Chapter 5, Problem 5.155P

(a)

Interpretation Introduction

Interpretation:

The density of each allotrope at $0°C$ and $760\text{ torr}$ is to be calculated

Concept introduction:

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

$d=\frac{PM}{RT}$

Here, $d$ is the density, $P$ is the pressure, $M$ is the molar mass, $T$ is the temperature, $R$ is the gas constant.

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 ratio of density of ${\text{O}}_3$ to density of ${\text{O}}_2$ is to be calculated.

Concept introduction:

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.