At fixed temperature and pressure, the volume of an ideal gas is directly proportional to the amount of gas measured in moles. This is Avogadro's law:

$$V\propto n,$$

so for two states at the same $T$ and $p$,

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

The relation means that equal volumes of ideal gases at the same temperature and pressure contain equal numbers of molecules, regardless of chemical identity.

Example

A gas sample occupies $3.00,\mathrm L$ when it contains $0.125,\mathrm{mol}$ at a fixed temperature and pressure. If the amount is increased to $0.200,\mathrm{mol}$ without changing temperature or pressure,

$$V_2=V_1\frac{n_2}{n_1} =(3.00,\mathrm L)\frac{0.200}{0.125} =4.80,\mathrm L.$$

Avogadro's law is especially useful in reaction stoichiometry because balanced chemical equations relate reacting amounts in moles. If two ideal gases are compared at the same temperature and pressure, their volume ratio is therefore also their mole ratio.

This does not mean that one mole of gas always occupies one universal fixed volume. The molar volume depends on temperature and pressure. The proportionality holds only while those conditions are specified and equal.