750
R. J. STEWART AND W. F. GRAYDON
TABLE XV THESORPTION OF WATERW (MOLES WATER/MOLE CBH~006) BY DYED DU PONT CELLOPHANE AT 25 AND 40" % dye in Sam le
R.E. (%)
0
1.09 1.68 Experimental values K
3.42
25 O 6.8 14.7 18.6 25.6 33.8 43.4 52.3 61.0 67.4 73.2 85.0
0.240 .409 .478 .576 .703 .842 * 974 1.132 1.279 1.470 2.070
0.235 .388 .456 ,566 .692 .828 .964 1.098 1.240 1.450 2.030
0.248 .400 ,468 ,567 ,694 .828 ,972 1.121 1.260 1.445 2.103
0.203 .311 .401 .486 .622 .784 .890 1.018 1.365 1,922
0.196 ,311 .405 .500 .617 .804 ,925 1.045 1.365 1.980
40'
8.0 13.9 20.0 26.5 34.4 45.6 52.8 60.3 73.8 84.8
0.231 ,343 .442 .540 .648 , .815 ,936 1.062 1.410 1.910
Vol. 60
Interpolated values W
10 20 30 40 50 60 70 75
0.327 .479 .618 .764 .931 1.118 1.379 1.589
25" 0.317 .491 .645 .792 .951 1.120 1.355 1.537
0.302 .482 .635 .783 .927 1.OS1 1.323 1.521
0.315 .486 .642 .784 .932 1.100 1.335 1.521
10 20 30 40 50 60 70 75
0.277 ,423 .558 .690 ,844 1.035 1.272 1.485
40 O 0.274 .441 .588 .731 .887 1.058 1.287 1.454
0.249 .407 .558 .702 .846 1.012 1.232 1.409
0.235 .410 .560 .711 .869 1.038 1.245 1.413
samples, ie., heated in water at 90-95' for two hours. The adsorption of water vapor by this sample differed slightly from that of cellophane sheet which had not been heated in water. Water adsorption isotherms on three dyed samples were determined at 25 and 40". The values obtained are given in Tables XIV and XV. It appears that there is no very marked difference in hygroscopicity between dyed and undyed cellulose.
ION-EXCHANGE MEMBRANES. 11. ION TRANSFER RATES1 BY R. J. STEWART AND W. F. GRAYDON Department of Chemical Engineering, University of Toronto, Toronto, Canada Received Augulrt $3, 1066
The rates of cation transfer for the sodium-hydrogen, and the calcium-hydrogen exchange across various polystyrenesulfonic acid membranes have been measured. Anion transfer rates for the chloride ion have also been estimated. I n all determinations the interdiffusion rates were measured directly using a modified diaphragm diffusion cell. The results are discussed in terms of the relative contribution of membrane resistance and liquid-film resistance to ion transfer. Cation diffusion coefficients are correlated empirically with membrane characteristics. Anion transfer rates are considered in terms of the Donnan membrane equilibrium and membrane potentials.
Introduction The membranes described in this report were prepared by the copolymerization of the propyl ester of p-styrenesulfonic acid with divinylbenzene and the subsequent hydrolysis of the polymer to produce polystyrenesulfonic acid. This method permitted the preparation of membranes of various capacities with the sulfonate groups distributed throughout the bulk of the membrane. The method of preparation also permitted independent variation of the divinylbenzene content of the membrane. Previous determinations of ion-diffusion coefficients in ion-exchange materials have been made by the radiotracer spread method, by the electrical conductance method, and by radiotracer ex(1) This report is abstracted from the the& of R. J. Stewart submitted for the degree of Master of Applied Science, University of Toronto, September. 1953.
change methods.2-6 These methods in general yield self-diffusion coefficients rather than the more useful interdiffusion coefficients. The method of calculation of interdiffusion coefficients from selfdiffusion coefficients is not immediately o b v i o u ~ . ~ By contrast, the ion-exchange diaphragm cell method used in this work yields values of interdiffusion coefficients directly. In addition the iontransfer rates may be measured by simple solution analysis. The values of interdiffusion coefficients may be obtained from the analytical data without curve fitting. (2) G. E. Boyd, W. Adamsonand L. S. Myers, J . Am. Chem. Soc., 69,2836 (1947). (3) G. E. Boyd, B. A. Soldano and 0. D. Bonner, TIIIB JOURNAL. 68, 456 (1954). (4) K. S. Spiegler and C. D. Coryell, ibid.. 67, 687 (1953). ( 5 ) h l . Tetenhauni and 11. P. Crecor, ibid.. 68, 11RG (1954).
