Chapter 14, Problem 55A

Interpretation Introduction

Interpretation: The volume of a gas at pressure $1.00\times {10}^2\text{ kPa}$ needs to be determined if the volume $1.20\times {10}^2\text{ kPa}$ is $1.50\times {10}^3\text{ mL}$

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 a gas are $1.20\times {10}^2\text{ kPa}$ and $1.50\times {10}^3\text{ mL}$ respectively. If the final pressure is $1.00\times {10}^2\text{ kPa}$ , the volume can be calculated as follow:

  $\left(1.20\times {10}^2\text{ kPa}\right)\left(1.50\times {10}^3\text{ mL}\right)=\left(1.00\times {10}^2\text{ kPa}\right)\left(V_2\right)$

On rearranging,

  $\begin{array}{c}{V}_2=\frac{\left(1.20\times {10}^2\text{ kPa}\right)\left(1.50\times {10}^3\text{ mL}\right)}{\left(1.00\times {10}^2\text{ kPa}\right)}\\ =1.8\times {10}^3\text{ mL}\end{array}$

Therefore, the volume of the gas is $1.8\times {10}^3\text{ mL}$ .