Chapter 6, Problem 6.96QE

Interpretation Introduction

Interpretation:

The gases $\text{Ar}$, ${\text{CH}}_{\text{4}}$, ${\text{N}}_{\text{2}}$ and ${\text{CH}}_2{\text{F}}_{\text{2}}$ has to be arranged in order of the average molecular speed of the particles.

Concept Introduction:

In accordance with the Kinetic molecular theory, not all of the gas particles will move at the same speed but with an average speed that is given by the expression as follows:

  $\overline{KE}=\frac{1}{2}m\overline{u^2}$

Here,

$\overline{KE}$ is the average kinetic energy.

$m$ is the mass of particle.

$u^2$ is the average of the speed.

The relation between rms speed $\left(u_{\text{rms}}\right)$, temperature and molar mass is given as follows:

  $u_{\text{rms}}=\sqrt{\frac{3RT}{M}}$

Since gas constant $R$, and temperature $T$ are constants so root mean square speed is inversely related to the square root of the molar mass and is represented as follows:

  $u_{\text{rms}}=\sqrt{\frac{1}{M}}$