Chapter 10, Problem 10.66SP

Interpretation Introduction

(a)

Interpretation:

Density of $\text{22}{\text{.414 L CH}}_4$ gas at $1\text{ atm}$ and $\text{273 K}$ is to be balanced.

Concept introduction:

The combination of all the gas laws namely Boyle’s law, Charles law and Avogadro’s lead to the ideal gas equation that can be used to relate all the four properties such as given below:

$PV=nRT$

The relation between number of moles and mass is as follows:

$\begin{array}{c}\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}\\ n=\frac{m}{M}\end{array}$

Substitute $n=m\text{/}M$ in ideal gas equation.

$\begin{array}{l}PV=nRT\\ PV=\left(\frac{m}{M}\right)RT\end{array}$

Rearrange to write the expression of Pressure.

$P=\left(\frac{m}{V}\right)\frac{R}{M}T$

The mass per unit volume is density $\left(\rho \right)$ hence replace $\text{m/V}$ in above equation with $\rho$.

$P=\rho \frac{R}{M}T$

Rearrange to obtain the expression of density.

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

Where,

• $\rho$ denotes density.
• $R$ is gas constant.
• $V$ denotes the volume.
• $M$ denotes the molar mass.
• $T$ denotes temperature.
• $P$ denotes the pressure.

Interpretation Introduction

(b)

Interpretation:

Density of $\text{22}{\text{.414 L CO}}_{\text{2}}$ gas at $1\text{ atm}$ and $\text{273 K}$ is to be balanced.

Concept introduction:

The combination of all the gas laws namely Boyle’s law, Charles law and Avogadro’s lead to the ideal gas equation that can be used to relate all the four properties such as given below:

$PV=nRT$

The relation between number of moles and mass is as follows:

$\begin{array}{c}\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}\\ n=\frac{m}{M}\end{array}$

Substitute $n=m\text{/}M$ in ideal gas equation.

$\begin{array}{l}PV=nRT\\ PV=\left(\frac{m}{M}\right)RT\end{array}$

Rearrange to write the expression of Pressure.

$P=\left(\frac{m}{V}\right)\frac{R}{M}T$

The mass per unit volume is density $\left(\rho \right)$ hence replace $\text{m/V}$ in above equation with $\rho$.

$P=\rho \frac{R}{M}T$

Rearrange to obtain the expression of density.

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

Where,

• $\rho$ denotes density.
• $R$ is gas constant.
• $V$ denotes the volume.
• $M$ denotes the molar mass.
• $T$ denotes temperature.
• $P$ denotes the pressure.

Interpretation Introduction

(b)

Interpretation:

Density of $\text{22}{\text{.414 L O}}_{\text{2}}$ gas at $1\text{ atm}$ and $\text{273 K}$ is to be balanced.

Concept introduction:

The combination of all the gas laws namely Boyle’s law, Charles law and Avogadro’s lead to the ideal gas equation that can be used to relate all the four properties such as given below:

$PV=nRT$

The relation between number of moles and mass is as follows:

$\begin{array}{c}\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}\\ n=\frac{m}{M}\end{array}$

Substitute $n=m\text{/}M$ in ideal gas equation.

$\begin{array}{l}PV=nRT\\ PV=\left(\frac{m}{M}\right)RT\end{array}$

Rearrange to write the expression of Pressure.

$P=\left(\frac{m}{V}\right)\frac{R}{M}T$

The mass per unit volume is density $\left(\rho \right)$ hence replace $\text{m/V}$ in above equation with $\rho$.

$P=\rho \frac{R}{M}T$

Rearrange to obtain the expression of density.

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

Where,

• $\rho$ denotes density.
• $R$ is gas constant.
• $V$ denotes the volume.
• $M$ denotes the molar mass.
• $T$ denotes temperature.
• $P$ denotes the pressure.