Chapter 1, Problem 1B.5BE

Interpretation Introduction

Interpretation: The most probable speed, the mean speed, and the mean relative speed of ${\text{H}}_{\text{2}}$ molecules at $20{}^{\text{ο}}\text{C}$ have to be calculated.

Concept introduction: The most probable speed is identified at the peak of the Maxwell-Boltzmann distribution curve.  It is calculated by the formula,

    $v_{\text{mp}}={\left(\frac{2RT}{M}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

The mean speed is calculated by the formula,

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

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}}$