THE JOURNAL OF
PHYSICAL CHEMISTRY
Registered in U.8. Patent O&ce
@ Copyright, 1968, by the American Chemical Society
VOLUME 72, NUMBER 4 APRIL 15, 1968
Pyrex Membrane Potential in Binary Nitrate Melts1 by A. G. Keenan, K. Notz, and F. L. Wilcox Department of Chemistry, University of M i a m i , Coral Gables, Florida
M I 2 4 (Receiaed November I S , 1967)
Electromotive force measurements at 350” are reported for cells with a Pyrex membrane and containing binary nitrate melts of the type RI1NO3-AgNOa. M is Li, Na, or K varying in Concentration from 0 to 90 mol %. The ion-exchange model fits the data, whereas the liquid-junction model does not. This result agrees with a previous fused-salt system involving an inert solvent and a lower concentration range but constitutes a more stringent test of the ion-exchange model, since both cations are potential determining and present over essentially the whole concentration range. Selectivity constants have the same rank order in the two systems as well as in aqueous solutions. The significance of this is discussed.
Membrane potentials have commonly been interpreted on the basis of either the liquid-junction2 or ion-exchange3 models. The physical basis of the liquid-junction model consists simply of a diffusion potential integrated from one liquid phase to the other according to the equation
E
=
- ( R T / F ) s 12 Z ( t , / Z t )d In at
The system in question consisted of a Pyrex membrane immersed in a solution of alkali metal or silver nitrates, singly or mixed, in fused ammonium nitrate solvent at 190”. The recent elegant derivation of the ionexchange equation by Conti and Eisenman5 reduces, for the case where one side of the membrane is exposed to a reference solution of constant composition, to
(1)
where t%is the transference number, 2, is the charge, ai is the activity, and the summation includes all ions which carry current. Thus the model is clearly inapplicable, in principle, to glass membranes, since the phase-boundary discontinuities, and the ion-exchange equilibrium which is known to occur at them, are completely neglected. Nevertheless, the model has been widely used to correlate emf data for glass membranes by invoking transference numbers (or relative ionic mobilities) with properties suitable for obtaining agreement with the experimental data. The moderately successful application of the liquid-junction model to glass-membrane potentials has been possible, in short, by use of the transference member as an adjustable parameter. In a recent p ~ b l i c a t i o n a, ~system was described in which the liquid-junction model failed completely to fit the data, whereas the ion-exchange model gave an excellent fit and meaningful values for the parameters.
E
=
E‘
+ ( R T / F ) In Bk,a,
(2)
where IC, =
(%/ul)K,
(3)
The ut are mobilities in the membrane and the K I t ion-exchange equilibrium constants at the surface, relative to a reference ion numbered 1. The order of the cation selectivity constants, IC,, was found to be the same as for aqueous solutions, indicating that the potential-determining ion-exchange processes at the (1) This work was supported by the Office of Naval Research under Contract Nonr-4008(07). It comprises parts of the Ph.D. Dissertation of K. Notz and the M.S. Thesis of F. L. Wilcox. (2) D. A. McInnes, “The Principles of Electrochemistry,” Reinhold Publishing Gorp., New York, N.Y., 1939, p 220. (3) R. H. Doremus in “Glass Electrodes for Hydrogen and Other Cations,” G. Eisenman, Ed., .Marcel Dekker, Inc., New York, N. Y., 1967, p 101. (4) K. Notz and A. G. Keenan, J . P h y s . Chem., 70, 662 (1966). (6) F. Conti and G. Eisenman, Biophys. J., 5, 247 (1965).
1085
A. G.KEENAN,K. NOTZ, AND F. L. WILCOX
1086
Table I: Emf Data for Pyrex Membrane Cells Containing the Binary Nitrate Melts MNOs-AgNOs a t 350’ AgNOs, mol %
100.0 79.8 40.0 19.6 10.0
-213.7b -212.1 -200.5 -181.0 -155.7 -126.4
100.0 90.4 80.3 70.5
-39.0 -29.5 -20.3 -15.3
60.0
...
50.3 39.9 30.4 20.0 10.4
0.0 9.5 17.9 36.6 64.0
60.0
Ag
Pyrex
&IN03
Ag+ in nitrate Ag eutectic
Cell potential for replicate on different bulbs, mV-
-run8
100.0 80.0 60.0 40.1 20.0 10.0 a
I
.
.
-211.6 -211.5 -209.7 -199.4 -179.5
Reference 6.
-Activity ooefficientaAgNO? MNOs
LiNOs-AgNOa -214.7 -219.4 -204.7 -209.3 -195.0 -199.7 -182.9 -184.8 -157.2 -157.4 -129.4 -126.9
1.00 1.04 1.14 1.30 1.59 1.75
NaNOa-AgNOs -38.8 -219.4b -30.7 .., -23.8 -200.9 -16.1 ... ... -184.3 0.0 ... 9 . 4 -166.8 ... 21.2 37.0 -137.8 68.6 -109.3
1.00 1.01 1.03 1.08 1.12 1.18 1.27 1.37 1.50 1.68
KNOa-AgNOs -214.1b -218.0 -214.9 -217.9 -215.2 -218.6 -212.5 -214.6 -201.3 -201.4 -178.0 -178.0
1.00 1.02 1.03 0.99 0.98 0 97
,
..
