Chapter 13.1, Problem 11PP

Interpretation Introduction

Interpretation:

The volume of the gas is to be calculated when pressure and temperature of the gas are given at two 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 11PP

The volume of the gas is $0.213mL$

Explanation of Solution

Given Information:

The initial pressure of the gas $P_1=1.02atm$

The initial temperature of the gas ${\mathrm{T}}_2=22°\mathrm{C}$

The final pressure of the gas $P_2=1.23atm$

The final volume of the gas $V_2=0.224mL$

The final temperature of the gas $T_2=100°\mathrm{C}$

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

$\mathrm{PV}=nRT$

Or

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Where

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

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

The initial temperature of the gas $T_1=22C$

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

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

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

Now converting the temperature values from Celsius to kelvin.

$\begin{array}{l}{T}_1(K)=T_1(C)+273\\ =22+273\\ =295K\\ T_2=100C\\ =100+273\\ =373K\end{array}$

Now substituting the values into formula,

$\begin{array}{c}{V}_1=\frac{P_2{V}_2{T}_1}{P_1{T}_2}\\ =\frac{1.23\times 0.224\times 295}{1.02\times 373}\\ =0.213mL\end{array}$

Therefore, the volume of the gas is $0.213mL$

Conclusion

The volume of the gas is $0.213mL$.