JOURNAL OF CHEMICAL EDUCATION
moles accompanying one unit of reaction. This equation expresses x, the extent of reaction a t equilibrium, as an implicit function of pressure and temperature. To determine how x changes with pressure one needs only to examine the sign of the derivative, (bx/bP),. Rearranging equation (2) and taking logarithms, wc obtain Pu
= rZCPCT)
(1
- z)""~"
21+m
aabD where r = a constant numerical ratio. l'mm'
To the Editor: v In P = In [1Kp(T)I + (a + b ) In ( 1 - 2) Recently Singh and Ebbing discussed the Le Chatelier ( 1 + nz) In s + u In N theorem from an algebraic standpoint (THIS JOURNAL, 33, 34 (1956)). Their argument is rather involved and Differentiating: I wish to point out a simpler method for illustrating the Le Chatelier theorem. Suppressing the subscripts in Singh and Ebbing's Multiplying out and simplifyingyields the result: equation (2), we obtain
where
v =
l+m-a-b,
the increase in number of
or
(2a)
VOLUME 33, NO. 6, JUNE, 1956 d- i=n-KP
dT
Every quantity contained in the bracket on the right side of equation (3) is positive. Thus, the sign of the derivative is determined by the sign of v. If v is positive, i. e . , if there is an increase in the number of moles of gases during the reaction, then ( b z / d P ) ? is negative, which is to say that an increase in pressure will decrease the extent of reaction a t equilibrium. If v is negative, then ( b x / b P ) , is positive and an increase in pressure will increase the extant of reaction a t equilibrium. An additional advantage of this argument over that of Ringh and Ebbing is that both cases, i. e., v is positive or negative, are covered a t once. By differentiating equation (2a) with respect to temperature at constant pressure, the temperature dependence of x is obtained.
Since
AH RTa
then
Again the quantities in the bracket are all positive and the sign of the derivative depends on the sign of AH. If the reaction is endothermic, AH is positive and the extent of reaction a t equilibrium increases with an increase in temperature. An exothermic reaction has a negative AH; consequently the extent of reaction a t equilibrium decreases with an increase in temperature. This method is given in general form by Prigogine and Defay ("Treatise on Thermodynamics," Vol. 1 (translated by D. H. Everett), Longmans, Green and Co., London, 1954, p. 270 ff.).
