stability constants of naco3-, naso4- and kco3- in water
TRANSCRIPT
Eastern Illinois UniversityThe Keep
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.
This is brought to you for free and open access by the Student Theses & Publications at The Keep. It has been accepted for inclusion in Masters Thesesby an authorized administrator of The Keep. For more information, please contact [email protected].
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 .
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75