IONTRANSFER RATES
June, 1956
Experimental Membranes.-The membranes used in this work were prepared by the methods described previously.6J The membrane characteristics of capacity, nominal cross-linking and moisture content have been given.' The same membranes as described? have been used in this work and are designated in the same way by two digits each, the second of which designates in each case the mole per cent. divinylbenzene used in the preparation of the membrane. The first digit represents the exchange capacity of each membrane to the nearest integer. Cation Diffusion Measurements.-The diffusion cell was a double-ended glass or Lucite cell consisting of two stoppered compartments, each of 11.5 ml. volume, separated by an ion-exchange membrane. The membrane was supported between two gaskets of 2.00 cm. internal diameter. The two flanged halves of the cell were bolted together. By means of a pipet 10-ml. portions of 0.1 N sodium nitrate and 0.1 N hydrochloric acid were placed in the cell compartments. The stoppered cell was then shaken mechanically at a measured rate in an air thermostat at 25 & lo. After 15 minutes, the solutions were removed and analyzed by acidimetric titration. This procedure was repeated until agreement between consecutive runs was obtained. The data for the initial runs were discarded. The same procedure was then repeated for various shaking rates and time intervals. Calcium-hydrogen interdiffusion data were obtained in a similar fashion uhing 0.1 N (0.05 M ) calcium nitrate solution and 0.1 N hydrochloric acid solution. Anion Diffusion Measurements.-The procedure used was similar to that described above except that all runs were for a shaking time of one hour. At the end of each run the nitrate solution was analyzed for chloride by potentiometric titration.
Results and Discussion The data which have been obtained for the transfer of hydrogen ion to the sodium nitrate solution during a 15-minute interval as a function of the shaking rate are given in Fig. 1. The plots for various membranes are similar in shape. All show a region a t low shaking rates which is characterized by an increasing rate of ion transfer, and a region at higher shaking rates for which the ion-transfer rate is independent of the shaking rate. This independence of shaking rate has been checked for several membranes up to 750 oscillations per minute and the rate of ion transfer has been found to be constant within a Sew per cent. The assumption may be made that at high shaking rates the resistance to ion transfer in the liquid is negligible and that a t low shaking rates, below the break in each plot, the ion-transfer rate is determined by both liquid film and membrane resistances. That this assumption is consistent with the data obtained is illustrated by the calculation below. A sufficient approximation may be obtained for the interdiffusion coefficient across the membrane at high shaking rates using the unintegrated diffusion equation where A
= change in concn. of either ion species on either side
of the membrane during the shaking time interval Clt = concn. of either ion species at the conclusion of the run in the compartment soln. more concd. with respect to that species. This quantity is the av. concn. difference across the membrane during a run D M = apparent interdiffusion coefficient for sodiumhvdrogen ions across the membrane. The term "kppayent" is used because this value is based on the concn. gradient between the liquids a t the membrane interfaces rather than the gradimt in the membrane
By means of equation 1 values of D M may be estimated for each membrane from the observed flux a t high shaking rates. These values of D M permit an estimation of the concentration difference across the assumed liquid films a t low shaking rates. where ACL represents the average concentration difference across either of the two liquid films a t the membrane surface. Thus the thickness of the liquid film layer may be estimated. (3)
where LL = liquid film thickness in cm. DL = interdiffusion coefficient in water, estimated as 2.4 X 10-6 cm.a/sec.
The values for the liquid layer thickness and the concentration gradient difference for various membranes and various shaking rates are given in Fig. 2 and Table I. 0.028
0,024
0.020
0.0I 6 T
& 0.012
0.000
= =
(6) I. H. Spinner, J. Ciric and W. F. Graydon, Can. J . Chem.. sa, 143 (1954).
(7) W . F. Craydon and R. J . Stewart, T I I I S . ~ O ~ ; R69,8(i N A L( ,I L J X )
- "
0,004
0
gross surface area of the membrane (3.14 cm.2) vol. of soh. on either side of the membrane (10 cc.) LM = thickness of membrane as measured by micrometer in em. At * = shaking time (900 sea.)
V
AC,
751
I
0
1-6
n r ,
I
40
I
I
80
I
I
120
I
160
~
I
200
I
,
I 240
Oscillations Per Minute. Fig. 1.-Cation transfer a t various shaking rates. [ H + ] is the acid concentration in thv solution originally 0.1 N NaNOs after a 15-min. shaking time; 28.0'; acid solution 0.1 N HCI.
