Molar volume is the volume occupied by $1 \; mol$ of any (ideal) gas at standard temperature and pressure ($STP$: $1 \; atm$ pressure,$0^{\circ} C$). Show that it is $22.4 \; L$.

(N/A) The ideal gas equation relating pressure $(P)$,volume $(V)$,and absolute temperature $(T)$ is given as:
$PV = nRT$
Where:
$R$ is the universal gas constant $= 8.314 \; J \; mol^{-1} \; K^{-1}$
$n = 1 \; mol$
$T = 273.15 \; K$ (Standard temperature)
$P = 1.01325 \times 10^{5} \; Pa$ (Standard pressure of $1 \; atm$)
Rearranging for volume:
$V = \frac{nRT}{P}$
Substituting the values:
$V = \frac{1 \times 8.314 \times 273.15}{1.01325 \times 10^{5}}$
$V \approx 0.02241 \; m^{3}$
Since $1 \; m^{3} = 1000 \; L$:
$V \approx 22.41 \; L$
Thus,the molar volume of an ideal gas at $STP$ is approximately $22.4 \; L$.