the equation takes the

form:

E + k log (1 yB)(1 yB/3) = EO 2k log lY.A + 2keyB

= A + ByB (6.12)

where A and B are determined by linear regression analysis.

For the ternary mixture, equation 6.12 takes the form:

E + k log (1 YB)(1 0.09802yB) = A + Byg (6.13)

The results for a C=B/2kl) and log yoA are given in Table 3,

along with the standard deviations of fit at each temperature

and ionic strength. Values of the temperature variation of

ar, dcr/dT, are given at the foot of Table 3.

Table 3, 2Values of -log y ~and the H~arnedl Coefficient (cL) for the Systems

H~lMg12and HCl-NaC MgC12 as a Function of Ionic Strength at 5 to 450C

HC1-MgCl2

I = 0.6729

--log yOA

0.1005 0.0509

O,1032 0.0498

O,1060 0.0489

0.1087 O,0479

0.1123 0.0462

0.1155 0.0456

0,1186 O,0443

0.1220 0.0434

0.1257 0.0418

HICl-MgC12

I = O,1

TOC _log_ yO c

HC1-MgCl2

I = 0.3809

u 104s

104sa

104s

-lg yoA

0.1132

O,1156

0.1174

0.1195

0.1220

0.1245

O,1266

O,1291

0.1316

0.0948

0.0956

0.0968

0.0980

0.0993

0.1005

O,1015

O,1030

0,1044

O,0569

0.0576

0.0550

0.0519

0.0493

0.0483

0.0456

0,0375

0.0362

0.0503

O,0492

0.0483

O,0472

0.0456

O,0441

0,0432

0.0416

0.0408

=-0,000552

-0.000247

-0.000224

s = standard deviation for regression.

Table 3 extended

HC1-MgC12

I = 0.8720

ogIs a~ c

HCl-NaCl-MgC12

I = 0.6729

104s

4

4

4

5

4

9

5

5

5

ac 104s

0.0428 3

0.0406 3

0.0389 3

0.03841 7

0.0362 3

0.0338 2

0.0324 2

0.0314 2

0.0303 3

-log y

0.1012

0.1040

0.1066

0.1091

0.1124

0.1157

0.1188

0.1222

0.1256

0.0865

0.0898

0.0930

0.0965

0.1002

0.1033

0.1076

0.1115

0.1156

0.0504

0.0492

0.0481

0.0468

0.0462

0.0441

0.0439

0.04230

0.0418

-0.000214

-0.000317

pK Standardization in Seawater

In an attempt to estimate the magnitude of liquid-

junction errors inherent in pH measurement in seawater of

varying salinity, measurements in a cell with liquid junction

have been carried out in buffered artificial seawater at

salinities of 30, 35, and 450/00, each containing Tris buffer

at molalities of 0.02, 0.04, and 0.06.

The results of these measurements were treated in two

ways, using the operational definition of pK Cequation 3.161.

First, values of pmHC~r were calculated where Es an~d pm CSI

referred to the 350/00 = 5, 0.04m Tris solution, Values of

pm (S) were obtained from Ramette et al.3 In the second

case, pHNBS was calculated by referencing Ex to the Es and

pH(SZ values for the NBS 1;3,5 phosphate buffer. The results

from these measurements and calculations are given in Table 4.

pH Standardization in Clinical Media

Attempts to establish a primary reference standard for

the measurement of pH near 7.4 at an ionic strength of 0.16,

corresponding to blood plasma and other clinical media,

have met with difficulty, Ideally, one would like to have

a standard with pH at or near that of the sample. Further-

more, the ionic strength of the standard should match that

of the sample. Although buffers have been proposed which

meet these requirements,416 they have been shown to be in-

consistent with the NBS primary scale, that is, the pK

values assigned based on measurements in cells without liquid

Table 4. Comparison of pmH(X) and pHNBS Obtained by EiMF

Measurements of the Cell Hg; Hg2Cl2, 3.5m KC1I1Soln.

S or X H2 (g, latm); Pt at 250C With Corresponding

pm (S) Values.

