Chapter 13.1, Problem 1PP

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 the gas decreases its volume. This law is known as Boyle’s Law.

According to this law,

  $P_1{V}_1=P_2{V}_2$

Where,

  $P_1$ is initial pressure of the gas

  $V_1$ is the initial volume of the gas

  $P_2$ is the final pressure of the gas

  $V_2$ is the final volume of the gas

Answer to Problem 1PP

The new volume of the gas is $157.98\mathrm{mL}$ .

Explanation of Solution

Given information:

The initial volume $V_1=300\mathrm{mL}$

The initial pressure $P_1=99\text{kPa}$

The final pressure is $P_2=188\text{kPa}$

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, the product of pressure and volume of a given mass of gas is constant at a constant temperature.

If $V_1$ is the volume of the gas at pressure $P_1$ and pressure is increased to $P_2$ , then the volume is decreased to $V_2$ . The formula used to calculate $V_2$ is

  $P_1{V}_1=P_2{V}_2$

Or

  $V_2=\frac{P_1{V}_1}{P_2}$

Where

• $P_1$ is the initial pressure of the gas
• $V_1$ is the initial volume of the gas
• $P_2$ is the final pressure of the gas
• $V_2$ is the final volume of the gas

On substituting the values in the formula:

  $\begin{array}{c}{V}_2=\frac{99\times 300}{\begin{array}{l}188\\ \end{array}}\\ =157.98\mathrm{mL}\end{array}$

Therefore, new volume is $157.98\mathrm{mL}$ .

Conclusion

The volume of the gas at $188\text{kPa}$ is $157.98\mathrm{mL}$ .