Chapter 7, Problem 7.24NP

Interpretation Introduction

Interpretation: Whether the attractive or repulsive interaction potential dominates for 42.1 g of Ar present in a container of volume 0.0885 L at 375 K needs to be determined with the help of pressure using ideal gas, van der Waals and Redlich-Kwong equation of state.

Concept Introduction: The ideal gas equation is the equation which gives the relations between P, V, n and T of gases. It can be written as:

PV = nRT

Usually, gases do not follow ideal behavior under all conditions of pressure, temperature and volumes. The relation of P, V, n and T of real gases can be given by Vander Waals equation:

  $\left(\text{P + }\frac{{\text{n}}^{\text{2}}\text{a}}{{\text{V}}^{\text{2}}}\right)\left(\text{V- n b}\right)\text{ = nRT}$

Hence $\text{P = }\frac{\text{RT}}{{\text{ V}}_{\text{m}}\text{- b}}\text{ - }\frac{\text{ a}}{{\text{V}}_{\text{m}}{}^{\text{2}}}$

The Redlich-Kwong equation of state can be written as:

  $\begin{array}{l}\text{P = }\frac{\text{R T}}{{\text{V}}_{\text{m}}\text{-b}}\text{ - }\frac{\text{a}}{\sqrt{\text{T}}{\text{V}}_{\text{m}}{\text{(V}}_{\text{m}}\text{+ b)}}\\ \text{P = }\frac{\text{n R T}}{{\text{V}}_{}\text{- nb}}\text{ - }\frac{{\text{n}}^{\text{2}}\text{a}}{\sqrt{\text{T}}{\text{V}}_{}\text{(V + nb)}}\end{array}$

Here, V_mis molar volume and a and b are constants.