Chapter 5, Problem 5.94P

(a)

Interpretation Introduction

Interpretation:

The sample that has the highest partial pressure of a gas $\text{A}$ is to be identified.

Concept introduction:

The ideal gas equation can be expressed as follows,

$PV=nRT$

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 partial pressure of the gas is as follows:

$P_{\text{gas}}=X_{\text{gas}}\cdot P_{\text{total}}$

Here, $P_{\text{gas}}$ is the partial pressure of the gas, $X_{\text{gas}}$ mole fraction of the gas and $P_{\text{total}}$ is the total pressure.

The expression to calculate the mole fraction of the gas is as follows,

$X_{\text{gas}}=\frac{\text{Moles of gas}}{\text{Total moles}}$

Here, $X_{\text{gas}}$ is the mole fraction of the gas.

(b)

Interpretation Introduction

Interpretation:

The sample that has the lowest partial pressure of a gas $\text{B}$ is to be identified.

Concept introduction:

The ideal gas equation can be expressed as follows,

$PV=nRT$

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 partial pressure of the gas is as follows:

$P_{\text{gas}}=X_{\text{gas}}\cdot P_{\text{total}}$

Here, $P_{\text{gas}}$ is the partial pressure of the gas, $X_{\text{gas}}$ mole fraction of the gas and $P_{\text{total}}$ is the total pressure.

The expression to calculate the mole fraction of the gas is as follows,

$X_{\text{gas}}=\frac{\text{Moles of gas}}{\text{Total moles}}$

Here, $X_{\text{gas}}$ is the mole fraction of the gas.

(c)

Interpretation Introduction

Interpretation:

The gas particles that have the highest average kinetic energy is to be determined.

Concept introduction:

The expression to calculate the kinetic energy is as follows:

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

Here, $E_{\text{k}}$ is the kinetic energy

The expression to calculate the root-mean-square velocity 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 kinetic energy is directly proportional to the temperature and inversely proportional to the molar mass.