94
JANC. TH.KWAKAND J. A. A. KETELAAR
Temperature Dependence of the Electrical and Diffusional Mobilities of 22Na and
13742s
in Molten LiNO,, NaNO,, and RbNO,
by Jan C. Th. Kwak and J. A. A. Ketelaar Laboratory for Electrochemistry, The University of Amsterdam, Amsterdam, The Netherlands
(Received June 19, 1968)
The diffusion coefficients and ionic mobilities of 22Na and 137Cs in molten LiN03, SaN08, and CsN03 are measured by a paper electrophoresis method in the temperature range of about 300-400". The values of the Arrhenius coefficients and of the preexponential factors are given. The Nernst-Einstein relation between mobility and diffusion coefficient is discussed.
Rleasurements of the diffusion coefficients and ionic mobilities of alkali tracer ions in pure molten alkali nitrates at 450" were performed in our laboratory by a method of paper chromatography and paper electrophoresis using a strip of paper impregnated with the molten solvent salt. 1-3 Formerly glass-fiber paper and a glass plate as a support were used, but now the paper consisted of quartz fibers and an alumina plate was used as a support. With these materials exchange of tracer ions, especially of sodium ions, was eliminated. Nevertheless, still 1-2% inactive salt of the tracer ion was added in general to the solvent melt, in order to decrease further the danger of absorption by the quartz fibers. The activity of W a arid 137Csthat could be detected in the fibers and the support after the experiment was negligible.4 For the interpretation of the results in terms of ionic size and mass and ionic interference it seemed useful to study also the influence of the nature of solute and solvent ions on the temperature dependence of diffusion coefficients and ionic mobilities. In this paper we report diffusion coefficient and ionic mobility measurements for 22Na and 13?Cs ions in Lil?;03 (270-400"), NaSO3 (310-450"), and RbNO3 (320-450"). and 137Cswere chosen because they are very diff erent in size and mass. The choice of LiN03, NaN03, and 12bX03 as solvents was made in order that the measurements could be performed in the same temperature range.
where AH* is calculated in kilocalories per mole and is often interpreted as an activation enthalpy. In Figure 1 our measurements of the diffusion coefficient of 22Nain S a x 0 3 are compared with the results of other investigations.5-* It is scen that the agreement is reasonable, indicating that the method used gives reliable results for the diffusion coefficient. In the previous investigations2~3too high values for D(221\a)in NaN03 were found, probably due to experimental conditions. N a S 0 3 does not wet the glass plate used as support in these investigations. This causes a rim of
28. 26-
*
2422 20:
%
1.8.
Results The diffusion coefficients and ionic mobilities are represented within 2-3y0 as well by a linear temperature dependence as by an Arrhenius equation. We chose to use the latter method, because it has become usual to discuss the temperature dependence of transport parameters in terms of Arrhenius coefficients, AH*, resulting from the equations
D
=
D, exp(-AHD*/RT); u = urnexp(-AH,*/RT)
The Journal of Physical Chemistry
*
1.
b
*t
+I+
(1) J. A. A. Ketelaar and E. P, Honig, J . Phys. Chem., 68, 1695 (1964). (2) E. P. Honig and J. A. A. Ketelaar, Trans. Faraday SOC.,62, 190 (1966).
(3) J. A. A. Ketelaar and J. C. Th. Kwak, J. Phys. Chem., 71, 1149 (1967). (4) J. C. Th. Kwak, Ph.D. Thesis, University of Amsterdam, 1967.
22N~AND la7Cs IN
MOLTEN LiNOs, NaNOa, AND RbNOa
95
-
0.600 0.500
-
0,400 -
5tlogD
-
1 0.300-
0.200
o.loot
,
I
135
1LO
I
145
1.55
150
---
1.60 +(oK-~)
1.65
I
1.70
1.75
1.80
I
I
1.85
1.90
103
Figure 2. Diffusion coefficients D (cmz sec-1) of 2aNa in: A, LiNOa, A, NaNOa, A, RbNOa.
