Stability Constants of NaCO3-, NaSO4- and KCO3- in Water ...

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Masters Theses Student Theses & Publications

1977

Stability Constants of NaCO3-, NaSO4- andKCO3- in Water at 25°CFrank Dennis BlumEastern Illinois UniversityThis research is a product of the graduate program in Chemistry at Eastern Illinois University. Find out moreabout the program.

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Recommended CitationBlum, Frank Dennis, "Stability Constants of NaCO3-, NaSO4- and KCO3- in Water at 25°C" (1977). Masters Theses. 3271.https://thekeep.eiu.edu/theses/3271

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pdm

STABILITY CONSTANTS OF NaCOs-' Naso�--

AND KC03 IN WATER AT 2s0c (TITLE)

BY

FRANK DENNIS BLUM ">

THESIS SUBMlmD IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

MASTER OF SCIENCE. DEPARTMENT OF CHEMISTRY IN THE GRADUATE SCHOOL, EASTERN ILLINOIS UNIVERSITY

CHARLESTON, ILLINOIS

1977 YEAR

• 1

I HEREBY RECOMMEND THIS THESIS BE ACCEPTED AS FULFILLING

THIS PART OF THE GRADUATE DEGREE CITED ABOVE

�2'1!!7� DATE /

� 2-(/!7'7 DATE /

ABSTRACT

Title of thesis: Stabi l i ty Constants of NaC03- , Naso,.- and KC03-

i n Water at 25°C.

Frank Denni s B lum, Master of Science , 1977

Thesis di rected by: David W . Ebdon , Associate Professor of Chemi stry

A new method for determining ion association constants in aqueous

sol utions usi ng ion selective el ectrodes has been developed. This meth

od has been appl ied to the NaC0 3- , Naso,.- and KC0 3- i on pairs at 25°C.

Association constants for NaC03- and Naso,.- were determined at various

ioni c strengths and ex�rapolated to zero i onic strength to yie l d 2 . 2 ±

0 . 2 for NaC03- and 5 . 3 ±. 0 . 4 for NaSOi.- . Values for the association

constants at an ionic strength near sea water ( I=0 . 70) we1e cal culated

to be 1 . 7 ± 0 . 1 for Naco; and 2 . 1 ± 0 . 2 for Naso,.- . The Kco3- asso-

ciation constant was determi ned to be between zero and one.

Other less d irect methods of determini ng these constants were

tested and evaluated. It was also evident sodi um m-benzenedisul fonate

i s a weakly associ ated electrolyte, which may associate to approximately '

the same extent as sodium carbonate . An Ori on model 94-11 Sodium Ion

Electrode, Orion model 93-19 Potassium Ion Electrode, Sensorex model

S810C03 Carbonate Sensitive El ectrode and Chemtrix model 1015M Sul fate

Electrode were used and compared i n this study.

VITA

Name: Frank Denni s Blum.

Pennanent Address: 400 N. Fairview, Mt . Prospect, I l l inoi s 60056.

Degree and date to be conferred: M .S . , 1977.

Date of bi rth: January 27 , 1955 .

Place of bi rth: Chicago, I l l inoi s .

Secondary education: Lane Techn ical High School , Chicago, " Il l inoi s , 1968-1969. Prospect High School , M� . Prospect , I l l inoi s , 1969-1972.

. .

Col l egi ate institution attended: Date

Univers i ty of I l l inois (Chi cago

Degree Date of Degree

Ci rcle Campus}, Chicago , I l l i nois 1972-1973

Eastern I l l i nois University Charleston , Il l i nois

Eastern I l l i nois Univers ity Charleston , I l l i nois

Major: Physical Chemistry .

1973-1976

1976-1977

B . S . May 1976

M . S . December 1977

Positions hel d: Graduate Assistant, Eastern I l l inois Universi ty , 1976-1977. Teaching Assistant, U�iversity of Minnesota, Mi nneapol i s , Minnesota, Present.

i i i

ACKNOWLEDGMENTS

The author woul d l i ke to express his sincere gratitude to

Professor David W . Ebdon for h is suggestion of thi s project , assi st

ance, gui dance, encouragement and patience during this study.

I would a l so l i ke to thank Ms. Li nda Blum for typing and cor

recting this manuscri pt.

Thi s work was parti ally funded by the Council on Facu lty

Research of Eastern I l l inois University.

I woul d like to dedicate thi s thesi s to the typi st, my wi fe ,

Linda.

i v

TABLE OF CONTENTS

ABSTRACT

VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

GLOSSARY OF SYMBOLS

I .

I I .

I I I .

IV .

v.

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

HISTORICAL REVIEW

STATEMENT OF PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A . Ion Association

B. Ion Selective El ectrodes

c. Detenni nation of Association Constants

EXPERIMENTAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .

A .

B .

c.

Reagents

Apparatus

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 . pH/mV Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 . Ion Selective El ectrodes

3. Waterjacketed Cel l

Experimental Methods

1. Sodium Ion El ectrode Runs . . . . . . . . . . . . . . . . . . . . . .

a. Determi nation of KA for NaC0 3- . . . . . . . . . . . . .

v

Page i i

i i i

iv

v

v i i

v i i i

i x

1 3

11

12

12

14

17

22

22

25

25

26

29

30

32

32

Page b . Detennination of KA for NaS04 - • • • • • • • • • • • • • • 34

c . Variation of Ioni c Strength . . . . . . . . . . . . • . . . . 35

d . Comparison of Salts Method . . . . . . . . . . . . . . . . . . 36

2 . Other Electrode Methods . . . . . . . . . . . . . . . . . . . . . . . . . 37

a . Potass ium Ion Electrode Measurements . . . . . . . . 37

b . Carbonate El ectrode Measurements . . . . . . . . . . . . 37

c . Sulfate Electrode Measurement . . . . . . . . . . . . . . . 38

VI . RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

A . Sodi um Ion Electrode Measurements . . . . . . . . . . . . . . . . . . . 39

1 . Detennination of KA for NaC0 3- • • • • • • • • • • • • • • • • • • 39

2 . Detenni nation of KA for NaS04- • • • • • • • • • • • • • • • • • • 48

3 . Variation of Ionic Strength • • . • • . • . . . . • • • . . . . . . . 53

4 . Comparison of Sal ts Method . . . . . . . . . . . . . . . . . . . . . . 5 7

B . Other Electrode Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

1 . Potassi um Ion Electrode . . . . . . . . . . . . . . . . . . . . . . . . . 57

2 . Carbonate Electrode Measurements . . . . . . . . . . . . . . . . 58

3. Sul fate Electrode Measurement _ :. . . . . . . . . . . . . . . . . . . 61

VI I . SUGGESTIONS FOR FUTURE RESEARCH . . . . . . . . . . . . . . . . . . . . . . . . . 63

APPENDIX 1 ·. SAMPLE CALCULATIONS FOR DETERMINATION OF THE SODIUM CARBONATE AND SULFATE ASSOCIATION CONSTANTS . . . . . . . . . • • . • . . . . . . . . . . . • . • . . . . . . . . . . • . 65

APPENDIX 2. COMPUTER PROGRAM-PAIR . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

vi

Figure 1 .

Figure 2 .

Figure 3 .

Fi gure 4 .

Figure 5 .

Figure 6 .

Figure 7 .

Figure 8 .

L I ST OF FIGURES dn Plot of Qf versus the radius for univalent i ons

of opposi te ( 1 ) and simi l ar ( 2 ) charge type . . . . .

Di agrams of a sodi um sensit ive sol i d state gl ass el ectrode ( a ) , a potassi um sensitive ion exchange el ectrode (b ) and a single junction reference electrode (c ) . . . . . . . . . . . . . . . . . . . . . . . . •

Di agram of the waterjacketed cel l and experi -menta 1 arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . • .

Typi cal cal i bration curve for sodium ion elec-trode at constant i on ic strength . . . . . . . . . . . . . • . .

Plot of Log KA versus IT for NaC03- . . . . . • . . . . . . . . .

Plot of Log KA (Nernstian) versus IT for NaC0 3- . . . .

P lot of Log KA versus If for NaSQ4- • . . . • . . . . . . . . . •

Plot of Log KA(Nernstian) versus IT for NaS04- • • • •

Page

8

27

31

41

45

46

51

52

Figure 9 . Plot of electrode response versus i on ic strength for salts with constant sodium ion concentra-ti on • • • • • • • • • • • • . • • • • • • • . • • • • • • • • . • • • • • . • • • • • • • 56

Figure 10 . Plot of el ectrode response versus Log [Na+] for comparison of Na2BDS and Na2C0 3 . . . . . . . . . . . . . 58

Figure 1 1 . Plot of electrode response versus Log [C03 2- ] using carbonate selective electrode . . . . • . . . . . . . 60

Figure 12 . Plot of electrode response versus pH for sulfate ion selective el ectrode . . . . . . . . . . . . . . . . . . . . . . . . . 62

v i i

LIST OF TABLES

Table 1 . Apparent and Zero Ionic Strength Association Constants for Naco�-

. . . . . . . . . . . . . . . . . . . . . . . . . . . • .

Table 2 . Apparent and Zero Ionic Strength Association Constants for Naso4- . . . . . . . . . . . • . . . . . . . . . • . . . . . .

Table 3 . Compari son of Data for Association Constants for NaC03 - and NaS04 - . . . . . . . . . . . . . . . . . . . . • . • . . . .

Table 4 . Cali bration Run Data-Output from PAIR . . . . . . . . � . . . .

Table 5 . Determ ination of Association Constant-Output from PAIR . . . . . . . • . . . . . . . . . . . . . . . • . . . . . . . • . . . . . . .

vi i i

Page

43

49

54 72

73.

a

a . 1

b

c

D

E

EO

Eo M E� M

F

I

k

GLOSSARY OF SYMBOLS

di stance of cl osest approach of i ons {cm)

activ ity of the i th ion (mol /l )

parameter i n Davies equation

concentration of species i ndi cated (mol/l )

dielectric constant of sol vent

el ectrode response (mV)

corrected el ectrode response (mV)

standard electrode potential (mV)

expanded scale correction factor (mV)

standard glass membrane potential (mV)

col l ection of EM terms (mV)

g lass membrane potential (mV)

i nternal el ectrode potential (mV)

reference electrode potential (mV)

Faradays constant ( 9 . 648 · 10� C/mol )

ionic strength (�LZiCi )

Bol tzman constant (1.381 · 10-16 erg/K); slope from Nernst

equation

KA thermodynami c association constant

K� apparent association constant ·A Kd di ssociation constant

K�el selectiv ity constant of i th i on 1

n1 number of ions with potenti al �i

i x

no total number of ions

r di stance between two ions (cm)

R gas constant 8 . 314 (J/(mol . K) )

T absolute temperature (K) Z; charge of i th ion ( s i�ned)

a degree of di ssociation

r. 1 activi ty coeffi cient of i

y± mean i onic acti vi ty coefficient

e: electronic charge (esu)

A mol ar conductance

Ao molar conductance at zero ionic strength

Pi charge density about ion i

'¥. J potential about ion i

v2 nab l a , l ap laci an operator

[F] concentration of F [F] I i ni ti al concentration of F [F]_T total concentration of F [F] F free i on concentration of F (F) acti vity of species F

x

I . INTRODUCTION

In recent years an increased i nterest in the thermodynamic

characterization of natural water systems has been observed. This

i nterest can be attributed to envi ronmental probl ems , production of

energy-resources and the characterization of the marine envi ronment.

The thermodynami c characterization of natural water systems requi res

knowledge of the pressure, temperature and solution composition .

The species in solution wi l l not only be simple ions , organi c mole

cules , and dissolved gases , but complex ions and i on pai rs . To

determ i ne the concentration of the l atter one needs the ir formation

constants.

A thermodynamic model of sea water has been developed1 and re

fined2 which uti l izes ion association constants to calculate the

free energies of formation of a l l the major and minor ion pai rs

which exist i n sea water. · Then using the el emental composition of

sea water, the total free energy of the system i s i teratively min

imized to achieve equi l i bri um speci ation. The cal culated results

for free ion concentrations and for prediction of precipi tation

agree wel l with experimental resul ts i n ocean ic waters .

