What Is Avogadro's Law?

Avogadro's law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Therefore, at constant temperature and pressure, the volume of a gas is directly proportional to its amount in moles.

The Reasoning

For a fixed temperature and pressure:

$$V \propto n$$

This can be written as:

$$\frac{V_1}{n_1} = \frac{V_2}{n_2}$$

Here, $V$ is gas volume and $n$ is the amount of substance in moles. If the number of moles doubles while temperature and pressure remain constant, the volume also doubles.

This relationship follows from the ideal gas equation, $PV = nRT$. Rearranging gives $V = \frac{nRT}{P}$. Because , , and are constant, volume depends directly on the number of moles.

At the particle level, adding gas particles at unchanged temperature does not change their average kinetic energy. To keep pressure constant, the gas expands, spreading collisions with the container walls over a larger area.

The law also explains why molar volume is constant only at a specified temperature and pressure. It does not mean every mole of gas always occupies the same volume; changing either condition changes the volume.

Worked Example

A gas occupies $2.40\text{ dm}^3$ when its amount is $0.100\text{ mol}$. Find its volume when the amount increases to $0.250\text{ mol}$, with temperature and pressure unchanged.

$$V_2 = V_1 \times \frac{n_2}{n_1}$$ $$V_2 = 2.40 \times \frac{0.250}{0.100} = 6.00\text{ dm}^3$$

A common misconception is that Avogadro's law and the Avogadro constant are the same. They are different: Avogadro's law relates gas volume to amount, whereas the Avogadro constant, $N_A$, gives the number of entities in one mole.

IB Exam Technique

This is SL and HL content in Structure 1.4. State explicitly that temperature and pressure are constant, show the mole ratio, and include units. Do not assume equal gas volumes contain equal numbers of molecules if their temperatures or pressures differ.