ION-EXCHANGE MEMBRANE POTENTIALS
3711
Ion-Exchange Membrane Potentials
by A. S. Tombalakian' and W. F. Graydon Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Ontario, Canada (Receited J u n e 27, 1966)
Direct measurements of electromotive force and transport numbers for sodium ion and water have been made across polystyrenesulfonic acid ion-exchange membranes separating different solutions of sodium chloride over a wide range of external solution concentration. The results indicate that the electrochemical potentials corresponding to the reversible transport of sodium chloride and water may be measured with a reasonably high degree of precision using polystyrenesulfonic acid ion-exchange membranes even in highly concentrated solutions. The measured electrical transference numbers for sodium ion verify the estimates of transference numbers which have been made from ion-interchange fluxes obtained in counterdiff usion experiments across the same membrane separating isotonic solutions of sodium nitrate and hydrochloric acid using the Nernst-Planck equation.
Introduction A previous study2 of membrane potentials across polystyrenesulfonic acid ion-exchange membranes in relatively dilute sodium chloride solutions has indicated that water transport causes the major deviation from ideality. Similar results for "untreated" collodion membranes in dilute potassium chloride solutions have been recently r e p ~ r t e d . ~The anion concentration in a cation-exchange resin immersed in solution increases markedly with increasing external solution concentrat i ~ n . The ~ xelative magnitudes of anion and water transport in potential measurements involving highly concentrated solutions are thus of interest. If the whole electrochemical process of the cell Ag,AgC1/NaCl(ml)lrnembranelNaCl(m") (AgC1,Ag is considered to be the reversible transport of sodium chloride and water and assuming no change in the composition of the membrane during an emf measurement, we may write2
E, = Ei
-
2RT a*(NaCl) I b 1 ~ 1 n a* (NaCl) I1
moles of chloride and water transferred per faraday. These transference numbers can readily be determined by independent measurements under experimental conditions similar to that of the membrane cell. The results of emf values and transference numbers obtained for polystyrenesulfonic acid ion-exchange membranes with sodium chloride solutions in the concentration range 0.05-4.0 M are presented in this report.
Experimental Section (1) Membranes. The polystyrenesulfonic acid ionexchange membranes used in this study were prepared by the bulk copolymerization of the n-propyl ester of p-styrenesulfonic acid with styrene, divinylbenzene, and benzoyl peroxide as catalyst and subsequent hydrolysis in 5% caustic soda solution following the procedure described previously. 2 ~ 6 The characteristics of these membranes are given in Table I. (2) Potential Measurements. The emf of the cell
Ag,AgCl/NaCl(m') /membrane/KaCl(m") (AgC1,Ag
+
RT a(Hz0)' tvIn F a(H2O)"
(1)
where E, is the measured cell electromotive force, Ei is the ideal potential for a hypothetical membrane permeable only to cations, bl and t, represent the
(1) Department of Chemistry and Engineering, Laurentian University, Sudbury, Ontario, Canada. (2) W. F. Graydon and R. J. Stewart, J . Phys. Chem., 59, 86 (1955). (3) N. Lakshminarayanaiah, ibid., 70, 1588 (1966). (4) H.P. Gregor and M. H. Gottlieb, J . Am. Chem. SOC.,75, 3539 (1953). (5) A. S.Tombalakian, H. J. Barton, and W*.F. Graydon, J . P h y s . Chem., 66, 1006 (1962).
Volume 70, Number 11
A'ovember 1966
3712
A. S. TOMBALAKIAN AND W. F. GRAYDON
Table I : Membrane Characteristics
Membrane
Mole
no.
1)VB
1
6 8 6
2 3
%
4
s
5
6
Capacity, mequiv/g of dry resin in Na form
Moisture content a t 100% re1 humidity, in Na form, moles of HzO/equiv
Thickness, 10.0002, cm
1.32 1.58 1.65 2.50 2.80
9.96 9.92 12.1 11.7 15.1
0.0664 0,0695 0,0620 0.0644 0.0602
stantiated by the close agreement obtained for the difference in chloride transport between experiments B and A and twice the value found in experiments C. The volume changes of solutions observed in the cell were corrected6 for partial molal volume changes of water and sodium chloride in these solutions and of silver and silver chloride at the eiectrodes. These data mere used to calculate the moles of water and sodium transferred per faraday.