Another important aspect of computer mode l i ng i s in oil wel l

brines. Secondary recovery techniques include water-flooding , where

available sources of water ( supply waters ) are pumped i nto the wel l

and the oi l i s displ aced al ong with produced water. Produced water

contains high concentrations of di ssol ved sal ts . This l eads to the

1

·-.

2

production ·of scale, usual ly al kal i ne earth carbonates and sul fate s ,

i n the pi pes and the producing fonnati on , a porous rock. The usual

solution to this problem i s to pul l out the oi l rigging and frac

ture the fonnation wi th explosives . Accurate data and a good com

puter model cou l d predict when sca l i ng wou ld occur and also what

mixtures of supply waters or what compl exing agents could be used

to reduce or prevent scal i ng i n the most economi cal ly feasible way .

In order to improve the re 1 i abi l ity of these computer mode 1 s ,

the present research was undertaken to more accurately detennine

the association constants of sodium carbonate , potassium carbonate

and sodi um sul fate. Carbonate and sul fate are important i n natural

water systems because of the i r effect on precipitation equi l i bria .

Carbonate i s a l so important because of i ts effect on the pH of these

systems . Even though the concentrations of carbonate and sul fate

are sma l l and the equi l i brium constants are also smal l , the effect

on i on pairing in respect to the concentrations of these anions i s

significant due to the relatively l arge concentrations of sodium

i on i n sea water and i n most bri nes .

3

I I . HISTORICAL REVIEW

. To und�rstand how the concept of i on pai ring relates to other

ionic solution processes , a bri ef summary of historical developments

leading to an understanding of ionic interactions in solution i s

appropriate. The concept of an ion, o r charged parti cle which could

carry electric ity, was proposed by Faraday i n 1833. C laus i us sug

gested i n 1857 that ions were produced by the breaking of chemical

bonds . This process occurred when an electrolyte dissolved in a

solvent. Arrheni us; 3 however, suggested that electrolytes were

only partially di ssoci ated i nto ions. The degree of di ssociation ,

a, can be detennined by the ratio of the molar conductance, A, at

concentration C to the molar conductance at i nfi nite di l ution, Ao,

or

a= A/Ao ( 1 )

Thi s concept works very wel l when appl ied to weak el ectrolytes .

The di ssociation i n general for a weak aci d , HA, can be expressed

usi�g the l aw of mass action as

= [H+] [A-] Kd [HA]

At equi l ibrium , [H+] =[A-] = cxC and.[HA]= ( 1-cx )C , where C i s the

( 2 )

stoichiometric concentration of HA . Substituting the rel ationships

i nto equation ( 2 ) we have

A2C K - ---...-d - Ao(Ao-A) ( 3 )

or rearranging,

1 _ 1 + .,.._.CA_.,.._. A - Ao KdA�

4

(3a )

Thi s equation, known as the Ostwa ld Dilution Law, describes the dis-

sociation of weak aci ds , such as acetic aci d , at l ow concentrations .

However i t breaks down when appl ied to the conductance of a "strong

electrolyte" , such as sodi um chloride .

This di l emma was partia l ly cl arified i n 1906 by Bjerrum4 from

research on hexaaquochromium ( I I I ) sal ts . He proposed that not

only these sal ts, but al l strong el ectrolytes dissoci ate completely

i nto i ons . This fact was l ater verified by x-ray crystal studies,

which showed that "strong electrolytes" in the sol i d state were

composed of discrete ions . "Weak el ectrolytes " such as acetic aci d ,

were shown to exist as undissociated neutral molecules .

The modern theory of el ectrolytes dates from the classic work

of Debye and Huckel5 i n 1923 . They assumed that a strong electrolyte

was completely dissociated i nto i ons i n aqueous sol utions and took .

as the ir model a rig id charged sphere i n a diel ectric continuum.6 A

Maxwel l -Bol tzmann distribution of i ons was assumed with the potential

due only to the electrical energy between a "centra l " ion and a l l

the other i ons in sol ution:

(4)

Here ni i s the number of i ons with a gi ven potential �j wi th re

spect to the jth ion, n0 i s the total number of i ons and e:, k and

T are the electron charge , Bol tzmann constant and absolute tempera-

5

ture, respect ively.

This di stribution was then used to calculate the charge densi ty ,

p, which coul d · be used in the Poisson Equation ,

( 5 )

where 'V� i s the l ap lac ian operator and D i s the diel ectric constant

of the sol vent. With proper simpl ifi cation and truncation of an

exponential series,equation ( 5 ) reduces to a simple second order

differential equation. The simpl i fi cation i nvolves assuming that

the i nterel ectronic potential for very di l ute solutions wi l l be much

less than the mean thennal energy . Therefore the second and higher

order tenns in 1/kT can be assumed neg l i gib le . The di fferential

equation when solved yields the el ectri c potenti al, which can be

rel ated to the chemical potenti al of the system. II The Debye-Huckel result for the mean ionic activity coeffi cient

can be stated as:

where Z 1,Z 2 are the charges of ions 1 and 2 ,

-y± i s the mean i on ic acti v ity coeffi ci ent,

a i s the di stance of cl osest approach of the i ons ,

I i s the ionic strength (=!zI:c.Z.2} , 1 1

and A and B are defined constants .

(6 )

This equation i s of great importance because i t can describe the

behavior of a strong electrolyte i n a di l ute solution wi thout the

use of an arbi trary constant. It agrees wel l with experimental re

sul ts for 1-1 el ectrolytes to an ionic strength of about O . lM . " There have been many attempts to extend the Debye-Huckel theory.

Guggenheim7 ( for 1-1 el ectrolytes) and Davies0 ( for 1-1 and 2-1

electrolytes ) have made the more successful attempts to calculate II acti vity coefficients� priori , based on the Debye-Huckel model and

assumed parameters . II

The Oebye-Huckel theory does have several l imitations . One

major problem i s that for smal l i ons , i ons of large charge type or

sol vents of low dielectric constant the electrical potential energy

i s not negl igi ble compared to the thermal energy . The Bjer�Jm9

treatment attempts to solve thi s problem. The treatment of Bjerrum

fi rst assumes that there i s a Bol tzmann di stribution of i ons in

solution and that the only energy that is important is the elec

troni c potenti al between two close ions . Therefore;

(-Z 1Z2£2 \ dn = n exp \ DrkT ) dV (7 )

where r i s the distance between ions 1 and 2 with charges of Z1 and

6

Z2 respecti vely, and the other variables are as previously defined.

With the assumption of spherical symmetry the equation can be simpl i

fied by replacing dV with 4�r2dr, yielding;

dn = n4�r2exp(-Z1Z2£�) dr DrkT

(8 )

Thi·s equation is pl otted i n figure ( 1 ) for charges of the same and

opposite charge types . For charges of opposite s ign there exists a

7

mi nimum which can be calcul ated by di fferentiating dn/dr with respect

to r, setting the result equal to zero and solving for r. Thi s proc

ess yiel ds a resu lt for the value of the radius rmin ' where the po

tential energy i s a minimum,

IZ1Z2le:2 rmin = 2 DkT (9 )

The distance rmin (3.sA for a 1-1 electrolyte) i s the "Bjerrum

Distance" which Bjerrum used to define an i on pai r. · Two ions of

opposite s ign within a di stance of rmin or less were said to be

paired. This equation can be rearranged to

IZ1Z2!e:2 2kT = ---Dr mi n

(9a)

Note that at rmin the electronic potenti al energy i s twice the mean

thennal energy. This contradicts the Debye-Huckel assumption that

the interelectronic energy i s negl igible compared to the thennal

energy.

I t should be noted here t.hat the Bjerrum treatment defi ni ti on

i s somewhat arbitrary and has been described as a mathematical

fiction!0 However the concept of an i on pai r i s important. It can

be thought of as a neutral di pole (for symmetrical electrolytes )

or a charged species ( for unsymmetrical el ectrolytes) th'e presence

of .whi ch wi l l alter the properties of solution� such as conductiv ity

and activi ty .

There have been many developments in the study of i on associa

tion. Conductiv ity measurements have been successful in d�tennining

.·

dn dr

1

0 5 10 15 20

Radius (�)

Figure 1 . Plot of �� versus the radius for univalent

i ons of opposite ( 1 ) and simi lar ( 2 ) charge type.

8

25

9

association constants. However, conductiv ity only works wel l when

the association constants are l arge , as i s the general case for 2-2

or 3-3 electrolytes . Another problem i s that conducti vity i s not a

"speci fic" technique but rel i es on the measurement of a bulk property

and .on the ion- i n-a-continuum model for detennination of association

constants.

A general l imitation of any thennodynami c method i s that it

can only separate a simple i on i nto two categories: free i ons and

ion pai rs . The constitution of the 11 thennodynamic11 ion pai r has

been the subject of debate for severa 1 years . The . Bjerrum theory

counts ions pai red i f they are closer than the arbitrary rmin value .

Some authors11 have suggested that only ions in di rect contact should

be counted as paired. Since then kineti c studies by Eigen and co

workers have shown that ion pair fonnation appears to take pl ace

through a step-wise mechani sm .12 This was further veri fied by

ultrasonic measurements of MnS04 1 3 and MgSQ4 . 1.4 The association

of MS04 i s bel ieved to take pl ace i n three steps , each of which has

characteri stic rate constants and equi l ibrium constant. Step I i s

assumed to be a diffusion control l ed process of free completely sol

vated i ons fanning an i on pai r separated by two water molecules . In

step I I the sulfate can l ose a water molecule to fonn an ion pai r

separated by one water molecule which can be l o�t i n step I I I to

fonn a contact ion p�i r . This process can be represented as

M2+(aq) + S042- ( aq} : M(WW)S04 : M(W}S04 ! MS04 KI KI I KIII

where W represents a water molecule between the ion pai r . This

..

· ..

10

model is i nstructive because i t considers speci fic ion-sol vent inter

actions rather than merely 11bul k11 sol vent properties . It a l so sug

gests that the contact ion pai r i s not necessari ly the most stable

.fonn of an i on pai r . The overa l l association constant for MgSO�

from .ul trasonics 15 agrees wel l with that determined by conductance . 16

Raman spectra , NMR , pol argraphy and kinetics have a lso been

.,used to study i on pai ring and these methods have been sunmarized

... by Davi es . 1 7 Most of these methods , howeve-r , do not work we 11

·when the . . association constant is sma 11 . A thermodynamic method

which i s both sensitive and specific i s the measurement of ion ac-

··. tivi ty by i on selective electrodes . With a mi nimum of assumpti oll$ ,

such measurements can yiel d precise values of i on association con

stants even when the magnitude of the constant i s not l arge. It i s

this method which wi l l be used in the present study.

II I . STATEMENT OF PROBLEM

The purpose of this study i s to detennine the apparent and

thennodynamic association constants for NaC03- , NaS04- and KC03-

11

ion pairs in aqueous soluti ons at 25° using i on selective electrodes .

Estimates of the fonnation constant of NaC0 3- from various exper

imental procedures are generally not i n agreement . I t i s hoped

that thi s more direct method wi l l yi el d a more accurate value for

this constant. The constant for Kco 3- is expected to be very smal l

and often has been assumed to be negl ig ib le . Values for NaS04- are

known from conductance and other methods which can serve as a veri

fication of our method.

Another area to be studied i s the association of the meta

benzenedi sul fonate ion with the sodi um ion . There i s some evi dence

from solution conducti vity that meta-benzenedi sul fonates ei ther do

not associate or associate to a very l imited degree . If these salts

do not associate they can be used as a standard for 2-1 el ectrolytes

just as sodi um chloride and potassium chloride are for 1-1 electrolytes.

In this study we wi l l attempt to calcul ate the equ i l i bri um con-· � stants and examine methods of detennining the constants with the use

of ion selective el ectrodes which respond only to the activity of

the free ion. I t is assumed that a paired i on cannot .affect th�

electrode potential .

I V . THEORY

A . I on Association

When a "weak electrolyte" (AaBb) dissolves in a solvent, an

e�u i l i brium. i s establ i shed between the di ssociated ions AX+, sYand the undi ssociated molecules AaBb . This equ i l ibrium can be

written as

A B ! aAX+ + bBYa b

where ax = by,and the corresponding equ i l i brium expression as

( 10 )

( 11 )

12

where the parentheses represent the activities of the various species

and Kd i s the thennodynamic di ssociation constant.

