Avogadro's law
Blow into a balloon and it grows; blow in twice as much breath and it grows to twice the size. Avogadro's law is the surprising and elegant fact behind this: at the same temperature and pressure, equal volumes of any gas contain equal numbers of molecules — and so the volume of a gas is proportional to how much of it there is.
Put precisely, at fixed temperature and pressure the volume V of a gas is directly proportional to the amount n in moles. Double the moles of gas and you double the volume. Remarkably, this holds whatever the gas is: a litre of hydrogen and a litre of carbon dioxide at the same conditions hold the same number of molecules, even though their masses differ greatly.
This deceptively simple idea was revolutionary. It let chemists count molecules by measuring gas volumes and underpins the very notion of the mole. As another special case inside the ideal gas law, it is also the reason chemical reactions between gases combine in simple whole-number volume ratios.
Because hydrogen and oxygen react in a two-to-one molecule ratio to make water, two litres of hydrogen gas react with exactly one litre of oxygen — the volumes mirror the molecule counts, just as Avogadro's law predicts.
Reacting gas volumes follow simple whole-number ratios.
Do not confuse Avogadro's law (about gas volumes and amount) with the Avogadro constant (the number of particles in one mole, about 6.022 times ten to the twenty-third). They are named for the same person but are different things.