Chapter 13.1, Problem 2PP

Interpretation Introduction

Interpretation:

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

Concept introduction:

When temperature and amount of gas are constant, pressure of gas is inversely proportional to the volume of the gas. 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 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 2PP

The new pressure of the gas is 0.494 atm.

Explanation of Solution

Given information :

The initial volume ${\mathrm{V}}_1=1\mathrm{L}$

The initial pressure ${\mathrm{P}}_1=0.988\mathrm{atm}$

The final volume ${\mathrm{V}}_2=2\mathrm{L}$.

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 $V_1$ is the volume of the gas at pressure $P_1$ and volume is increasedto $V_2$ Then pressure is decreased to $P_2$. The formula used to calculate $P_2$ is

$P_1{V}_1=P_2{V}_2$

Or

$P_2=\frac{P_1{V}_1}{V_2}$

Where

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

Now initial volume is $1\mathrm{L}$

Initial pressure is 0.988 atm

Final volume is 2 L

On substituting the values in the formula:

$\begin{array}{c}{P}_2=\frac{1\times 0.988}{2}\\ =0.494\mathrm{atm}\end{array}$

Therefore, new pressure is 0.494 atm.

Conclusion

The pressure of the gas on changing the volume to 2 L is 0.494 atm.