Chapter 13.2, Problem 20PP

Interpretation Introduction

Interpretation: The volume of the gas is to be calculated when pressure, temperature and number of moles of the gas are given.

Concept introduction:

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

  $\mathrm{PV}=nRT$

Where,

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

  $\mathrm{V}$ is the 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 20PP

The volume of the gas is $1.029L$ .

Explanation of Solution

Given information:

The number of moles of gas is $0.0459mol$ .

The Pressure $\mathrm{P}=1atm(atSTP)$

The Gas constant is $0.0821Latm{K}^{-1}mo{l}^{-1}$

The temperature of the gas $\mathrm{T}=273K$

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

  $\mathrm{PV}=nRT$

Or

  $\mathrm{V}=\frac{nRT}{P}$

Where

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

  $\mathrm{V}$ is the 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

Now substituting the values into the formula,

  $\begin{array}{c}V=\frac{nRT}{P}\\ =\frac{0.0459\times 0.0821\times 273}{1}\\ =1.029L\end{array}$

Therefore, the volume occupied by the gas is $1.029L$ .

Conclusion

The size of the container should be $1.029L$ .