For a strong electrolyte an equ i l i brium i s establ i shed between

the free ions and ion pai rs . Simi l arly thi s equi l i brium can be ex

pressed by

CX+ + [)Y- ! CX+[)Y- ( i on pair )

with the equi l i brium expression

( cx+(}Y-) K = ----A ( cX+)([}Y-)

( 12 )

(13 )

where KA i s the thermodynamic association constant. The thermody

namic association constant should be a constant at any i onic strength .

However i t i s often convenient to use the apparent or stoichiometric

constant , KA , where the activities are replaced by the stoichiometric

conce_11t rations:

K"' = A

·[CX+()Y-]

ccx+JcoY-J (14)

13

Note �hat the stoichiometric equi l i brium constant can be converted

to the thermodynami c constant by mul ti plying by the appropriate ac-• .I

�i v i ty coeffi cients to obtain .•

( 15 }

where the y's represent the act iv ity coefficients of the species

i nd.i ca ted . '

The fonnation of an ion pai r resul ts in the fonnation of a

species which no l onger has the properties of the free i ons. For

example i t wi l l reduce the conductiv ity of a solution , produce an

u l trasoni c absorption or not respond to an ion selective electrode .

Formation of the ion pai r wi l l reduce the concentration and activity

of the free i ons .

Si nce the association constants for the alkali metal sul fates

and carbonates are smal l , conductiv ity or ultrasonics may not be

the best method for determining these constants . A better method of

determining these constants i s by means of ion selective el ectrodes .

I n theory the ion selective electrode responds only to the act iv ity

of free ions. Therefore i f free ions exist i n equi l ibrium with i on '

pai rs , the measured activity of the free i ons wi l l be l ess than that

calculated assuming complete di ssociati on . If we can then attribute

..

14

thi s decrease sol ely to the fonnation of ion pai rs , we can calcul ate

the concentration of i on pai rs . Using the l aw of mass action and

the free ion and i on pai r concentrations , we can calcul ate the equi

l i bri um constant.

B . Ion Selective El ectrodes

Recently qua l i ty el ectrodes of high selecti vity for certain

i ons have been developed. A sol i d state sodi um gl ass el ectrode,

potassium ion exchange electrode and precipi tate electrodes selec

tive to carbonate and sul fate wi l l be di scussed.

Consi der a glass specifi c ion and reference el ectrode i n con-tact with a solution of interest. This set-up can be represented as:

i nternal I internal I gl ass I solution I reference electrode solution

. membrane

1of i nterest .electrode

v EI E EM Eref

where EIE' EM and Eref are the potentials of the i nternal electrode,

membrane and reference el ectrode, respecti vely. For a gi ven tem

perature and pressure the potential E1E i s expected to be constant

because the el ectrode i s sealed and. the composition of the i nternal

sol ution can not be a ltered. For most electrodes the Eref wi l l be

constant or nearly constant for a given temperature and pressure.

ine glass membrane potential , EM , how=ver wi l l not be a constant

i f the sol ution of interest i s changed. Thi s potential depends on

the potentia l s at the gl ass- l iquid boundries and possibly a di ffu

s i on potential. Us i ng the Nernst equation and the selecti vi ty

15

constants for various interfering i ons one can arrive at the fol l ow-i ng equation;1 8'19

. RT E = E0 + - l n M . M nF

{16)

where a1 and a2 refer to the acti vities of the specific ion in the

internal or external sol utions , respecti vely,

K�el i s the selectiv ity constant for the i th i nterfering ion ,

ani represents the act ivi ty of the ith i on i n the i nternal

{n=l) or external {n=2 ) sol ution ,

and EM i s the glass membrane standard potenti al .

The EM shou ld be the same on both g lass surfaces and therefore be I

zero. ' However because s i des of the glass can have di fferent environ-

ments {one surface i s always i n contact with the i nternal surface

whi l e the other i s conti nua l ly bei ng changed) the potential i s often

. not zero. Thi s has been tenned the asymmetry potential and mainly

depends on the hi story of the gl ass . Because of this asymmetry

potential the electrode must be "cal i brated" before use.

Si nce the i nternal solution i s of constant composi tion the

activi ties of the i ons i n equation ( 16 ) wi l l be constant and ca·n

be grouped w�th the asynvnetry potential to yield

E, RT l EM = M + n F n . a 2 { 17 ).

where

EM� = E 0 - RT l n a 1 (18) M nF

(Note that the K�el ai tenns have been omitted for simpl icity . I n

our experimental work the effects of possible interfering ions are

neg l ig ible . )

I t i s possible to write the overal l voltage for the cel l as

or by substi tuting and combining constants as

RT E = E0 + � ln a2 nF

(19)

( 20 )

where E0 is the col l ection of constants and a2 i s the activity of

16

the specific ion i n the external solution. Therefore i n theory an

ion selective el ectrode is responsive to the activity of the selected

ion in the absence of any i nterfering ions . The same bas i c equa

tion (20) wi l l al so hol d for an ion exchange or precipitate electrode.

The main di fference i s that i nstead of a g lass membrane the ion ex

ch�nge el ectrode has an ion exchange reservoi r i n contact with the

internal solution , which exchanges the outer solution through a

porous membrane. The precipitate electrode has a membrane composed

of an insoluble salt of the ion of i nterest pressed into a pel let ,

precipitated on the electrode surface or impregnated into a s i l i con

or pl astic matrix . A more compl ete treatment of these electrodes

·-�

17

can be found i n the l i terature. 18�20

It i s important to note here that due to the asymmetry potenti a l s

i t i s very diffi cul t to relate the electrode readings of two solu

tions taken at different times. One solution to the problem i s to use

a reference solution of constant i on activity and make alternate read

ings i n the reference and unknown solutions. The unknown solution

vol tage can then be corrected for electrode "drift . " Another method

of avoiding this problem wi l l be di scussed i n the fol l owing section.

C . Detenni nation of Association Constants

The formation of an ion pair (NaC0 3- for example ) can be repre

sented by;

(21 )

From the laws of mass balance i t i s possib l e to express the total

concentration of sodium ion , [Na+]T as the amount of free sodium ion,

[Na+] F p lus the amount of ion pai r, [NaC0 3-] or

(22)

Simi larly ,

(23 )

Since [Na+ ]T and [C032-1T are known, i t would be possible to express

the concentration of the ion pai r and hence the association constant

i f the free ion concentration of ei ther the carbonate or the sodium

I

18

ion i s known . The free ion concentrations can be calcul ated through

the use of an ion selective el ectrode .

In theory the electrode shou l d obey the Nernst equation. From

equation (20) we have

or

E = E0 + RT l n a nF

E = E0 + 0 . 05915 log a

(20)

for a singly charged i on such as sodium i on where a represents the

"free i on" activity. The Nernstian sl ope for a doubly charged ion

shoul d be 0 . 05915/2. The s lope however i s not always Nernstian but

varies with el ectrode composition and must be experimentally deter

mined . Equation (20) wi l l then become

E = E 0 + k l og a ( 25)

where k is the experimentally determined s lope . The activity of the

ion can also be rewri tten as a = ye where Y i s the acti vity coeffi-'� cient and c i s the concentration (moles/l i ter) of the free ion .

The acti vity coeffi cient shoul d be a function of ionic strength.

Si nce the act·ivi ty coeffi cient wi l l be constant at constant ionic

stre.ngth and the E0 term wi l l be invariant , the d ifference between

two vol�age readings taken at constant i onic strength wi l l be due

to a dffference i n the concentration of the free ion. We can express

the voltage at a concentration C as

19

E = E0.+ k l og C + k l og Y ( 26)

and for a concentration c·' at the same i onic strength

E' = E0 + k. log C' + k. l og Y ( 26a)

Then the di fference can be g iven by

E - E' = k .1 og C - k l og C' = k. l og .�, ( 27)

A change in voltage can then be di rectly related to a change i n

concentration of the free i on .

Two types of measurements w'il 1 be done. F i rst , a run where the

concentration of the sodium ion i s varied at constant i oni c strength

in the absence of any signifi cant complexing ions . This wi l l al l ow

us to calculate k , the slope, by

E - E' k = ----

1 og (c:/c ') (27a)

Once the sl ope is known the results of the second run can be i nter

preted. To a sol ution of sodi um chlori de (where al l Na+ i s i n the

free i on) a solution of sodium i on and tetramethyl ammonium carbonate

i s added. This sol ution has the same sodium i on concentration and

ionic strength.

When a l iquots of the carbonate solution are added the voltage

wi l l be l owered even though the total sodium i on concentration has

not changed. It i s proposed that thi s decrease i n el ectrode response

20

and the corresponding decrease in the free sodium i on concentration

is due to the fonnation of the i on pai r , NaC0 3- . The el ectrode

response can be compared to the known voltage and concentration of

the i ni tial sodium chloride solution to yield the free sodium i on

concentrati on . Rearrangi ng equation (27) we have

(27b)

where [Na+] F is the free sodium ion concentration with an el ectrode

response of E; and [Na+]1 i s the initial sodi um i on concentration

with a voltage of E. Then using equation (27b) the free carbonate

ion concentration can be calculated.

· Once the free i on and ion pair concentrations are known i t i s

possible to express the apparent equi l i brium constant , KA,from equa

tion ( 14 )

[NaCO 3- ] K; = -----

A [Na+] [CO 3 �-] (28)

As noted previously the apparent constant, KA. can be converted to

the ·thennodynami c constant by mul tipl i cation of the proper activity

coefficients , equation ( 15 ) . The activity coefficients for the sodi um

carbonate ion pair and the sodium i on can be estimated at l ow ioni c

strengths using the Davies equation . 17 However, si nce both are of the

same charge typ� i t-can be·expected that i n d i l ute so1utjons both wi l l

have approximately the same acti vity coeffi cient so that equation (15 )

'

21

becomes

·:: (29)

The thennodynamic association constant can be calcul ated by

�taking the logari thm of both s ides of equation (29) yiel ding

logKA = logKA - l ogYCO 2-3 (30)

'The logYc032- can be estimated by pl otting the . l ogKA versus the

square root of the ionic strength or by the use of

If l ogY = -o .sz2 ---

1 + all - bl ( 3 1 )

··which i s the functional fonn of the Davies equation where a and b

are detennined constants . A plot of l ogKA + 0 . 5Z 2 If versus 1 + all

I woul d have an intercept of l ogKA (at zero i on ic strength) and a

s l ope of 0 . 5Z 2b . Davies has suggested that the parameters of a=l

and b=0 . 3 work best for most sal ts .

> V . EXPERIMENTAL

! A . Reagents

The fol l owing chemical s used were reagent grade and dried

over.night at approximately 100° i n a vacuum oven and stored i n a

desi ccator before usage: NaCl , KCl , Na2C0 3 , K2C0 3 , Na2S04 and

K2S04 .

22

Tetramethylammonium chloride , (CH3)4NCl . (97%, Al drich Tl ,952-6)

A stock so lution of tetramethyl anmonium chloride (usual ly l-2M) was

prepared. The salt was not weighed di r�ctly because of i ts hygro

scopic nature . The stock solution was analyzed by passing a known

volume of the solution through a col umn of Dowex SOW-XB·cation ex

changer charged with H+ . The HCl produced was then ti trated with

a standardized base to a phenolphthalein endpoint .

Tetramethylammonium carbonate , [(CH 3 ) 4NJ2C03• A Dowex 50W-X8

cation exchange column i n the aci d fonn was charged with tetra

metnylammonium i on . At least a five fold excess of tetramethyl

a1T1noniu� chloride was passed through the column and the effluent

solution was tested wi th pHydrion paper unti l there was no further

evidence of hydrogen i on being displaced from the column. Then a

sma l l amount of tetramethylammonium hydroxide ( 20% in a methanol

solution , Aldrich Tl , 954-2 ) was passed through the column to el im

i nate any residual amounts of acid present. A weighed amount of

sodium carbonate was passed through the column and the tetramethyl

ammonium carbonate was col l ected and used . A second method of

23

preparation was also used . A Dowex l-X8 anion exchange col umn was

changed from. the chlori de fonn to the carbonate fonn using potassium

carbonate ( ca . 4M) . The charg ing continued unt i l the effluent solu

tion contained no chloride. A known volume of a r.ecently standard

ized. tetramethyl ammoni um chloride solution was passed thr�ugh the

column and the tetramethyl ammoni um carbonate was col l ected and used.

