M. V. KULKARNI AND P. A. LYONS
2336
Diffusion of Potassium Chloride in Methanol-Water Solutions
by M. V. Kulkarni and P. A. Lyons Department of Chemistry, Yale University, New Haven, Connecticut
(Received January 22, 1966)
Diffusion coefficients for dilute KC1 solutions in a mixed solvent of methanol and water have been measured a t 25”. Methanol concentrations were 10, 20, and 38.6% by weight. Theory based on pseudo-binary behavior correctly predicts the results over the entire range of concentrations in 10% methanol solutions, is valid a t the lowest concentrations for the 20% methanol data, and yields values about 1% below experiments for the 38.6% methanol case. The diffusion data may be used to compute precisely the salt activity coefficients for the 10 and 20% data and these data are compared with some experimental values and with results deriving from accepted electrochemical theory. The success of this procedure suggests that this method may be used to estimate activities in mixed solvents which are presently experimentally inaccessible.
Introduction Although a great deal of transport data have been amassed for electrolytes in aqueous solutions and in mixed solvents, relatively little is known about pure diffusion in mixed solvents.’ In dilute solutions there are no precise results, yet there are several questions for which such measurements would provide answers. First, would diffusion in very dilute mixed solvent solutions mimic the analogous behavior in simple binary systems; when would it become necessary to deal with these systems as ternary systems? Beyond this, would the concentration dependence follow the classical Onsager-Fuoss theory? Finally, could diffusion data obtained for such mixed solvent systems be used for the practical computation of the electrolyte chemical potential? The potassium chloride-methanol-water system was the obvious choice for this initial study for several reasons. Accurate transference numbers are available for K + and C1- in these mixtures and they are nearly equal. The cell lubrication problem for these solutions is not as serious as for other mixed solvent choices (dioxane-water for an example). Diffusion data for aqueous KC1 soIutions conform to theory over a greater range of concentrations than for any electrolyte yet studied. Experimental Procedure. Because of the nature of the system and the low concentrations of KC1 involved the natural The Journal of P h y 8 k l Chemistry
choice of experimental technique was the conductometric method. The procedure followed has been described. In this method a cell is placed on a heavy brass platform in an air thermostat which, in turn, is submerged in a water bath. By appropriate manipulation, a small quantity of electrolyte is introduced into the bottom of a cell which previously had been filled with solvent. After introduction of the electrolyte, the cell contents are isolated and, after a period of time sufficient to develop restricted diffusion, the further flow of electrolyte is followed by measuring the conductivity a t positions one-sixth of the distance from the top and bottom of the cell. The all-glass cell used in this work was patterned after one used earlier in this laboratory for studying diffusion in partially dissociated electrolytes. For the current experiments it was desirable to collect data over a rather long period of time. As a consequence, the height of the new cell was 6 cm. (the previous height was 3.6 cm.). The resulting unit was a glass rectangular parallelepiped 1.0 X 3.0 X 6.0 cm. in dimension with platinum electrodes 1 mm. thick and 30 mm.
(1) H. S.Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd Ed., Reinhold Publishing Corp., New York, N. Y., 1958; R. A. Robinson and R. H. Stokes, ”Electrolyte Solutions,” Butterworth and Co., Ltd., London, 1955. (2) H. S. Harned and R. L. Nuttall. J . A m . Chem. SOC., 69, 736
(1947). (3) E. Holt, Ph.D. Thesis, Yale University, 1961.
