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

May 25, 2014

The Molar Volume of an ideal gas at STP, which we define to be ${0}^{\circ} \text{C}$ and $\text{1 atm}$ arbitrarily (because we're old-fashioned and stuck in 1982) is $\text{22.411 L/mol}$.

To calculate this we can use the Ideal gas law of $P V = n R T$

At STP (Standard Temperature and Pressure), we CHOSE:
$P = \text{1 atm}$
V = ?
$n = \text{1 mol}$
$R = \text{0.082057 L"cdot"atm/mol"cdot"K}$
$\text{T = 273.15 K}$

$V = \frac{n R T}{P}$

$= \left(1 \cancel{\text{mol")) (0.082057 (cancel("atm")cdot"L")/(cancel("mol")cdotcancel("K")))(273.15cancel("K"))/(1 cancel("atm}}\right)$

$=$ $\text{22.411 L}$

This is the volume of one mole of ideal gas at STP, in 1982 or before...