Chapter 14, Problem 56A

Interpretation Introduction

Interpretation: The new volume of the gas needs to be calculated if the gas of volume 4.0 L at 90.0 kPa expands and pressure drops to 20.0 kPa at a constant temperature.

Concept Introduction: According to Boyle’s law at a constant temperature, the volume of gas of a fixed number of moles is inversely proportional to its pressure.

This can be represented as follows:

  $P\propto \frac{1}{V}$

Thus, the relation between the initial and final pressure and volume of gas will be:

  $P_1{V}_1=P_2{V}_2$

Here, P is pressure and V is volume.

Explanation of Solution

At constant temperature, the relationship between the initial and final volume and pressure of the gas is as follows:

  $P_1{V}_1=P_2{V}_2$

Here, the initial pressure and volume of gas are 90 kPa and 4.0 L respectively. If the final pressure is 20.0 kPa, the volume can be calculated as follow:

  $\left(90\text{ kPa}\right)\left(4.0\text{ L}\right)=\left(\text{20 kPa}\right)\left(V_2\right)$

On rearranging,

  $\begin{array}{c}{V}_2=\frac{\left(90\text{ kPa}\right)\left(4.0\text{ L}\right)}{\left(\text{20 kPa}\right)}\\ =18\text{ L}\end{array}$

Therefore, the new volume of the gas is 18 L.