Tetramethyl ammonium sul fate, [{CH3)3N]2S04 . A Dowex l-X8 anion

exchange column was charged with hydroxide (�. 4M) ion and a known

amount of tetramethylammonium was passed through the column. The

tetramethylammonium hydroxide solution was immediately titrated with

standardized sulfuric aci d to a pH 7 endpoint using a pH electrode.

A second method of preparation involved charging a Dowex 1-X8 column

di rectly wi th su lfuric acid (4M) and sodium sul fate. The sodium

sulfate (�. 2M) was used unt i l the pH of the effluent solution was

neutral . A known amount of tetramethyl ammonium chlori de solution was

passed through the column. The tetramethylammonium sul fate was . col

lected and used . The col umn charging with sul fate ion seemed to be

the fastest most efficient process whi l e charg ing with hydroxide ,

tetramethylamnonium o r carbonate ions took a l ong time and used a

much l arger excess of these i ons .

Benzyltriethylammoni um chlori de , C6HsCH2N(C2H5 ) 3Cl . (97% ,

Aldrich 14 ,655-2) A stock solution of ben�yl triethylammonium chlo

ri de was prepared and analyzed by the same method described for

tetramethyl ammoni um chlor ide .

Benzytriethyl ammonium sulfate, l.£6HsCH2N(C2Hs) 3)2S04 . Benzyl - ·

24

triethylammonium sulfate was prepared by charging a Dowex 1-X8 anion

exchange column with sul fate and passing a known amount of benzyl

triethylarnnonium chloride through the column. The same process

described for the preparation of tetramethyl arrmonium sul fate was

used.

Tetramethyl ammoni um m-Benzenedi sulfonate , [(CH3)4N)2CGH4($0 3)2 .

·retramethyl amnoni um .m-benzenedisu lfonate, abbreviated [ (CH 3 ) 4N] 2BDS ,

was prepared from .m.-benzenedisul foni c aci d ( H2BDS, Eastman , T 4147 ) .

The acid was neutra l i zed with barium carbonate which should extract

any sulfate impurity. The BaBDS was then recrystal ized from con

ducti vi ty grade water and exchanged for H+ from a Dowex 50W-X8 cation

exchange column. The acid produced was then ti trated with a tetra

methylarrmoni um hydroxide solution in methanol . The solution was then

heated to drive off the methanol and the [ {CH 3 )4N] 2BDS was then

crystal i zed from conductivity grade water. The [{CH 3 ) 4N] 2BDS was

dried at 110°c i n a vacuum oven overnight before use .

Sodium m-Benzenedisulfonate, Na2C6H4(S03)2· Purified H2BDS was

prepared by the method described for tetramethyl ammonium m-benzene-

di sul fonate . The acid was then ti trated with NaOH and the salt pro

duced was recrystal i zed and dried i n a vacuum oven at 110°c before use .

Sodi um-4a4'-Biphenyl di sul fonate, Na2(SQ3C6H4C6H4S0 3 ) . Sodium-4 ,

4'-biphenyl di sul·fonate, abbreviated Na2BPDS , was prepared i n the same

method described for sodium m-benzenedi su lfonate . The starting ma

terial used was 414'-bi phenyldi sulfoni c acid (Eastman , P 4590) .

B . Apparatus

1 . pH/mV Meter

All measurements were made using an Orion 801 digi tal pH/mV

meter. The readings were taken on the mV scale to a preci sion of

25

± 0 .01 mV. The meter nonnally reads to ± 0 . 1 mV, but additional

preci s ion was achi eved as fol l ows: (1 ) an external �ource (Leeds

and Northruo, Model K-3 potentiometer and galvanometer) was cal

i brated with a standard cel l { Eppley #100 735837) wi th a voltage of

1 . 01925V. ( 2 ) The Orion 801 meter was then zeroed using the zero

adjust on the back panel with a shorting strap across the standard

and·reference electrode i nputs . ( 3 ) A voltage of 99 . 0V was then ,

dialed on the potentiometer and the output from the GO and EMF- post

was placed across the standard and recorder input posts on the back

of the meter. (4) The recorder span was then adjusted to the known

vol tage ( 99 . 9()nV) and subsequent measurements were made across the

standard and recorder inputs . This mode of measurement wi l l here

after be referred to as the "expanded scale" mode. ·'

When the meter i s i n this mode the decimal point i s not auto-

mati cal ly moved but will remai n between the third and fourth digit

when it shou l d be between the second and third digit . In this

mode a sma l l correction must also be made because when the meter i s

zeroed i n the nonnal mode (±0 .lmV) i t wi l l not necessari ly read

o.ocmv on the expanded scale . A correction for thi s i s necessary

and. takes the fonn of

26

E' = E + (1 - E/99 .9 ) EO (32)

where E' is the corrected reading , E i s the meter reading and EO

is the meter reading with the shorting strap on expanded scale .

Each reading i s then corrected , but the correction i s usual ly sma l l

if not ·neg l i g i bl e because each reading i s "adjusted" by the same

amount.and the di fference between two readings , which i s important,

is sti l l the same .

2 . Ion Selective Electrodes

The measurements on the sodium sal ts were made using an Orion

94-11 ion selective el ectrode , figure (2a ) . Thi s i s a g lass el ectrode

wi th a s i l ver-si l ver chloride reference electrode in contact wi th

an internal sod ium chloride solution. Thi s el ectrode shows a good

selectivity for sodium over potassium . In a 10- 3M Na+ solution a

change of K+ acti vity of 10-1M. wou l d cause a 10% error i n the read

i ng . 21 Selectivities for sodium ion over tetraalkylafTl11oni um ions

are l arge and the effect of a change i n tetramethyl�11Tionium i on i s

negl ig ib le . Thi s i s veri fied by runs done for the sodi um carbonate

ion pai r where both the potassium and tetramethylammonium ions were

used. The tetramethylammonium ion concentration was changed by

�i fferent amounts, but the results i n each case were sti l l wi thin

experimental error.

The Orion 94-11 sodi um i on el ectrode has a fast response time

(98% of reading i n two minutes) . The response time , sensit iv ity

... ..\• (a )

Internal Aqueous Reference Solution

Porous Plastic Ion Exchanger Reservo ir

Internal Reference Electrode (Ag/AgCl)

Electrode Body

Internal Solution

Na+ Sensitive Glass Membrane

r---, I I I I I I I I

Filling Solution

Refe·rence Element

27

( c )

Internal Reference El ement (Ag/AgCl)

Internal Sensing Assembly

��--- Porous Organophi l i c Membrane

Ion Sensitive Area

{ b )

Figure 2 . Di agrams of a sodium sensi tive solid state g lass electrode

ia) , a potass i um sensi tive i on exchange electrode ( b ) and a s i ngle

junction.reference electrode ( c ) .

28

and selectiv ity make the Orion el ectrode more suitabl e than the

comparable Beckman model 39278 which has a thi cker gl ass membrane.

Due to the i nterference of the hydrogen ion , the pH was kept greater

than 10 for both the sodium and potassium runs .

The potass i um ion el ectrode used was an Orion model 93-19 , fig

ure ( 2b ) . It consi sted of a sol i d state electrode body and a replace

! 1 j able electrode sensing modu le . The electrode sensing module was con

posed of a s i l ver-s i l ver chloride reference el ectrode i n contact with

an i nternal reference soluti on . 22 These in turn are i n contact with

an i nternal sensing assembly and porous organophi l i c membrane sur

rounded by the ion exchange resevoir . The el ectrode shows good se-, · lecti vity over sodium and the effect of tetraa l kylammonium i ons was to

be tested. This electrode a l so shows an i nterference at l ow pH· and

therefore the pH of the tested soluti ons i s adjusted to greater than

9 .

The reference electrode used with the sodium and potassium

electrodes was an Orion model 90-01 , fi gure ( 2c ) , s ingle junction

reference electrode. The fi l l i ng solution used for the sodium runs

was a l i thi um trichloroacetate solution (Ori oh 90-00-19)1 and 0 .06M

NaCl wi th a few drops of s i l ver ni trate added was used for the po

tass ilJTl runs .

A Sensorex model S810C03 carbonate sensitive el ectrode was used

for the carbonate soluti ons . A carbonate selective electrode has

been reported i n the l i terature, 2 3 however this electrode has a

l i qu i d exchange m'embrane . The electrode used i n our study i s be-

•

l i eved to be a preci pi tate electrode with a membrane composed of

i nsoluble carbonate salts . The Sensorex el ectrode i s able to oper

ate . i n solutions of sodium carbonate without pH adjustment whi l e

the l i quid membrane el ectrode has strong OH- i nterference at a pH

greater than 9 .

The sulfate electrode used was a Chemtrix model 1015M. This

electrode is bel ieved to have a membrane made of i nsoluble sul fate

sal ts such as one described in the l i terature . 2 4 This electrode i s

expected to show an i nterference to carb<?nate, chromate, phosphate

and lead ions probably .due to l ead and s i l ver ions in the membrane.

The value for the slope is a function of the el ectrode compos it ion

.and surface· condi tioning. This sul fate electrode accor�ing to the

manufacturer has a sma l l pH working range, 5 . 00: ± 0.05. However

our experimental work i ndi cates that a pH range of 6 . 5 to 8 . 5 may

29

be the best range for measurement . Presumably at l ow pH values

bisul fate fonnation wi l l i nterfere and at high pH values the hydrox

i de ion wi l l i nterfere.

The reference electrode used for the sul fate and carbonate runs

was a Sensorex model S701RD Refi l l able Double Junction Reference

Electrode . The upper and l ower compartments were fi l l ed with Gel l ed

KCl F i l l i ng Solution {Sensorex ,S-18) and Gel l ed KN03 Fi l l i ng Solution

{Sensorex , S-19) , respecti vely .

3 . Waterjacketed Cel l

The cel l used, [figure {3� was waterjacketed to maintain con-

30

stant temperature and was fitted with a frame to a magneti c stirrer.

The cel l was i nsul ated from the sti rrer with a one-i nch thi ckness of

insulation. The sti rrer and a l l other equipment were pl aced upon

and grounded to a copper sheet. The cel l was fi tted with a rubber

stopper which had holes dri l l ed for the electrode s , thennometer,

nitrogen i nlet and pipettes . The holes were dri l led on an angle

of about 15°-20° to reduce the chance of trapping a ir bubbles be

l ow the e lectrode surface.

The waterjacketed cel l was connected to a �· 20 gal . constant

temperature bath fi l l ed wi th deionized water. The water was heated

and ci rculated wi th a Brownwi l l heater-circulator (Brownwi l l Scien

tific) and cooled through a copper cool i ng coi l through which col d

water was ci rculated . In the winter tap water was used for cool i ng

and i n the summer cool water was produced and ci rculated with a

Fonna Jr . bath and ci rculator ( Fonna Scienti fic) .

C . Experimental Methods

The solutions were made using di sti l led , deionized water and

cal i brated vol umetri c gl assware. Stock solutions of NaCl , KCl , Na2C03 ,

K2C0 3 , Na2SO� , K2so� and Na2BDS were prepared by weighing dried sol i ds

to ± 0. 00002g on a Mettler model H semimicro balance , dissolv ing the

sol i d an-0 di l uting to volume. Stock solutions of tetramethyl ammomi um

and benyzl tri ethyl ammonium salts were prepared and analyzed by the

methods described i n the reagents section.

N in l �t

,

Water ·

Thennometer

Fl ow __ ,__...,_

CJ

31 801 pH/mV

meter

to Constant -----Temperature Bath

Magnetic _..-+-__ sti rrer

Figure 3. Diagram of the waterjacketed cel l and experimental

arrangement.

