Molar Volume Calculation: Ideal Gas Vm = RT ÷ P

This calculator finds the molar volume of an ideal gas, the volume one mole occupies at a given temperature and pressure. Enter the temperature in °C, the pressure in kPa and, optionally, a gas volume in litres; you get the molar volume in L/mol, the moles of gas in that volume and the number of molecules.

Formula

V_m = R × T ÷ P, with T = t + 273.15, and n = V ÷ V_m.

• V_m: molar volume; with P in kPa the result is in litres per mole (1 J = 1 kPa·L)
• R = 8.31446261815324 J/(mol·K), the molar gas constant (exact in the SI)
• T: absolute temperature in kelvin; t: temperature in °C
• P: pressure in kPa; 1 atm = 101.325 kPa, 1 bar = 100 kPa
• N = n × N_A, with N_A = 6.02214076 × 10²³ mol⁻¹

Worked Example

An ideal gas at 0 °C and 101.325 kPa (1 atm), and a 10 L sample of it.

1. T = 0 + 273.15 = 273.15 K
2. R × T = 8.31446 × 273.15 = 2,271.095 J/mol
3. V_m = 2,271.095 ÷ 101.325 = 22.414 L/mol
4. Moles in 10 L: 10 ÷ 22.41397 = 0.4462 mol
5. Molecules: 0.44615 × 6.02214076 × 10²³ = 2.687 × 10²³

Assumptions

• The gas is ideal. Real gases at 0 °C and 1 atm come within about 1% of 22.414 L/mol for most permanent gases such as N₂, O₂ and He.
• The temperature is converted to kelvin by adding 273.15.
• The pressure is absolute, not gauge pressure; add atmospheric pressure to a gauge reading first.

How to read the result

The molar volume depends only on temperature and pressure, not on which gas it is. Reference values: 22.414 L/mol at 0 °C and 101.325 kPa, 22.711 L/mol at 0 °C and 100 kPa (the current IUPAC standard), and about 24.465 L/mol at 25 °C and 101.325 kPa. To find a pressure from moles and volume, use the ideal gas law calculator; for gases far from ideal, the van der Waals calculator.

Limits and common mistakes

• Using 22.4 L/mol at room temperature: at 25 °C the molar volume is about 9% larger.
• Mixing standard conditions: STP has been defined both as 101.325 kPa and as 100 kPa at 0 °C; state which one you use.

Frequently Asked Questions

What is the molar volume of a gas at STP?

22.414 L/mol at 0 °C and 101.325 kPa; 22.711 L/mol if STP is taken as 0 °C and 100 kPa.

What is the formula for molar volume?

V_m = RT ÷ P, with T in kelvin.

Is the molar volume the same for every gas?

For an ideal gas, yes. Real gases differ slightly, most at high pressure and low temperature.

How many moles are in 10 L of gas at STP?

About 0.4462 mol at 0 °C and 101.325 kPa.

in t | Temperature | °C | 0 | -273.15
in p | Pressure | kPa | 101.325 | 0.000001
in v | Volume of gas | L | 10 | 0
out vm | Molar volume | L/mol | 8.31446261815324 * (t + 273.15) / p | 3
out n | Amount of gas in the volume | mol | v / vm | 4
out nn | Number of molecules in the volume | - | n * 6.02214076e23 | 3