Chapter 5, Problem 5.140P

(a)

Interpretation Introduction

Interpretation:

The moles of ${\text{Cl}}_{\text{2}}$ gas at $298\text{ K}$ is to be calculated.

Concept introduction:

According to Boyle’s law, the volume occupied by the gas is inversely proportional to the pressure at the constant temperature.

The relationship between pressure and volume can be expressed as follows,

$PV=\text{constant}$

Here, $P$ is the pressure and $V$ is the volume.

According to Charles's law, the volume occupied by the gas is directly proportional to the temperature at the constant pressure.

The relationship between pressure and temperature can be expressed as follows,

$V\alpha T$

Here, $T$ is the temperature and $V$ is the volume.

According to Avogadro’s law, the volume occupied by the gas is directly proportional to the mole of the gas at the constant pressure and temperature.

The relationship between volume and mole can be expressed as follows,

$\text{V }\alpha n$

Here, $n$ is the mole of the gas and $V$ is the volume.

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.

(b)

Interpretation Introduction

Interpretation:

The tank pressure at $298\text{ K}$ by the van der Waals equation is to be calculated.

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 of the van der Waals equation is as follows:

$\left(P_{\text{VDW}}+\frac{n^{2}a}{V^2}\right)\left(V-nb\right)=nRT$ (3)

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.

(c)

Interpretation Introduction

Interpretation:

The engineer fills the tank to the desired pressure is to be predicted.

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 of the van der Waals equation is as follows:

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

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.