Chapter 6, Problem 6.61P

Interpretation Introduction

(a)

Interpretation:

The equations used to calculate the bubble-point temperature for the given mixture in the form $f\left(T\right)=0$ are to be written. Also, the equations to calculate the vapor mole fraction of the first bubble formed in terms of the calculated temperature of the system are to be written.

Concept introduction:

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$   ...... (1)

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,

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$   ...... (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, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.

Interpretation Introduction

(b)

Interpretation:

A spreadsheet is to be prepared to show the calculations by equations written in part (a). Also, test this spreadsheet for the given mixture at different pressures.

Concept introduction:

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$   ...... (1)

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,

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$   ...... (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, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.

Interpretation Introduction

(c)

Interpretation:

The spreadsheet prepared in part (b) is to be modified to incorporate the given Antoine equation and the bubble point temperature of the mixture is to be calculated at the given pressure.

Concept introduction:

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$   ...... (1)

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,

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$   ...... (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, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.