Chapter 8.5, Problem 6E

(A)

Interpretation Introduction

Interpretation:

The fugacity of butane at temperature 300 K and pressure 0.5 bar.

Concept Introduction:

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

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

Here, parameter is $\kappa$.

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, pressure is $P$, 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 to obtain the reduced temperature $\left(T_r\right)$ 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,

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

Here, gas constant is $R$.

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 $\left(Z\right)$ for liquid phase is,

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

The expression of the dimensionless group that include the Peng-Robinson parameter $\left(A\right)$ is,

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

The expression of the dimensionless group that include the Peng-Robinson parameter $\left(B\right)$ is,

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

The fugacity $\left(f\right)$ of a compound as described by the Peng-Robinson equation is,

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

The expression of compressibility factor $\left(Z\right)$ is,

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

(B)

Interpretation Introduction

Interpretation:

The fugacity of butane at temperature 350 K and pressure 5 bar.

(C)

Interpretation Introduction

Interpretation:

The fugacity of butane at temperature 400 K and pressure 1 bar.

(D)

Interpretation Introduction

Interpretation:

The fugacity of butane at temperature 500 K and pressure 10 bar.