Chapter 6, Problem 6.70P

Interpretation Introduction

(a)

Interpretation:

It is to be shown that there are two degrees of freedom for the given system using Gibbs phase rule.

Concept introduction:

A $PVT$ system consisting of $N$ chemical species along with $\pi$ phases in equilibrium, characterized by its intensive variables, $T\left(\text{temperature}\right),P\left(\text{pressure}\right),\text{ and }N-1$ mole fractions for each of the species is used to define the intensive state of this system.

According to the Gibbs phase rule, degree of freedom $\left(F\right)$ for any system is used to define the number of independent intensive variables which can be used to specify the system completely.

$F=2-\pi +N$ ....... (1)

Here, $\pi$ is the number of phases present in the system, and $N$ is the number of components present in the system.

Interpretation Introduction

(b)

Interpretation:

The liquid and vapor compositions are to be calculated for the given system.

Concept introduction:

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$ ....... (2)

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

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

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$ ....... (3)

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, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.

Interpretation Introduction

(c)

Interpretation:

The pressure and vapor composition are to be calculated for the given system.

Concept introduction:

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$ ....... (2)

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

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

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$ ....... (3)

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, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.

Interpretation Introduction

(d)

Interpretation:

The temperature and vapor composition are to be calculated for the given system.

Concept introduction:

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$ ....... (2)

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

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

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$ ....... (3)

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, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.

Interpretation Introduction

(e)

Interpretation:

The temperature and liquid composition are to be calculated for the given system.

Concept introduction:

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$ ....... (2)

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

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

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$ ....... (3)

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, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.

Interpretation Introduction

(f)

Interpretation:

The temperature and pressure are to be calculated for the given system.

Concept introduction:

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$ ....... (2)

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

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

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$ ....... (3)

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, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.