Chapter 13, Problem 13.39P

(a)

Interpretation Introduction

Interpretation:

The experimental values of $G^E/RT$ are to be calculated and plotted on a single graph along with the experimental values of $\ln {\gamma }_1\text{ and }\ln {\gamma }_2$ .

Concept Introduction:

The formula to calculate the value of $G^E/RT$ for a binary system is:

  $\frac{G^E}{RT}=x_1\ln {\gamma }_1+x_2\ln {\gamma }_2$ .......(1)

(b)

Interpretation Introduction

Interpretation:

A valid correlation for the composition dependence of $G^E/RT$ is to be developed. Also, the lines on the graph prepared in part (a) are to be shown to represent these correlations.

Concept Introduction:

Margules equation for excess Gibbs energy in terms of the composition of the binary system in VLE is:

  $\frac{G^E}{RT}=\left(A_{12}{x}_1+A_{21}{x}_2\right)x_1{x}_2$ .......(2)

Here, $A_{12}\text{ and }{A}_{21}$ are the temperature dependent parameters, specific for a system.

The equations used to calculate $\ln {\gamma }_1\text{ and }\ln {\gamma }_2$ are:

  $\begin{array}{c}\ln {\gamma }_1=x_2^2\left[A_{12}+2\left(A_{21}-A_{12}\right)x_1\right]\\ \ln {\gamma }_2=x_1^2\left[A_{21}+2\left(A_{12}-A_{21}\right)x_2\right]\end{array}$ .......(3)

(c)

Interpretation Introduction

Interpretation:

The consistency test is to be applied on the given data and the result is to be concluded.

Concept Introduction:

The formulas for the residuals of a property used to check the consistency of a system is:

  $\delta {\left(\frac{G^E}{RT}\right)}_i={\left(\frac{G^E}{RT}\right)}_{\text{calc}\text{.}}-{\left(\frac{G^E}{RT}\right)}_{\exp .}$ .......(5)

  $\delta \ln {\left({\gamma }_1{\gamma }_2\right)}_i=\ln {\left(\frac{{\gamma }_1}{{\gamma }_2}\right)}_{\text{calc}\text{.}}-\ln {\left(\frac{{\gamma }_1}{{\gamma }_2}\right)}_{\exp .}$ .......(6)

The formula for absolute mean deviation in the residual is:

  $\text{Mean deviation}=\left|\frac{\left(\delta X_i\right)}{n}\right|$ .......(7)

Here, $X$ is the residual of the property, and $n$ is the number of entries.