Chapter 8.6, Problem 21P

(A)

Interpretation Introduction

Interpretation:

The vapor pressure at $T=25°\text{C}$.

Concept Introduction:

The Peng-Robinson equation is,

$P=\frac{RT}{\underset{\_}{V}-b}-\frac{a}{\underset{\_}{V}\left(\underset{\_}{V}+b\right)+b\left(\underset{\_}{V}-b\right)}$

Here, molar volume is $\underset{\_}{V}$, parameters of Robinson equation are a, b, gas constant is R, temperature and pressure is T and P respectively.

The expression of the parameter used in calculation of a for Peng-Robinson EOS is,

$\kappa =0.37464+1.54226\omega -0.26993{\omega }^2$

The expression to obtain the relative temperature at the critical point is,

$T_r=\frac{T}{T_c}$

Here, system temperature is T.

The expression to obtain the value of $\alpha$ expressed as a function of the reduced temperature is,

$\alpha ={\left[1+\kappa \left(1-T_r^{0.5}\right)\right]}^2$

The expression to obtain the value of parameter a at the critical point is,

$a_c=\frac{0.45724R^2{T}_c^2}{P_c}$

The expression to obtain the parameter $a$ is,

$a=a_c\alpha$

The expression to obtain the parameter b is,

$b=\frac{0.07780R{T}_c}{P_c}$

The expression of compressibility factor is,

$Z=\frac{P\underset{\_}{V}}{RT}$

The residual properties of A is,

$A=\frac{aP}{R^2{T}^2}$

The residual properties of B is,

$B=\frac{bP}{RT}$

The expression of fugacity of a compound as described by the Peng-Robinson equation is,

$\ln \left(\frac{f}{P}\right)=\left(Z-1\right)-\ln \left(Z-B\right)-\frac{A}{2B\sqrt{2}}\ln \left[\frac{Z+\left(1+\sqrt{2}\right)B}{Z+\left(1-\sqrt{2}\right)B}\right]$

(B)

Interpretation Introduction

Interpretation:

The fugacity at the critical point.

(C)

Interpretation Introduction

Interpretation:

The fugacity of saturated liquid at $T=25°\text{C}$.

(D)

Interpretation Introduction

Interpretation:

The fugacity of compressed liquid at $T=25°\text{C}$ and $P=500\text{ bar}$.

Concept Introduction:

The Poynting equation to obtain fugacity in liquid phase at 500 bar is,

$f_L=f_{sat}\exp \left[\frac{\underset{\_}{V}\left(P_2-P_{sat}\right)}{RT}\right]$

Here, saturated pressure is $P_{sat}$, molar volume is $\underset{\_}{V}$, and saturated vapor fugacity is $f_{sat}$.

(E)

Interpretation Introduction

Interpretation:

The normal boiling point.