I t may be noted that the liquid film thickness calculated is independent of the membrane and the flus and is determined by the shaking rate. The
]
R. J. STEWART AND W. F. GRAYDON
752
Vol. 60
The data were evaluated using the integrated form of the diffusion equation given by Gordon.8
-
32
-
28
ro
The linearity of the plots as shown in Fig. 3 indicates the adherence of the data obtained t o an -0.7
20
0
Fig. 2.-Liquid
40
60
80
100
// / 3-2 3-4
3-68
P4“..=a
120
Oscillations Per Minute. layer thickness at various shaking rates.
values obtained indicate that a hydrodynamic limit is being approached but that it is by no means attained a t a shaking rate of 110 oscillations per minute. The values of ACL are of more direct interest. These values are dependent on flux as well as liquid-film thickness. The observed flux is expected to be essentially independent of shaking rate when the value of ACT, becomes small relative to the over-all concentration difference. Thus the break in plot on Fig. 1 occurs a t a higher shaking rate the greater DM. In Table I it may be seen, for example, that ACL is small for the 1-6 membrane relative t o the 2-6B membrane a t the shaking rate of 50 0.p.m. although the liquid film thickness has been assumed the same in both cases. TABLE I LIQUIDFILMCONCENTRATION DECREASE
30 35 50 55 73 86 92 110
(4)
ACO = initial concn. difference between the 2 bulk soln. a t time zero ACr = final concn. difference between the 2 bulk soln. at time t k = constant containing the diffusion coefficient and terms describing the geometry of the cell as shown in eq. 5
20 -
Shaking r,ate min.-l
- kt
where
-
24
5
In 3 ACo
0 1-6 0 1-4 a 2-60 @ 2-6A 0 3-4
-
1-6
1-4
ACL. rnoles/l. 2-6B
2-6A
3-4
0.0135 0.0176 0.0053 0.0092 0.0033
0.0152 .0127 .0079 0.0124 0.0141 .0048 0.0053 0,0099 0.0014 0.0038
All of the measurements of interdiffusion coefficients reported below were obtained at shaking rates greater than 160 0.p.m. Each diffusion coefficient is the average of the values obtained for five or six runs of different duration up t o one hour.
Fig. 3.-Sodium-hydrogen interdiffusion across various membranes; 25’; approximately 0.1 N solution concentrations.
equation of the form of equation 4. The constant k in equation 4 has been analyzed according to equation 58 k
=
~DMA/VLM
(5)
where the symbols have the same significance as previously. This integrated equation has been used to calculate the values of apparent membrane interdiffusion coefficients as given in Table 11. These values are integral diffusion coefficients. Although it might be expected that the diffusion coefficients would be dependent on the ion composition of the membrane, the linearity of the plots in Fig. 3 indicates that this dependence is small over most of the range studied. Differential diffusion coefficients measured in this Laboratory indicate that composition dependence is small for the sodium-hydrogen interdiffusion over this range but may be appreciable for systems involving large ions. The values for anion diffusion coefficient listed in Table I1 have been calculated directly from the chloride-ion flux and the Concentration difference which was assumed t o be a constant, 0.1037 mole/ 1. These values may be expected to be somewhat high because the bi-ionic potential gradient has been neglected. At any rate the values are indicative only because of the very small anion’flux. After one hour chloride concentrations of the order of loq4N were found in the nitrate solution. (8) A. R.Gordon, Ann. N. Y. Acad. Sci., 48, [ 5 ] 285 (1945).
IONTRANSFER RATES
June, 1956
753
I n Table IV are listed the ratios of the interTABLE I1 diffusion coefficients for sodium-hydrogen to those APPARENT MEMBRANEINTERDIFFUSION COEFFICIENTS~ for chloride. These values have been compared 25.0°, solution concentrations 0.1 N Membrane no.
DN~+-B+, cm.s/sec. X 1 os
Dol-9
cm.l/aec. X 100
DCa++- E+*
cm.s//sec. X 10s
1-6 0.46 0.88 1-4 0.97 1.8 1-2 2.9 22 2-6A 3.8 8.3 1.9 2-6B 3.1 2-4 4.1 18 2.3 2-2 6.1 57 3-6A 6.3 16 3.6 3-6B 5.8 16 3-4 6.5 50 4.6 3-2 7.4 215 a The word "apparent" is used since these values are calculated on the basis of the liquid concentrations rather than membrane concentrations.