S(0/00)

ReHS)34

8.185

8.185

8.187

8.198

8.201

8.201

8.216

8.217

8.220

Soln. X or S

-ECVI a (XJ HNS

0.73473 8.190 8.198

0.73506 8.195 8.203

0.73494 8.193 8.202

0.73515 8.197 8.205

0.73538 8.201 8.209

0.73522 8.198 8.206

0.73552 8.203 8.211

0.73563 8.205 8.213

0.73563 8.205 8.213

sw + 0.02m

sw + 0.04m

sw + 0.06m

sw + 0.02m

sw + 0.04m

sw +0.06m

sw + 0.02m

sw + 0.04m

sw + 0.06m

Tris

Tris

Tris

Tris

Tris

Tris

Tris

Tris

Tris

1:3.5 Phosphate

I = 0.1m 0.68841 (pH(S) = 7.415)

junction do not agree with the pK values determined by

measurements in cells with liquid junction and the opera-

tional definition (equation 3.7). Pursuant to this problem,

extensive measurements involving the buffers of TES, HEPES,

and Tris have been carried out in conjunction with the NBS

1:3,5 phosphate "blood buffer" in an effort to reveal the

causes of the discrepancies.43 Factors investigated were

a) the possible failure of the convention for log yC1 at

ionic strengths above 0,1m, and b) the appreciable residual

liquid-junction potential when the relatively dilute NBS

reference solutions are replaced by buffers at I = 0.16m.

Measurements have been made in cells without liquid

junction to determine the EMF for solutions of the NBS

phosphate "blood buffer" containing 0.01, 0.02, 0.04, and

0.06 mol kg-1 NaC1 as an independent check on the value of

pHCS). The solution with the highest concentration of NaC1

(0.06m) corresponds to an ionic strength of 0,16 mol kg-1

Figure 3 is a plot of plaH C1) from equation 3.4 as a func-

tion of molality of NaC1 added at 25 and 37*C. The inter-

cepts, p~aH C1)o at mCl = 0, found by linear regression anal-

ysis, were 7.520 and 7.499 at 25 and 370C, respectively,

with a mean deviation slightly greater than 0.001. Intro-

duction of the pH convention to equation 3.5 gave values of

pH(S) of 7.411 and 7,387 at the two temperatures; these com-

pare well with the NBS assigned values. Table 5 gives the

results of these and similar measurements involving the TES,

KIEPES, and Tris buffers and the phosphate buffer, where its

contribution to the total ionic strength was varied by ad-

justing the phosphate-NaC1 ratio. All solutions contained

enough NaCl to bring the ionic strength to 0.16 mol kg-1

Assuming the pH convention is valid at this ionic strength

(above its intended limit of 0.1ml, pH(S1 values were as-

signed to these buffer solutions based on equation 3,4,

They are listed in Table 5 with the corresponding EM~F's and

temperatures.

Measurements in a cell with liquid junction have been

carried out on the same solutions, and these results are

listed in Table 6. The pH values listed here were calculated

from the EMF values and equation 3.7T, referenced to the EMF

of the dilute phosphate buffer and its assigned pKCS). value.

The values of pHCX1 calculated In this manner differ appre-

ciably from those assigned by the conventional approach.

Both sets of values are summarized for the TES, KEPES, and

Tris buffers in the second and last columns of Table 7, It

is discrepancies of this sort that have led others296 to

postulate that a residual liquid-junction potential exists

between dilute and higher ionic strength buffers when meas-

ured in cells with liquid junction.

