704
COMMUNICATIONS TO THE EDITOR
Vol. 65
parallel increase in acetylene formation. Alternate explanations might involve the bimolecular reaction of long-lived excited species, multiple ionization of a single molecule or of near neighbors, or other specific effects which could occur a t the end of the path of the ionizing particle. Further detailed studies are in progress.
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EIDGENOSSISCHE TECHNISCHE HOCHSCHULE TINOGAUMANN ZURICH,SWITZERLAND MELLONINSTITUTE ROBERTH. SCHULER PITTSBURGH, PENNSYLVANIA, AND BROOEHAVEN NATIONAL LABORATORIES UPTON,NEW YORK RECEIVED MARCH 20, 1961
T H E OXSAGER COEFFICIENT L12 I N TRANSPORT OF BIXARY ELECTROLYTES Sir: &filler1 has pointed out the importance G f the coefficient L12 in the Onsager phenomenological equations for diffusion, conductance, and transference of a binary electrolyte. He suggests that Llz/I (where I is ionic strength) approaches a common slope for electrolytes of different valences. As a matter of fact, the slope for a given electrolyte computed from the Debye-Onsager theory depends somewhat on specific properties, but turns out to be almost constant for various electrolytes. The theoretical expression for ,512 can be written compactly in terms of the equivalent concentration, ce, Hittorf transference numbers, tl and t2, and the so-called kinematic diffusion coefficient, D, which is equal to the Fick diffusion coefficient divided by (1 d In y/d In c)
+
where z2 < 0 is the valence of the anion, and the other symbols have their usual significance2 ( Y is used in place of Miller’s r ) . Differentiation by ./c, gives the limiting slope of the L12/ce curve in terms of the limiting slopes SA)^ and (SA)2 for equivalent ionic conductances and SDfor diffusion:
Expressions for the S A ’ S and SDcan be taken from standard works2 and evaluated for salts for which values of t l , t2, and A are available a t infinite dilution. The theoretical values are given in Table I (1) D. G. Miller, J. Phys. Chom.,64, 1598 (19130). ( 2 ) &. g., H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd Edition, Reinhold Publishing Corp., New York, N. Y., 1958.
0.00
0.10
0.05
6
Figure 1.-Experimental and theoretical values of -LIZ/C,. The intercepts are separated by 0.1 X 10-18.
TABLE I THEORETICAL VALUESOF S12X l O l 6 LiCl NaCl KCl CaC12 2.248 2.361 2.536 2.206
LaCla 2.145
for several chlorides in water. Comparison with experimental values is shown in Fig. 1. The four lower-valent salts exhibit an exceptional conformance with the linear limiting laws (solid lines), up to ce>O.1, aproperty that is not shared by other quantities associated with electrolytes, including the Onsager coefficients Lll and LZ2. It is a curious fact for these electrolytes that diffusion coefficients can be obtained more accurately from the theoretical value of Llz and the experimental value of A, than directly as the theoretical value on which calculation of L12is based. The data on LaCI3 appear to be approaching a slope (dashed line) about 35% higher than the theoretical. PETROLEUM RESEARCH CENTER BUREAU OF MINES PHILIPB. LORENZ U. S. DEPARTMENT OF THE INTERIOR BARTLESVILLE, OKLA. RECEIVED JANUARY 16, 1961
