Chapter 13.1, Problem 3PP

Interpretation Introduction

Interpretation:

The volume of the gas is to be calculated for a given new pressure when the temperature and amount of gas are constant.

Concept introduction:

When temperature and amount of gas are kept constant, increasing the pressure of gas decreases its volume. This law is known as Boyle’s Law.

According to this law,

${\mathrm{P}}_1{V}_1=P_2{V}_2$

Where

${\mathrm{P}}_1$ is initial pressure of the gas

${\mathrm{V}}_1$ is initial volume of the gas

${\mathrm{P}}_2$ is the final pressure of the gas

${\mathrm{V}}_2$ is the final volume of the gas

Answer to Problem 3PP

The new volume of the gas is $116.56\mathrm{mL}$

Explanation of Solution

Given information:

The initial volume ${\mathrm{V}}_1=145.7\mathrm{mL}$

The initial pressure is ${\mathrm{P}}_1=1.08\text{kPa}$

The change in volume on changing the pressure of the gas keeping the temperature fixed is studied by a law named as Boyle’s Law. According to this law, Product of pressure and volume of a given mass of gas is constant at constant temperature.

If ${\mathrm{V}}_1$ is the volume of the gas at pressure ${\mathrm{P}}_1$ and pressure is increased to ${\mathrm{P}}_2$ then volume is decreased to ${\mathrm{V}}_2$. The formula used to calculate ${\mathrm{V}}_2$ is

${\mathrm{P}}_1{V}_1=P_2{V}_2$

Or

${\mathrm{V}}_2=\frac{P_1{V}_1}{P_2}$

Where

• ${\mathrm{P}}_1$ is initial pressure of the gas
• ${\mathrm{V}}_1$ is initial volume of the gas
• ${\mathrm{P}}_2$ is the final pressure of the gas
• ${\mathrm{V}}_2$ is the final volume of the gas

Now initial volume is $145.7\mathrm{mL}$

Initial pressure is $1.08\text{kP}a$

Final pressure is increased by $25\%$ of the initial pressure. Therefore

$\begin{array}{c}{\mathrm{P}}_2=1.08+\frac{25\times 1.08}{100}\\ =1.08+0.27\\ =1.35\text{ kPa}\end{array}$

On substituting the values in the formula:

$\begin{array}{c}{\mathrm{V}}_2=\frac{1.08\times 145.7}{\begin{array}{l}1.35\\ \end{array}}\\ =116.56\mathrm{mL}\end{array}$

Therefore, new volume is $116.56\mathrm{mL}$

Conclusion

The volume of the gas on increasing $25\%$ pressureis $116.56\mathrm{mL}$.