Figure 3. Plot of p(aH C1) for the NBS phosphate "blood

buffer" as a function of molality of added NaCl

CI

O

r

r

u

Morality of NaCl

Table 5. Electromotive Force of Cells of Type 2.7: Pt; H2(g, latm))Buffer Soln.l

AgCl; Ag, at 25 and 37 C, in Volts

buffer, ionic

phosphate

phosphate

phosphate

phosphate

phosphate

phosphate

0.02 TES

0.04 NaTE~S

0.04 TES

0.04 NaTES

0.02 HEPES

0.04 NalIEPES

0.05 Tris-HIC1

0.01667 Tris

strength, I

0.1

O.1

0.1

0.08

0.06

0.04

0.04

NaCl I

0.02

0.04

0.06

0.08

0.10

0.12

0.12

E25

0.76675

0.74775

0.73644

0.72860

0.72232

0.71723

0.74340

0.72560

0.74619

0.73529

pH1(S), 250C

7.385

7.360

7.339

7.331

7.323

7.315

7.758

7.457

7.805

7.746

E-37

0.77917

0.75945

0.74768

0.73950

0.73295

0.72769

0.74276

0.72429

0.75051

0.72849

pH(S), 370C

7.360

7.334

7.314

7.306

7.297

7.290

7.535

7.235

7.661

7.427

0.04

0.04

0.05

0.12

0.12

0.'11

EO = 0.22242

EO = 0.21440

,

buffer, ionic

phshte

phosphate

phosphate

phosphate

phosphate

phosphate

phosphate

0.02 TES

0.04 NaTES

0.04 TES

0.04 NaTES

0.02 HEPES

0.04 NaHEPES

0.05 Tris-HICI

0.1667 Tris

Hg2C12, 3.5M KC1I Buffer

Table 6. Electromotive Force of Cells of Type 3.6: Hg

SolnIH2 (g, latm), P-t, at 25 and 370C, in Volts

strength

0.1a

0.1

0.1

0.1

0.08

0.06

0.04

0.04

NaC1, I

0

0.02

0.04

0.06

0.08

0.10

0.12

0.12

PH, 250C

(7.411)b

7.308

7.294

7.281

7.265

7.714

7.414

-25

0.6885

0.68242

0.68159

0.68082

0.67988

0.70644

0.68869

-E37

0.6999

0.69779

0.69588

0.69397

0.69324

0.69250

0.69151

0 .70702

pHI, 370C

(7.387)b

7.353

7.322

7.291

7.279

7.267

7.251

7.503

0.04

0.04

0.05

0.12

0.12

0.11

0.68862 7.204

0.71490 7.631

0.70939 7.764

0.70472

7.685

0.69951

7.381

" Each phosphate buffer was composed of KH2O and Na2HO in the mole ratio 1:3.5.

b

Reference values.

Respective contributions of

Table 7. Operational pH Values Calculated by Equation 3.7 from the EMF of Cell 3.6

vs. Phosphate-Chloride Standard Reference Solutions at 25 and 370C

standard reference solution

NBS 0.1P + O.1P + 0.1P + 0.08P + 0.06P +

0.1Pa 0.02NaC1 0.04NaC1 0.06NaCl 0.08NaCl 0.10NaC1

25aC

7.714 7.745 7.751 7.756

7.414 7.445 7.451 7.456

7.764 7.795 7.801 7.806

7.685 7.716 7,722 7.727

37oC

7.503 7.510 7.515 7.526 7.530 7.533

7.204 7.211 7.216 7.227 7.231 7.234

7.631 7.638 7.643 7.654 7.658 7.661

7.381 7.388 7.393 7.404 7.408 7.411

buffer solution

TES,0.04 NaTES,0.12 NaCL

TES, 0.04 NaTES,0.12 NaC1

HEPES, 0.04 NaHEPES, 0.12 NaC1

Tris-HICL O.01667 Tris,0.11 NaC1

TES,O0.04 NaTES, 0. 12 NaC1

TES,0.04 NaTES,0.12 NaC1

HIEPES, 0.04 NaHEPES,0.12 NaCl

Tris-HCL, O.01667 Tris,0.11 NaCl

0.02

0.04

0.02

0.05

0.02

0.04

0.02

0.05

P = Phosphate buffer (1:3.5); the numbers indicate the

phosphate buffer and NaC1 to the total ionic strength.

Table 7 extended

0.04P +

0.12NaC1 pHI(S)

7.764

7.464

7. 814

7.735

7.542

7.243

7.670

7.420

7.758

7.457

7. 805

7.746

7.535

7.235

7.661

7.427

Isopiestic Measurements

NaC1-SrC12 Mixtures

Of the aqueous systems MIX-NX2, where Md = Na, K, and

N = Mg, Ca, Sr, Ba, only the system NaCl-SrCl2 has not been

studied by the isopiestic technique. Thermodynamic proper-

ties of this system are of interest to the chemical ocean-

ographer, since both components are present in seawater.

The literature values for the osmotic coefficients of

strontium chloride in water are based upon the results of

two isopiestic studies, one using KC17 and the other CaC127

as isopiestic reference. Downes72 has drawn attention to the

poor agreement between values derived from these studies and

has made measurements using KC1 as a reference. Measurements

have been made in this laboratory73 using NaCl as a reference

up to about 3 mol kg-1 these are in excellent agreement with

Downes" results. Comparison of the literature values with

those from the present study are given in Table 8.

Data for the single electrolytes, NaC1 and SrCl2, have

been fitted to equations 4.6 and 4.8, and the best-fit param-

eters have been obtained.74 These parameters, listed in

Table 9, were used in fitting the data on the mixtures. The

compositions of the mixtures in isopiestic equilibrium are

given in Table 10, along with the molalities of the NaCl

reference solutions, and the osmotic coefficients calculated

from equation 4.3. Osmotic coefficients for the NaC1 refer-

ence solutions were obtained from the tables of Robinson and

Stokres.B

The osmotic coefficients of the mixtures were fitted to

the Scatchard neutral-"electrolyte treatment (equation 4.11);

the best-fit parameters and standard deviatcions a- (4) are

given in Table 11. The computer program allows the inclusion

of any or all parameters at the choice of the operator. This

enables one to see the significance each parameter has on

the standard deviation of fit.

