Chapter 1, Problem 1B.4BE

Interpretation Introduction

Interpretation: The relative mean speed of ${\text{O}}_{\text{2}}$ and ${\text{N}}_{\text{2}}$ in a gas at $2{\text{5 }}^{\text{ο}}\text{C}$ has to be calculated.

Concept introduction: The relative mean speed refers to the mean speed at which one molecule approaches the similar type of another molecule.  The relative mean speed for identical molecules is calculated by the formula,

    $v_{\text{rel}}=2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{v}_{\text{mean}}$

The relative mean speed of two dissimilar molecules of masses $m_{\text{A}}$ and $m_{\text{B}}$ is calculated by the formula,

    $v_{\text{rel}}={\left(\frac{8RT}{\pi \mu }\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$