Chapter 8.6, Problem 12P

(A)

Interpretation Introduction

Interpretation:

The best estimate of the triple point pressure and temperature.

Concept Introduction:

The Clausius Clapeyron equation to obtain the value of $\Delta {\underset{\_}{H}}^{vap}$ using the 3^rd and 4^th phases is,

$\Delta {\underset{\_}{H}}^{vap}=-\frac{\ln \left(\frac{P_3^{sat}}{P_4^{sat}}\right)R}{\left(\frac{1}{T_3}-\frac{1}{T_4}\right)}$

Here, temperature for phases 3 and 4 is $T_3\text{and}{T}_4$, gas constant is R, vapor pressure for phases 3 and 4 is $P_3^{sat}$ and $P_4^{sat}$ respectively, and change in molar enthalpy of vaporization is $\Delta {\underset{\_}{H}}^{vap}$.

The Clausius Clapeyron equation to obtain the value of $\Delta {\underset{\_}{H}}^{sub}$ using the 1^st and 2^nd phases is,

$\Delta {\underset{\_}{H}}^{sub}=-\frac{\ln \left(\frac{P_2^{sat}}{P_1^{sat}}\right)R}{\left(\frac{1}{T_2}-\frac{1}{T_1}\right)}$

Here, temperature for phases 1 and 2 is $T_1\text{and}{T}_2$, gas constant is R, vapor pressure for phases 1 and 2 is $P_1^{sat}$ and $P_2^{sat}$ respectively, and change in molar enthalpy of sublimation is $\Delta {\underset{\_}{H}}^{sub}$.

The expression to obtain the pressure at triple point is,

$\ln \left(\frac{P_T}{P_1^{sat}}\right)=\frac{-\Delta {\underset{\_}{H}}^{sub}}{R}\left(\frac{1}{T_T}-\frac{1}{T_1}\right)$

Here, temperature at transition point is $T_T$.

The expression to obtain the pressure at transition point is,

$\ln \left(\frac{P_T}{P_1^{sat}}\right)=\frac{-\Delta {\underset{\_}{H}}^{vap}}{R}\left(\frac{1}{T_T}-\frac{1}{T_1}\right)$

(B)

Interpretation Introduction

Interpretation:

The best estimate of pressure at which solid-liquid equilibrium occurs at $T=50°\text{C}$.

Concept Introduction:

The Clapeyron Equation to model solid-liquid equilibrium is,

$\begin{array}{l}\frac{d{P}^{sat}}{dT}=\frac{\Delta {\underset{\_}{H}}^{fus}}{T\left({\underset{\_}{V}}^L-{\underset{\_}{V}}^S\right)}\\ d{P}^{sat}=\frac{\Delta {\underset{\_}{H}}^{fus}}{T\left({\underset{\_}{V}}^L-{\underset{\_}{V}}^S\right)}dT\end{array}$

Here, molar volume for liquid and solid state is ${\underset{\_}{V}}^L$ and ${\underset{\_}{V}}^S$, temperature is T, change in molar enthalpy of fusion is $\Delta {\underset{\_}{H}}^{fus}$, and change in vapor pressure with respect to change in temperature is $\frac{d{P}^{sat}}{dT}$.

The change in molar enthalpy of sublimation is,

$\begin{array}{l}\Delta {\underset{\_}{H}}^{sub}=\Delta {\underset{\_}{H}}^{vap}+\Delta {\underset{\_}{H}}^{fus}\\ \Delta {\underset{\_}{H}}^{fus}=\Delta {\underset{\_}{H}}^{sub}-\Delta {\underset{\_}{H}}^{vap}\end{array}$

(C)

Interpretation Introduction

Interpretation:

The best estimate of the temperature at which the liquid vapor equilibrium occurs at $P=0.15\text{bar}$.

Concept Introduction:

The expression to obtain the temperature at which liquid-vapor equilibrium occurs at $P=0.15\text{bar}$ is,

$\ln \left(\frac{P_T}{P_1^{sat}}\right)=\frac{-\Delta {\underset{\_}{H}}^{vap}}{R}\left(\frac{1}{T_T}-\frac{1}{T_1}\right)$