Chapter 13.1, Problem 12PP

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 12PP

The volume of the gas is $72.2mL$

Explanation of Solution

Given information:

The initial pressure of the gas $P_1=1.30atm$

The initial volume of the gas $V_1=146mL$

The initial temperature of the gas $T_1=5C$

The final pressure of the gas $P_2=2{\mathrm{P}}_1$

The final temperature of the gas $T_2=2°C$

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

${\mathrm{T}}_1$ 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

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

Now

$\begin{array}{l}{T}_1(K)=T_1(C)+273\\ =5+273\\ =278K\\ T_2=2C\\ =2+273\\ =275K\end{array}$

Now substituting the values into formula,

$\begin{array}{c}{V}_2=\frac{P_1{V}_1{T}_2}{P_2{T}_1}\\ =\frac{1.30\times 146\times 275}{2.60\times 278}\\ =72.2mL\end{array}$

Therefore, volume of the gas is $72.2mL$

Conclusion

The volume of the gas is $72.2mL$.