The values of apparent diffusion coeficients as given in Table I1 are derived directly from the analytical data and are subject to no assumptions as to the diffusion mechanism in the membrane. These values are not comparable to membrane selfdiffusion coefficients. Values that are more nearly comparable may be obtained by assuming that the effective concentration gradient is the concentration gradient for the ion species in the membrane. Because of the high effective concentration in the membrane this concentration gradient may be of the order of 20 to 30 times the gradient between the two solutions. The method of estimating the gradient in the membrane is also a matter for speculation. However, without regard t o the precise method of computation it is apparent that the concentration gradient in the membrane will be relatively insensitive to external solution concentrations. The data given in Table I11 illustrate this effect.
to the values estimated on the basis of an ideal Donnan equilibrium. Assuming that activity coeficients are unity and solution mobility ratios for the sodium and chloride ions we would expect
-[Na+]m =
[Cl-lm
h a +
D X
-
[RS0,-12,
[NaCl]as [RSOs-1' 1.35 [NaCll2. 2;03
where [ ] indicates concentration in gram ions or gram moles per liter and subscripts m and s refer to membrane and solution, respectively. The values calculated for this expression are given in Table IV. The agreement in general is within the limits of error of the chloride analyses. However, for the 3-4 and the 3-2 membranes the deviations are very large. For these membranes a gross mechanical leak may be suspected. TABLE IV RELATIVE ANION-CATION DIFFUSIVITIES Membrane concn.
[RSO:-1,
Membrane no.
meq./g. water
1-6 1-4 1-2 2-6A 2-4 2-2 3-6A 3-6B 3-4 3-2
3.33 3.16 1.90 3.20 2.65 1.58 3.01 3.11 2.17 1.37
obrd
740 670 243 692 47 1 168 610 654 315 126
522 540 132 460 233 106 403 374 77 35
The data given in Table IV are also of interest in connection with the interpretation of membrane potentials. The values of diffusion coefficients TABLE I11 CORRECTED DIFFUSION COEFFICIENTS FOR A 2-6 MEMBRANE, are not completely suitable for the estimation of 25.0" Soh. concn. total, moles/l.
0.10 0.30 0.60
Membrane concn.. meq./g. water
3.70 4.02 4.35
Apparent Diva +-H cm.'/sec.
+
3.3 x 10-6 1 . 2 x 10-6 0.78 X 10-6
Cor. membrane interdiffusion coefficients, cm.P/sec.
x x 9.0 x 8.9 9.0
lo-' 10-7 10-7
It will be noted that the apparent diffusion coefficients show a considerable dependence on solution normality indicating that the flux is essentially independent of the external solution concentration. However, if these apparent diffusion coefficients are multiplied by the ratio of the solution concentration t o the membrane concentration, the products, which may be considered as membrane interdiffusion coefficients, are quite independent of external solution concentration and are of the same order of magnitude as reported self-diffusion coefficients for polystyrenesulfpnic acid resins. For example, Boyd, Soldano and Bonner give a value of 8.44 X 10-7 cm.2/sec. for the self-diffusion of sodium in a resin of capacity 1.91 meq./g. and 8.6% D.V.B.
Fig. 4.-Empirical correlation of interdiffusion coefficients. D is interdiffusion coefficient for sodium-hydrogen ions in cm.2/sec.; 25.0'; solution concentration a proximately 0.1 N. C is membrane capacity in meq.fg. dry hydrogen form. Wd is the moisture content of the membrane expresse.d as grams of water per gram of dry hydrogen resin.
I. T. OIWA
754
sodium chloride membrane transport numbers because of the simultaneous hydrogen-ion diffusion. However, this error will be less in the diffusion coefficient ratio than in the individual values, and in any case should be less than a factor of two. On the basis of the diffusion coefficient ratios in Table IV, membrane chloride transport numbers may be estimated to be between 0.002 and 0.004 for the six membranes of lowest chloride-ion transfer. Membrane potentials for these membranes' show considerably larger deviations from ideality than would be expected for anion transport numbers of this order. Thus the ion-transfer rate data provide confirmation for the previous conclusion7 that the transfer of water electroosmotically is a major factor in the deviation of membrane potentials from ideal values. Since it is difficult to prepare a membrane of precisely a given capacity or cross-linking, membranes
VOl. 60
cannot be reproduced identically. For this reason, it is of considerable usefulness in the routine preparation of ion-exchange membranes t o have an empirical correlation of the experimental data. Preferably such a correlation should involve only quantities which may be measured with some precision. The sodium-hydrogen ion-transfer rates may be correlated empirically as shown in Fig. 4. The experimental poihts have been obtained by a number of workers in this Laboratory using membranes prepared from different batches of ester monomer and divinylbenzene. The membranes used were of capacity between one and three milliequivalents per gram, and between 2 and 12 mole yodivinylbenzene. Acknowledgment.-The authors are indebted to the National Research Council, Ottawa, and to the Advisory Committee on Scientific Research, University of Toronto, for financial support.
