Chapter 6 : Solution Thermodynamics and Principles of Phase Equilibria
Section 1 : Partial Molar Property
While deriving eqn. 6.8 no specific constraints on the values of either have been applied. This suggests that the equation is valid for any arbitrary values of these two variables. Thus n and dn are independent of each other. Therefore, eqn. 6.8 can only be valid if the coefficients of these two variables are identically zero. On putting the coefficients to zero the following equations obtain:
(6.9)
(6.10)
From eqn. 6.10, it follows, that
(6.11)
And also:
(6.12)
Equating (6.19) and (6.21) yields the well-known Gibbs/Duhem equation (GDE):
have been applied. This suggests that the equation is valid for any arbitrary values of these two variables. Thus n and dn are independent of each other. Therefore, eqn. 6.8 can only be valid if the coefficients of these two variables are identically zero. On putting the coefficients to zero the following equations obtain:
