Molar Volume of Ideal Gases at STP

The molar volume of an ideal gas at STP (standard temperature and pressure) is the volume occupied by one mole of the gas under standard conditions, and it is 22.414 L at 0 °C and 1 atm (101.325 kPa), or 22.711 L at 0 °C and 1 bar (100 kPa). In brief: at STP, 1 mol of any ideal gas occupies about 22.4 L, so 5.60 L of oxygen is 0.250 mol, which has a mass of 8.00 g; the molar mass of a gas can be found from its density: M = density × 22.4 L/mol.

The molar volume follows from Avogadro’s law, which states that equal volumes of gases at the same temperature and pressure contain the same number of molecules. It connects the volume of a gas to the amount of substance, which makes it a powerful tool for calculations with gases. This article explains Avogadro’s law and the molar volume, the definitions of STP and other standard conditions, shows how to calculate gas volumes and densities, how to use the ideal gas law for other conditions, includes tables, works through examples and gives some history.

What does Avogadro’s law say?

Avogadro’s law states that at the same temperature and pressure, equal volumes of all gases contain equal numbers of particles. Expressed differently, the volume of a gas is directly proportional to the amount of gas: V ∝ n (at constant T and P), or V ÷ n = constant. The constant is the molar volume, V_m. It does not depend on the kind of gas, since in an ideal gas the particles are far apart and the volume is determined by their number and not by their size. Real gases differ slightly from this behavior.

What is STP?

Different organizations use slightly different definitions of “standard” conditions, so always check which one is meant.

• STP (traditional, widely taught): 0 °C (273.15 K) and 1 atm (101.325 kPa). The molar volume is 22.414 L/mol.
• STP (IUPAC since 1982): 0 °C (273.15 K) and 1 bar (100 kPa). The molar volume is 22.711 L/mol.
• SATP (standard ambient temperature and pressure): 25 °C (298.15 K) and 1 bar. The molar volume is 24.790 L/mol.
• Room conditions: 25 °C and 1 atm give 24.465 L/mol, which is often rounded to 24.5 L/mol.

Most school problems use 22.4 L/mol at STP. The calculation comes from the ideal gas law V_m = RT ÷ P = 0.082057 L·atm/(mol·K) × 273.15 K ÷ 1 atm = 22.414 L/mol.

Molar volume under different standard conditions

How do gas densities depend on molar mass?

The density of a gas is its mass divided by its volume: ρ = M ÷ V_m. A gas with a larger molar mass has a higher density. Gases lighter than air (average molar mass 28.96 g/mol) rise, and heavier ones sink.

Worked examples

1. Moles from volume. How many moles are in 5.60 L of oxygen at STP? n = 5.60 L ÷ 22.4 L/mol = 0.250 mol. The mass is 0.250 × 31.998 = 8.00 g.
2. Volume from mass. What volume do 10.0 g of CO₂ occupy at STP? n = 10.0 ÷ 44.009 = 0.2272 mol. V = 0.2272 × 22.4 = 5.09 L.
3. Number of molecules in a volume. How many molecules are in 1.00 L of nitrogen at STP? n = 1.00 ÷ 22.4 = 0.04464 mol. N = 0.04464 × 6.022 × 10²³ = 2.69 × 10²² molecules. (This number is called the Loschmidt number per liter.)
4. Molar mass from density. A gas has a density of 2.86 g/L at STP. M = 2.86 × 22.4 = 64.1 g/mol. This matches SO₂ (64.07 g/mol).
5. Gas volumes in a reaction. In 2H₂ + O₂ → 2H₂O(g), the volume ratio equals the mole ratio: 10.0 L of H₂ reacts with 5.0 L of O₂ to give 10.0 L of steam (at the same temperature and pressure).
6. Hydrogen from zinc at STP. Zn + 2HCl → ZnCl₂ + H₂. 6.54 g of Zn (0.100 mol) gives 0.100 mol of H₂, which has a volume of 2.24 L at STP.
7. Decomposition of potassium chlorate. How many liters of oxygen at STP come from 24.5 g of KClO₃ (122.55 g/mol)? n(KClO₃) = 0.2000 mol. From 2KClO₃ → 2KCl + 3O₂, n(O₂) = 0.3000 mol. V = 0.3000 × 22.4 = 6.72 L.
8. Density of ammonia at STP. NH₃ has a molar mass of 17.031 g/mol: ρ = 17.031 ÷ 22.414 = 0.760 g/L, lower than the density of air (1.29 g/L at STP), so ammonia rises in air.

What if the conditions are not standard?

Use the ideal gas law, PV = nRT, with T in kelvin and a consistent set of units. With R = 0.082057 L·atm/(mol·K): V = nRT ÷ P.

Example: What volume do 0.250 mol of oxygen occupy at 30 °C and 0.950 atm? T = 303.15 K. V = 0.250 × 0.082057 × 303.15 ÷ 0.950 = 6.55 L.

The combined gas law is also useful: P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂ for a fixed amount of gas. A volume of 2.00 L at 25 °C and 1.00 atm becomes at STP V₂ = 2.00 × (273.15 ÷ 298.15) = 1.83 L.

When is the ideal gas model not accurate?

The ideal gas model works best at low pressure and high temperature, since the particles are far apart and the attractive forces are small. Gases such as ammonia and carbon dioxide, with stronger intermolecular forces, deviate slightly: the real molar volume of CO₂ at STP is 22.26 L/mol, and that of ammonia is about 22.09 L/mol. At high pressures the finite size of molecules becomes important, and the van der Waals equation is used. The molar volume applies only to gases; solids and liquids have very different molar volumes (for liquid water 18.0 mL/mol).

How was the molar volume discovered?

Joseph Louis Gay-Lussac found in 1808 that gases react in simple ratios of volumes (for example, 2 volumes of hydrogen with 1 of oxygen). Amedeo Avogadro explained this in 1811 with his hypothesis that equal volumes contain equal numbers of molecules, and that elementary gases are diatomic. Stanislao Cannizzaro used the idea in 1858 to 1860 to determine reliable molar masses from gas densities. The molar volume at STP was determined accurately by Lord Rayleigh and others by weighing gases in the late 19th century.

Which mistakes are common?

Mistake 1: Using 22.4 L/mol at any temperature

The value applies only at 0 °C and 1 atm. For 25 °C use 24.5 L/mol or the ideal gas law.

Mistake 2: Using the molar volume for liquids and solids

It applies only to gases. 1 mol of liquid water is 18 mL, not 22.4 L.

Mistake 3: Mixing Celsius and kelvin in the gas law

Convert to kelvin: T(K) = t(°C) + 273.15.

Mistake 4: Assuming that the molar volume depends on the gas

For ideal gases it is the same for all gases. Differences between gases come from the molar mass, not the molar volume.