Chapter 6, Problem 6.4P

Interpretation Introduction

(a)

Interpretation:

A semi log plot for the given data is to be prepared and a linear expression relating $\ln p^{\ast }$ to $1/T\left(\text{K}\right)$ is to be determined. Using this expression, heat of vaporization of ethylene glycol is to be estimated. Also, vapor pressures at each of the given temperature are to be calculated using Clausius-Clapeyron equation.

Concept introduction:

The Clausius-Clapeyron equation is defined as:

$\ln \left(p^{\ast }\right)=-\frac{\Delta H^{lv}}{R}\left(\frac{1}{T}\right)+C$   ...... (1)

Here, $p^{\ast }$ is the vapor pressure of the gas at temperature $T$, $\Delta H^{lv}$ is the latent heat of vaporization, and $R$ is the universal gas constant. $C$ is the constant.

The equation of a straight line on semi-log plot is, $\ln y=\text{m}x+\ln \text{b}$.

Given two points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$, the slope $\left(\text{m}\right)$ for this equation is calculated as:

$\text{m}=\frac{\ln y_2-\ln y_1}{x_2-x_1}$   ...... (2)

Interpretation Introduction

(b)

Interpretation:

A semi log plot for the given data is to be prepared and a linear expression relating $\ln p^{\ast }$ to $1/T\left(\text{K}\right)$ is to be determined using Slope and Intercept functions of APEx. Using this expression, heat of vaporization of ethylene glycol is to be estimated. Also, vapor pressures at each of the given temperature is to be calculated using Clausius-Clapeyron equation.

Concept introduction:

The Clausius-Clapeyron equation is defined as:

$\ln \left(p^{\ast }\right)=\frac{\Delta H^{lv}}{R}\left(\frac{1}{T}\right)+C$   ...... (1)

Here, $p^{\ast }$ is the vapor pressure of the gas at temperature $T$, $\Delta H^{lv}$ is the latent heat of vaporization, and $R$ is the universal gas constant. $C$ is the constant.

APEx is a tool in Excel to carry out process calculations.

Interpretation Introduction

(c)

Interpretation:

Vapor pressures of ethylene glycol at given temperatures are to be determined using equation of part (b). Also, the boiling point temperature at given system pressures are to be estimated and all these results are to be compared with the values calculated by APEx.

Concept introduction:

The Clausius-Clapeyron equation is defined as:

$\ln \left(p^{\ast }\right)=\frac{\Delta H^{lv}}{R}\left(\frac{1}{T}\right)+C$   ...... (1)

Here, $p^{\ast }$ is the vapor pressure of the gas at temperature $T$, $\Delta H^{lv}$ is the latent heat of vaporization, and $R$ is the universal gas constant. $C$ is the constant.