1.600-
Table I : Arrhenius Coefficients AH* (kcal/mol) and Preexponential Constants u, (cma V-l sec-l) and D, (cmz sec-1) for Electrical Migration and Diffusion of 2aNa and 1Ws in LiNOa, NaNOs, and RbNOa
1,500-
6+r,:*o: 1.400-
W a AHn*
12M)-
lO'D, 1.100-
AH, *
108u,
1.000-
1.35
1.40
lk5
150
155
160
165
1.70
185
1.80
,1.90L
185
(320-450')
NaNOs
RbN03 (320-460°)
3.55 10.20 4.3 1 0 . 6
4,06 1 0.24 6.3 11.0
4.56 10.24 6.9 1 1 . 2
3.53 1 0 . 1 8 8.2 1 1 . 3
2.36zt0.10 2.6 l t 0 . 3
3.28 i r 0 . 3 0 2.3 f.0.5
4.54f0.25 6.6 1 1 . 4
4.74ztO.24 8.8 k l . 6
5.4710.40 1.0.2 1 2 . 0
3.44 1 0 . 1 6 5.4 1 0 . 7
2.8110.18 2.9 1 0 . 4
3.28 f . 0 . 2 6 2.3 1 0 . 4
187Cs AHn*
104D, AH,,*
10au,
free salt a t the sides of the paper strip, where turbulence can easily occur. This rim is not present with an alumina support. We find D ( W a ) = 3.73 10.l0at45O0, resulting in a Nernst-Einstein parameter RTuIFD of 0.84 f 0.04 at that temperature. Figures 2-5 show the log D and log u us. 1jT plots for W a and 137Csin LiN03, NaN03, and RbNO3. Within the standard deviation no curvature could be found in the temperature region investigated. The full lines are calculated with a least-squares method. The coefficients D,, AHD*, u,, and AH,* are given in Table I. The standard deviations in u and D vary between 1.5 and 2% for the different cases. Our results agree reasonably well with other investigations. We find for A H D * ( ~ ~inNLiN03 ~ ) 3.55 f 0.20, compared with 4.4 i 0.G reported by Lantelme.7 I n NaNOa our value for AH~*(''r\la) (320-450") is 4-06 f 0.24, compared with 4.97 f 0.08 (310-380°),5 5.0 i 0.7 (320-400°),1 and
LiNOa (265-400')
4.30 i 0.30 (350-420°).e Our value for AHD*(~~~CS) in NaNO3 is 4.74 f 0.24, compared with 4.69 & 0.21.7 Although our temperature dependence in this case is identical with the value of Nagarajan and Bocltris,6 our absolute values of D(la7Cs)in NaN03 are about 15% lower than the values reported in their work. For the ionic mobilities only comparison with the work of Lantelme7 can be made. We find AH,*(22PI'a)in Lito be 3.53 f 0.18 and in NaN03 2.36 f 0.10. The corresponding values of Lantelme are, respectively, 3.9 0.6 and 2.7 f 0.4. All AH* values are expressed in kilocalories per mole. (6) A. 8. Dworkin, R. B. Esoue, and E. R. van Artsdalen, J. Phys. Chem., 64, 872 (1960). (6) M. K. Nagarajan and J. O'M. Bockris, ibid., 70, 1854 (1966). (7) F. Lantelme, Ph.D. Thesis, Paris, 1965. (8) C.A. Angell and J. W. Tomlinson, Discussions Faraday SOC.,32, 237 (1961).
Volume 78, Number 1 Januarg 1969
96
JANC. TH. KWAKAND J. A. A. KETELAAR
I
0.640
0.56(-t
4+log U
1.30
1.35
1.40
1.45
1.50
1.55
1.60 +(OK-$
1.65
1.70
1.75
1.80
1.85
190
x 103
Figure 4. Ionic mobilities u (cm2 V-1 sec-1) of 22Na in: ALiNOs; A, NaN03; A, RbNOs.
i
0.700
-
0.600
a5004+1og
u .
f
OAOO-
0.300-
exception. Also in mixtures of Lii\'o3 with Ca(W03)z9 and CdClz with alkali chlorides,'O it was observed that the values of AH,* of the cations are equalmithin experimental error. This difference in temperature dependence of diffusion coefficients and ionic mobilities is the cause of a different temperature dependence of the Nernst-Einstein parameter a = RTu/FD in the different cases. When AHD" - AH,* < RT, isda/dT > 0 and when AHD* - AH,* > RT is da/dT < 0. I n LiX03 the Wernst-Einstein parameter of both 22Na and 13?Csbecomes larger than unity at higher temperatures. This is of course related to the differences in u and D when comparing LiW03 with NaN03. As can be seen from the figures, the diffusion coefficient of 137Cs, and a t higher temperatures also that of W a , is smaller in LilC'O3 than in NaN03. Also the fluidity of KaN03 is larger than that of LiXO3.l1 However, the ionic mobilities of both 13?Cs and W a are both appreciably higher in LiW03 than in NaN03. In our opinion this different behavior of u and D is due to an influence on the ionic mobilities of Ia7Csand W a in LiN03 from a smaller drag effect on the cations from the anions than in the other solvents, caused by a polarization of the NOS- ion by the small Lif ion.
I 1
0.200 0.100
Qooo130
U5
1AO
lk5
150
1.55
--F
160
1.65
170
135
180
Is
CSin:
185 190
+~d)~103
Figure 5. Ionic mobilities u (om2V-' sec-l) of 0, LiNOs; 0, NaNOs; 0, RbNOs.