DIFFUSION OF POTASSIUM CHLORIDE IN METHANOL-WATER SOLUTIONS
long inserted in the cell walls 1 cm. from the top and bottom of the cell. This new cell was found to perform very well, so a second cell of the same general design with three chambers (1.0 X 2.0 X 6.0 cm.) was made. While both cells were assembled and bonded in the same wayShell Epon VI11 epoxy cement cured a t 200°F.-the cement in the second cell was softened by 38.6% methanol-water solutions, whereas the first cell was not perceptibly affected. The second cell was also more strained; a number of cracks appeared in this cell after several months of use. Although none of these cracks interfered with the function of the cell, it seems that the single chamber cell is a safer design even if it does result in stretching out the data collection a bit. A great advantage of both cells is their large electrode areas, 0.3 and 0.2 cme2for the single and triple units, respectively. For this conductometric experiment, the normal computational procedure employs a correction for the inequality of the cell constants of the top and bottom electrode pairs.2 In earlier work this quantity, which can have an appreciable effect on the derived results, was estimated by an iterative process which minimized the temporal drift in the computed diffusion coefficients. Since larger electrodes can be more easily matched, it is not surprising that the correction for the new cells is very small. With the improved electrode design it is possible to evaluate the correction directly by measuring the cell constant for each pair; no longer is the correction employed as a parameter to minimize drift in the data. Sliding surfaces of the cell were lubricated with Apiezon M which had been extracted with methanol for about 1 week. Concentrations of the final (infinite time) cell contents were obtained by measuring the conductances of those solutions in an auxiliary cell. A relation between the resistance of the solutions and the square root of the concentration was established through a series of measurements on carefully prepared solutions of known composition. All experiments were carried out a t 25". The outer water bath was controlled a t 25 f 0.01'. Within the air thermostat the control was much better; no fluctuations could be observed with a Beckmann thermometer immersed in water in that unit. Reagents. Fisher certified reagent grade methanol was used without purification. Deionized distilled water with a specific conductance less than 10+ was used. Both liquids were deaerated before the preparation of the solvent mixtures. KC1 precipitated from a saturated solution by passage of HC1 through the solution was dried for several days in a vacuum desic-
2337
cator,. placed in a platinum dish, dried under vacuum at 100" for 1 hr., and fused a t 800" under
Results and Discussion Diffusion coefficients were computed a t various concentrations using the equation
D
=
u2 A In ( K B - KT - AK) --
(1)
At
I?
where a is the total height of the diffusion chamber, K B and KT are conductances of the bottom and top electrode pairs, At is the time interval corresponding to A In ( K B - K T - AK), and AK = Kgm - KTm, as measured after shaking the cell a t the end of the run. These diffusion data will be compared with values predicted by the Onsager-Fuoss theory, which leads to the expression'
D
=
(vi
+ vz)1000RT 1.0741 X 10-zO-
XioXzo
vllzllAo
I AB' c
+-AB")
(2)
C
where v, A, AO, z , and y, have their accepted electrochemical meanings, and the electrophoretic terms, A B ' and are given by the equations
An",
-An' =
(I zz/XI O
- /zl/A20)23.132 X 10-19 c y / r
+
Ao2/z1zz/(vl vz)
qo(d')''*
(1
4-KU) (3)
and
E
is the dielectric constant, qo is the solvent viscosity,
I' is the ional concentration, and ( ~ ( K uis) defined and tabulated in ref. 1. The equation used to fit the b In y*/b In c) is developed thermodynamic term (1
+
later (eq. 12). In Table I are listed the experimental values for the diffusion coefficients and those supplementary data needed for a comparison with theory. The results are also plotted in Figure 1. It is apparent that the agreement with theory is excellent for the 10% pethanol data and surprisingly good for the 20% data. At 38.6% methanol, the results are about 1% higher than theory in the range of concentrations covered. While in some cases the conductometric method can yield data with an apparent precision of +O.lyo,the results reported here for 10 and 20% methanol are no more reliable than =k0.20/,and an uncertainty of *0.30j, (4)
T.Shedlovsky, J. A m . Chem. Soc., 54, 1411 (1932).