The same procedure has been applied to the Pitzer treat-

ment (equation 4.12), and the results are given in Table 11.

It can readily be seen that the Pitzer treatment for the

single electrolytes is far superior to that of Scatchard,

in that these equations alone fit the data for the mixtures

with a standard deviation a C4) = 0.002 without the inclusion

of any mixing parameters, while the Scatchard treatment re-

quires at least one mixing parameter.

Natl.-Na2CO3 Mixtures

The carbonate system in seawater is important from the

standpoint of acid-base processes which influence the pH and

buffering capacity of this medium as well as the solubility

of marine carbonates. It is of interest to investigate the

mixtures NaC1-Na2CO3 at various compositions and ionic

strengths to elucidate osmotic coefficient behavior and

obtain thermodynamic information based on interactions of

these electrolytes.

Data for the single electrolytes have been obtained,75

and the useful parameters for treatment of the mixtures are

given in Table 12 along with the standard deviations of fit.

The isopiestic molalities and osmotic coefficients of the

mixtures are listed in Table 13. Blanks in the ta'ole are

where data were not included due to poor precision between

duplicate cups. Results of fitting the mixtures to the

Scatchard and Pitzer treatments are given in Table 14.

Table 8. Osmotic Coefficients in Aqueous SrC12 Solutions

at 250C; Comparison of Results

4 (KC1 ref.)70 O (CaC12 ref.271

4

0.850

0.854

0,864

0,880

0.899

0,918

0.937

0.959

0,983

1.009

1.061

1.116

1.173

1.232

1.292

1.454

1.631

1.802

1.966

$ Ol~aC1 ret.2a

0,8487

0.8501

0.8815

0,8768

0.8946

0,9140

0.9349

0.9570

0.9802

1.OO45

1,0558

1,1104

1.1674

1.2281

1.2905

1,4551L

1.6300

1,8010

1.9669

2.0302

m8rC12

0.1

0.2

0.3

0.4

0.5

0.6 .

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

2.5

3.0

3.5

0.8494

0,8491

0.8590

0.8734

0.8906

0.9097

0,9303

0.9520

0.9746

0.9978

1.0460

1.0953

1.1460

1.1982

1.2530

0,8490

0.8514

0.8636

0.8797

0.8979

0.9177

0,9388

0.96~11

0.9843

1.0086

1.0598

1.1144

1.1718

1.2320

1.2944

1.4585

1.6294

1.8009

1.9669

2.0302

SPresent work.

Table 9. Parameters for Eqs. 4.6 and 4.8 Used in the

Treatment of NaC1-SrC12 20 M~ixtures

Parameters for Ea. 4.6

S =-1,17202

NaCla SrCl b

1,4635 1,60~1

0.041340 0,031312

0.020830 0.0095259

-0.0016130 -0.00051960

0.000043460 0,000013640

6,0 9.0

0,0004 0.0012

Paramet rs for Eq. 4.8

AL = -01392

NaC1c Sr~C1 b

0.07669 0.28994

0,26461 1.5795

0.0012193 -0.003755

6.0 6.0

0.0007 0.0017

A

B

C

D

E

I Cmax. )

aC4)

CO)

UC)

I Cmax.)

&[4)

a

Parameters taken from ref. 74.

b

Combined fit to results of

/Table 8).

ref, 72 and-present work

SParameters obtained by fitting smoothed values of 4NC

from ref. 4. NC

Table 10. Compositions and (Osmotic Coefficients) of

System NaCl(A) SrC12(D 120

S= 0.0 0.1722 0.3528 0.5259

Isopiestic Solutions in the

0.6717

0.8291

I =0.6035

0.9757

1.4578

2.0146

2.4670

2.7057

3.0150

3.3386

3.6711

43.0015

0.6633(0.9189)

1.0698(0.9328)

1.5915(0.9565)

2.1882(0.9914)

2.6716(1.0215)

2.9231(1.0392)

3.2524(1.0613)

3.5934(1.0860)

3.9453(1.1117)

4.2946(1.1377)

0.7419(0.9119)