1.61 1.28 1.12 1.03 1.02
.,. 1.79 1.59 1.38 1.29 1.20 1.14 1.08 1.05
1.03
... 0.989 0.948 0.992 0.998 0.999
’ These data are shown in Figures 1 and 2.
duce the values for the other nitrates shown in Table I. The data, now plotted according to eq 4,again showed pronounced curvature. Some representative graphs are shown in Figure 1. Thus the liquid-junction model does not apply to these systems. Combining the usual Nernst expression for electrode potentials with the ion-exchange equation (eq 2) for membrane potential gives ECell
= E’
+ ( R T / F ) In klal +a1 kzaz
(5)
Since silver is the common ion in these systems, it is convenient at first to standardize the selectivity ratio scale relative to silver by putting ICl = 1. E’ then is evaluated at a2 = 0 and eq 5 may be recast in the form log-‘ Y = log-’
[F(Ei:iRiE’)] 1 + ICz(6) =
a2
a1
When plotted according to eq 6, all the data gave excellent straight lines, some representative examples (6) M.Bakes, J. Guion, and J. P. Brenet, Electrochim. Acta, 10, 1001 (1965). (7) R. W.Laity, J . Anzer. Chem.. SOC.,79, 1849 (1967). (8) I. M. Klotz, “Chemical Thermodynamics,” W. A. Benjamin, Inc., New York, N. Y., 1964. The Journal of Physical Chemistry
1087
PYREX MEMBRANE POTENTIAL IN BINARY NITRATEMELTS EMF (rn v)
- 120
-160
-
200
- 0.4
0 LOB
0.4
0.8
1;L
% concentration. The anomalous behavior of lithium on glass is well known.4 Although emf readings were taken between 0 and 10 mol yo MNOB, it was not possible to study this phenomenon further because the activity coefficient data could not be read sufficiently accurately in this range from the published values.6 I n any case, the selectivity constants discussed below are calculated from the slope and are not affected appreciably by the variation in E'. The agreement of the data in functional form with eq 5 thus demonstrates that the ion-exchange model applies to the binary melts used. Selectivity constants calculated from the slope of eq 6 and converted to a basis of I G N ~ = 1 are given in Table 11. It is seen that the rank order of selectivity constants is the same in fused ammonium nitrate solvent at 190" and in binary nitrate melts at 350". The values for the other ions relative to sodium are, however, an order of magnitude larger at the higher temperature, presumably due to the increased mobility in glass.
aI
Figure 1. Cell emf a t 350" us. log of activity ratio, according to liquid-junction model: 0 , Na-AgNOa (bulb 26); 0, Li-AgN08 (bulb 29); V, K-AgN03 (bulb 31). AgNOa is component 1. 0
2.0
Table 11: Selectivity Constants (IC) for Pyrex in Nitrate Melts
4.0
Binary nitratesa
NH,NO~*
Ion
(350')
(1900)
Na+ Ag+ Li +
1.00 0.78 0.63 0.070
1.00 0.32 0.065 0.007
K+ a
6.0
-
4.0
'01 0
J
2 .o
0
4.0
8.0
Figure 2. Emf data a t 350" vs. activity ratio, according to ion-exchange model.
being shown in Figure 2. All except the lithium lines passed through unity on the ordinate axis. The lithium lines could also be made to pass through unit intercept by making a correction of about -6 mV to E'. Since E' was evaluated from a pure silver nitrate solution, it seems probable that this correction represents a bias which is introduced by an initial etching of the glass surface by lithium ion below 10 mol
This research.
' Reference 4.
I t was pointed out in the previous work4 that the rank order of selectivity constants in Table 11, for fused salts, is the same as found by Eisenmang for aqueous solutions. This might at first appear unlikely, considering the large variation in extent of hydration and, therefore, effective size of the ions in question. These data have been interpreted'" recently to indicate that in fused salts the whole glass membrane takes on the transport and exchange functions of the hydrated gel layer in aqueous systems at room temperature. Since in most cases the gel layer occupies only a small fraction of the transport path, an alternative explanation of these data is that in aqueous systems the hydrated ion on entering the gel layer prior to adsorption loses its hydration sphere in a preequilibrium which does not influence the membrane potential. The potential-determining ion-exchange equilibrium constant at the lattice adsorption site, which enters into the selectivity constant according to eq 3, then corresponds to that in fused salts. J., 2, 259 (1962). (10) G. A. Rechnitz, Chem. Eng. News, 45, 146 (1967). (9) G. Eisenman, Biophya.
Volume 7.2, Number Q ApriE 1988
