Chapter 5, Problem 5.126P

(a)

Interpretation Introduction

Interpretation:

Whether argon or xenon will show greater deviation from ideal behavior at the same set of the condition is to be identified.

Concept introduction:

Gases that obey the ideal gas equation at all temperature and pressure are known as an ideal gas.

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 of Van der Waals equation is as follows:

  $\left(P+\frac{n^{2}a}{V^2}\right)\left(V-nb\right)=nRT$

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature, $n$ is the mole of the gas, $R$ is the gas constant, $a$ and $b$ are van der Waals constants.

At low pressure and high temperature, real gas will obey the gas laws.

The value of van der Waals constants depends upon the nature of the gas. The constant $a$ is the measure of the attractive force between the molecules and the constant $b$ is the measure of the effective size of gas molecules.

(b)

Interpretation Introduction

Interpretation:

Whether water vapor or neon will show greater deviation from ideal behavior at the same set of the condition is to be identified.

Concept introduction:

Gases that obey the ideal gas equation at all temperature and pressure are known as an ideal gas.

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 of Van der Waals equation is as follows:

  $\left(P+\frac{n^{2}a}{V^2}\right)\left(V-nb\right)=nRT$

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature, $n$ is the mole of the gas, $R$ is the gas constant, $a$ and $b$ are van der Waals constants.

At low pressure and high temperature, real gas will obey the gas laws.

The value of van der Waals constants depends upon the nature of the gas. The constant $a$ is the measure of the attractive force between the molecules and the constant $b$ is the measure of the effective size of gas molecules.

(c)

Interpretation Introduction

Interpretation:

Whether mercury vapor or radon will show greater deviation from ideal behavior at the same set of the condition is to be identified.

Concept introduction:

Gases that obey the ideal gas equation at all temperature and pressure are known as an ideal gas.

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 of Van der Waals equation is as follows:

  $\left(P+\frac{n^{2}a}{V^2}\right)\left(V-nb\right)=nRT$

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature, $n$ is the mole of the gas, $R$ is the gas constant, $a$ and $b$ are van der Waals constants.

At low pressure and high temperature, real gas will obey the gas laws.

The value of van der Waals constants depends upon the nature of the gas. The constant $a$ is the measure of the attractive force between the molecules and the constant $b$ is the measure of the effective size of gas molecules.

(d)

Interpretation Introduction

Interpretation:

Whether water vapor or methane will show greater deviation from ideal behavior at the same set of the condition is to be explained.

Concept introduction:

Gases that obey the ideal gas equation at all temperature and pressure are known as an ideal gas.

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 of Van der Waals equation is as follows:

  $\left(P+\frac{n^{2}a}{V^2}\right)\left(V-nb\right)=nRT$

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature, $n$ is the mole of the gas, $R$ is the gas constant, $a$ and $b$ are van der Waals constants.

At low pressure and high temperature, real gas will obey the gas laws.

The value of van der Waals constants depends upon the nature of the gas. The constant $a$ is the measure of the attractive force between the molecules and the constant $b$ is the measure of the effective size of gas molecules.