Chapter 13, Problem 31A

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 31A

The volume of the gas is $464mL$

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

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

The following data is given:

  $\begin{array}{l}{P}_1=1.05atm\\ P_2=0.997atm\\ V_1=459mL\\ T_1=27°C\\ T_1(K)=T_1(°C)+273\\ =27+273\\ =300K\\ T_2=15°C\\ =15+273\\ =288K\end{array}$

Now substituting the values into formula,

  $\begin{array}{c}{V}_2=\frac{P_1{V}_1{T}_2}{P_2{T}_1}\\ =\frac{1.05\times 459\times 288}{0.997\times 300}\\ =464mL\end{array}$

Therefore volume of the gas is $464mL$

Conclusion

The volume of the gas is $464mL$ .