1. Sodium Ion Electrode Runs

a . Detenni nation of KA for NaC0 3-

32

Potassi um Chlori de-Tetramethyl ammonium Chloride Runs. Three

solutions were prepared from stock solutions for these runs . Solu

tion I was a NaCl solution contain ing KCl and (CH 3) 4NCl to control

the ioni c strength. Sol ution I I was a solution contai ning K2C0 3

and NaCl or Na2C0 3 and Sol ution I I I contained KCl and (CH 3 ) 4NCl

but no Na+ . To each solution a smal l amount of KOH or {CH 3) 4NQH

was added to adjust. the ·pH of the solutions to 1 1 . 3-1 1 . 5 . Each

of the solutions had the same pH , K+ concentration and ionic strength .

Solutions I and I I had the same Na+ concentration.

The sod i um i on and reference el ectrodes were pl aced in a sma l l

amount o f Solution I for periods of three to twel ve hours before the

runs were to be made. Thi s seemed to reduce the time needed for the

el ectrode reading to stabi l i ze . Before a run was made the shorting

strap was pl aced across the standard and reference inputs and the

i nstrument zeroed (O .OnV) . Then the shorting strap was pl aced across

the standard and recorder outputs and the voltage was recorded on the

"expanded scal e . " This voltage was then used i n equation (32) for

the correction factor discussed earl ier .

A 75ml portion of Solution I was then pipetted i nto the clean

dry cel l , the stirring bar added and the constant temperature bath

connected and adjusted to 25°C . The el ectrode assembly was rinsed,

the thennometer wiped and the el ectrodes bl otted dry . Every second

33

day the reference electrode fi l l i ng solution was changed. Purified

nitrogen was passed through water in a gas bubbler at a flow rate of

about io ml/min and the electrode assembly was placed in the cel l .

Ni trogen was used over the solutions to el iminate absorption of C02

from a i r which would add more carbonate to the solution. The elec-

trodes were connected to the recorder and standard output junctions

for "expanded scale" (±0. 0lmV) measurement . Since the vol tages for

a l l sodium electrode runs were between +100 and -100 mV and the

readings were stable to ±0.01 mV , the "expanded scale" was used .

The solution was l eft to equ i l i brate at l east one to two hours . ,

The i ni ti al reading was taken when the electrode d id not show any

dri ft, or i nstabi l i ty at 25°C. Then 1 and 5 ml al iquots of Solution

I I I were pipetted i nto the cel l through a hol e in the stopper.

Care was taken so that the pi pette d id not contact the solution i n

the ce� l . The corresponding new vol tage was recorded when the new

solution equi l i brated, whi ch usually took 2-10 mi n . The prec ision

in the voltage readings is bel i eved to be ±0. 02 mV. This process

was continued until a total solution volume of ca . 100 ml was reach-

ed. Thi s run was the "ca l i bration run" and was used to check the

11Nernstian11 S lope , l::inV/6. l og [Na+] .

The cel l was emptied� rinsed and dri ed. A new 75 ml al iquot

of Solution I was pi petted into the cell and a l l owed to equi l ibrate

i n th� manner described earl ier . Then 10 and 20 ml al iquots of

Solution II were pi petted i nto the cel l and the corresponding voltages

34

recorded . This procedure was repeated either with success ively di

luted or freshly prepared soluti ons . Sufficient base was added to

the di l uted solutions to maintain the pH at 1 1 . 3-1 1 . 5 .

. Tetramethylammoni um Chl ori de Runs . The same procedure de-

s·cri bed for the potass i um chloride-tetramethyl amrnonium chloride runs

was used except that no potass ium ion was used . The potassium chlo

ri de and potassium carbonate were replaced with tetramethylamrnonium

chloride and tetramethylanunonium carbonate, respecti vely. Tetra-

.methyl anmoni um hydroxide was used to adjust the pH to 11 . 5 . These

runs were made to test any dependence of our experimental ly detennined

constants on potassium ion .

b . Detennination of KA for Naso�-

Tetramethyl ammonium Chloride Runs . The sodium sulfate association

constants were determined i n the same manner as that described for

sodium carbonate . However , s i nce the potassium i on interacts with

sulfate to about the same degree as the sodium i on , previous solu+ tions containing K were not used . Tetramethyl arrmonium chl oride and

sul fate were therefore used i n Solutions I and I I , respectively.

Benzyl triethyl arrmonium Chloride Runs . To check the dependence of

the experimental ly determined association constant for Naso�- on the

presence of tetramethyl anvnonium i on , benzyltriethyl anmonium chl oride

and sul fate were used. The same procedure was used except that tetra

methylammonium chloride and sul fate were replaced with benzyl triethyl

arrmonium chloride and sulfate .

c . Variation of Ionic Strength

Separate solutions of NaCl , Na2C03 and Na2BDS were prepared . ,

35

by .weight and d i l uted to 250 ml i n a vol umetric flask. The concen

tration of sodium ion i n each solution was very nearly equal .

Tetramethyl ammonium Chloride Runs . To the clean dry cel l a

100 ml al iquot of the NaCl solution was added. To thi s solution

15 ml of a (CH 3 ) 4NC1 - (CH 3) 4NQH solution was added to .control the

pH (=11 . 5 ) and ionic strength . The el ectrodes were pl aced i nto the

solution and a l l owed to equi l i brate whi l e carbon dioxide free ai r was

passed over the solution . Carbon dioxide free air was produced by

passing a i r through three gas bubblers , containing H2S04 , NaOH and

deionized water, i n sequence . The ai r flow rate was adjusted to

about 10 ml/min and the a i r was passed into the cel l through the

N2 gas i nl et .

When the electrode response was stab le , pr.evi-ously dried .and

weighed amounts of ( CH 3 ) 4NCl were added d i rectly to the cel l . Usu

ally three or four additions of (CH 3 ) 4NCl were made , and each time

the voltage was recorded . After the final addition the electrodes

were pl aced i n a reference solution of Na2BDS which was used to ad

just each reading for electrode drift over a period of time. For

example , i f i t was found that the reference solution reading had

changed by +0 . 35 mV between two runs , 0 . 35 mV was subtracted from

a l l the voltage readings of the l atter run. By thi s method the .

reference solutions would always have the same basel ine voltage , and

36

one can compare di fferent Na+ solutions at different times .

T.hi s procedure was repeated for other NaCl solutions of s l ightly

different sodium ion concentrati ons , which a l lows one to compare the

change i n vol tage to a change i n sodium ion concentration at constant

ioni c strength. A Na2C0 3 solution with the same sodium i on concen

tration was then pl aced i n the cel l and the same procedure used .

Tetramethyl ammonium m-Benzenedi sul fonate Runs . Si nce [ (CH 3 ) 4N] 2BDS

i s of the same charge type as Na2C0 3 i t i s bel ieved that i f the BOS ion

does not pai r signifi cantly with sodium it may be a good standard for

a 2-1 electrolyte. Solutions of Na2BDS and Na2C0 3 were prepared from

the dried salts. The same procedure as the tetramethyl ammonium chlo-

· ride r.uns was used except that tetramethylalTlllonium m.-be�zenedi sul fonate

was used for the i on ic strength addi tions . The sal t was dried and

weighed before the additions were made, and the electrode response was

recorded after each addi tion. Again each measurement was corrected

for the apparent drift of the el ectrode by measurement on. a reference

solution.

d. Comparison of Salts Method

Solutions of Na2BDS and Na2C03 were prepared by weight from the

dried sal ts . One hundred ml of the Na2BDS solution was pipetted into

the cel l and 15 ml of the (CH 3)4NCl - ( CH 3) 4NQH solution was added to

control pH. The electrodes were pl aced i n the solution and the po

tenti al recorded. The electrodes were then pl aced i n the reference

Na+ solution and the response was recorded. One hundred ml of the

..

37

Na2BDS solution was then di luted to 250 ml and the above procedure

repeated for the di l uted samp le . Four or five d i lutions were usu

al ly ·done and each time the reference Na+ solution was checked and

the other readings adjusted for the electrode drift due to the asym

metry potential .

The same procedure was then used for the Na2C03 sol ution . An

other four or five di luti ons were made and the voltage of each of

these recorded .

2 . Other El ectrode Methods

a . Potass i um Ion Electrode Measurements

Solutions and procedures simi lar to those described for the deter

mination of. the NaS04- constant with tetramethyl anmonium chloride �uns

were used . The only di fference was that KCl was used in Sol utions

I and I I instead of NaCl and Na2C�.

b . Carbonate Electrode Measurements

Comparison of Sal ts . Solutions of Na2CO� and K2C0 3 were pre

.pared by weight from the dried salts . Several solutions of these

salts at di fferent concentrations were placed i n the cel l and meas

ured .

Addition Method. Solutions of Na2C0 3 and K2CQ 3 of the same

carbonate concentrations were prepared from stock sol uti ons . A

75 ml a l iquot of a NaCl solution was pl aced in the cel l and 3-25

38

ml al iquots of the K2C0 3 were added. The voltage after each addi tion . '

was recorded.

c . Sul fate Electrode Measurement

: A 0 .5 M Na2SO� was pl aced i n the cel l and the pH was adjusted

to 10.5 wi th KOH . The pH of the solution was then s lowly changed

to 3 . 75 by adding smal l addi tions of HCl and recording the voltage

after each addi tion.

39

VI . RESULTS AND DISCUSSION

•.

A. Sodium Ion Electrode Measurements ··. ·

·.

' The sodium i on electrode seemed to be the most stable and had

the fastest response time . . This was the only el ectrode which could

be used on the expanded scale because the voltage readings were all

between +100 mV and -100 mV and the el ectrode readings were stable

to ±0. 01 mV. The electrode response was a l so near 11Nernstian . 11

1 . Detennination of KA for NaC03-

Potassium Chloride-Tetramethyl ammonium Chloride Runs. To i l l us

trate:i the method of ca 1 cu 1 ati on a samp 1 e run is fo 1 1 owed from the raw

data to the calculation of the constant i n Appendix I . This method

and other important points wi l l be out l i ned here. It was found that

in order to obtain reasonable voltage changes a relatively l arge a-

·mount .of C032- should be added to a small amount of Na+ . In this

manner, after addi tion of the carbonate the percentage of sodium

'that i s i on pai red i s from 5-20% for concentrated samples and 1-5%

for the more di l ute samples . One problem associated with thi s method

i s that a large amount of K+ must be used to adjust the i onic strength.

Usual ly a 7 5 : 1 to 25: 1 excess of [K+] : [Na+] i s used. At these con

centrations of sodium ion , 10-4-10-2 M a change of potass i um i on of

10- 3- 10- 1 M , respecti vely, wi 1 1 cause a 1% error i ·n the reading .

Therefore the [K+] was kept constant i n a l l three solutions and

(CH 3 ) �NC1 was used to adjust the i onic strength of Solutions I and

.,

40

I I I . . The ionic strength and [K+] of a l l three solutions were equal

and the [Na+] T of Solutions I and I I were also equal .

The first run was a cal i bration run where Solution I I I was added

to Solution I . Since thi s run was done at constant ionic strength

and .. hone of the i ons present was expected to i nteract suffi ciently

with Na+ to reduce i ts free ion concentration, a p l ot of log [Na+]

versus E should be a straight l i ne as shown in figure (4) . The slope

estimated by a l east squares fit from Part I of the FORTRAN program

PAIR (Appendix I I ) was 59 .3 ± 0 . 4 mV/decade . Slopes were usual ly

found to be near Nernstian or 57-61 mV/decade . There were however,

a few sl opes which were non-Nernstian, 45-49 mV/decade , which wi l l be

exami ned l ater.

After the s lope was calcul ated, i t was used in Part II of PAIR,

which calculates the equi l i bri um constant from values of the [Na+]T ,

[Na+] F ' [C03 2-]T and [C032- ] F . The second run was done by adding

known amounts of Solution I I to Solution I in the cel l . Si nce ions

known to complex Na+ were not present i n the solution corresponding to

the first data poi nt , i t was assumed that the [Na+] T was equal to

[Na+] F ." This a 1 1 ows us to have a "reference point" where the voltage

and [Na+] F are known preci sely. The [Na+] F at other volumes can then

be calcul ated from the change i n voltage using equation (26b) and

the experimentally detenni ned s l ope. The [NaC03- ] and the [C0 32-] F can then be calcul ated from equations (22 ) and ( 23 ) . From these

concentrations the apparent association constant can be cal cu l ated from

-1.0

0 ---��-----��-------------------------·�-

----�-------------------------�------------------------------�--,

f'T'1

_..

