Avogadro's Law Calculator – Gas Volume and Amount at Constant T and P
Avogadro's law says that at constant temperature and pressure, the volume of a gas is proportional to the amount of gas. Put twice as many molecules into a balloon at the same temperature and pressure and it swells to twice the volume. This Avogadro's law calculator solves the two-state form for any one unknown and also works out gas volumes in chemical reactions from the balanced coefficients.
V₁ / n₁ = V₂ / n₂ (T and P constant, ideal gas)The hypothesis behind the law
In 1811 Amedeo Avogadro proposed that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. He was explaining Joseph Gay-Lussac's law of combining volumes (presented in 1808 and published in 1809): gases react in simple whole-number volume ratios. Two volumes of hydrogen and one of oxygen give two volumes of steam, not one. That only works if hydrogen and oxygen exist as diatomic molecules, H₂ and O₂, which John Dalton rejected. The idea was largely ignored for decades until Stanislao Cannizzaro championed it (his Sunto of 1858, circulated at the 1860 Karlsruhe Congress), and it became the basis for consistent atomic weights.
Molar volume and the "22.4 L" confusion
For an ideal gas the ratio V/n is the molar volume, V/n = RT/P. It is the same for every ideal gas at a given temperature and pressure, which is the hypothesis in one line. The number you see depends on which "standard" conditions are meant:
| Conditions | Molar volume |
|---|---|
| 0 °C, 1 atm (older textbook STP) | 22.41 L/mol |
| 0 °C, 1 bar (IUPAC STP since 1982) | 22.71 L/mol |
| 25 °C, 1 atm | 24.47 L/mol |
| 25 °C, 1 bar (SATP) | 24.79 L/mol |
Answer keys disagree because they use different standards. The calculator's molar-volume card shows your own V/n on this scale and the temperature or pressure it implies.
Using mass instead of moles
If the gas is the same in both states, the molar mass cancels: m₁ / m₂ = n₁ / n₂, so grams work directly. With two different gases, equal volumes hold equal numbers of molecules but not equal masses. A 2 L flask holds 0.327 g of helium or 3.595 g of carbon dioxide at the same T and P, because the masses are in the ratio of the molar masses, 4.003 : 44.01.
Gas reaction volumes
Because volume ratios equal mole ratios at shared conditions, the coefficients of a balanced equation are the volume ratios. In the Haber process, N₂ + 3 H₂ → 2 NH₃, four volumes of gas become two, so the mixture contracts by half. Burning 4 L of propane needs 20 L of oxygen and gives 12 L of CO₂. Water formed below 100 °C condenses, so it drops out of the gas volume. When several reactant volumes are supplied, the gas that allows the fewest "volumes per coefficient" is the limiting one.
Avogadro's law vs Avogadro's number
The law is a proportion between gas volume and amount. Avogadro's number, N_A = 6.02214076 × 10²³ mol⁻¹, is the number of particles in one mole. This calculator only uses N_A to convert molecule counts to moles. To work with particle counts themselves, use the Avogadro's Number Calculator.
Limits of the law
- Real gases follow it closely at everyday conditions and less well at high pressure or near condensation.
- Temperature and pressure must not change. If they do, use Charles's, Boyle's, Gay-Lussac's or the combined gas law.
- Only gases count. Liquids and solids have volumes set by how their particles pack, so they get no volume from the coefficients.