Chapter 8.5, Problem 8E

Interpretation Introduction

Interpretation:

The fugacity of the compound in the liquid phase at temperature 300 K and various pressures 1, 10, 100 and 1000 bar.

Concept Introduction:

The Poynting equation to estimate the fugacity $\left(f\right)$ of the compound in the solid phase is,

$f=f^{sat}\exp \left\{\frac{\underset{\_}{V}\left(P-P^{sat}\right)}{RT}\right\}$

Here, molar volume is $\underset{\_}{V}$, pressure is $P$, vapor pressure is $P^{sat}$, gas constant is $R$, temperature is $T$, and the fugacity of a liquid or vapor that is at its vapor pressure is $f^{sat}$.

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 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,

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

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 to obtain the compressibility factor $\left(Z\right)$ is,

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

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

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

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

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

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

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

The vapor pressure using Antoine equation is,

$P^{sat}={10}^{\left[A-\frac{B}{C+T\left(°\text{C}\right)}\right]}$

Here, temperature in degree Celsius is $T\left(°\text{C}\right)$, and Antoine coefficients are $A,B,\text{and}C$.