HERBERT S. HARNED AND CLARENCE L. HILDRETH, JR.
650
their comments and suggestions on this work. Particular thanks are expressed to H. Mark and T. Alfrey, Jr., and B. R. Sundheim for their valuable criticism, and to Mr. 11.1. Pope for his invaluable assistance. The author is also indebted to the Office
[CONTRIBUTION FROM
THE
VOl. 73
of Naval Research for the considerable support rendered to this work. BRooKLVN
RECEIVED SEPTEMBER 27, 195OZ4
2, N. y,
(24) Original manuscript received March 31, 1949.
DEPARTMENT OF CHEMISTRY OF YALE UNIVERSITY ]
The Differential Diffusion Coefficients of Lithium and Sodium Chlorides in Dilute Aqueous Solution at 25' BY HERBERT S.HARNEDAND CLARENCE L. HILDRETH, JR. Recent accurate measurement^^^^^^ of the diffusion coefficients of potassium chloride in water from 4 to 30' have shown excellent agreement with the theory4 a t concentrations from 0 to 0.3 molar. As a further test of the theory for 1-1 electrolytes, we have employed the conductometric method for measuring the diffusion of lithium and sodium chlorides in dilute aqueous solutions. The results obtained by this method for potassium chloride solutions have received excellent verification by their agreement with values obtained by Gosting3 who employed the Gouy layer optical method. This agreement increases our confidence in the value of the conductometric method for the investigation of the theoretical aspects of electrolytic diffusion in dilute solution.
J.(d) =
+
ad/& 0.001 (2M1 - Mz) d 0.001c(2M1 Md
+
-
(4)
where y t is the mean activity coefficient of the electrolyte on the molar concentration scale, Sa) is the limiting theoretical expression of the Debye and Hiickel theory for activity coefficients, and B is an empirical constant. The density term, &(d), in equation (3), was calculated by equations (4) and (5)8a in which d is the density of the solution, do the density of the solvent, MI and i M 2 are the molecular weights of the solvent and solute, respectively, 4: is the apparent molal volume a t infinite dilution and S, is the experimental slope of the apparent molal volume versus ,...
VC. Theoretical Calculations The limiting value of the diffusion coefficient, The theoretical values of the diffusion coefficients DO,may be obtained from were computed by the following equations6applicable to 1-1 electrolytes: (6)
and the slope, S p ) , of the limiting law 3
P O
- S(D) 4
(7)
may be computed by =
'(')
3.754 x lo-* D'/nT1/9
xO,xO, 3.683 X xo ( x) + D'/aT-l/a (*) (8)
+
where& = 10, A!; KU = A & = A ' d i ; A = a35.559 X lO*/(DT)'/a. a> is the diffusion coefficient in c m 2sec.-l, A! and XO, and the equivalent limiting ionic conductances of the cation and anion, t o is the viscosity of the solvent, D is the dielectric constant of water, T is the absolute temperature, +(A'
