Units, the Constant R, and Molar Volume

Choosing Your Units Carefully

Before any calculation with PV = nRT, you need to put all quantities into the same unit system. With R = 8.314 J/(mol·K), you must use:

• P in pascals (Pa) — watch out, 1 bar = 1.0×10^5 Pa and 1 atm ≈ 1.013×10^5 Pa,
• V in cubic meters (m³) — watch out, 1 L = 1.0×10^-3 m³,
• T in kelvins (K),
• n in moles (mol).

Molar Volume

The molar volume Vm is the volume occupied by one mole of gas, under given pressure and temperature conditions:

Vm = V / n = R*T / P

Under so-called standard conditions (0°C, i.e. 273.15 K, and 1 atm, i.e. 101,325 Pa), the molar volume of an ideal gas is about 22.4 L/mol, a classic value worth knowing. At 20°C (293 K) and 1 atm, this molar volume is a bit larger, about 24.0 L/mol, because a warmer gas takes up more room at the same pressure.

Vm(0 deg C, 1 atm) = R*273.15 / 101325 = 0.02241 m3/mol = 22.4 L/mol

What It's Used For

Molar volume lets you go directly from an amount of substance to a volume (or the other way around) without going back through the whole equation, as long as the pressure and temperature remain the same as those used to calculate Vm.

V = n * Vm

Common Mistake

Don't confuse 22.4 L/mol (valid only at 0°C and 1 atm) with a universal constant: molar volume changes as soon as the temperature or pressure changes. Always check the conditions under which it is given before using it.