Question

Why is $22.4$ liters called the molar volume of a gas?

Answer 1

Standard temperature and pressure

• Always the Standard temperature and pressure (STP) are specified as $273.15\mathrm{K}$ and $1\mathrm{atm}$ pressure.
• At STP an ideal gas law is as follows:

$V=\frac{nRT}{P}$

Here, $V$ is the volume, $n$ is the number of moles, $R$ is a gas constant, $T$ is the temperature and $P$ is the pressure.

Molar volume of a gas

• The molar volume of a gas is the volume of one mole of a gas at STP.
• Substitute the values $n=1\mathrm{mol}$, $R=0.082057\mathrm{L}\mathrm{atm}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$, $T=273.15\mathrm{K}$ and $P=1\mathrm{atm}$ in the above equation as follows:
  $\begin{array}{rcl}V& =& \frac{nRT}{P}\\ & =& \frac{1\mathrm{mol}\times 0.082057\mathrm{L}\mathrm{atm}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}\times 273.15\mathrm{K}}{1\mathrm{atm}}\\ & =& 22.4\mathrm{L}\end{array}$
• At STP, one mole of any gas occupies a volume of $\begin{array}{rcl}& & 22.4\mathrm{L}\end{array}$.