Chapter 7.7, Problem 13P

(A)

Interpretation Introduction

Interpretation:

Using Joback method, estimate the critical temperature and critical pressure

Concept Introduction:

The expression to calculate the critical temperature $\left(T_c\right)$ is given by:

$T_c=T_b{\left[0.584+0.965{\displaystyle \sum T_b}-{\left({\displaystyle \sum T_b}\right)}^2\right]}^{-1}$

Here, boiling temperature is $T_b$, and the sum of the contributions of boiling temperature groups to the property is ${\displaystyle \sum T_b}$.

The expression to calculate the boiling temperature $\left(T_b\right)$ is given by:

$T_b=198.2+{\displaystyle \sum T_b}$

The expression to calculate the critical pressure $\left(P_c\right)$ is given by:

$P_c={\left(0.113+0.0032n_a-{\displaystyle \sum P_c}\right)}^{-2}$

Here, number of atoms is $n_a$, and the sum of the contributions of critical pressure groups to the property is ${\displaystyle \sum P_c}$.

(B)

Interpretation Introduction

Interpretation:

Find the acentric factor.

(C)

Interpretation Introduction

Interpretation:

The molar volume at $P=5\text{ bar, T=500 K}$

Concept Introduction:

Write the expression to calculate the reduced temperature.

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

Here, critical temperature is $T_c$ and system temperature is T.

Write the expression to calculate the reduced pressure $\left(P_r\right)$.

$P_r=\frac{P}{P_c}$

Here, pressure is $P$.

Write the expression to calculate the parameter a for Peng-Robinson EOS.

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

Write the expression to calculate the $\alpha$ expressed as a function of the reduced temperature.

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

Write the expression to calculate the value of parameter a at the critical point $\left(a_c\right)$ .

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

Write the expression to calculate the van der Waals parameter $a$.

$a=a_c\alpha$

Write the expression to calculate the van der Waals parameter $b$.

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

Write the expression to calculate the molar volume $\left(\underset{\_}{V}\right)$ using the Soave equation.

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

(D)

Interpretation Introduction

Interpretation:

The molar volume at $P=5\text{ bar, T=800 K}$

Concept Introduction:

Write the expression to calculate the reduced temperature.

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

Here, critical temperature is $T_c$ and system temperature is T.

Write the expression to calculate the reduced pressure $\left(P_r\right)$.

$P_r=\frac{P}{P_c}$

Here, pressure is $P$.

Write the expression to calculate the parameter a for Peng-Robinson EOS.

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

Write the expression to calculate the $\alpha$ expressed as a function of the reduced temperature.

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

Write the expression to calculate the value of parameter a at the critical point.

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

Write the expression to calculate the van der Waals parameter $a$.

$a=a_c\alpha$

Write the expression to calculate the van der Waals parameter $b$.

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

Write the expression to calculate the molar volume $\left(\underset{\_}{V}\right)$ using the Soave equation.

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