1.1890(0.9313)

1.7586(0.9605)

2.4037(1.0015)

2.9217(1.0365)

3.1938(1.0554)

3.5442(1.0807)

3.9076(1.1082)

4.2820(1.1366)

4.6517(1.1655)

0.8336(0.9067)

1.3299(0.9304)

1.9543(0.9658)

2.6563(1.0127)

3.2127(1.0533)

3.5033(1.0752)

3.8774(1.1039)

4.2646(1.1347)

4.6630(1.1663)

5.0533(1.1989)

0.9320(0.8999)

1.4784(0.9288)

2.1577(O,9708)

2.9115(1.0254)

3.5052(1.0714)

3.8141(1.0959)

4.2092(1.1285)

4.6174(1.1630)

5.0355(1.1986)

5.4447(1.2349)

1.0671(0.8917)

1.6788(0.9279)

2.4283(0.9786)

3.2476(1.0428)

3.8872(1.0959)

4.2170(1.1245)

4.6382(1.1617)

5.0699(1.2016)

5.5097(1.2427)

5.9396(1.2841)

Table 11. Best-Fit Mixing Parameters for the System

NaC1(A) SrC12(B) H20

1. Scatchard neutral-electrolyte treatment

-01 -02 -03 bl2 13

-0.0050

0.0096 -- 0.0017

0.0212 -0.00274 0.0011

0.0235 -0.00402 0.00016 0.0011

0.0243 -0.0038 -0.0014 0.0005

0.0178 0.00023 -0.00054 -0.00037 -0.00027 0.0005

2. Pitzer treatment

-3la,Sr --~a,Sr ~Na,Sr,C1 0( ).

- -0.0021

0.0036 0.0017

-0.0096 0.0031 -0.0014

-0.0084 -0.0036 0.0015

-0.0076 0.0068 -0.0052 0.0013

Table 12. Parameters for Eq. 4.6 and 4.8 Used in the

Treatment of NaC1-Na2CO3-h20 Mixtures

Parameters for Eq. 4.6

S =-1.17202

NaCla Na C

1.4226

-0.065322

0.0084332

-0.00028700

0.0000018700

9.0

0.0020

A

B

C

D

E

I(max)

aS)

1.4635

0.041340

0.020830

-0.0016130

0.000043460

6.0

0.0004

Na2COd

0.040822

1.4679

0.0042374

9.0

0.0020

Parameters for Eq. 4.8

A~ = -0.392

NaC1c

8(0)

B(1)

C

I(max)

oC()

0.076690

0.026461

0.0012193

6.0

0.0007

aParameters taken from ref. 74.

Parameters obtained by fitting smoothed values of $Na C

from ref, 75. 2 03

c Parameters obtained by fitting smoothed values of #NaC1

from ref. 4.

d

Parameters taken from ref. 75.

Table 13. Compositions and (Osmotic Coefficients) of Isopiestic Solutions in the

System NaC1(A) Na2CO3(B) H20

S= 0.0 0~.1713 O,3500 0.5371 0,6996 O,8518

I = 0.2936

0.3081

0.9202

1.3451

2,0026

2.0985

2.3039

2.4158

0.3223(0,9182)

1,0470(0.9056)

1.5113(0.0238)

2.2562(0.9547)

2.3657(0.9594)

2.5986(0.9706)

2.7270(0.0764)

0.3656(0,8971)

0.4983(0,8912)

1,2002(0.8756)

1,7404(0.8890)

2,6073(0.9156)

2.7338(0.9202)

3,0031(0.9308)

3,1576(O,9346)

O,4273(O,8659)

O,5845(0.8570)

1.4192(0.8351)

2.0716(O,8424)

3,1197(O,8631)

3.2708(O,8675

3,5942(0.8772)

3.7852(0,8793)

0.4978(0.8362)

O,6837(O,8243)

1.6015(0,7883)

3.9464(O,8083)a

4,3412(0.8166)

4.5809(O,8174)

0.5872(0.8028)

O,8111(0.7868)

2.0590(O,7334)

3,0705(0.7242)

4.6840(O,7324)

4.9021(0,7357)b

5.3943(O,.7429)b

5.6896(0.7454)

a B is actually 0,6988,

b

yB is actually 0.8490,

Table 14, Best-Fit Mixing Parameters for the System

NaC1(A) Na2CO3(B) H20

1. Scatchard neutral-electrolyte treatment

401 4-2 b-03 12 bl3

-0.047

S0.0081

-0.0081

S0.0073

-0.0047

0,001723 0.0047

-0.1099

-0.09562

-0.1744

-0.1654

-0.136

-0.00366

0.04240

0.01971

-0.0243

-0.00619 -

~0,01802

0.003921 0.01478

2. Pitzer treatment

e e' d

-Na, Sr '-\a, Sr ~Na,Sr, C1

o(d6)

