The molar excess Gibbs free energy, $${{\text{G}}^{\text{E}}}$$, for a binary liquid mixture at T and P is given by, $$\left( {\frac{{{{\text{G}}^{\text{E}}}}}{{{\text{RT}}}}} \right)$$ = Ax1x2, where A is a constant. The corresponding equation for ln y1, where y1 is the activity co-efficient of component 1, is
A. Ax22
B. Ax1
C. Ax2
D. Ax12
Answer: Option A
Solution(By Examveda Team)
Given, $$\frac{{{G^E}}}{{RT}} = A{x_1}{x_2} \Rightarrow \frac{{n{G^E}}}{{RT}} = \frac{{A{n_1}{n_2}}}{n}$$On partially differentiating it $$\left( {\frac{{\partial \frac{{n{G^E}}}{{RT}}}}{{\partial {n_1}}}} \right)T,P,{n_2} = \frac{{A{n_1}{n_2}}}{n} = A{x_2}^2$$
As $$\left( {\frac{{\partial \frac{{n{G^E}}}{{RT}}}}{{\partial {n_1}}}} \right)T,P,{n_2} = \frac{{\overline {n{G^E}_l} }}{{RT}} = ln{\gamma _1}$$
Hence $$ln{\gamma _1} = A{x_2}^2$$
Related Questions on Chemical Engineering Thermodynamics
A. Maxwell's equation
B. Thermodynamic equation of state
C. Equation of state
D. Redlich-Kwong equation of state
Henry's law is closely obeyed by a gas, when its __________ is extremely high.
A. Pressure
B. Solubility
C. Temperature
D. None of these
A. Enthalpy
B. Volume
C. Both A & B
D. Neither A nor B
Join The Discussion