564
J. Phys. Chem. 1982, 86, 564-571
Electrolyte Oiffusion in Multicomponent Solutions Derek G. Lealst and Phlllp A. Lyons" Department of Chemistry, Yale UnlverslCY, New Maven, Connecticut 06520 (Received: July 21, 1981; In Final Form: October 7, 1981)
Diffusion coefficients are reported for dilute electrolytes in the system hydrochloric acid/potassium chloride/methanol(lO wt %)/water at 25 "C. The experimental diffusion coefficients and the derived Likphenomenological coefficients are in very good agreement with predictions based on pseudo-ternary mixed electrolyte diffusion theory. The results suggest that reliable electrolyte diffusion properties can be predicted from limiting ionic mobilities for any arbitrary ionic mixture at low ionic strength in any arbitrary mixed solvent, as long as the dielectric constant is high enough to give effectively total dissociation. Nernst expressions are provided for the limiting diffusion Coefficients of mixed electrolyte solutions containing up to four kinds of ions. Strong coupling between diffusive flows of electrolytes may be anticipated in solutions containing polyelectrolytes, and in aqueous systems containing acids (or hydroxides). Restricted diffusionexperiments for the conductimetric determination of ternary diffusion coefficients are described. Introduction Studies of the diffusion of dilute electrolytes in multicomponent solutions have been reported recently. The fmt dealt with solutions containing several electrolytes and a single solvent component;1,2in these systems electrolyte flows can be strongly coupled by electrostatic interaction. Given limiting ionic conductivities, accurate multicomponent transport coefficients (Dikand Lik)can be predicted by using Onsager-Fuoss theory. Experimentally determined transport coefficients for the system HCl/KCl/ water agree well with their predicted values. The diffusion of a single electrolyte dissolved in mixed solvents was discussed in other paper^.^^^ Because of the weak interaction between diffusive flows of electrolytes and nonelectrolytes, electrolyte diffusion in these systems is pseudo-binary. Experimental data for the systems HCl/methanol/water and KCl/methanol/water support this simple concept. Precise electrolyte activity coefficients were determined from the diffusion data. In this paper we propose to combine those earlier ideas with an extension which will allow us to describe the diffusion of mixed electrolytes in mixed solvents with only limited experimentation and, at low ionic strength, the description should be accurate. To test our proposal, we have measured the diffusion of dilute HCl and KC1 in the quaternary system HC1/ KCl/methanol(lO w t %)/water (25 "C) and compared the results with the anticipated pseudo-ternary behavior. The system was chosen because diffusion studies have already been performed on the respective pseudo-binary systems, electrolyte activity coefficients are available, and ion association is In the Discussion section we provide Nernst expressions7 for the limiting diffusion coefficients of mixed electrolytes in solutions containing up to four kinds of ions. With these simple expressions we point out some intriguing examples of coupled diffusion which may be of interest to a wide range of workers interested in electrolyte transport in complex systems. Experimental Section Equipment and Procedure. Because of the low electrolyte concentrations involved, the diffusion coefficients (1)D. G.Leaist and P. A. Lyons, A u t . J. Chem., 33, 1869 (1980). (2)D.G.Leaist, Dissertation, Yale University, 1980. (3)M. V. Kulkarni and P. A. Lyons, J. Phys. Chem., 69,2336(1965). (4)D.G.Leaiat and P. A. Lyons, J. Solution Chem., 10,95 (1981). (5)H. S.Harned and H.C. Thomas, J.Am. Chem. Soc., 58,761(1936). (6)I. T.Oiwa, J.Phys. Chem., 60,754 (1956). (7)W." u t , Z.Phys. Chem., 2, 613 (1888).
were determined by the conductimetric technique. In that method an electrolyte concentration gradient is created along a vertical column of solution. With small electrodes set in the column walls, the electrical conductivity of the solution is measured at one-sixth of the distance from the top and bottom of the column and the rate of diffusion of the electrolytes is determined from the rate of change of the difference in conductivity between the bottom and top electrode pairs. Both equipment* and experimental procedures1V2have been described. A 1-mL precision syringe (Hamilton Co.), fitted with a 7-cm, 20-gauge stainless steel needle, was used to prepare the initial concentration gradient by injecting a small amount of more concentrated electrolyte into the bottom of the solution column. The needle tip had been crimped shut, ground back and polished to leave a very small, leak-free opening. All experiments were carried out at 25(*0.01) "C. Experience showed that controlling the laboratory air temperature to f l OC for the duration of the experiment improved the reliability of the experiment. All solutions were prepared by weight with reagents described in an earlier paper.4 The density equation d = 0.9799
+ 0.018ml + 0.047m2
(1)
was used to convert from molal to molar concentrations (1 = HC1,2 = KC1, d is the solution density in g ~ m -and ~, mi is the molality of electrolyte i). Solutions to the Diffusion Equations. The general equations describing ternary and pseudo-ternary diffusion are
(3)
The solute concentrations c1 and c2 are expressed in moles per unit volume, Dll and D22 are the main diffusion coefficients, and the cross-term coefficients DI2 and DZl measure the coupling between flows of solutes 1 and 2. Because we will be dealing with dilute solutions, it is unnecessary to distinguish between the laboratory and solvent-fixed frames of reference. In obtaining eq 2 and 3, the usual assumption that the diffusion coefficients are independent of solute concentration has been made and (8)T. A. Renner and P. A. Lyons, J . Phys. Chem., 78, 1667 (1974).
0022-3654/82/2086-0564$01.25/00 1982 American Chemical Society
The Journal of Physical Chemistry, Vol. 86, No. 4, 1982 565
Electrolyte Diffusion in Muiticomponent Solutions
possible errors arising from this assumption are minimized by using very small concentration gradients. To establish the coordinate x , the coordinate origin will be located at the bottom of the diffusion column and the positive direction will be taken upward along the column. The requirements that no material shall diffuse out of the ends of the column supply the restricted diffusion boundary conditions acl/ax: = o x = 0;x = A (4) ac2/ax =
o
x = 0;x = A
= C2
+ (1- [/A)Aczo
~1
= E l - ([/A)AClo
~2
= E2 - ([/A)Ac,o
0