0.030

0.012

0.010

0.0047

0.0047

-0.0495

-0.08981

-0.1605

-0.1607

0.01031

~0.05030

-0.002544 0.05488

CHAPTER 7

DISCUSSION

Electromotive Force Measuremients

Activity Coefficient of HC1 in Seawater

For the HC1-MgC12 system, two values of the Harned

slope, a, at I = 0.1 mol kg-1 and 250C have been reported

previously. That of Downes,6 based on measurements made

by Smith,77 is 0.0521, while Khoo et al,78 found a = 0.0326.

This is a rather large discrepancy. The value obtained

from this work, a = 0.0493, tends to support the value

reported by Downes.

The primary purpose of this study was to derive values

of al at ionic strengths corresponding to those-of seawater

of salinities 20, 35, and 450/00, and thus to elucidate

the behavior of activity coefficients in solutions resem-

bling seawater. It is also of interest to evaluate the

trace activity coefficient of HC1 in the mixtures and com-

pare it to earlier measurements. This has been done in

two ways. First, values of a obtained from the present

work involving HC1-MgC12 (Table 3) were combined with

those of an earlier study of ECl-NaC1, weighting the two

in accord with the relative contributions of the two salts

to the total ionic strength of a seawater solution con-

taining only those two salts (equation 2.40). In another

approach, YHC1 was calculated from the Harned slope ob-

tained from HC1-NaC1-MgC12 mixtures at I = 0.6729 CTable

3), treating NaC1 + MgC12 as one component (equation 2.38),

where y is the ionic strength contribution of the two salts

to the total ionic strength. In Table 15, the values of

tr

YHC1 obtained in these two ways are compared with the

values obtained by Khoo et al. from EMF measurements of

0.01m HC1 in synthetic seawater. Although sulfate was

omitted, the salt mixture used in the latter study approached

closely the composition of natural seawater, being composed

of NJaC1, MgC12, CaC12, and KC1 in the correct proportions.

tr

An examination of the table shows that YKC derived from

the Harned rule, using a measured for HC1 in the salt mix-

ture composed of both NaC1 and MgC12, agrees well with that

calculated by equation 2.40 from the individual values of

a from the KC1-NaC1 and HC1-MgC12 systems. Furthermore,

tr

it is evident that THC is nearly the same in a mixture of

the two salts as in a mixture of the same ionic strength

but containing the four salts predominant in seawater, The

average difference at the nine temperatures is less than

0.001; for a solution of NaC1 alone (I = 0.6729 mol kg-1~

tr

YHC1 differs from that in seawater on the average by about

0.006. Thus, the drop in YHC1 from pure HC1 to seawater is

accounted for by the effect of the two major salts, NaC1

and MlgC12'

Table 15. Comparison of the Trace Activity Coefficient of

HCI (y r) in NaC1-MgC12 Mixtures With That Determined

Experimentally in Synthetic Seawater (sw)

I = O8720

S = 450/00)

Eq, 2.40 sw

0.752 0.752

0.747 0.748

0.747 0.745

0.744 0.741

0.739 0,738

0.737 0.734

0,731 0.730

0.726 0.726

0.722 0.722

I =0.3809

CS = 200/00)

It _* Eq. 2.40a sb

I =

CS =

Eq. 2,40

0.741

0.739

0.736

0.734

0,730

0.726

0,722

0.718

0.713

0.6729

350/00)

Eq. 2.38c sw

0.741 0.741

0,739 0.738

0.736 0.735

0,733 0.732

0.730 0.729

0,727 0.725

0.723 0.722

0.719 0.718

0.714 0.714

5

10

15

20

25

30

35

40

45

0.740

0.738

0.739

0.733

0.730

0.727

0.725

0.722

0.718

0.740

0.738

0.739

0.737

0.733

0.730

0.728

0.726

0.722

a Calculated by Eq. 2,40

(reference 24) and for

from a values for HC1-NaC1 mixtures

HIC1-MgCl2 mixtures [present work).

From experimental data, reference 25,

c Calculated by Eq. 2.38 from a for KC1-NaCl-MdgC12 mixtures,

YNaC1/MgC12 = 1.

