PETER,J. DUNLOP
26
polluted atmosphere. Until more precise information on the nature of the inorganic compounds present in the atmosphere is at hand further speculation is unwarranted.
Acknowledgment. The authors are grateful for the support given this work by grants from the Division of Air Pollution, Bureau of State Services, U. S. l’ublic Health Service, arid the Xational Science Foundation.
Frictional Coefficients for Binary and Ternary Isothermal Diffusion
by Peter J. Dunlop Departmetit of Ph?jsical a7kd Irlorganic Chmistry, University of Addaide, Adelaide, South Australia (Heceiwd May 2, 1868)
Starting from a general set of flow equations, relations are deduced which define a set of frictional coefficients for isothermal multicomponent diffusion. These relations are essentially identical with those previously proposed by Lamm, Onsager, Klemm, Laity, and Rearman. Equatioiis are then derived which permit these frictional coefficients to be computed for binary and ternary diffusion from experimental values of diff usiori coefficients and corresponding thermodynamic data.
I n the past two decades, means of describing multicomponent isothermal diff usiori in terms of experimentally measurable diffusion coefficients have been suggested.’-4 The diffusioii coefficients which appear in one of the above sets of generalized flow equations1have been measured for several tcrriary systems6-’*and used, together with the pertinent thermodynamic data, to test the Onsager reciprocal relation (ORR) for ternary isothermal diffusion.Y-lY Iliffusiori in multicomponent systems may also be described in terms of sets of frictional coeficients*~ l 4 - l s which cannot be measured directly but which, unlike the experimental diffusion coefficients, arc: independent of the coordinate system of measurement. I t is the purpose of this papcr t o deduce from a set of generalized flow equations a corresponding set of relations which define frictional coefficients for multicomponent diffusion. ‘I’hcse relations are esscntially identical with those proposed by I,amm, Onsager,* Iv]11
+ Cl(bl11 ~1t’bC1]T,p (41)
where DV = [ ( l ) l l ) ~ ~ ] c 2isr o~ i o wthe mutual diffusion coefficirnt for a binary system and y1 is the solute
(32) (26)
Equatioris 35 and 36 haw bcen tcstt*ti c~xgorirnentally; see ref. 6, 7, arid 10.
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PETERJ. DUNLOP:
30
activity coefficient on the concentration scale moles per cc. The above equation may be used to compute values of Rlo'for binary systems from the experimental factors on the right-hand side of the equation. We note that knowledge of the concentration dependence of the activity coefficients for the solutes 1 and 2 in a ternary system permits (Rlo)cl= 0, (Rlz)cZ= 0, and (Rzo)cz = o to be determined as follows. If we assume that solutes 1 and 2 are both nonelectrolytes, then the logarithms of the solute activity coefficients, ut, may be expressed by Taylor series of the form 2
In
= j=l
BijCj
+
2
2
j=l k-1
BtjtCjCt
+ . . . (i
=
1,2) (42)
where
The Journal of Physical
and from the.Bt, and Bijk in eq. 42 the appropriate p C j may be determined. These values together with the ( D l j ) vvalues then permit ( R I o )=~0, , (R1dci = 0, ( R d c ,= 0, and (Rzo)cz = to be computed by eq. 38 and 39.
Acknowledgments. The author is grateful to Dr. B. J. Steel for many helpful discussions during the course of this work and to Messrs. H. D. Ellerton and D. E. Mulcahy €or checkinq wme of the equations. This work was supported in part by a research grant from the National Institutes of Health (AM-06042-02).
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