Gas volumes: every mole gets 24 dm³

By the end of this lesson

By the end you can convert between moles and gas volumes using the molar gas volume, and use gas-volume ratios to solve reacting-volume problems.

The heavy balloon and the light balloon

Fill one party balloon with hydrogen and an identical one with carbon dioxide, at the same temperature and pressure. The $\text{CO}_2$ inside is 22 times heavier, and that balloon sinks like a sad pancake. But both contain the same number of molecules.

That's Avogadro's law: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. So one mole of any gas takes up the same volume.

Definition

Molar gas volume, Vₘ

The volume occupied by one mole of any gas at a stated temperature and pressure. From the Data Booklet:

$V_m = 24.0\ \text{dm}^3\ \text{mol}^{-1}$ at room conditions
$V_m = 22.4\ \text{dm}^3\ \text{mol}^{-1}$ at s.t.p. (273 K and 101 kPa)

Why the gas doesn't matter

A gas is almost entirely empty space: the molecules themselves fill well under 0.1% of the container. So the volume is really "space per molecule", and that is set by temperature and pressure, not by how big or heavy each molecule is.

Where it breaks down: real gases aren't perfect, so 24.0 dm³ is a very good approximation rather than exact. (Ideal and real gases come back in topic 4.)

The toolkit

$n = \frac{V}{V_m} \qquad\qquad V = n \times V_m$

Match the units:

volume in	use $V_m$ =
$\text{dm}^3$	$24.0\ \text{dm}^3\ \text{mol}^{-1}$
$\text{cm}^3$	$24\,000\ \text{cm}^3\ \text{mol}^{-1}$

$1\ \text{dm}^3 = 1000\ \text{cm}^3$ (a dm³ is a litre). And this works only for gases: never for liquids, solids or solutions.

Quick check

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