In this respect, it is of interest to consider the

results in light of Pitzer's recent treatment concerning

electrolyte mixtures. The data for HCI in mixtures of NaC1

and MgCl2 have been fitted to the Pitzer equation Cequation

4.12) in an attempt to estimate the pertinent mixing terms.

The parameters B and 66 for the single electrolytes

wpere taken from Pitzer s tabulated values.48 Strictly,

the CX terms should have been included. K-owever, they

were unavailable and were taken to be zero. The best-fit

values of interaction terms 9MN' 9.N, and $31NXi were derived

by curve-fitting. The results are summarized in Table 16.

It is evident from the standard deviations given in the

last column that the properties of the mixtures are not

well accommodated by 6(0 and 6(1 for the idvda

electrolytes alone. Inclusion of the cation-cation mixing

term, 6i, produces considerable improvement. The parameter,

6', which represents a dependence of 9 on ionic strength,

appears to be of little importance in fitting the data.

The ternary interaction term, 9, produces some improvement;

however, its inclusion would result in a term quadratic in

y~C2in Pitzer's equation for the activity coefficients

in the mixture. Since the data obey Harned's rule without

such a term, the necessity of Jl is questionable.

The Harned slope appears to be linearly dependent on

temperature, as shown by the slope da/dT given at the foot

of Table 15, Since -aygI = 10g (YHC1 THC1), the quantity

Table 16, Mixing Parameters

System KC1-MgC12 20O

(Pitzer Treatment) for the

0 1039 a

-I, Mg, C1

30.9

8

-K,Mg

-0.2904

-0.3430

-0.4357

-0.4651

O'

-HMg

0.2728

-0.1401

0,3843

0.5337

aStandard deviation of log y ,

da/dT may be related to the difference in partial molal

heat content of HC1 in its pure solution and in a mixture

with MgC12 by the equation:

-460RT I(da/dT) = 2RT2d In(HC1 HC1

dT

=HCr( MgC12 = 0) EC1( gC12)

(7.1)

Thus, the partial molal enthalpy appears to be linearly

dependent on yB, and in this respect an analog of Harned's

rule exists, at least for 50C < T < 450C and 0.1 < I < 0.9.

pH Standardization in Seawater

Comparison of results (Table 4) for pmR(X) obtained by

the operational definition with pmH(S) values calculated from

equation 3.15 shows that a discrepancy does exist when salin-

ity is varied. At a salinity of 300/00, for example, this

amounts to an average of 0.007 pH unit higher for the pmH(X)

values, while at S = 400/00, the operational values are, on

the average, 0.013 pH unit lower than the corresponding

pm I(S) values. Within a given salinity, however, pm (X)

values are essentially identical regardless of the Tris

buffer concentration, indicating a stabilization of the

residual liquid-junction potential by the seawater medium.

It is interesting to note that when the operational

definition is employed using Ex with Es and pH(S) of the NBS

1:3.5 phosphate buffer, the resulting pHNBS values are very

close (0.007 pH unit on the average) to the corresponding

pmH(S) values, even though there is a large difference in

ionic strength between the seawater solutions and the dilute

(I = 0.1m) phosphate buffer.

Since pH(X) differs from pH(S) (= -log mH H) by the

liquid-junction term, E /k, the relationship between pHNBS

and pmH(S) can be written as:

pmH(S) = pHNBS + log YH + E /k (7.2)

The close agreement between pHNBS and pm (S) must then be

attributed to a cancellation of the liquid-junction poten-

tial and activity coefficient terms. Robinson and Bates

have recently estimated TC = 0.639 in seawater of 350/00

salinity, based on an hydration number method developed

earler.7 UingTHC= 0.729 at 250C, one obtains083 o

YH H=Y;Cl/Cl). Using this value in equation 7.2 with

pmH(S) pHNES = -0.007 at 350/00 salinity, the residual

liquid-Junction potential is estimated to be about 4.3mV.

pH Standardization in Clinical Media

As pointed out in Chapter 6, discrepancies between

column 2 and the last column of Table 7 are thought to arise

as the result of an appreciable residual liquid-junction

potential caused by the difference in ionic strength between

the relatively dilute NBS phosphate "blood buffer" and the

higher ionic strength (I = 0.16m) Tris, HEPES, and TES

buffers.

The pH(S) values obtained for the phosphate buffer +

NaC1 by measurements in a cell without liquid junction in all

likelihood lie close to the NBS standard scale, based on the

same pH convention. The reasoning is as follows.

