Chapter 8.5, Problem 2E

(A)

Interpretation Introduction

Interpretation:

The vapor pressure of n-pentane using the Antonie equation.

Concept Introduction:

Write the Antoine equation.

${\log }_{10}\left(P^{sat}\right)=A-\frac{B}{T+C}$

Here, Antoine constants or coefficients are A, B, and C, vapor pressure is $P^{sat}$, and temperature is T.

(B)

Interpretation Introduction

Interpretation:

The vapor pressure of n-pentane using the Clausius-Clapeyron equation.

Concept Introduction:

Write the Clausius-Clapeyron equation.

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

Here, gas constant is R, temperature at state 1 and 2 is $T_1\text{and}{T}_2$ , vapor pressure at state 1 and 2 is $P_1^{sat}\text{and}{P}_2^{sat}$, and change in molar enthalpy from vaporization is $\Delta {\underset{\_}{H}}^{vap}$.

(C)

Interpretation Introduction

Interpretation:

The vapor pressure of n-pentane using the shortcut equation.

Concept Introduction:

Write the shortcut vapor pressure equation.

$\begin{array}{l}{\log }_{10}{P}_r^{sat}=\frac{7}{3}\left(\omega +1\right)\left(1-\frac{1}{T_r}\right)\\ P_r^{sat}=\left(P_c\right)e^{\frac{7}{3}\left(\omega +1\right)\left(1-\frac{T_c}{T}\right)}\end{array}$

Here, reduced temperature is $T_r$, critical temperature is $T_c$, critical pressure is $P_c$, acentric factor is $\omega$, and reduced pressure at saturated point is $P_r^{sat}$.