Chapter 6, Problem 6.100QE

Interpretation Introduction

Interpretation:

Root mean square speed of ${\text{SO}}_{\text{2}}$ at $\text{127 }°\text{C}$ as well as the rms speed when temperature on Kelvin scale is doubled has to be calculated.

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 by the equation,

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

Here,

$\text{R}$ is the universal gas constant.

$T$ denotes temperature in kelvins.

$M$ denotes the molar mass in $\text{kg/mol}$.