Chapter 13.2, Problem 30PP

Interpretation Introduction

Interpretation:

The volume of the gas is to be calculated when pressure, temperature and number of moles of the gas are given at two different conditions.

Concept introduction:

Ideal gas equation helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Where

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

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

$\mathrm{n}$ is the number of moles of the gas

$\mathrm{R}$ is the ideal gas constant

$\mathrm{T}$ is the temperature of the gas

Answer to Problem 30PP

The volume of the gas is $12L$

Explanation of Solution

Ideal gas equation helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Or

$\frac{P_1{V}_1}{n_1{T}_1}=\frac{P_2{V}_2}{n_2{T}_2}$

Where

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

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

${\mathrm{n}}_1$ is the initial number of moles of the gas

${\mathrm{T}}_1$ is the initial temperature of the gas

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

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

${\mathrm{n}}_2$ is the final number of moles of the gas

${\mathrm{T}}_2$ is the final temperature of the gas

$V_2=\frac{P_1{V}_1{n}_2{T}_2}{P_2{n}_1{T}_1}$

Now, according to the statement:

$\begin{array}{l}{P}_1=P\\ P_2=P\\ {\mathrm{V}}_1=3L\\ T_1=T\\ T_2=2T\\ n_1=n\\ n_2=2n\end{array}$

Now substituting the values into formula,

$\begin{array}{c}{V}_2=\frac{P_1{V}_1{n}_2{T}_2}{P_2{n}_1{T}_1}\\ =\frac{P\times 3\times 2n\times 2T}{P\times n\times T}\\ =12L\end{array}$

Therefore, volume of the gas is $12L$

Conclusion

The volume of the gas is $12L$.