Chapter U3.59, Problem 3E

Interpretation Introduction

Interpretation: The volume occupied by the given air needs to be determine if it is allowed to expand until the pressure $1.0\text{ atm}$ is reached.

Concept Introduction:The law which states the relation between pressure, $\text{P}$ and volume, $\text{V}$ under constant temperature, $\text{T}$ is said to Boyle’s law. According to this law, the pressure of an ideal gas has inverse relation with its volume:

  $\text{P}\propto \frac{1}{\text{V}}$

Answer to Problem 3E

The volume occupied by the given air is $720\text{ L}$ if it is allowed to expand until the pressure $1.0\text{ atm}$ is reached.

Explanation of Solution

Given:

Initial:

Volume = $18.0\text{ L}$

Pressure = $40\text{ atm}$

The Boyle’s law can be expressed as for two different sets of condition for the same substance at constant temperature as:

  ${\text{P}}_{\text{1}}{\text{V}}_{\text{1}}{\text{ = P}}_2{\text{V}}_2$

Where 1 and 2 indicates conditions at set 1 and condition at set 2.

The value of ${\text{V}}_{\text{1}}\text{ = }18.0\text{ L}$ , ${\text{P}}_1\text{ = }40\text{ atm}$ and ${\text{P}}_2\text{ = }1\text{ atm}$ . Substituting these values as:

  $\begin{array}{l}\text{40 atm }\times \text{18 L = }1.0\text{ atm}\times {\text{V}}_2\\ {\text{V}}_2\text{ = }\frac{\text{40 atm }\times \text{18 L}}{1.0\text{ atm}}\\ {\text{V}}_2\text{ = }720\text{ L}\end{array}$

Hence, the volume occupied by the given air is $720\text{ L}$ if it is allowed to expand until the pressure $1.0\text{ atm}$ is reached.