Chapter 8.6, Problem 13P

(A)

Interpretation Introduction

Interpretation:

Estimation of the triple point pressure and temperature.

Concept Introduction:

The Clausius-Clapeyron equation for vapor-liquid equilibrium to calculate the change in molar enthalpy from vaporization is,

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

Here, vapor pressure is $P^{sat}$, change in molar enthalpy from vaporization is $\Delta {\underset{\_}{H}}_{vap}$, gas constant is $R$, and temperature is $T$.

The Clausius-Clapeyron equation for solid-vapor equilibrium to calculate the change in molar enthalpy from sublimation is,

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

Here, change in molar enthalpy from sublimation is $\Delta {\underset{\_}{H}}_{sub}$.

The equation for saturated pressure in solid-vapor equilibrium is,

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

The equation for saturated pressure in liquid-vapor equilibrium is,

$P_2^{sat}=P_1^{sat}\exp \left[\frac{-\Delta {\underset{\_}{H}}_{vap}}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)\right]$

(B)

Interpretation Introduction

Interpretation:

Estimation of pressure at which solid-liquid equilibrium occurs at $T=25°\text{F}$.

Concept Introduction:

The Clapeyron equation to fit solid-liquid equilibrium is,

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

Here, change in vapor pressure is $d{P}^{sat}$, change in temperature is $dT$, change in molar enthalpy from fusion is $\Delta {\underset{\_}{H}}_{fus}$, liquid molar volume is ${\underset{\_}{V}}^L$ and solid molar volume is ${\underset{\_}{V}}^S$.

The expression to obtain the change in molar enthalpy from fusion $\left(\Delta {\underset{\_}{H}}_{fus}\right)$ is,

$\Delta {\underset{\_}{H}}_{fus}=\Delta {\underset{\_}{H}}_{sub}-\Delta {\underset{\_}{H}}_{vap}$

(C)

Interpretation Introduction

Interpretation:

Estimation of the normal boiling point.

Concept Introduction:

The expression of the best normal boiling point is,

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