Volulne 69, Number 7 July 1966
M. V. KULKARNI AND P. A. LYONS
2338
1.60
I
Table I CI, mole/l
D X 106, om.2 sec.-1
D X 106 calcd., cm.2 Bec. -1
0.00211 0.00273 0.00395 0.00425 0.00529 0.00943 0.01250 0.01382 0.02108 0.02905
10% CHiOH 1.559 1,549 1,545 1.542 1.533 1,521 1,513 1,513 1.505 1.491
1.557 1.552 1.545 1.543 1,538 1,523 1.516 1,513 1.502 1.490
0.01476 0.01587 0.01863 0.02102
20% CHIOH 1.251 1,249 1,249 1.246
I . 248 1.246 1,243 1.239
1.05
0.00240 0,00302 0,00757 0.01050 0.01513
38.6170 CHSOH 1.026 1.027 1.005 1.008 0,9992
1.017 1.014 0.996 0.989 0.978
1.00
Methanol, wt. %
vo x 103, poises" b
e
Si A' X°K +'
xo,
I-
a for KC1
=
10.00%
12.40 74.1 0.5587 1.186 60.1 59.8
20.00%
14.80 69.2 0.6184 1.227 50.0 49.4
38.61%
17.00 60.2 0.7622 1,314 39.7 39.4
1.55
1.30 .3'
P X
9
0.00
0.10
0.05
0.15
d C .
Figure 1. Diffusion of potassium chloride in different methanol-water mixtures: top curve, 10% CHaOH; middle curve, 20% CHsOH; lower curve, 38.61% CHIOH.
3.5 A.
C. Carr and J. A. Riddick, Ind. Eng. Chem., 43, 692 (1951). See ref. 1. R . Kay, Mellon Institute, private communication.
is associated with the 38.6Oj, methanol values. Since our cells did give diffusion values for very dilute aqueous KCl solutions within 0.05% of the theoretical value, it is assumed that for this mixed solvent system distillation losses attendant upon filling the cell and analyzing the final cell contents tended to scatter the results because of imprecision in both the diffusion coefficients and the concentrations. In any event, the 10% methanol data agree with simple binary theory over the entire concentration range covered. The 20% data just meet theory a t the lowest concentrations and the 38.6% data are about 1% above theory. Significantly, in the work-up of the data for all methanol concentrations there was no systematic variation in the values of D computed from various pairings of time. The time invariance of D and AK will be shown to be consistent with first-order departure from pseudo-binary behavior. The Journal of Physienl Chemistry
Of course, the agreement with theory does not require identical interaction of ions with either methanol or water. This is obviously not the case. The conductance data and transference nclmbers which are used to compute the limiting values of the diffusion coefficients already admit of differences in specific interactions. Where results agree with theory it can only be stated that the variation with concentration of the diffusion coefficient follows the same rule as a very dilute aqueous solution of a 1-1 electrolyte. I t may be of some interest to consider in a rough approximation how results such as these might be expected to depart from pseudo-binary behavior. Calling the concentrations of KC1 and methanol c1 and c2, respectively, in moles per liter, and assuming as is reasonable that a preferential coupling of ions with water would result in a lowered concentration of methanol as a result of salt flow into a given volume element, and if the initial concentration of methanol in the mixed solvent were czo, moles per liter, then where n = the net number of moles of water transported by KC1, the methanol concentration in the solvent at any
DIFFUSION OF POTASSIVM CHLORIDE IN METHANOL-WATER SOLUTIONS
level in the cell would be c2 % cz0 - ncl. The apparent diffusion coefficient measured for this system by the Harned method is related to the flow of salt, J1, by Fick’s second law
b (J1) = bCl = DaPP b2C1 _- bX bt bX2
(5)
Following Fujita and G ~ s t i n gwe , ~ may also write
Using the approximation c2 g c20 - ncl, and comparing ( 5 ) and (6), we find D,,, is given approximately by the difference, D I I - nD12. In this first-order estimate, the pseudo-binary diffusion coefficient would approach the Onsager-Fuoss value for D under circumstances where nDlz was very small. Since we expect D12 to be both small and negative and also that n, the net water transport, is small, we expect the deviation to be small and positive. Additionally, since n should increase with methanol concentration, the deviation should increase also. Finally, the pseudo-binary constant should appear to be a time invariant quantity g (Dl1 - nDlz) for higher methanol concentrations. All of these features are consistent with the observed data. (Unfortunately, the positive deviation cannot be considered to be particularly dwisive since this is the direction of departure from theory for 1-1 electrolytes in simple aqueous solutions.) It is appropriate to consider how well activity coefficients for the salt can be computed from the diffusion data for this mixed solvent system. The theoretical value for the diffusion coefficient may be written in a simple form
2339
where the Debye-Huckel limiting slope
Sf =
1 - (ZlViZi2)*’2 V
1.290 X lo6 (cT)”’
(11)
A graphical integration of the plot of D’/cl/‘ us. cl” yields log yk. These values can then be compared with experimental values. For convenience, values of y* obtained from the diffusion data, from limited experimental data, and from a Debye-Huckel fit of the data are presented a t round concentrations in Table 11. (See also Figure 2 . )
0.7
1
0.7
\
4 I
0.8
0.7
0.00
0.10
0.05
0.15
4;.
