GLASS ELECTRODE DETERMISATION OF SODIUM
I S NaCl-KC1 MIXTURES* BY F R A S K T R B A S A S D ALEXASDDR STEINER
I t has been shown by Horovitz' and Schiller*that a glass electrode can also function as a Na, K, Zn, or Ag electrode. In the presence of more than one ion, a mixed electrode potential is obtained, which, according to Michaelis and F ~ j i t a and , ~ HorovitzJ4may be represented by the equation
where Clk and c,, indicate concentrations of cation and anion of salt' i; (Yik and distribution coefficients of the cation and anion of salt i. In our studies of mixtures of NaOH, NaC1 and KC1, we kept KC1 and KaC1 constant in a given series of mixtures and varied KaOH only. It was found that log cxa plotted against E always gave a straight line. Moreover, a change in C K C I caused a parallel displacement of this straight line. We attempted to derive this straight line from the Michaelis-Horovitz equation. For alkaline solutions containing SaOH, S a C l and IiCl:
E
=
RT -1n1
F
' a y , ~ y ,+ U K C K UOHCUH
+ oicicci
In studying a series of mixtures of S a c 1 and NaOH, such that the sum of C N ~ C ~ cNaOHwas kept constant, we observed that the glass electrode potential remained nearly constant. The following mixtures were used:
+
+
i\l NaOH ,233 ,466 '932 I
,864
31 KaC1
Nols per liter 2.329 2.329 2.329
0.46j
2.329
-
2.329
-
2.096 I . 863 1.397
2.329
On the basis of this observation, it may be permissible to put
But
COH
+
CCI =
cs0
+
CK.
Substituting in (3) and dividing by
CYOH =
aci.
CYOH,CI:
* From the Laboratory of Biological Chemistry, Kashington Cniversity School of Medicine, Saint Louis, Missouri. ' K. Horovitz: Z. Physik, 15, 369 ( 1 9 2 3 ) . H. Schiller: Ann. Physik, 14) 7 4 , l o j I 1924). L. Michaeh and A. Fujita: 2. physik. Chem., 110, 269 (1924). * K. Horovitz: Z. physik. Chem., 115, 424 i 1 9 z j ) ,
GLASS ELECTRODE DETERMINATION OF SODIUM
E
(4)
= Eln /a’rvacNS
F
Ch’a
+ +
3059
~’KcK
CK
Neither equation ( 2 ) or (4) represent our experimental findings. The glass’ used by us had the following composition: Li Xa20
70% 155
K
very small amount
CaO 6% RIgO - X1203 - HBO3 - Fez03 - BaO
9 7
The equation proposed byHorovitz*for the potential of the glass electrode in alkaline solutions containing iTa+ is:
When potassium ions are introduced into such a solution, the Ka+ distribution coefficient a x a changes. If we assume that the number of sodium ions on the surface is in adsorption equilibrium with the number of sodium ions in s ~ l u t i o nthen, , ~ upon the addition of potassium ions to the solution, some of the latter will be driven into the interface, displacing a number of sodium ions. If we apply the adsorption isotherm to this polar adsorption, the number of potassium ions adsorbed (per unit area) will be k’.c‘l”; and the Ka+ distribution coefficient will now be equal to aNa(I-k.c”n). The isotherm does not contain a correchion for the adsorption of the solvent and, furthermore, it does not hold in concentrated solutions. It is very probable that the true adsorption isotherm shows a pronounced maximum.‘ K i t h these reservations, we substitute the corrected sodium ion distribution coefficient in ( j ) : E=-lncNa RT i I - kc’ ”) or
1
F
RT E =-lncNa+-ln- R T
F
ZF
asi
axa
asiKci
KGI
+ RT -ln(I-kc””) ZF
I t may logically be objected that aNncannot be independent of cg,, even in solutions in which S a + is the only predominant cation. This objection is justified. We found a constancy of ax, between 0.004 and 1.0 31 NaOH. Above and below these concent,rations, a ~ is. no longer constant. The theoretical reasons for the constancy of a distribution coefficient have been discussed by Freund1ich.j Glass and analysis by Kimble Glass Co., Vineland, S . J. Chem., 115, 424 (192j). Similar views have been brought forward by B. von Lengyel: Z. physik. Chem., 153A, 425 (1931); and by K. Lark-Horovitz: Naturwiss., 19, 397 (1931). ‘Evans: J. Phys. Chem., 10, 290 (1906), quoted by Freundlich. Freundlich: “Kapillarchemie,” p. 2 5 1 (1931).
* Z. physik.
3060
FRANK U R B A S A S D ALEXASDER STEINER
Equation (;) is in agreement with our findings. The glass electrode potential, in alkaline solution containing both S a " and IC', is linearly related to log exRJas long as C K is kept constant in the mixtures. A change in c K causes Z constant. The a displacement, the slope 2 . 3 0 3 RTjF = O . O ~ ~ Iremaining value of the slope was found to be equal to 0.060 v. (Average of 5 determinations). The term 0.0296 loglo ( I - k c1 ") represents the parallel displacement due to K+. 0.0296 log,,
asi h o i
represents the intercept, in the absence of K+.
