Chapter 6, Problem 6.74P

Interpretation Introduction

(a)

Interpretation:

The temperature of the mixture of benzene and toluene is to be calculated.

Concept introduction:

The formula to convert mass fraction $\left(x_m\right)$ to mole fraction $\left(x\right)$ of a two-component system is:

$x=\frac{\left(\frac{x_{m1}}{{\text{MW}}_1}\right)}{\left(\frac{x_{m1}}{{\text{MW}}_1}+\frac{x_{m2}}{{\text{MW}}_2}\right)}$

             …… (1)

Here, ${\text{MW}}_1{\text{ and MW}}_2$ are the molecular weight of components 1 and 2 in the mixture.

For two phase binary mixture, Raoult’s law states that,

$P=x_{\text{A}}{P}_{\text{A}}{}^{\ast }+x_{\text{B}}{P}_{\text{B}}{}^{\ast }$

             …… (2)

Here, $x_{\text{A}}\text{ and }{x}_{\text{B}}$ are the mole fractions of A and B in liquid phase respectively, $P_{\text{A}}{}^{\ast }\text{ and }{P}_{\text{B}}{}^{\ast }$ are the vapor pressure of A and B respectively, and $P$ is the total pressure of the system.

Also, the partial pressure of the components in the two-phase binary system in terms of their vapor phase mole fraction is,

$\begin{array}{c}{y}_{\text{A}}P=x_{\text{A}}{P}_{\text{A}}{}^{\ast }\\ y_{\text{B}}P=x_{\text{B}}{P}_{\text{B}}{}^{\ast }\end{array}$

             …… (3)

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$

             …… (4)

Here, $A,B\text{ and }C$ are the constants specific for a substance given in table B.4 of appendix B.

Interpretation Introduction

(b)

Interpretation:

The fraction of system’s mass present in the liquid phase is to be determined.

Concept introduction:

The formula to convert mass fraction $\left(x_m\right)$ to mole fraction $\left(x\right)$ of a two-component system is:

$x=\frac{\left(\frac{x_{m1}}{{\text{MW}}_1}\right)}{\left(\frac{x_{m1}}{{\text{MW}}_1}+\frac{x_{m2}}{{\text{MW}}_2}\right)}$

             …… (1)

Here, ${\text{MW}}_1{\text{ and MW}}_2$ are the molecular weight of components 1 and 2 in the mixture.

For two phase binary mixture, Raoult’s law states that,

$P=x_{\text{A}}{P}_{\text{A}}{}^{\ast }+x_{\text{B}}{P}_{\text{B}}{}^{\ast }$

             …… (2)

Here, $x_{\text{A}}\text{ and }{x}_{\text{B}}$ are the mole fractions of A and B in liquid phase respectively, $P_{\text{A}}{}^{\ast }\text{ and }{P}_{\text{B}}{}^{\ast }$ are the vapor pressure of A and B respectively, and $P$ is the total pressure of the system.

Also, the partial pressure of the components in the two-phase binary system in terms of their vapor phase mole fraction is,

$\begin{array}{c}{y}_{\text{A}}P=x_{\text{A}}{P}_{\text{A}}{}^{\ast }\\ y_{\text{B}}P=x_{\text{B}}{P}_{\text{B}}{}^{\ast }\end{array}$

             …… (3)

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$

             …… (4)

Here, $A,B\text{ and }C$ are the constants specific for a substance given in table B.4 of appendix B.

The formula to calculate density $\left(\rho \right)$ from its mass $\left(m\right)$ and volume $\left(V\right)$ is:

$\rho =\frac{m}{V}$

             …… (5)

The density of a mixture is calculated as:

${\rho }_m=\sum _i{x}_i{\rho }_i$

             …… (6)