In 1808 Joseph Louis Gay-Lussac found that gases react in simple whole-number ratios by volume, when the volumes are measured at the same temperature and pressure.
One volume of hydrogen and one of chlorine give two volumes of hydrogen chloride, and two volumes of hydrogen and one of oxygen give two volumes of water vapour.
Nitrogen and hydrogen combine in the ratio 1 : 3 to give two volumes of ammonia. This is the law of combining volumes, and as these examples show, the total volume of gas can shrink in a reaction.
If equal volumes of gases held equal numbers of atoms, one volume of hydrogen and one volume of chlorine would hold the same number of atoms, say four of each.
The two volumes of hydrogen chloride would then hold eight particles, and each would need half a hydrogen atom and half a chlorine atom.
Dalton held that atoms cannot be split, so he rejected the idea of equal numbers in equal volumes and doubted the accuracy of Gay-Lussac's measurements.
In 1811 Amedeo Avogadro proposed that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, and that the molecules of an element can contain more than one atom.
If hydrogen and chlorine are made of molecules of two atoms, four \mathrm{H_2} and four \mathrm{Cl_2} molecules give eight \mathrm{HCl} molecules without splitting any atom: \mathrm{H_2 + Cl_2 \longrightarrow 2HCl}.
The eight \mathrm{HCl} molecules fill two volumes, just as the four \mathrm{H_2} and four \mathrm{Cl_2} molecules filled one volume each. This idea, now called Avogadro's law, was widely accepted only after 1860.
Above 100 °C, two volumes of hydrogen and one volume of oxygen give two volumes of water vapour. With diatomic molecules, four \mathrm{H_2} and two \mathrm{O_2} give four water molecules.
Each water molecule must therefore contain two hydrogen atoms and one oxygen atom, so the formula is \mathrm{H_2O}: \mathrm{2H_2 + O_2 \longrightarrow 2H_2O}.
Water is 1 : 8 hydrogen to oxygen by mass, and one oxygen atom goes with two hydrogen atoms, so an oxygen atom is 16 times as heavy as a hydrogen atom. The value of 8 that follows from \mathrm{HO} was only half the true one.
Since equal volumes of gases hold equal numbers of molecules, the masses of equal volumes are in the same ratio as the masses of single molecules.
At 0 °C and 1.013 × \mathrm{10^5} Pa, 1.00 L of hydrogen weighs 0.0893 g, nitrogen 1.25 g and oxygen 1.43 g, a ratio of 1 : 14.0 : 16.0.
Taking the hydrogen molecule as 2.0 gives relative molecular masses of 28.0 for nitrogen and 32.0 for oxygen. Each molecule has two atoms, so the relative atomic masses are H 1.0, N 14.0 and O 16.0.
Stanislao Cannizzaro used this reasoning in 1858 to set out a consistent table of atomic masses, which ended decades of confusion.