# How would you determine the volume that 1 mol of a gas at 0°C and 1 atm occupies?

Nov 22, 2015

By means of the Ideal gas law.

#### Explanation:

$P V = n R T$; where $P$ is pressure; $V$ is volume; $R$ is the appropriate gas constant (usefully $R$ $=$ $0.0821$ $L \cdot a t m \cdot {K}^{- 1} \cdot m o {l}^{- 1}$), and $T$ is the absolute temperature in Kelvin, $K$.

You will always be given these constants, but you must manipulate them so that you get an answer with the appropriate units.

If $V$ $=$ $\frac{n R T}{P}$, then $V$ $=$ $\frac{1 \cdot m o l \times 0.0821 \cdot L \cdot a t m \cdot {K}^{- 1} \cdot m o {l}^{- 1} \times 273 K}{1 \cdot a t m}$ will give me an answer in litres.

Alternatively, it is a given that 1 mole of ideal gas will occupy a volume of $22.4$ ${\mathrm{dm}}^{3}$ at $273$ $K$. And $1$ ${\mathrm{dm}}^{3}$ $=$ ${\left\{1 \times {10}^{- 1} m\right\}}^{3}$ $=$ $1 \times {10}^{- 3} \cdot {m}^{3}$ $=$ $1$ $L$ (a litre is a 1000th of a cubic metre).