-2.0

0

-3.0

0

� -4

.00

rt

�

0

0..

Cl> � �

-5.0

0 0

�

(/)

Cl)

- 3

.::. -

6.00

-7.0

0

-8.0

0

.... �

Slo

pe

= 59

.3 ±

0.4

mV

/dec

ade

--�

�--

��

�--

��

--�

��

·-+-�

��

��

�-+

-----

��

-r-�

�..

..,.�

��

-t-�

�--

-1�-'

-2

- . 00

-2.0

2 -2

.04

-2.0

6 -2

.08

�

Log

Na

' c

onc

ent

ra

tio

n

(mo

l/1

)

Fig

ur

e 4

. Ty

pic

al

Cal

ibr

at

ion

Cur

ve f

or

So

diu

m

fon

E

lect

ro

de

at C

ons

tan

t I

onic

St

ren

gt

h.

-2.1

0

.i:i.

.....

42

: equation (28) . Thi s procedure was repeated for each data pai r and a ., · · series of constants was calcul ated. The calcul ated constants appear

i n table ( 1 ) a l ong with other pertinent data .

The error was estimated from two values , the standard deviation �"-

< of the sl ope from Part I and the standard deviation of the mean value

of KA. The error from the solution compositions and di lutions i s

1< negl igible compared to these two . The total error o� KA was calcu-,•. :: l ated by summing the "slope error" and the standard deviation of the

di fferent points (see Appendix I ) . The "slope error" was estimated

' by assuming 1 standard deviation of error in the sl ope and using the

new sl ope to calcul ate a new set of apparent association constants

at that ionic strength. The di fference between the means of both sets

then was used as the "slope error. "

It was noted that a few runs yiel ded unusual ly high constants .

These runs however seem to have very l ow s lopes as detennined from

the cal i bration run. Therefore Part I I was recal cul ated assuming a

.Nernsti an , 59 . 1 5 mV/decade sl ope. These results are al so shown in

Jab le ( 1 ) .

Tetramethyl ammoni um Chloride Runs . The data for the .tetramethyl

anmonium ion runs were analyzed i n the same manner as described for

the KCl - ( CH 3 ) �NCl runs . In these runs no K+ was present and the

results , g i ven i n table (1) are wi thin experimental error of those

runs which contained K+ . I t was apparent that the electrode was

s l.ightly less stable for these runs , which could possibly be due to

the fol lowing reaction,

KCl- ( CH s ) �NCl Runs

. I K"' A S lppe KA(Nernstian)

. 0 . 098 2 .00 ± 0 . 15 56 . 42 ± 0 . 19 1 . 90 ± 0 . 24

0 . 099 *' 3 . 85 ± 0 . 25 42 .8 ± 1 . 3 2 . 7 ± 1 . 2 'It

0 . 193 1 . 93 ± 0. 28 65 . 0 ·± 3 . 7 2 . 14 ± 0 . 38

0 . 200 2 . 18 ± 0 . 11 49.60 ± 0 . 17 1 . 80 ± 0.49

0 . 380 1 . 99 ± 0 . 10 48 . 70 ± 0 . 60 1 . 61 ± 0 . 43

0 . 383 1 . 80 ± 0 . 14 60.56 ± 0 . 51 1 . 84 ± 0 . 16

0 . 764 1 . 65 ± 0 . 04 59.25 ± 0 . 36 1 . 65 ± 0 . 03

(CHshNCl Runs

I K ... . A S lope KA(Nernsti an ) .

0 . 105 1 . 83 ± 0 . 05 57 . 87 ± 0 . 10 1 . 79 ± 0 . 05

0 . 175 2 . 04 ± 0 . 1 1 57 . 90 ± 0 . 18 2 . 00 ± 0 . 1 5

0 . 193 1 ..71 ± 0 . 20 59 . 15 ± 0 . 27 1 .71 ± 0 . 21

Extrapolation to Zero Ionic Strength

2 . 4 ± 0 . 2

2 . 2 ± 0 . 2

2 . 1 ± 0 . 2

2 . 1 ± 0 . 2

KC1 - (CH 3 ) �NC1 Runs only

Both sets of Runs

Table 1 . Apparent and Zero Ionic Strength

Associ�tion Constants for NaC0 3- .

* Not used i n extrapol ation procedure

43

· These resul ts verify that there i s no dependence of the experi

mental ly detennined KA on potassi um i on i f its concentration i s

not. significantly changed.

44

Extrapolation to Zero Ionic Strength . The apparent associa

tion constants g iven i n Table ( 1 ) were corrected to I = 0 by plot

ti ng l og KA versus I . Thi s plot i s shown for the association con

stants detennined usi ng the experimentally detennined sl ope [figure

(5 } ] ,and assumed Nernstian s lopes , figure (6) . The "best fit" l i nes

shown on the plots were detennined by the method of least squares.

Of th� values of KA l i sted in table ( 1 ) , 2 . 2 ± 0 . 2 was chosen to

· be the final estimate of the thennodynami c constant. Thi s value

was chosen because i t i ncl udes the points from both sets of runs

and uses the apparent constants derived from the experimental ly

detennined s l opes . I n this case i t i s assumed that si nce many

experimental s l opes were "non-Nernsti an" , the el ectrode response

for the carbonate runs woul d a l so be non-Nernsti an.

Plotting l _og KA versus IT and extrapolating to I = 0 seems

to be the best choice of data analys i s . Using the Davies equation

i s questionable because i t has an upper useful l imit of I = 0 . 1 .

A best fit l i ne was calculated for a plot of log KA� + 2 IT I

T 1 + I

versus I , which yiel ded a constant at I = 0 of KA = 5 . 9 ± 0 .3

(standard deviation ) . This value i s somewhat l arge and probably

not correct due to the "over-extension" of the Davies equation.

_,,

0

c.o

"'

)> \

0.6

•

o. 5

.

. 0.4

I In

terc

ept

= 0.

33 ±

0.0

4

Slop

e =

-0

.11

± 0.

07

• 0.

3 A

• •

•

0,2

I •

0.1

----

-�--

-------

--�

----

-�--

�--

---�

--�

�--

�--

-�·--

--J-�

.......... --

----

0 0.

1 0.

2 0.

3 0.

4 0.

5 0 .

6 0.

7

IT

Figu

re 5

. Pl

ot o

f �o

g K A

ver

sus

IT fo

r Na

C03-

(e KC

1 -(C

H3)1t

NCl

Runs

,•

(CH3

)1tNC

l Ru

ns)

0.8

0.9

.i:.

<.11

__,

0

�

�

)> \ - ::z

Cl)

�

::

::3 V)

r+

.J

. Il

l ::

::3 ..

......

0.6

0.5

I o.

4 r

o.3

I 0.

2 .

0.1 0.

0 0.

1

• In

terc

ept

= 0.

31 ±

0.0

4

Slop

e=

-0.1

1 ±

0.06

A.•

•

A

• •

A

•

0.2

0.3

0.4

0.5

0.6

0.7

0'.8

IT

Figu

re 6

. Pl

ot o

f Lo

g K A

(Ner

nsti

an)

vers

us I

T fo

r Na

C03-

(. KC

l -( C

H 3) ..

Ncl

Runs

, �

(CH

3) .. N

cl R

uns)

0.9

.f¥

0)

47

Another possi bi l i ty of calcul ating KA from KA values i s by div i .di.ng

the. KA ·values _by the appropri ate single ion activity coefficients

for co,2- . These activ ity coeffi cients have been measured i n K2C0 3

solutions . 2 5 Thi s procedure assumes that KC03- ion pair fonnation

i s i nsignificant and that the acti v ity coeffi cients for NaC03- and

Na+ cancel . The fi rst assumption may be true , but i t woul d seem

that i n solutions > 0 . 2 M the l atter may not. Calculations of thi s

type yield values of KA from 4 to 9 and average to about 7 . I t

shoul d be noted however, this method i s highly uncerta in .

Comparison with Other Data. Our data are compared wi th other

KA values i n table ( 3 ) . The value of Garrel s and Thompson 1 i s

unusua 1 l y 1 arge and probably should not be trusted. Nakayama'·s

value2 6 at I = O i s 3 . 5 and i s more i n the range of thi s work.

Apparen� association constants of Lin and Atkinson,2 7 Butler and

Huston.28. and Hawley29 are a l so g i ven . These apparent association

values are sometimes more useful than the thennodynami c constant

because s ingle ion acti vity coeffi cients are very difficu l t to

predict at i onic strengths greater than a few tenths . Our values

shown are calcul ated, at a g i ven ionic strength , using the l east

squares data from the plot of l og KA versus II. The uncertai nty

for a calcul ated KA at a g i ven i on ic strength i s taken to be

approximately the same as the uncertai nty for the experimental

values near that i on ic strength .

I t i s bel ieved that our values represent better estimates of

�he true constants because all of the other methods , except for

that of L i n and Atkinson, depend on a "second order" effect to ·.

measure· the constant. The constant detennined by Nakayama , for '

eiampl�, depends upon a variation of the fi rst and second d i sso-cia�ion constants of carbonic aci d in the presence of varying

amounts of sodium ion . Our method i s di rectly sensitive to the

fr�e sodium ion concentration which can be d irectly related to

the concentration of the sodium carbonate i on pai r .

' : . .

2 . Detennination of KA for NaSO_i.-

Tetramethylammonium Chlori de Runs . The data fran the tetra

methylctmmonium chloride runs were analyzed with the same procedure

as that described for the NaC03 - association constant. In these

48

runs the el ectrode seemed to be very stab l e . The electrode response t was n�arly Nernstian for most of the cal i bration runs. The Nernstian

response coul d perhaps be due to a seasoning effect of the el ectrode

membrane or to the fact that for these runs the (CH3 ) i.NC1 was not

al lowed in the basi c . soluti.on .for more than 3 hr before the runs ·were made.

the calculated constants and other data are g i ven in table ( 2 ) .

t'he error analysis was made i n exactly the same manner as i n the

Naco3- detenni nati on . Part I I of PAIR was also repeated assuming

a'' Nernstian slope and values of the recal c1Jl ated constants , KA(Nernstian)

are g iveQ i n table ( 2 ) .

Benzyl tri ethyl ammonium Chl oride Runs . The data for the benzyl

triet.ttylammonium chloride runs are g iven i n table ( 2 ) . These data

. . .

I

' 0 . 042

0 .118 "

0 . 173

0 . 234

0 . 347

0 . 373

0 . 466

0 . 739

> . ..

I i -0 . 039

0 . 083

0 .:.141

K .. A * 6 . 17 ± 0 . 71

3 .85 ± 0 . 32

3 . 19 ± 0 .13

3 . 54, ± 0 . 62

2 . 55 ± 0 . 40

2 . 45 ± 0 .14

2 . 35 ± 0 . 07

2 . 21 ± 0 . 05

4 .10 ± 0 . 25

3 . 86 ± 0 .10

3 . 90 ± 0 . 05

Slope

58.65 ± 0 . 20

58. 7 ± 1. 6

59 . 43 ± 0 .10

58.19 ± 0 . 10

57. 96 ± 0 .11

58 . 73 ± 0 . 07

58.69 ± 0 . 08

58.75 ± 0 . 25

Slope

57 . 50 ± 0 .13

58.19 ± 0 . 11

58. 35 ± 0 . 12

KA(Nernstian)

6 .14 ± 0. 72 *

3 . 82 ± 0 . 21

3 . 20 ± 0 .14

3 . 48 ± 0 . 65

2 . 49 ± 0 . 40

2 . 43 ± 0 . 15

2 . 33 ± 0 . 07

2 . 20 ± 0 . 06

KA(Nernstian)

3 . 98 ± 0 . 34

3 . 79 ± 0 . 16

3 . 84 ± 0 . 09

; Extrapolation to Zero Ionic Strength

5 . 4 ± 0 .8

5 . 4 ± 0 .8

5 . 4 ± 0 . 4

5 . 3 ± 0 . 4

( CH 3 ) 4NCl Runs only

Both sets of Runs

1:

Tabl e 2 . Apparent and Zero Ionic Strength

AssociatiQ� Constants for NaS04- . 1 •

* Not used i n extrapolation procedure

49

.

