Chapter 6, Problem 6.9NP

(a)

Interpretation Introduction

Interpretation: An expression needs to be derived for the entropy of mixing as a function of $\xi$

Concept Introduction:

The change in entropy of mixing can be represented as follows:

  $\Delta S_{mixing}=-nR{\displaystyle \sum _i{x}_i}\ln x_i$

Here, n is total number of moles, R is Universal gas constant, $x_i$ is the mole fraction of the gas i in the mixture.

(b)

Interpretation Introduction

Interpretation: The value of $\xi$ needs to be determined graphically as the function of entropy of mixing.

Concept Introduction: The change in entropy of mixing can be represented as follows:

  $\Delta S_{mixing}=-nR{\displaystyle \sum _i{x}_i}\ln x_i$

Here, n is total number of moles, R is Universal gas constant, $x_i$ is the mole fraction of the gas i in the mixture.

(c)

Interpretation Introduction

Interpretation: An expression for $G_{pure}$ as a function of $\xi$ needs to be determined.

Concept Introdiction: For the mixture of gases, the $G_{pure}$ at equilibrium can be represneted as follows:

  $G_{pure}=n_A\Delta G_f^o\left(\text{A},g\right)+n_{\text{B}}\Delta G_f^o\left(B,g\right)$

Here, $n_A$ and $n_{\text{B}}$ are number of moles of gases A and B respectively at equilibrium.

(d)

Interpretation Introduction

Interpretation: The plot of $G_{\text{mixture}}$ which is $G_{pure}+\Delta G_{mixing}$ as a function of $\xi$ needs to be plotted. The value of $\xi$ needs to be calculated for minimum value of $G_{\text{mixture}}$ . The calculated value needs to be compared with the value of $\xi$ in part (b).

Concept Introduction: The change in Gibbs free energy of mixing can be calculated as follows:

  $\Delta G_{\text{mixing}}=nRT{\displaystyle \sum _i{x}_i}\ln x_i$

Here, n is total number of moles of mixture at equilibrium, R is Universal gas constant, T is temperature and $x_i$ is mole fraction of i gas at equilibrium.