under combined chemical and electrostatic potential gradients as the negative gradient of the electrochemical potential (-X = V l = V p zeV$) results in a formulation of the particle flux J of which the laws of Fick and Ohm are special cases. I t is interesting that more than two decades before the electrochemical potential function was defined in the literature, Gibbs2recognized that the "force necessary to prevent migration" of an ion in solution is dpldz ze (d$/dz).
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LETTERS
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To the Editor: The recent article "An Introduction to Nonequilibrium Thermodynamics" by H. J. M. Hanley [THIS JOURNAL 41, 647 (1964)] contains statements in the section on Lmear Laws which may be misleadmg. The form of Ohm's law, namely I = LV, which Dr. Hanley uses as illustration of the phenomenological relation between fluxes and forces is an unfortunate choice for these reasons: (a) The "voltage" (difference in electrostatic potential) is a scalar and not avector quantity, as stated, and so cannot be the force producing the electric current. The actual driving force is the product of the charge on the carriers of current and the electric field vector. (b) The coefficient L may be a scalar quantity (if I in Dr. Hanley's formulation is taken to be the magnitude of the current) but is more generally a tensor. Moreover, since L contains the mobilities and concentrations of the current carriers as well as dimensions of the conducting medium, it is hardly appropriate to refer to it as a "scalar constant." A perhaps more convincing basis for the formulation of the phenomenological equations of particle flow than the "linear law" of Hanley's article and other sources is that the average velocity for a collection of like particles subject to the same driving force is postulated to be proportional to that force:
where n is the concentration. Since in the steady state, driving force and retarding force must be equal, the foregoing statement of the basic postulate is closely related to Stokes' law (viscous drag = 6mqv). The comparison may be even closer than a t first apparent, for in both cases the proportionality between velocity and force must be valid only in first approximation. (Gurney1 stated that the more exact expression for the viscous drag is
The constant in equation (1)can for charged particles be evaluated in terms of physically measurable quantities by considering the special circumstance where the only driving force acting is that of the electrical field: GO XO= constant X (-rev$) (2) The velocity of drift under unit potential gradient definesthe mobility; for particles of charge ze:
'GURNEY,R. W., "Ionic PrOceaSeS in Solution," Dover Publications, Inc., New York, 1962, p. 66. "Collected Works of J. Willard Gibbs. Volume I, Thermodynamics," Yale Univemity Press, New Haven, 1957, p. 430.
To the Editor: While trying to solve a numerical example given to a graduate class concerning the kinetics of the thermal formation of hydrogen iodide from iodine and hydrogen, I discovered that the equation given by Bodenstein' for this classical case is wrong. This is certainly due to an oversight in proof reading or a printing error and the equation following the one in question is correct. However, the incorrect equation appears in several popular physical chemistry texts. The incowect equation that appears in the original Bodenstein report andis found in various texts is:
This is for the reaction written as:
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where K = k / k l , and m = [(a b)%- 4ab(l - 4K)I"'; a and b are the initial concentrations of iodme and hydrogen respectively; and x is the amount of hydrogen iodide formed a t time t, starting initially with x = 0. It can be seen a t a glance from the boundary conditions (t = 0, x = 0 ) that the equation, as given, cannot be correct. The negative sign in front of the first logarithmic term is missing. The correct equation should be:
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It is suggested that readers check the books they use and help to eliminate this particularly long-lived printer's error. H. H. G. JELLINEK
whence the constant is equal to u&le and
The identification of the driving force for diffusion 344
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Journol o f Chemkol Educafion
BODENSTEIN, M., Z. Phyaik. C h . (Leipig), 29, 307 (1899); dm BODENSTEIN, M., "Gs.sres.ktionen in der chenischen Kine-
tik," Htthilitationsschrift,Leipzig, 1899, p. 26.
