Chapter 10, Problem 151E

Interpretation Introduction

Interpretation:

The temperature, masses, average velocities, and average kinetic energy of the three kinds of gases should be described along with similarities and differences and how are these properties related should be identified.

Concept introduction:

Gas is a collection of a very large number of very small size (10⁻¹⁰m ) particle. The volume of gas particles is very smaller than the volume of the container in which it is placed.

The kinetic theory of gas explains the behavior of gas based on the assumption gas as made up of a very small particle moving continuously with high speed. The force of interaction between atom or molecules of gas is short range force. A collision between gas particle and wall of the container is the relation between pressure, temperature, volume no of moles of gas.

(1)According to the kinetic theory of gases, the average kinetic energy for all gas at the

Given temperature T is same.

The average kinetic energy of a gas molecule

$\frac{1}{2}m{v}^2\mathit{ }\mathit{=}\mathit{ }\frac{\mathit{3}}{\mathit{2}}{K}_{\mathit{B}}T$

(2)The average velocity depends on temperature and mas of gas.

${\mathrm{V}}_{\mathrm{avg}}=\sqrt{\frac{8\mathrm{RT}}{{\mathrm{\pi M}}_{\circ }}}=\sqrt{\frac{8\mathrm{RT}}{\mathrm{\pi m}}}$

M_° = Molecular weight

m= Mass of molecules