(a/c) is the combined mobility term.
where Calling
Figure 2. Plots for computing activity coefficients from eq. 9: top curve, 10y0CHsOH; middle curve, 2097, CHIOH; lower curve, 38.617, CHsOH.
For the above comparison the experimental activity data were fit to an equation of the form gives6 The value of A ’ in methanol-water mixtures was estimated using the approximate relation At the limit
A ’(water) A ’(mixturej
€mixture
=
‘/2
(13)
Fujita and L. J. Gosting, J . Am. Chem. Soc., 78, 1099 (1956). (6) H. S. Hamed, PTOC. .VatZ. Acad. Sci. L’. 8.. 40, 551 (1954). (5) H.
Volume 69, lvumbeT 7 J u l y 1966
M. V. KULHARNI AND P. A. LYONS
2340
Table I1 g* from g+ from
76 methanol
Cl
equation
Harned rulea
10 10 10 10 10
0 0 0 0 0
001 010 020 030 050
0.962 0.892 0.856 0.832 0.797
0.959 0.892 0.857
20 20 20 20 20
0 0 0 0 0
001 010 020 030 050
0.957 0.881 0.843 0.817 0.786
0.960 0.883 0.849
0 0 0 0 0
001 010 020 030 050
0.948 0.857 0.813 0.782 0.741
0.951 0.858 0.812 ... 0,737
38 38 38 38 38
61 61 61 61 61
...
0.803
...
0.791
g* from
e.m.f.b , . .
... 0.857 ... 0.794
... ...
0,849 ... 0.776 ... ...
0.812 ... 0.717
v* from Figure 2
0.962 0.891 0.856 0.831
... 0.957 0.881 0.844 0.820 ...
0,955 0.879 0.840 0.821 ...
H. S. Harned, a Values of y* were obtained from 7 ~ See . J . Phys. Chem., 66, 589 (1962). Revised values (see ref. a). G . Akerlof, J . Am. Chem. SOC.,52, 2353 (1930).
A choice of B’ = 0.02 for both 10% methanol and 20% methanol fits the data over the entire range of concentrations (c up to 0.03 and 0.02, respectively). An interesting method proposed by Harned for estimating log ~ j &may also be testedS7 His rule empirically relates the activity coefficients of two different electrolytes in the same solvent. The rule is 71
log-
72
The Journal of Physical Chemistry
=
where y is the activity coefficient on the molal scale, m is the molality, and B is a constant which can be evaluated from the activity data for both electrolytes in pure water. Values of B for the KC1-HC1 system are tabulated for concentrations above 0.01 m.7 Since precise e.m.f. data exist for hydrochloric acid-methanolwater mixtures, yrt and then y* may be computed for potassium chloride-methanol-water solutions. Values of these are included also in Table 11. The agreement is very good. In sum, these measurements show that KC1 solutions in 10 and 20% methanol-water mixtures behave as pseudo-binary systems as confirmed by the close agreement with the Onsager-Fuoss theory for binary solutions. As a consequence, the salt activity coefficient can be determined from diffusion data a t low KCl concentrations. The results presented here are the first experimental values for solutions of electrolytes in mixed solvents below 0.02 m. They also refer unambiguously to the infinitely dilute solution as the reference state. In addition, the results support the utility of the Harned rule. However, it has not been shown that either this diffusion technique or the Harned rule can be used successfully a t higher concentrations than those for which activity coefficients could be computed with a modified Debye-Huckel equation of the form of Guggenheim with judiciously selected constants.
Acknowledgment. This work was supported by Atomic Energy Commission Contract No. AT(30-1)1375.
Bm (7) See footnote a in Table 11.
