Two cylinders with free pistons, at the same pressure and the same temperature: one holds n1 moles, the other n2. The gas columns are drawn to one shared scale, so the height ratio you see is the mole ratio. Change the pressure or the temperature and the molar volume moves; change the gas and the mass and the density move — but the volumes, the ratio and the molecule count do not.
Volume before22.71 L
Gas added+1.00 mol added
Molar mass28.96 g/mol
Gas density1.275 g/L
Temperature273.15 K
Molecules after1.204e24 molecules
WhyAt 100 kPa and 0 °C one mole of any gas fills 22.711 L, so 2.00 mol fills 45.42 L.
The other two gasesSame amount in the other two gases: helium 8.006 g · carbon dioxide 88.02 g, all in the same 45.42 L.
What to noticeEqual volumes of any two gases at the same pressure and temperature hold the same number of molecules. That is Avogadro's law, and it is why the volume readings do not change when you press a different gas button.
R = 8.314462618 J/(mol·K) · Avogadro's number = 6.02214076e23 per mole · both exact in the SI. Avogadro's law is the statement that the volume follows the amount of gas; Avogadro's number is the count of entities in a mole — two different things. The law needs a container free to change size against a fixed outside pressure — a piston, a balloon, a gas holder, a lung; pump gas into a rigid bottle and the volume cannot move, so the pressure rises instead. Air is a mixture, so its 28.96 g/mol is a mean molar mass and not the molar mass of a substance. These are ideal-gas volumes.
Volume after V2 = V1 · n2/n1
45.42 L
volume after, at the same pressure and temperature
Molar volume Vm = R T / P
22.711 L/mol
molar volume: the same for every gas at this pressure and temperature
Volume ratio
2.000
V2/V1, and n2/n1 — the same number
Mass of the gas
57.92 g
mass of the gas afterwards — the volume does not depend on it
Amount before1.00 mol
Amount after2.00 mol
Pressure100 kPa
100 kPa is IUPAC's standard pressure; 101.325 kPa is 1 atm