. ·-were calculated as mentioned previously. lt is assumed that the s expe,rimental ly detennined constants are independent of the ionic

\

strength bui l ders used because the calcul ated constants using

C6H5CH2N(C2H s ) 3Cl are within experimental error of the constants

detenni ned· using (CH 3 ) .. NCl .

Extrapolation to Zero Ionic Strength. The apparent constants

g i ven i n table ( 2) were used to estimate the thennodynamic asso

ciation constant, KA for Naso .. - . A plot of l og KA versus IT and

log KA(Nernsti an ) versus IT were extrapolated to I = 0 i n figures

(7 ) and (8) , respecti vely . It i s i nteresting that the sl opes

s hown 1 n figures ( 5 ) and (6 ) for the Naso .. - runs are much l arger

than those for NaC0 3- i n figures (7) and (8 ) . Perhaps the car@

50

bonate i on or sodium carbonate ion pai r has a different effect on

the water structure than the sul fate or sodium sul fate i on pai r·.

The s l opes and intercepts were calcul ated by the method of l east

squares . The value of 5 . 3 ± 0 . 4 was chosen to be the best estimate

because i t represents the points from both sets of runs and assumes

Nernstian .response . Nernstian response can be assumed i n thi s case

because the experimental ly detennined slopes for i ndi vidual runs

are very cl ose to the theoreti cal response. ([

A plot of log KA + 21 + If versus I for the Naso .. - data

yields an association constant of KA = 1 1 . 8 ± 0 .8 ( standard devia

tion ) . Thi s value, l i ke that for NaC03- , can be disregarded be

cause i t i s very unl i kely that the Davies equation works at I > 0 . 1 . •

......

0

l.O

"'

)> \

0 .9

---r------....------....---,----.----ro---.------......---r------..---.....------..----

.�·.'.

0.8

•

0.7

0.6

0.5

0.4

.... " •

•"'°'.'..,

"' ,,.,.

',,.,

.......

•

Inte

rcep

t =

0.

73 ±

0.0

3

Slop

e =

-0

.49

± 0.

06

• ••

• ,.·,{ ·'

.... .t/_

�' .. ,i"'il

.

0.3: 0--

""-�

�--

-:�--1.

.--.JL-

-_J__j_

�J_

__j___J

L._.j_

_J,,.�

1-..

..J....._j�

.:L:::: �

0.

1 0.

2 0.

3 0.

4 0.

6 0.

7 0.

8 0.

5 0.

9 IT

Fi

gure

7.

Plot

of

Log

K A v

ersu

s IT

for

NaS0

4-

(e (C

H3)4

NCl

Runs

, .4 C

6HsC

H 2N(

C 2Hs

)3Cl

Run

s)

01

-

- 0

'°

;io;:

)> \ - :z

It>

"1

:J

"'

c-+

..

... Il

l :J

-

0.9

r--:r--i-�.--r��r-.--;-�.-.----,-�r-.--+�r-------__:_

"'--

· ...

0.8

l-•

l 0.

7

r �

0.

6 t-

A

�

-

I 0.

5

0.4

.. ...

. . �

. .,, �-

.. -�

·� . . ..

...

�

•

.. .. � �:1�

-:...,.,1 \

Inte

rcep

t=

0.72

± 0

.03

Slop

e =

-0

.48

± 0.

06

••

•

0.1

03

, I

I I

I I

• .

0 '

' t

I

' I

I'

''

'>r 0.9

0.2

0.3

0.4

0.6

0.7

0.8

0.5

II

Figu

re 8

. Pl

ot o

f Lo

g KA(

Nern

stia

n ve

rsus

IT fo

r Na

S04-

(e (C

H3)t.

NCl

Runs

, .A

Ci;Hs

CH2N

(C2H

s)3C

l Ru

ns)

(J'1

N

Comparison to Other Data. Our values for the formation con

st�nt �d errors are calculated i n the same manner as described ..'

for NaC03 - . These and other values are shown in table ( 3 ) . L i t-

erature val ues for the NaS04- association constants are bel i eved

to be more rel i ab le than the values for NaC03- . The reported

value from Jenkins and Monk 3 0 from conductance measurements i s

most often cited i n the l i terature . The values reported by

Fi sher and Fox3 1 are much higher than the other constants at I = 0

i ncl uding those cal culated by Reardon . 3 2 Reardon 1 s value was

calcul ated from measured Na2S04 stoi chi ometric activ ity coef

fi cients. He� used the dissociation constant of Kso-- and the

mean �al t method (YK+ = Yc1 - = Y±KCl ) to estimate the activ ity

coeff� cient of su lfate . Two values at i on ic strengths of 0 . 5

53

a�d 0 . 61 were reported by Santos et !l_. 3 3 and Kester and Pytkowicz3 4 ,

respecti vely. Each of these values 'is within experimental error

of our values. The work of Santos et !}_. was done using an Orion

sodium selective ion e lectrode , but wi th a di fferent method.

The fact that our extrapolated value agrees wel l wi th the

value reported by Jenkins and Monk i s a strong veri fication of our

method. However i t i s important to point out that values closer

to I = 0 are needed to estimate KA with great certainty. The

l ower ioni c strength l imit of this method i s from 0 . 05 to 0 . 01 .

3 . Variation of Ionic Strength

Tetramethyl ammoni�m Chloride Runs . Plots of the electrode

54

Table 3 . Comparison of Data for Association

� Constants for NaCOa- and NaS04- .

Sodium Carbonate Association Constants

I K.,\( thi s work)* K.,\(other workers ) ref. Comments

0 . 00 2 . 2 ± 0 . 2 18.5 1 pH measurements of �a2COa-NaHCO a

3 . 5 ± 0 . 1 26 From Kd of H2C0 a

0 . 19 1 . 9 ± 0 .3 4 . 2 ± 0 .8 27 Sodium ion electrode

0 . 50 1 . 8 ± 0 . 2 1 ± 1 28 Harneds Rule data

0 . 70 1 . 7 ± 0. 1 Sea Water

o . 72 1 . 7 ± 0 . 1 · 4 . 25 ± 0 .3 29 • -}

�detenni ned from least square. fi t data

� Sodium Sulfate Association Constants

I K.,\(this work)* KA(other works) ref. Comments

0 . 00 5 . 3 ± 0 . 4 12 .5 ± 2 31 Conductance

10 .3 ± 0 . 3 31 Conductance

6 . 6 3 2 From Y±Na2S04 5 . 3 30 Conductance

� Sodium ion 0 . 50 2 . 4 ± 0 . 2 2 . 5 ± 0 . 2 33 el ectrode 0 . 61 2 . 2 ± 0 . 3 2 . 02 ± 0 . 03 34

0 . 70 2 . 1 ± 0 . 2 Sea water

*determined from least square fit data

55

respon�e versus the total i on ic strength are shown i n figure ( 9 ) .l for a s;}.>dium chlori de and sodium carbonate run of the same total

,•

sodi um ion concentration. The ionic strength i s changed with

addi tion of (CH 3 ) 4NCl . Even though the total sodi um ion concen

trations for both soluti ons i s equal , the Na2C0 3 run has l ower

vol tages than the NaCl run at the same i on ic strength . It i s

evident that thi s reduction o f the free sodi um i on concentration

for the Na2C03run i s due to the fonnation of NaCQ 3- . If we assume

that the NaC1 - (CH3 ) 4NCl sol ution contains only free sodium, we can

attempt to calcul ate the free sodium ion concentration for the

Na2CO r(CH3hNCl solution from equation ( 27b ) . It i s then pos s i ble •

to express the free carbonate and sodium carbonate ion pai r con-centrations , which can be used to express the equi l i bri um constant.

f

Equi l l'-brium constants calcul ated i n this manner do not yield rea

sonab}e results because the uncertai nty i n the voltage readings are

large.

Tetramethyl a111J1oni um m-Benzenedi sulfonate Runs . For these runs

the concentration of sodi um ion i n the Na2BDS solution was 3% higher

than that i s the Na2CP 3 solution . Thi s i s apparent by the higher

'°E reading with the Na2BDS sol ution than with the Na2CO 3SOlution at

the ihitial point where no extra BOS has been added. However after

the fi rst and subsequent additions of [ {CH 3 ) 4N] 2BDS the response with

Na2BDS i s l ower than that with the Na2C03 at the same ionic strength.

It fol lows that the free sodi um ion concentration i s l ower i n the

Na2BDS solution and therefore the concentration of NaBos- ion pai r

f'T'1 �

ct> (") rt--s 0 c... l'D ::0 ct> (11 -0 0 :::> (11 ct> -3 < -

70

60

50

. . . ;,,'· •'

40 · .

30

0

.

0 . 1 0 . 2 0 .3 0 . 4 0 . 5 0 . 6 0 . 7 I (total )

Figure 9 . Plot of Electrode Response Versus Ionic

Strength for Salts with Constant Sodium Ion Concentration

( • NaCl with (CH 3 ) i.NCl , A Na2C0 3 with (CH 3 ) t.NCl ,ANa2C0 3 with [ (CH3 ) ..N] 2BDS and CJ Na2BDS with [ (CH 3) ..N] 2BDS)

;JV

--'

0

57

);.

i s ·hiQher than the concentration of NaC0 3- i n the Na2C0 3 solutions . ' "' �!'·" ... Thjs suggests that the sodium and m-benzenedisul fonate ions wi l l

pai r to a signifi cant degree, perhaps as much as NaC03- . Thi s seems

a bit surpri s ing because the charge in the BOS i on is spread out

over a much l arger framework than in either carbonate or sulfate.

4. Comparison of Sal ts Method

The resul ts of the compari son of salts method are shown in

figure ( 10) for a typical run . It was noted that the sl opes deter

mined by this method are cl ose to Nernstian (54 to 52) , whi ch i s

good consi dering we are plotting l ogarithm of concentrations and not ;

acti vities . This method i s not acceptable for determining constants

becaµ,5€ the l i nes for Na2C03 and Na2BDS are almost co-l i near. Ei ther ' .

thi s· ·i s due to experimenta 1 error or the fact that Na2BOS i s not

a good standard. Perhaps BOS ion pairs with sodium ion to almost

the same extent as carbonate. This wou l d explain the curve crossing

i n · figure ( 9 ) and the co-l i near behavior i n figure ( 10) .

B . Other Electrode Methods

1 . Potassi um Ion El ectrode

The potassium ion el ectrode was unable to g i ve stable readi ngs

for any of the solutions tested. Electrode i nstabi l i ty of ±2 mV/5min

was noted which cou l d mask any sma l l change in the free i on concen

tration of potass i um. It i s possib le that the tetramethyl ammonium

60 ..-.�

��---,--�----�---�----------�----��--.----.--------�----��----...

,,· ·.-.

m

40

...;..,

(1)

0

r+ d 0..

(1)

:::0

ct>

VI

"O

0

:3

VI

ct>

.....-..

3

<

........

20 0

-20

-40

�--

------ �

__.,

____

__ _.

__

____

__.�

��

_.�

----

---- --

-"----�

------'

----�

----_.

�-

-2.5

-2

.0

-1. 5

lo

g [N

a+]

Figu

re 1

0.

Plot

of

Elec

trod

e Re

spon

se v

ersu

s

Log

[Na+

] fo

r Co

mpar

ison

of

Na2B

DS a

nd N

a2C0

3.

(eNa

2C03

, A

Naz

BDS)

-1

.0

(1'I

CX>

59

i on attacked the ion exchanger i n the potassium el ectrode. Tetrar:

alky,1. anmon ium i ons have been known to affect the electrode reaction

of a Ag/AgCl el ectrode . 3 5

2 . Carbonate Electrode Measurements

Compari son of Sal t s . A p lot of the data for thi s method i s

shown i n figure ( 1 1 ) . The p lot of E versus l og [C032-] for Na2CQ 3 . .

and K2C0 3 were practi cally co-l inear. Th i s method seems too i n

sensitive for the determi nation of a sma l l constant . For sma l l

constants such as these a method of compari_ng di fferent soluti ons

i s probably not goi_ng to work because between points the e 1 ectrode

must be placed i n di fferent sol utions . Due to a sma l l asymmetry

potent� al the uncertai nties of the electrode response are i n-'1

creased when measurements are made i n this manner.

