Chapter 19, Problem 90A

Interpretation Introduction

Interpretation: The volume of the gas is to be calculated when the pressure and temperature of the gas are given at two conditions.

Concept introduction:

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

  $PV=n\text{R}T$

Where

  $P$ is the pressure of the gas

  $V$ is the volume of the gas

  $n$ is the number of moles of the gas

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

  $T$ is the temperature of the gas

Answer to Problem 90A

The volume of the gas is $26.53\text{ mL}$

Explanation of Solution

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

  $PV=n\text{R}T$

Or

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

Here,

  $\begin{array}{l}{P}_1=0.75atm\\ P_2=1atm\\ V_1=32.4mL\\ T_1=-23°C\\ T_1(K)=T_1(°C)+273\\ =-23+273\\ =250K\\ T_2=273K\end{array}$

Now substituting the values into the formula,

  $\begin{array}{c}{V}_2=\frac{P_1{V}_1{T}_2}{P_2{T}_1}\\ =\frac{0.75\times 32.4\times 273}{1\times 250}\\ =26.53\text{ m}L\end{array}$

Therefore, volume of the gas is $26.53mL$ .

Conclusion

The volume of the gas is $26.53\text{ mL}$ .