The number of particles in a mole is called Avogadro's number or, more accurately, Avogadro's constant. For most calculations, three (6.02 x 1023) or at most four (6.022 x 1023) significant figures for Avogadro's number are enough.

Gay-Lussac's law of combining volumes was announced only a few years after John Dalton proposed his atomic theory. The link between these two ideas was first recognized by the Italian physicist Amadeo Avogadro three years later, in 1811. Avogadro argued that Gay-Lussac's law of combining volumes could be explained by assuming that equal volumes of different gases collected under similar conditions contain the same number of particles.

HCl and NH3 therefore combine in a 1:1 ratio by volume because one molecule of HCl is consumed for every molecule of NH3 in this reaction and equal volumes of these gases contain the same number of molecules.

Anyone who has blown up a balloon should accept the notion that the volume of a gas is proportional to the number of particles in the gas.

V a n

The more air you add to a balloon, the bigger it gets. Unfortunately this example does not test Avogadro's hypothesis that equal volumes of different gases contain the same number of particles. The best way to probe the validity of this hypothesis is to measure the number of molecules in a given volume of different gases, which can be done with the apparatus shown below.

 The apparatus used to demonstrate Avogadro's hypothesis

A small hole is drilled through the plunger of a 50-mL plastic syringe. The plunger is then pushed into the syringe and the syringe is sealed with a syringe cap. The plunger is then pulled out of the syringe until the volume reads 50 mL and a nail is inserted through the hole in the plunger so that the plunger is not sucked back into the barrel of the syringe. The "empty" syringe is then weighed, the syringe is filled with 50 mL of a gas, and the syringe is reweighed. The difference between these measurements is the mass of 50 mL of the gas.

The results of experiments with six gases are given below. The number of molecules in a 50-mL sample of any one of these gases can be calculated from the mass of the sample, the molecular weight of the gas, and the number of molecules in a mole. Consider the following calculation of the number of H2 molecules in 50 mL of hydrogen gas, for example.

0.005 g H2 x 1 mol H2 x 6.02 x 1023 molecules = 1 x 1021 H2 molecules

2.02 H2 g 1 mol

The last column below summarizes the results obtained when this calculation is repeated for each gas. The number of significant figures in the answer changes from one calculation to the next. But the number of molecules in each sample is the same, within experimental error. We therefore conclude that equal volumes of different gases collected under the same conditions of temperature and pressure do in fact contain the same number of particles.

Experimental Data for the Mass of 50-mL Samples of Different Gases

 Compound Mass of 50 mL of Gas (g) Molar Mass of Gas  (g / mol) Number of  Molecules H2 0.005 2.02 1 x 1021 N2 0.055 28.01 1.2 x 1021 O2 0.061 32.00 1.1 x 1021 CO2 0.088 44.01 1.2 x 1021 C4H10 0.111 58.12 1.15 x 1021 CCl2F2 0.228 120.91 1.14 x 1021