?The molar volume (cm3·mol?1) of a binary liquid mixture at T and P is given by:\(V=120

Chapter 10, Problem 10.13

(choose chapter or problem)

The molar volume (cm3·mol−1) of a binary liquid mixture at T and P is given by:

\(V=120 x_{1}+70 x_{2}+\left(15 x_{1}+8 x_{2}\right) x_{1} x_{2}\)

(a) Find expressions for the partial molar volumes of species 1 and 2 at T and P.

(b) Show that when these expressions are combined in accord with Eq. (10.11) the given equation for V is recovered.

(c) Show that these expressions satisfy Eq. (10.14), the Gibbs/Duhem equation.

(d) Show that \(\left(d \bar{V}_{1} / d x_{1}\right)_{x_{1}=1}=\left(d \bar{V}_{2} / d x_{1}\right)_{x_{1}=0}=0\).

(e) Plot values of V, \(\bar{V}_{1}, \text { and } \bar{V}_{2}\) calculated by the given equation for V and by the equations developed in (a) vs. x1. Label points \(V_{1}, V_{2}, \bar{V}_{1}^{\infty}, \text { and } \bar{V}_{2}^{\infty}\) and show their values.

Text Transcription:

(cm^3 cdot mol^-1)

V=120x_1+70x_2 + (15x_1 + 8x_2) x_1x_2

(dbarV_1/dx_1)_x_1 = 1 = (dbarV_2/dx_1)_x_1 = 0 = 0

barV_1, and barV_2

V_1, V_2, barV_1^nfty, and barV_2^infty