Addi t ion Method. In itial ly the solution i n the cel l contains

on�y Na2C0 3 at a concentration of 0 . 124 M . A KA for NaC0 3- was

assumed from our work to be l.88 at this ioni c strength . Using thi s

value the concentration of free carbonate was calcul ated. When

the K2C0 3 was added the el ectrode response changed. Th is change

represented an additional amount of free carbonate. Once again

the free carbonate response was calcul ated assuming a Nernstian

slope . The KA for KC03 - was i terated upon using the known con

sta�t to estimate [C03 �-J F and the relationship [C03 2-]T = IC0 32-] F + [KC0 3- ] + [NaC03 -] . The calcul ated constants show great ex-

. perimental error, but a l l of the constants were below 1 , wi th a

,.,,

.....

ct>

(')

�

�

0

a.

ct>

::0

ro

"'

-0

0

::s

"'

ro

- 3

<

-

40·0

·.

I '1

..

, I

I ..

. . f

.1

--1 -

I I

I .J

,, I

-

I• I

. • I

' .

I I

•. "

,_

, -.

--·.

. '

-.......

. ··-·

·'

. �·

....

�-�=·�

•

f i.·: ..

:.._ .. '�

·�· .. .

.

-430

A

-460

-490

-520

-550

..._--.�--�._---�--�_,__..�--�-----.....__.._�.._�.__-"-�-'-�"--__.�--�----

-4.5

-4

.0

-3.5

-3

.0

-2.5

lo

g [C

O 32

-]

Figu

re 1

1.

Plot

of

Elec

trod

e Re

soon

se v

ersu

s Lo

g [C

032-

]

Usin

g Ca

rbon

ate

Sele

ctiv

e El

ectr

ode

(� N

a 2CO

3, A

K2C

O 3)

O'I

0

few . a�ound 0 . 5 . I t therefore seems that �he KA for KCOs- i s very "'

smalf and less than 1 . This i s an interesting result when one

considers that the association of KS04- i s greater than that of

NaS04- .

3 . Sul fate Electrode Measurement

61

A plot of electrode response versus pH i s plotted in figure

( 1 2 ) . At high pH values the el ectrode probably responds to OH

and at l ow pH values HS04- formation affects the membrane potenti al .

lhe regi on we feel should be used for sul fate determination i s

betwe�� p H 7-8 . 5 . The manufacturer recommends pH 5 . 00 ± 0 . 05 , but

in tfrf·s area the e 1 ectrode response cJiange fpr a g:i ven change i n

pH-· i s/�uch larger than i n the "pl ateau" area. Using pH 5 . 00 ± 0 . 05

a l so :"requires much more work to assure that al l solutions are ad

Justed to a very narrow pH range .

,.,,

__,

Cl)

(')

rt

�

0

0..

Cl)

::0

Cl)

VI

"'O

0

::I

VI

Cl)

- 3

<

.._...

580

,,..,.

-I

I

I I

I I

I

I I ..

I

I, I

?. 1

I

I

-560

-540

-520

-500

-480

-460

4 5

6

·...

,•

·;,.

�.

"{;.

7

pH

8 9

Figu

re 1

2.

Plot

of

Elec

trod

e Re

spon

se v

ersu

s pH

for

Sulf

ate

Ion

Sele

ctiv

e El

ectr

ode.

10

11

, ...

:-_•

• _ ..

. '. : 1t'.

...

�

"'

N

.�

- ... ..

VI I . SUGGESTIONS FOR FUTURE RESEARCH

63

Thi s research could be extended to other methods for the deter-

: mination of association constants. The two most productive areas

. should be the detenni nation of the stabi l i ty constants of KS04- and

NaBDS- . The KS04- constant could be determined using a potassium

"> sensitive electrode. Using benzyl triethyl ammoni um or tetraethyl

ammonium sal ts to control i onic strength may be preferable to using

.. tetramethyl anmonium salt because they should not undergo a reaction

· '

in the presence of bas�. The electrode woul d not be expected to

have sensitivi ty tQ these ions.

trhe NaBDS- association constant shoul d be detenninable in the ,I

. same'.:nianner as NaC03 - and NaS04 - . When a constant for NaBDS- i s • i> • # � .

'_ detetmi ned , i t wi l l probably be l arge enough to exclude Na2BDS for

use as an unassociated standard. Prel iminary work has i ndi cated that

sodi um 4 , 4'-bi phenyl disulfonate may be an unassociated el ectrolyte .

However , because of i ts low solubi l i ty , its usefulness may be l imited .

Perhaps the sodium para-benzenedisul fonate with i ts greater solubi l ity

cou l d serve as a more useful standard for 1-2 el ectrolytes , but thi s

awai ts experimental verifi cation .

Work with the sul fate electrode coul d a l so lead to interesting

results . The addi tion method mentioned for the carbonate el ectrodes

could be used for sul fate runs . Thi s was not possible using tetra

methyl anmonium salts because the pH of the solution coul d not be

control led to ±0 . 05 units . This i s probably due to the reaction

64

..

prev.tously menti oned. Runs of K2S04 and Na2S04 wou ld serve as a ,-.e

go� verification of thi s method. It i s bel i eved that the pH range \, .. ,!<

from 7 to 8 . 5 shoul d be used rather than the man�facturer ' s sug

gested range , 5 . 00 ± 0 . 05 . I t shoul d be noted that this method

wi l l be l ess exact because the s lope i s only about 30 mV/decade and

the expanded scale can not be used . .r ... • "�

, .

. .

65

Appendix I . � .. ·:. ·samEl e Calculations for the Determination of the Sodium Carbonate

and Sul fate Association Constants . Sample cal cul ations and raw data I

are gi ven here for one sod i um carbonate run . This method can al so be

used for the sodium sul fate runs .

Solution Composi tions :

Solution I

[NaCl] 9 . 9953 · 10- 3 M

[KC l ] 0 . 500214 M

[ ( C� 3 ) ,NCl ] 0 . 2500 M

IONIC STRENGJ'H

I�' , . ·� ...

0 . 7634

Solution I I

[Na2C0 3] 4 . 97818 · 10- 3 M ' .

[K2C03] 0. 24864 M

0 . 7640

Solution I I I

[KCl ] 0 . 501338 M

[ ( CH 3 ) 4NC1 ] 0 . 2550 M

0 . 7595

Cal i bration Run . Al i quots of Solution I I I were pi petted i nto

75 ml of Sol ut i on I i n the cel l . The vol t age , E and the ·vol ume , V

were recorded and corrected for the expanded sca l e , equation (32 ) .

The resu l ts were :

0 . 0 mV ( regular scal e ) = - 1 . 59 mV (expanded scale)

Ll!!!U E (mV} E "' (mV) V (ml) E (mV) E "' (mV)

7 5 . 00 -3 . 59 -1 . 94 80 . 00 -5 .36 -3 . 68

76.00 -3 . 94 -2 . 29 85 . 00 -6 . 92 -5 .21

77 . 00 -4 . 28 -2 . 62 90 . 00 -8 . 40 -6 . 68

78.00 -4 . 66 -3 . 02 95 .00 - 9 . 78 -8 . 03

79 . 00 -5 . 04 -3 . 37

66

-'

For each total volume, V , the [Na+] was calcul ated from [Na+] =

'-�JS x 9 .9953 x 10- 3 M)/V. Then a cal i bration curve was prepared of

_E' versus log [Na+] . A plot of this i s shown in figure ( 4 ) . Part

1 of a FORTRAN program PAI R , Appendix I I was used to evaluate the

sl ope and i ntercept of the cal i bration curve. The resul ts of the

least squares fit and other results are gi ven i n table (4) . For this

run it was found that the s lope was 59.25 ± 0 . 36 mV/decade. The

estimated error i s ± 1 standard deviation.

Determination of Constant. Once the sl ope· i s known i t i s then

possible to estimate the equ i l i brium constant by appropi ate calcu l a

tion of the resul ts of the other run . A l iquots of Solution I I were �

added �tp 75 ml of Solution I . The total volume, V and the el ectrode

� -resp�.nse, E were recorded and the corrected response , E ' cal cul ated .

.. . ·

The resul ts were :

V (ml ) E (mV) E' (mV) V (ml ) E (mV) E' (mV)

75 .00 -3 . 64 - 1 . 99 125 . 00 - 7 . 73 -6 . 02

85 . 00 -4 .87 - 3 . 20 145 . 00 -8. 52 - 6 . 79

95 .00 -5.85 . -4 .17 165 . 00 - 9 . 14 - 7 . 40

105 . 00 -6 . 60 -4.90

These results were analyzed by Part 2 of PAIR . It is assumed that

the first reading of - 1 . 99 mV i s due to the [Na+] T a l l of which i s

expected to be "free . " From equation ( 27b) a di fference i n voltage

can be di rectly related to a di fference in free ion concentration.

For examp l e , i f we use the experimental ly determined sl ope and the

data ·for 75 and 85 m� , we have: ... . . ,. ,,

67

• f; �i�' { ( 3 20 + 1 99)/59 25 + l og 9 . 99528 · 1 0- 3}

[Na+] F = 10 · · ·

This yie l ds a value of [Na+] F = 9 . 541 · 10- 3 M . The concentration

of the ion pai r , [NaC0 3- ] can then be cal cul ated from the d i fference

between [Na+]T and [Na+] F or from equation (22 )

[NaC03- ) = 9 . 907 · 10- 3 M - 9 . 541 · 1 0- 3 M = 4 . 50 · 10-4 M • '

� - The total carbonate concentration, [C0 32- ] T and the free carbonate

�concentration, [C0 32�] F can be calcul ated from equation ( 23 ) ; '· I ·r:�·.. . ;-��0 32- ] F

= 2 . 9836 • 10- 2 M - 4 .50 · 10- i. M = 2 . 9386 · 10-2 M =1': :.·:· ...

· Then from equation (28) the apparent equi l i bri um constant, KA can �

· · · be cal culated.

K"' ---------- = 1 . 61 A -( 9 . 541 · 10- � (2 . 9386 · 10-2 )

This procedure was then repeated for each data pai r and the average

constant and the standard devi ation cal cul ated. The standard devia-

tion i s beli eved to be a reasonable estimation of error for Part 2 .

The resu l ts of a l l these cal cul ati ons are shown i n table ( 5 ) .

Fi nal ly a Nernstian sl ope i s assumed and part two i s once again

recal culated to yi eld another constant. The constants are compared

i n table ( 1 ) .

68

Uetenni nation of Error. The total estimation of error for each

, ��" i s assumed to be the sum of the standard devi ation of the i ndi -

vi dual KA val ues (di scussed i n the previous paragraph) plus the

"slope error. " This first error i s cal cu l ated and shown i n table ( 1 ) .

For our example KA i s 1 . 648 ± 0 . 024. The "slope error" i s detennined

by adding 1 standard deviation to the sl ope and recalcu l ating the

;mean value of KA usi ng Part 2 . The di fference between this aver

age constant and the previous average constant i s the "s lope erro r . "

Thi s di fference i s ca l cu l ated ( 1 . 648-1 . 637) and then added t o the

-:l .: other estimated error or (error from points) + ( s l ope error) ; (total

> error) . In our exampl e

.i'

0 . 024 + 0 . 011 = 0 . 035

./ . :.,

Therefore the experimental ly determined constant i s bel i eved to be

1 . 65 ± 0 .04 at I = 0 . 76 .

The error for the constant calcul ated from assuming a Nernstian

s lope wi l l be the sum of the di fference between the two average con

stants p lus the standard deviation of the constant calcul ated assum

ing the Nernsti an sl ope. From table (4) this wou l d be 1 . 65 ± 0 . 03 ,

which i s smal l . This method of error treatment for other runs wi th

non-Nernstian s l opes wi l l probably yiel d an estimated error which i s

too l arge .

c

(.. r: c c c c c

c

c c c c c c c c c c c

PR

OG

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1\IG

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• (H

t.:.JT

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IS

f

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75

Stability Constants of NaCO3-, NaSO4- and KCO3- in Water ...

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