Chapter 5, Problem 69QAP

Interpretation Introduction

(a)

Interpretation:

The average translational kinetic energy of the two given gases has to be compared.

Concept introduction:

The average translational energy of an ideal gas depends only on the gas temperature and don’t depend of the quantity of the gas.

Interpretation Introduction

(b)

Interpretation:

The partial pressure of the two given gases in the mixture has to be compared.

Concept introduction:

An ideal gas in a mixture of gases enclosed in a rigid container will occupy the whole volume of the container when the other gases are not present, that is the partial pressure of the gas is equal to the pressure which the gas will exert if it is present alone in the container. Therefore, the ideal gas law can be used to compute and compare the partial pressures of the two gases.

Interpretation Introduction

(c)

Interpretation:

The mole fraction of the two given gases in the mixture has to be compared.

Introduction:

The mole fraction of an ideal gas in a mixture of gases is simply equal to the ratio of the partial pressure of the gas to the total pressure in the system. The total pressure of the system is equal to the sum of the partial pressures of the gases.

$\begin{array}{l}\text{mole fraction of component i in a mixture of ideal gases,}\\ {\chi }_{\text{i}}=\frac{{\text{P}}_{\text{i}}}{{\text{P}}_{\text{tot}}}\end{array}$

Interpretation Introduction

(d)

Interpretation:

The rate of effusion of the two given gases has to be compared.

Introduction:

The rate of effusion of a gas can be calculated using Graham’s law of diffusion. As per Graham’s law, the rate of effusion of a gas has inverse relation with mass of the gas taken, that is

$\text{rate of effusion }\alpha \frac{1}{\sqrt{\text{w}}}$

Where w is the mass of the gas taken.