Calculations from equation 3.3 for the logarithm of the

activity coefficient of chloride ion at 250C give -0.110 at

I = 0.01m and -0.128 at I = 0.16m. These values are nearly

the same as the logarithm of the mean activity coefficient

(log y ) of NaC1 at I = 0.1m (-0.109) and at I = 0.16m

(-0.126). At 370C, log TC1 is -0.130 at I = 0.16m, while

log y, is -0.128. Furthermore, the hydration convention79

yields -0.130 for log TC1 in a solution of NaCl of molality

0.16 mol kg-l

One expects that log y, and log yC1 will vary linearly

as phosphate is added to a solution of NaCl maintaining a

constant ionic strength.5 To estimate the magnitude of

this change, the sodium glass electrode was employed in a

cell of the type:

NalSEIPhosphate buffer + NaCl AgC1, Ag (7.3)

and the following EM1F data were obtained:

ionic strength E(V)

phosphate NaC1 250C 370C

0 0.16 0.0432 0.0465

0.04 0.12 0.0540 0.0574

0.10 0.06 0.0767 0.0814

The standard potential of cell 7.3 was derived knowing

log y, in the 0.16m NaCl solution, and the activity coeffi-

cients in the mixtures were calculated by:

log y, = 1- + 1 log (mNa Cl) (7.4)

2k

The results, plotted in Figure 4, are not of high accuracy

but do demonstrate a linear increase of-log ye when NaC1 is

replaced by buffer. This increase amounts to only 0.001 in

log y, for each increment of 0.01 in the ionic strength con-

tribution of phosphaT~e. Therefore any discrepancy in calcu-

lation of -log TC1 by the convention for a solution of

phosphate (I = 0.06) and NaC1 (I = 0.1) would not amount to

more than 0.006, small when compared with the difference of

0.042 at 25"C and 0.030 at 370C in pH values derived from

cells with and without liquid junction (see Tables 5 and 6).

Having values of pH(S) for buffer solutions with NaCl

(last column, Table 7) that appear to lie close to the NBS

standard scale, it was possible to examine the effect of

ionic strength and composition of the phosphate standard on

the pH(X) values determined for the TES, HEPES, and Tris

buffers from the cell with liquid junction. By taking

values of Es and pH(S) for the reference phosphate-NaC1

solutions from Tables 6 and 5 respectively and the values of

Ex for the other buffers (Table 6) and applying equation 3.7,

the pH(X) values listed in Table 7 were calculated; each

column heading being the reference buffer composition. The

Figure 4. Variation of the logarithm of the mean activity

coefficient of NaC1 in phosphate-chloride

mixtures of I = 0.16m, as a function of compo-

sition at 25 and 37* C

0 0.05 OJ1

Phosphate lonic Strength~

results are shown graphically in Figure 5. The horizontal

dotted lines indicate the values of pH(S) assigned to the

respective buffers.

It is clear from Figure 5 that the greater part of the

discrepancy between the operational pH(X) and the conventional

activity pH(S) is removed simply by matching the ionic

strength of the standard to that of the unknown sample. By

increasing the NaC1 molality further at the expense of phos-

phate such that I(phosphate) = 0.06m and I(NaC1) = 0.10m, the

residual liquid-junction potential is completely eliminated

for the TES and HEPES buffers although a difference of about

0.9mV (0.015 pH unit) persists for the Tris buffer.

Estimates of liquid-junction potentials at the junction

buffer l3.5M KC1 bave been made by use of the Henderson

equation.33 Using available limiting ionic conductances at

250C and estimating those of HPO4, TES HEPES and

TrisH the following values have been obtained:

1:3.5 phosphate 0.10 1.9

P(0.10) + NaC1(0.06) 0.16 1.5

P(0.08) + NaC1(0.08) 0.16 1.4

P(0.06) + NaC1(0.10) 0.16 1.3

P(0.04) + NaC1(0.12) 0.16 1.3

1:1 TES(0.04) + NaC1(0.12) 0.16 1.3

1:2 TES(0.04) + NaC1(0.12) 0.16 1.3

1:2 HEPES(0.04) + NaC1(0.12) 0.16 1.3

1:3 Tris(0.05) + NaCl(0.11) 0.16 0.8

It is evident that the residual liquid-junction potential

when the blood buffer (I =0.1m) is replaced by a TES buffer

(I = 0.16m), for example, should not exceed 0.6mV (0.01 pH

unit), whereas the observed differences are three times this