Chapter 6, Problem 6.121QP

Interpretation Introduction

Interpretation: The given gases ${\text{SO}}_{\text{2}}\text{,}{\text{NO}}_{\text{2}}$ and ${\text{CO}}_{\text{2}}$ are to be arranged in order of increasing root-mean-square speed at $\text{0}{}^{\text{o}}\text{C}$.

Concept introduction: The root-mean-square speed is used to find out the single value of speed of the gas molecules that move in random directions having different speed and the formula is,

$v_{rms}=\sqrt{\frac{3\text{R}T}{M}}$

According to kinetic theory of molecular gases, gases are hitting continuously against the walls of container when the temperature increases. Hence their total energy also increases. The kinetic energy $\text{(K}\text{.E)}$ is given by the formula is,

$\text{K}\text{.E}=\frac{1}{2}m{v}^2$

To determine: The rank of given gases ${\text{SO}}_{\text{2}}\text{,}{\text{NO}}_{\text{2}}$ and ${\text{CO}}_{\text{2}}$ in order of increasing root-mean-square speed at $\text{0}{}^{\text{o}}\text{C}$.