To the Editor, Missen and Spinner are correct in their assertion that G, may be held constant in one step of the derivation of the Gihbs-Duhem equation and varied in the next if one assumes that the line integrals of Gdn, are independent of the path.
composition a t given T and P by adding together small increments of the phase a t the given T and P. Now G is (assumed to be) a state function, singlevalued in T, P and the n,. Therefore the result expressed by equation (1) should be independent of the path of integration of equation (2). Equation (1) can then be differentiated in any manner desired, including with respect to variable GI, and there is no contradiction, because the integration of (2) has no bearing on the differentiation of (1). This is the point which seems to have been overlooked. In order to get an expression fordGfrom (1)comparable with that in (2), we must differentiate (1) "generally," that is, with respect to the same variables as in (2), expressed explicitly or implicitly. These are T, P, and composition (upon which the G, depend), and the mole numbers. This gives
+ Z n,do