Results and Discussion The average emf values of the cell
1
Ag,AgC11KaCl(nz') lmembranel KaC1(m1I) AgC1,Ag was measured using a two-compartment cell made of Lucite. Each compartment, separated from the other by a membrane 1.5 cm in diameter, was filled with sodium chloride solution from reservoirs and left to stand for 24 hr. The solutions in the cell were then renewed and the potential was measured using a Leeds and Northup Type K2 potentiometer and a movingcoil galvanometer of sensitivity lo-" amp/cm, resistance 866 ohms. The procedure was repeated with fresh solutions until constant potential was obtained. No significant asymmetry for the membranes and silver-silver chloride electrodes used was noted. The data reported here are average values for eight measurements taken at 25 f 0.1" with the solutions at rest in the cell. The solutions of sodium chloride used were in the concentration range 0.05-4.0 M . (3) Measurements of Transference Numbers. A two-compartment Lucite cell fitted with capillary tubes and silver-silver chloride electrodes was used to measure the moles of sodium and water transferred across a membrane (1 cm in diameter) separating different solutions of sodium chloride in three series of experiments (A, B, and C). In experiments il,a charge of about 10-5 faraday at a current density of about 3 ma/ cm2 was passed froni the dilute to the concentrated side for a time measured by a stopwatch, and the changes in the heights and contents of solution in the cell were determined, I n experiments B, the above procedure was repeated passing the same quantity of electricity from the concentrated to the dilute side. In experiments C, the transfer of salt and water induced by chemical potential difference between the two solutions for the same time interval was determined. All measurements were made at 25 + 0.1" with sodium chloride solutions in the concentration range 0.054.0 M. The experiments C were used to correct experiments A and B for sodium chloride leak and osmotic water transport. The validity of this correction is subThe Journal gf Physical Chemistry
measured for various membranes and solution concentrations are given in Table 11. These results are compared with values of ideal potentials (Ei)for a hypothetical membrane permeable only to cations calculated by eq 2.
E , - __ 2RT In a*(SaCl)' F a* (XaCl)" I -
I t can be seen that the deviations from the ideal potential increase with increasing external solution concentration. The ratio of measured to ideal potentials ( E o / E i ) even in the case of the least selective membrane (no. 5) is smaller than the measured cation transference number (ha)because of water transfer over the entire range of solution concentration as shown in Table 111. It is of interest to determine the relative contributions of chloride and water transport to the observed deviations of the membrane potentials from the ideal values over the entire range of solution concentration investigated. Samples of results calculated by the last two terms in eq 1 using experimental transference numbers for membrane 5 are also given in Table 111. It can be seen that the deviation from cation transport only is in major part due to transport of water even in the cases of most concentrated solutions. This is observed in spite of the increase of anion concentration in the membrane and increase in anion transport by the membrane. In fact, the data would indicate that anion transport constitutes at most only about 20% of the observed deviation from ideal potentials even in the most concentrated solutions. Within the limits of experimental error and the uncertainty in the values of activity coefficients used in this calculation, good agreement is found between the observed deviations and the values calculated. This indicates that the membrane potential measured is (6)
R. J. Stewart and W. F. Grwdon, J . Phys. Chem., 61,164 (1957).
ION-EXCHANGE MEMBRANE POTENTIALS
3713
Table I1 : Membrane Potentials Nominal NaCl soln molarities
Ideala potentials (Ei),
mv
0.05-0.1 0.1-0.2 0.2-0.4 0.5-1.0 1.0-2.0 2.0-4,O
Membrane 1
Membrane 2
32.95 31.96 31.10 31.65 32.40 35.82
32.93 31.92 31.02 31.60 32.10 35.30
33.05 32.70 32.08 33.78 36.47 43.78
Measured potentials ( E c ) , Membrane 3
32.83 31.78 31.00 31.53 32.40 34.87
Membrane
Membrane
4
5
32.85 31.80 30.83 31.50 31.90 34.63
32.75 31.62 30.45 30.78 30.64 33.80
Based on cation transfer only.
Table 111: Transference Numbers and Potential Deviations (Membrane No. 5) Nominal NaCl soln molalities
0.05-0.1 0.1-0.2 0.2-0.4 0.5-1.0 1 0-2.0 2.04.0
fNa,
tw,
E,/Ei
exptl, direct meast
exptl, direct meast
0.988 0.966 0.950 0.912 0,839 0.772
0,999 0 I990 0.984 0.981 0.974 0.955
8.1 7.3 6.7 5.5 4.7 3.2
EcI,’ mv
E,,” mv
0.03 0.33 0.51 0.64 0.95 1.97
0.24 0.69 1.07 2.58 4.50 7.38
(Ei
- Ed, mv
(Ei
- Ec) -
+
(ECI E w ) , mv
+0.03
0.30 1.08 1.63 3.00 5.83 9.98
$0.06 $0.05 -0.22 $0.38 f0.63
a Ecl and E , are the potential deviations calculated from experimental values of chloride ion and water transference numbers using the last two terms in eq 1.
