Chapter 8, Problem 160CP

Interpretation Introduction

Interpretation: How wander Waals equation simplifies to the ideal gas law under low pressure and high temperature should be explained.

Concept introduction:

By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law.

According to ideal gas law,

$PV=nRT$

Where,

          P = pressure in atmospheres

          V= volumes in liters

          n = number of moles

          R =universal gas constant ( $0.08206L\cdot atm/K\cdot mol$)

          T = temperature in kelvins

Ideal gas law tends to hold best at low pressure and high temperature

A modified ideal gas equation on account of molecular size and molecular interaction forces is termed as Van der Waals equation.

That is,                $\left[P+a{\left(\frac{n}{V}\right)}^2\right]\left(V-nb\right)=nRT$

‘a’ and ‘b’ is called Van der Waals coefficient and are characteristic of the individual gas

•  a is a measure of intermolecular attraction
• b is a measure of size of the molecule

Where,

          P = pressure in atmospheres

          V= volumes in liters

          n = number of moles

          R =universal gas constant ( $\text{0}\text{.08206L×atm/K×mol}$)

          T = temperature in kelvins