Avogadro’s Law and Molar Gas Volume
Avogadro’s law states that equal volumes of all gases at the same temperature and pressure contain the same number of particles, so the volume of a gas is directly proportional to the amount in moles: V1/n1 = V2/n2. In brief: at standard temperature and pressure (0 °C and 1 atm), one mole of any ideal gas occupies about 22.4 L, so 11.2 L of oxygen is 0.500 mol.
Avogadro’s law connects the macroscopic quantity volume to the microscopic quantity number of particles. It lets chemists count molecules by measuring a volume, and it is the basis for molar volume calculations in gas stoichiometry. This article states the law, gives the molar volume values, shows worked examples and traces the history of the idea.
What does Avogadro’s law say?
At constant temperature and pressure, the volume of a gas is proportional to the number of moles:
V / n = k, or V1/n1 = V2/n2
If you double the number of moles, the volume doubles. The type of gas does not matter, because in an ideal gas the particles are so far apart that their size and mass have no effect on the volume. A balloon filled with helium and one filled with the same number of moles of chlorine have equal volumes under the same conditions, although the chlorine balloon is much heavier.
What is molar gas volume?
The molar volume is the volume occupied by one mole of gas. It follows from the ideal gas law, Vm = RT / P, and it depends on the temperature and pressure but not on the identity of the gas. Two reference conditions are in common use:
- STP (0 °C, 1 atm): 22.414 L/mol, usually rounded to 22.4 L/mol.
- SATP (25 °C, 1 bar): 24.79 L/mol.
The current IUPAC definition of standard pressure is 1 bar (100 kPa), which gives 22.711 L/mol at 0 °C. Many textbooks still use 1 atm and 22.4 L/mol, so always check which definition a problem uses.
Molar volume at different conditions
| Conditions | Temperature | Pressure | Molar volume (L/mol) |
|---|---|---|---|
| STP (older definition) | 273.15 K | 1 atm | 22.414 |
| STP (IUPAC since 1982) | 273.15 K | 1 bar | 22.711 |
| Room temperature | 293.15 K | 1 atm | 24.055 |
| SATP | 298.15 K | 1 bar | 24.790 |
| Body temperature | 310.15 K | 1 atm | 25.450 |
How do you use Avogadro’s law?
Worked example 1: finding the volume from moles
What volume do 0.250 mol of nitrogen occupy at STP (0 °C, 1 atm)?
V = n × Vm = 0.250 mol × 22.4 L/mol = 5.60 L.
Worked example 2: finding moles and mass from volume
A sample of carbon dioxide occupies 8.96 L at STP. How many moles and what mass does it contain?
- n = 8.96 L / 22.4 L/mol = 0.400 mol.
- The molar mass of CO2 is 44.01 g/mol.
- m = 0.400 mol × 44.01 g/mol = 17.6 g.
Worked example 3: changing the amount of gas
A balloon contains 0.80 mol of helium and has a volume of 19.6 L. More helium is added until the balloon holds 1.20 mol at the same temperature and pressure. What is the new volume?
V2 = V1 × n2 / n1 = 19.6 L × 1.20 / 0.80 = 29.4 L.
Worked example 4: volume ratios in a reaction
In the reaction 2H2 + O2 → 2H2O(g), the mole ratio is 2 : 1 : 2. Because volume is proportional to moles, 10 L of hydrogen react with 5 L of oxygen to give 10 L of steam, all measured at the same temperature and pressure.
How did Avogadro’s hypothesis develop?
In 1808 Gay-Lussac found that gases react in simple volume ratios, such as 2 volumes of hydrogen to 1 of oxygen. John Dalton rejected the idea that equal volumes contain equal numbers of particles because it seemed to imply that a molecule of oxygen could split in half. In 1811 Amedeo Avogadro resolved the problem by suggesting that elemental gases such as hydrogen and oxygen exist as diatomic molecules. His hypothesis was ignored for about 50 years until Stanislao Cannizzaro revived it at the Karlsruhe Congress of 1860. The Avogadro constant, 6.02214076 × 1023 mol−1, was named after Avogadro, although he never measured it. Jean Perrin determined it experimentally in the early 1900s.
Where is molar volume used?
- Gas stoichiometry: converting between the volume of a gas product and the moles of reactant.
- Airbag design: the amount of nitrogen produced by sodium azide determines the airbag volume.
- Medicine: calculating doses of anesthetic gases.
- Gas analysis: volume fractions of gases in a mixture equal their mole fractions.
Which mistakes are common?
- Using 22.4 L/mol at any conditions: the value applies only at 0 °C and 1 atm.
- Applying molar volume to liquids and solids: the idea works only for gases.
- Forgetting diatomic molecules: 22.4 L of oxygen is one mole of O2, which contains two moles of oxygen atoms.
- Mixing STP definitions: 1 atm and 1 bar give slightly different molar volumes.