probably the reversible emf for the cell reaction considered in the development of eq 1. A comparison may be made between the measured electrical transference numbers and the values of transference numbers estimated from interdiffusion coefficients (Dsl;+-H-) as measured previously’ in masstransfer experiments. The limiting evaluation of the interdiffusion coefficient ( 0 1 2 ) from the Nernst-Planck equationS for initial diffusion conditions of the membrane is (3) for D1 # D2, where D1, D2are the single-ion diffusion coefficients of the counterdiffusing ion species 1 and 2 in the membrane. The single-ion diffusion coefficient is related to the electrochemical mobility (Vi) by the Nernst-Einstein equation.
By substituting (4) into (3), the interdiffusion coefficient in terms of the mobilities of the ion species is obtained.
(5)
The results of this calculation using the above relationships are shown in Table IV. It may be seen that the calculated values of the transference numbers
Table IV: Membrane Transference Numbers for Sodium Ion (Membrane No. 5) Nominal NaCl soln molarities
0.05-0.1 0.1-0.2 0.2-0.4 0.5-1, 0 1.0-2.0 2.04.0
_______ Exptl direct meast
0.999 0,990 0.984 0,981 0.974 0.955
tN
Calcd for “dilute“ soln
0,998 0.995 0,990 0.976 0.946 0.901
(7) M. Worsley, A. 8. Tombalakian, and W. F. Graydon, J. Phys. Chem. 69, 883 (1965). ( 8 ) F. Helferich, Discussions Faraday SOC.,21, 83 (1956).
Volume 70, Number 11 .Vovember 1966
3714
ARVINS. QUIST
deviate to the low side from measured electrical transference numbers a t higher sodium chloride solution concentrations. I n general, fair agreement is found between the transference numbers calculated from ioninterchange data and membrane transference numbers
AND
WILLIAM L. MARSHALL
obtained by direct measurement for our experimental conditions of the membrane cell. Acknowledgment. The authors are indebted to the National Research Council, Ottawa, Ontario, Canada, for financial support.
Electrical Conductances of Aqueous Solutions at High Temperatures and Pressures.
111. The Conductances of Potassium Bisulfate Solutions
from 0 to 700"and at Pressures to 4000 Bars1
by Arvin S. Quist and William L. Marshall Reactor Chemistry Dioiswn, Oak Ridge National Laboratory, Oak Ridge, Tennessee (Received J u n e 27, 1966)
91880
The electrical conductances of dilute aqueous potassium bisulfate solutions have been measured from 0 to 700" and at pressures to 4000 bars. From these measurements, the second ionization constant of sulfuric acid was calculated a t temperatures to 300" and a t densities to 1.0 g em+. At temperatures above approximately 400", KHS04 behaves as a uni-univalent electrolyte, dissociating into K + and HSOI- ions only. I n this region, limiting equivalent conductances were obtained and dissociation constants for the equilibrium KHSOl & K + HSOo- were calculated. KHSOo behaves as a weaker electrolyte as temperature increases (at constant solution density) and as solution density decreases (at constant temperature).
+
Introduction Earlier papers in this series presented the results of conductance measurements on aqueous K2S042and H2SOh3solutions at temperatures from 0 to 800" and a t pressures to 4000 bars. As part of a continuing program a t this laboratory studying the behavior of aqueous solutions at high temperatures and pressures, conductance measurements mere made on potassium bisulfate solutions in the same ranges of temperature and pressure. These measurements were carried to very low concentrations (0.00007 m) in an effort to determine the lowest practical concentration range that could be studied with the present conductance cell. From the T h e Journal of Physical Chemistru
measurements, the second ionization constant of H2SO was calculated a t temperatures from 100 to 300" and a t Values reported solution densities to 1.0 g herein for this constant are considered to be more reliable than those calculated previously from the measurements on H2S00abecause of the better reproducibility of the KHSOl measurements. From the present (1) Research sponsored by the U. S. Atomic Energy Commission under contract with Union Carbide Corp. (2) A, S. Quist, E. U. Franck, H. R. Jolley, and W. L. Marshall, J . Phys. Chem., 67, 2453 (1963). (3) A. S. Quist, W. L. Marshall, and H. R. Jolley, ibid., 69, 2726 (1965).
