Chapter 13, Problem 74A

Interpretation Introduction

Interpretation:

The pressure inside the containers is to be calculated given is the mass and volume of gas.

Concept introduction:

Ideal gas equation helps to calculate pressure of a gas at given temperature and volume. According to this law,

$\mathrm{PV}=nRT$

Where

$\mathrm{P}$ is pressure of the gas

$\mathrm{V}$ is volume of the gas

$\mathrm{n}$ is the number of moles of the gas

$\mathrm{R}$ is the ideal gas constant

$\mathrm{T}$ is the temperature of the gas

Answer to Problem 74A

The pressure inside the container containing propane is $66.1atm$ and nitrogen is $76.2atm$.

Explanation of Solution

Ideal gas equation helps to calculate pressure of a gas at given temperature and volume. According to this law,

$\mathrm{PV}=nRT$

Or

$\mathrm{P}=\frac{nRT}{V}$

Given data for propane is:

$\begin{array}{l}\text{m=0}\text{.52}\text{Kg}\\ \text{=0}{\text{.52×10}}^{\text{3}}\text{g}\end{array}$

$\mathrm{V}=4L$

$\text{R=}0.0821Latm{K}^{-1}mo{l}^{-1}$

$\text{T=273}\text{K}$

To convert mass into moles,

$\begin{array}{c}\text{n=}\frac{\text{m}}{\text{M}}\\ \text{=}\frac{\text{0}{\text{.52×10}}^{\text{3}}}{\text{44}}\\ \text{=11}\text{.8}\text{mol}\end{array}$

Now substituting the values into formula,

$\begin{array}{c}P=\frac{nRT}{V}\\ =\frac{11.8\times 0.0821\times 273}{4}\\ =66.1atm\end{array}$

Given data for nitrogen is:

$\begin{array}{l}\text{m=0}\text{.38}\text{Kg}\\ \text{=0}{\text{.38×10}}^{\text{3}}\text{g}\end{array}$

$\mathrm{V}=4L$

$\text{R=}0.0821Latm{K}^{-1}mo{l}^{-1}$

$\text{T=273}\text{K}$

To convert mass into moles,

$\begin{array}{c}\text{n=}\frac{\text{m}}{\text{M}}\\ \text{=}\frac{\text{0}{\text{.38×10}}^{\text{3}}}{28}\\ \text{=13}\text{.6}\text{mol}\end{array}$

Now substituting the values into formula,

$\begin{array}{c}P=\frac{nRT}{V}\\ =\frac{13.6\times 0.0821\times 273}{4}\\ =76.2atm\end{array}$

Conclusion

Thus,

$\begin{array}{l}\text{P(propane)=66}\text{.1}\text{atm}\\ \text{P(nitrogen)=76}\text{.2}\text{atm}\end{array}$