Chapter 13, Problem 13.45P

Interpretation Introduction

Interpretation:

The $P_{x-y}$ diagram for one of the binary systems in table $13.10$ is to be drawn using NRTL equations and equation $13.19$ .

Concept Introduction:

Antoine equation is used to determine the vapor pressure of any substance at the given temperature by the equation:

  $\ln P^{\text{sat}}\left(\text{kPa}\right)=A-\frac{B}{\left(T^{\circ }\text{C}\right)+C}$ ......(1)

Here, $A,B\text{ and }C$ are the constants specific for a substance given in table B.2 of appendix B.

Equation $13.19$ to be used for Modified Raoult’s law is:

  $y_{i}P=x_i{\gamma }_i{P}_i{}^{\text{sat}}$ ......(2)

NRTL equations to be used are:

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

Here, the parameters ${\tau }_{12}\text{ and }{\tau }_{21}$ are calculated by the formula:

  $\begin{array}{l}{\tau }_{12}=\frac{b_{12}}{RT}\\ {\tau }_{21}=\frac{b_{21}}{RT}\end{array}$ ......(4)

And, $G_{12}\text{ and }{G}_{21}$ are calculated by the formula:

  $\begin{array}{l}{G}_{12}=\exp \left(-\alpha {\tau }_{12}\right)\\ G_{21}=\exp \left(-\alpha {\tau }_{21}\right)\end{array}$ ......(5)

Where, $\alpha \text{, }{b}_{12}\text{ and }{b}_{21}$ are the NRTL equation parameters given in table $13.10$ for binary systems.