The linear relationship between E and log cs., can be made the basis for a potentiometric determination of ?;a in the presence of IC If to an unknown mixture of XaC1 and KCl, we add a known amount of SaOH, the potential found satisfies (7). (8) El= m log (x c,) b x = unknown SaCl (mols), c1 = SaOH added. For an amount c2 of S a O H added, Ez = rn log (x c2) b (9) Subtracting (9) from (8): x c1 (IO) EI - E2 = m logx C?
+
+
+
+
+
+
m being known' from a series of calibration determinations, equation (IO) may be solved for x. This can be done conveniently by plotting both (Et-E2)/m+log (x+cP), and log (x c l ) against x (for vari.3 I 51, ous values of x) (Fig. I ) . The abscissa representing the intersection of these FIG.I two curves is the desired value for the unknown amount of KaC1 i n the original KaC1-KC1 mixture. As a reference electrode, a HPelectrode was used, mainly for the purpose of eliminating liquid junction potentials. The potentials of the H Pelectrode were calculated from S a O H activity coefficients according to Harned.' The small salt error was neglected. When the E.M.F. of the cell glass electrode-solution-H2 electrode wae plotted against log c X a , parallel straight lines were also ~ b t a i n e d . ~(Fig. 2 ) . These are more convenient to use for the calculation of x, as the H Pelectrode potential does not have to be calculated. The procedure is the same as before, with the exception that m in (8) and (9) now represents the slope of the line obtained when log S a is plotted against E b I F of the whole cell; while El and E2 represent the EMFs of the cell. The following mixtures were analyzed in the latter manner. 1 The value of m depends,on the electrode used; ELand ESshould therefore be determined
-
,,
+
with the same electrode, which was used for determination of m. 'H. S. Harned: J. Am. Chem. SOC., 47, 682 (1925). 3 Activity coefficient deviations are apparently within the percentage error of the method.
3061
GLASS ELECTRODE DETERMIXATION O F SODIUM
Mixt
Mols NaOH
A B C D E
0 2j
Mols KC1 o 125
NaOH found o 26
25
o
242
0 25
0 50
0
24;
25
I 00
0
0 25
2 00
0 0
25
0
Error
4 % 3 3% 1.27 2 or; 6 4%
215 o 266
3 .6y6
average
Sufficient NaOH was added to make c1 and cp 0.233 r\; and 0.698 S respectively. A third point was obtained by adding sufficient NaOH to make C'p
0.349
x.
The following cell potentials were observed: (Fig.
2).
.a
x
.I
a
a
FIG.2
S XaOH added
Mixture h
el = 0.233
c2
= 0.698
0'5440
0.5025
0.5025
B
0.5720
0.5295 0.5291
0.5721
c
0.5320 0.5319
D
0.5329 0.5330
0.5460 0.5465
0 .j;40
0.5402
0.5535
0.5814
E
0.5745 0 .j
i70
Glass electrode potentials calculated form NaOH activity coefficients. (Fig. 3 ) .
FRAKK U R B A S AND ALEXASDER STEISER
3062
S a O H added
CI = 0.233
0.349
C'z
PIlixture A
-0
-0
c
2804 2536
-0
B
-0
2509
-0
D
-0
2199
-0
E
-0
2327
-0
Kormal Hz potential
-0
2754 2474 2339 2341 2369
cz
=
o 698
-0
2631 2351 2326 2315
-0
2257
-0 -0
-0
= 0.
'I,
.4rd
-
1 .3
2
.I
LOG
CN,
FIG.j
In order to decrease the percentage error, c1 and cp should be approximately of the order of magnitude of x. A11 determinations were carried out in an oil bath at 2 j°C ri: 0.01'. Hydrogen was purified by passing over platinized asbestos at red heat. Solutions were kept under oil during the determination, to protect them from Cog. Readings were made by connecting electrodes in series with a 5 m.f. condenser t o the EhiF leads of a Leeds-Sorthrup type K potentiometer, so that at balance the condenser was unchanged. A 10-8 5 amp. sensitivity galvanometer was used, 0.2 millivolt giving a detectable deflection.' All leads were carefully insulated. As a rule, equilibrium was reached within less than I j minutrs. The glass electrode was of the Ilaber type, filled with 0.1 HC1; a Ag, AgC1 electrode, properly screened from light was used. The ruggedness of this type makes it useful in alkaline solutions.
Summary (I)
h method for the detn. of S a in mixtures of S a C l and KCl by means
of the glass electrode has been outlined. ( 2 ) An equation for the mixed electrode potential has been developed. 1
G. H. Bishop: R o c . Soc. Expt. Biol. Med., 21,
260-2
(19301.