-
THE ACTIVITY COEFFICIENTS OF HYDROCHLORIC ACID IN METHANOLWATER MIXTURES BY I. T. OIWA Department of Chemistry, Faculty of Science, Toholczl University, Sendai, Japan Received August 10,1966
Electromotive force measurements were made on cella: Hz(1 atm.)/HCl(m), X% CHaOH, Y% HzO/AgCI-Ag over the molalities of hydrochloric acid from 1 X 10-8 to 0.1, at 25' and methanol contents of 0, 20 40, 60, 80 and 90 in weight per cent, From the data obtained, standard potentials of silver-silver chloride electrode and ion-size arameters, 5.6, 4.6,4.3, 4.3,5.3 and 5.5 A., respectively, in these solvents are determined. The activity coefficients of hy&ochloric acid, which are referred to unity at infinite dilution in pure water, are calculated. Further, for the free energy change of the reaction transferring hydrochloric acid of unit activity from a ueous solution to the methanol-water mixture, equations are introduced which consider the change of ionic solvation an% proton transfer from water to methanol molecule over the electrostatic energy change. These equations elucidate the experimental results. The proton transfer is accompanied by an increase of free energy of 0.0834e.v. per mole of hydrochloric acid.
I. Introduction
It seems desirable, in elucidating the various experimental results of non-aqueous solution of electrolytes to determine the activity of strong electrolytes in non-aqueous solution with the same scale as that in aqueous solution. In this study electromotive forces of the reversible cells Hz( 1 atm.)/HCl(m), X% CHsOH, Y% HaO/AgCI-Ag (1)
were measured, and the standard potentials of the silver-silver chloride electrode were calculated. The activity coe%cients of hydrochloric acid of concentration C, designated by f, in any methanolwater medium, are given by the relation
f
=
Pfc
(2)
where y is the activity coeacient of the acid a t zero concentration in the non-aqueous solvent referred to unity a t the standard state (aqueous solution a t infinite dilution) and fc is that a t concentration C referred to unity a t the reference state (each particular solution a t infinite dilution) , were determined. The free energy change G(C) at the time of transferring 1 mole of free ion of vapor phase into (1) I. T. Oiwa, J . Chem. SOC.Japan, 7 6 , 1047 (1954).
a solution of concentration C is shown by the equation2 G(C) Gs" Gi,s(C) Gi(C) (3) where G,O and Gi,8are the free energy changes of the interaction between the ion and the solvent, and Gi, that between ions. Gi,s is a portion of Gs, which changes with concentration by ionic atmosphere. Gi and Gi,, become zero a t infinite dilution. Therefore, G,O shows the ionic state of each solution a t infinite dilution. Correlations of G,O with the properties of the solvent are examined. 11. Experimental
+
+
Material Used.-Methanol, Extra Pure Grade Reagent of the Wako Pure Chemical Industries (&o = 0.7916, nl*~ 1.330) was distilled. The amount of aldehydes was determined as less than mole/l. by the polarographic method. Distilled water passed through a column of ionexchange resin ( K < 1 X 10-6 ohm-' cm.-l) was used. Hydrochloric acid, Special Reagent Grade of Mitsubishi Chemical Industries, wm distilled twice a t a constant pressure. The concentration was calculated from the Foulk tablea and also determined by the gravimetric method; the results agreed with an accuracy of 0.01%. Cell Solutions.-An aqueous stock solution of hydrochloric acid of one molal concentration m'as prepared and (2) Cf.R. H. Fowler and E. A. Guggenheim, "Statistical Thermodynamics," Cambridge University Press, 1939, p. 383. (3) C. W. Foulk and M. HoUingsworth, J . Am. Chem. SOC..46, 1220 (1923).
