Chapter 5, Problem 5.74P

(a)

Interpretation Introduction

Interpretation:

Three different flasks that contain ${\text{H}}_{\text{2}}$, $\text{He}$, and ${\text{CH}}_{\text{4}}$ gas are to be ranked in order of pressure.

Concept introduction:

The ideal gas equation can be expressed as follows:

  $PV=nRT$        (1)

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature, $n$ is the mole of the gas and $R$ is the gas constant.

The expression to calculate the moles of gas is as follows:

  $\text{Moles of gas}=\frac{\text{Mass of gas}}{\text{Molar mass of gas}}$        (2)

(b)

Interpretation Introduction

Interpretation:

Three different flasks that contain ${\text{H}}_{\text{2}}$, $\text{He}$, and ${\text{CH}}_{\text{4}}$ gas are to be ranked in order of average kinetic energy.

Concept introduction:

The expression to calculate the average kinetic energy of gases is as follows:

  $\text{Average kinectic energy of gases}=\left(\frac{3}{2}\right)\left(RT\right)$

Here, $T$ is the temperature and $R$ is the gas constant.

The expression to calculate the kinetic energy is as follows:

  $E_{\text{k}}=\left(\frac{1}{2}\right)\left(\text{mass}\right){\left(\text{speed}\right)}^2$

The kinetic energy is directly proportional to the temperature.

(c)

Interpretation Introduction

Interpretation:

Three different flasks that contain ${\text{H}}_{\text{2}}$, $\text{He}$, and ${\text{CH}}_{\text{4}}$ gas are to be ranked in order of diffusion rate.

Concept introduction:

Effusion is explained as the movement of the gas molecule through a pinhole.

Diffusion can be explained as the mixing of one gas molecule with another gas molecule by random motion.

According to Graham’s law of effusion, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

The mathematical expression of Graham’s law of effusion is as follows:

  $\frac{\text{Rate of A}}{\text{Rate of B}}=\frac{u_{rms\text{ of A}}}{u_{rms\text{ of B}}}=\frac{\sqrt{M_{\text{B}}}}{\sqrt{M_{\text{A}}}}=\frac{\text{time B}}{\text{time A}}$        (3)

Here,

$M_{\text{B}}$ is the molar mass of gas $\text{B}$

$M_{\text{A}}$ is the molar mass of gas $\text{A}$.

(d)

Interpretation Introduction

Interpretation:

Three different flasks that contain ${\text{H}}_{\text{2}}$, $\text{He}$, and ${\text{CH}}_{\text{4}}$ gas are to be ranked in order of total kinetic energy.

Concept introduction:

The expression to calculate the root-mean-square speed is as follows:

  $u_{rms}=\sqrt{\frac{3RT}{M}}$

Here, $M$ is the molar mass, $T$ is the temperature and $R$ is the gas constant.

The expression to calculate the average kinetic energy of gases is as follows:

  $\text{Average kinectic energy of gases}=\left(\frac{3}{2}\right)\left(RT\right)$

Here, $T$ is the temperature and $R$ is the gas constant.

The expression to calculate the kinetic energy is as follows:

  $E_{\text{k}}=\left(\frac{1}{2}\right)\left(\text{mass}\right){\left(\text{speed}\right)}^2$

The kinetic energy is directly proportional to the temperature.

(e)

Interpretation Introduction

Interpretation:

Three different flasks that contain ${\text{H}}_{\text{2}}$, $\text{He}$, and ${\text{CH}}_{\text{4}}$ gas are to be ranked in order of density.

Concept introduction:

The expression to calculate the density of the air is as follows,

  $d=\frac{PM}{RT}$

Here, $P$ is the pressure, $M$ is the molecular mass, $T$ is the temperature, $d$ is the density of the air and $R$ is the gas constant.

Rate of diffusion is inversely proportional to the square root of the density of the gas.

The expression to calculate the density of a gas is as follows:

  $\text{Density of the gas}=\frac{\text{Mass of gas}}{\text{Volume of gas}}$        (4)

(f)

Interpretation Introduction

Interpretation:

Three different flasks that contain ${\text{H}}_{\text{2}}$, $\text{He}$, and ${\text{CH}}_{\text{4}}$ gas are to be ranked in order of collision frequency.

Concept introduction:

The mean free path can be defined as the average distance traveled by the gas molecule during a collision. There are many factors that affect the mean free path such as pressure, temperature, density and radius of the molecule.

The collision frequency is defined as the ratio of the most probable speed to the mean free path.