Question

The excess gibbs free energy of a binary liquid mixture at t and p is given by: T = (−2.6 x1 − 1.8x2)x1x2 , a) find expression of ln 1 and ln 2 at t and p. show that (d ln 1/dx1)x1=1 = (d ln 2/dx1)x1=0=0

Answer 1

The student's question is about deriving expressions for the natural logarithms of activity coefficients, ln γ1 and ln γ2, from a given excess Gibbs free energy equation for a binary liquid mixture and showing that certain derivatives equal zero.

Step-by-step explanation:

The student is asking for the expression of the natural logarithm of the activity coefficients (ln γ1 and ln γ2) for a binary mixture described by a given excess Gibbs free energy function. According to thermodynamics, the activity coefficient γi is related to the excess Gibbs free energy function (G^ex) by the equation:

ln γi = ∂(G^ex/RT)/∂ni at constant T, P, and nj (j ≠ i).

In this case, the function provided for G^ex is a function of mole fractions x1 and x2, and the student is seeking to show that the derivative of ln γ1 with respect to x1 at x1=1 and the derivative of ln γ2 with respect to x1 at x1=0 are both equal to zero. The correct differentiation and simplification of the given function will lead to the desired result.