Discussion As can be seen from Table I and from literature data, the trends in the Arrhenius coefficients are different for electrical and diffusional transport. I n all three salts studied AHD*(Va) < AHD*(I~~?CS) < AHD*(hTo3-),6 which is clearly a size effect. AHD*((22Na) and AHo*(13'Cs) increase with increasing solvent cation radius; the value of AHD*('~~CS) is largest in CsNOa (6.47 f 0.326 or 5.61 f 0.275). However, AH,*(22Na) and AH,*(137Cs) are about equal in the three solvents studied; WaN03 is hardly a significant The Journal of Physical Chemktry
(9) J. C. Th. Kwak, J. A. A. Ketelaar, and A. J. H. Boerboom, unpublished data. (10) J. C. Th. Kwak and J. A. A. Ketelaar, submitted for publication in Electrochim. Acta. (11) I. G. Murgulescu and S. Zuca, Electrochim. Acta, 11, 1383 (1966).
97
COUNTERION TRANSFERENCE NUMBERS I N ION-EXCHANGE MEMBRANES This polarization causes a decreased interaction of the larger tracer ions with the NOa- i0n.12~13 It is clear that this effect especially influences the ionic mobility, resulting in a high Nernst-Einstein parameter.
tions have been carried out under the auspices of the Netherlands Foundation for Chemical Research (SON) and with financial aid from the Netherlands Organization for the Advancement of Pure Research (ZWO).
Acknowledgments. The authors wish to thank Mr. J. Roele for technical assistance. The present investiga-
(12) C. T. Moynihan and R. W. Laity, J . Phys. Chem., 68, 3312 (1964). (13) F. LanteIme and M. Chemla, Electrochim. Acta, lo, 663 (1965).
Counterion Transference Numbers in Ion-Exchange Membranes
by N. Lakshminarayanaiah Department of Pharmacology, University of Pennsylvania, Philadelphia, Pennsylvania
1910.4
(Received June 20,1968)
Transference numbers of counterions in ion-exchange membranes have been determined by both emf and Hittorf’s methods. In general, the transference number derived from the emf data, €+‘fnPp), is lower than the value derived by the Hittorf method, f+, for any given external electrolyte concentration. This difference is attributed to transport of water occurring across the membrane. The theoretical relationship between these parameters has been derived by Oda and Yawataya. This derivation contains some minor errors which have been clarified in this presentation. The transport number and other relevant data obtained for a crosslinked phenolsulfonate membrane have been used to check the relationship between €+ and t+(aap).
Introduction The efficiency with which a membrane transports selectively any particular ionic species is usually inferred by measuring the transference number of the species in the membrane. Two methods are normally used to measure the transport number.’S2 They are the emf methods14 and the Hittorf m e t h ~ d . I~n the emf method, the potential E arising across the membrane when it separates electrolyte solutions of concentration C1 and Cz is measured. If reversible electrodes without forming any liquid junctions are used in membrane cell of the type Ag-AgC1 IRIC1 solnlcation exchange1 (a& membrane lMCl solnlAgC1-Ag
(1)
( 4 2
the transport number is evaluated from the
where (a& and (a*)l are the mean activities of the two solutions, and R, T, and F have their usual significance. The transport number so derived has been called the apparent transport number t+(npp), because in this type of measurement no correction has been applied for the transport of water occurring across the membrane,
but if very dilute solutions are used, I+(aDP)will be very close to the true value I+. I n the Hittorf method, a known quantity of electricity is passed through the membrane cell containing an electrolyte solution of known concentration on either side of the membrane. By estimating the concentration change brought about in the two chambers, the true transport number I+ is determined. Here again, how true the value of I+ is depends on the procedure employed in the estimation which may be carried out either volumetrically or gravimetrically. I n the volumetric method, correction for water transport must be introduced to get the true value, whereas in the gravimetric method, true value is obtained provided other factors like concentration polarization and electrolyte back-diff usion which have been considered in detail elsewhere’ are properly controlled. (1) J. R. Wilson, Ed., “Demineralization by Electrodialysis,” Butterworth and Co., Ltd., London, 1960,p 203. (2) Y.Oda and T. Yawataya, BUZZ. Chem. SOC.Jap., 29, 673 (1956). (3) C. A. Kumins and A. London, J . Polymer Sci., 46, 395 (1960). (4) N.W.Rosenberg, J. H . B. George, and W.D. Potter, J . Electrochem. SOC.,104, 111 (1957). (5) T. M. Ellison and H. G . Spencer, J . Polymer Sci., B1, 707 (1963). (6) D. K. Hale and D. J. McCauley, Trans. Faraday SOC.,57, 136 (1961). (7) N.Lakshminarayanaiah and V. Subrahmanyan, J . Polymer Sci., A2, 4491 (1964). Volume 79, Number 1 January 1969
