Chapter 13, Problem 13.66P

Interpretation Introduction

Interpretation:

The expressions for ${\widehat{\varphi }}_1$ and ${\widehat{\varphi }}_2$ for a binary gas mixture are to be determined.

Concept Introduction:

Equation $3.38$ used to describe the binary gas mixture is:

  $Z=\frac{PV}{RT}=1+\frac{B}{V}+\frac{C}{V^2}$ .....(1)

Here, $B\text{ and }C$ are virial coefficients which is substance dependent and a function of temperature.

Equation $10.62$ gives the mixing rule of $B$ for a binary mixture as:

  $B=y_1^2{B}_{11}+2y_1{y}_2{B}_{12}+y_2^2{B}_{22}$ .....(2)

The virial coefficient $B_{ij}$ represents the bimolecular interaction between the molecules of species $i\text{ and }j$ . Thus, $B_{ij}=B_{ji}$ .

The equation used to find the value of ${\widehat{\varphi }}_i$ is:

  $\ln {\widehat{\varphi }}_i=\frac{\partial \left(n{G}^R/RT\right)}{\partial n_i}-\frac{\partial \left(nZ\right)}{\partial n_i}+n\frac{\partial \left(\ln Z\right)}{\partial n_i}+1$ .....(3)

Equation to be used for $G^R$ in terms of virial coefficients is:

  $\frac{G^R}{RT}=2B\rho +\frac{3}{2}C{\rho }^2-\ln Z$ .....(4)