Topic 2 of 3
Use pV = nRT
Choose consistent units and determine a molar mass.
A-Level 9476 (2026-2027)
Convert the units before substituting
With R = 8.31 J mol-1 K-1, pressure is in Pa and volume in m3.
The ideal-gas equation is pV = nRT. It relates pressure p, gas volume V, amount n and absolute temperature T. With R = 8.31 J mol-1 K-1, use Pa and m3, since Pa m3 = J. A value of R with different units requires the matching pressure and volume units.
| Given quantity | Convert for SI substitution |
|---|---|
| 100 kPa | 100000 Pa |
| 250 cm3 | 250 × 10-6 m3 = 2.50 × 10-4 m3 |
| 1.00 dm3 | 1.00 × 10-3 m3 |
| 25.0 degrees C | 298.15 K; 298 K when consistent with the precision given |
Worked example
Find a gas molar mass
A 0.444 g sample occupies 250 cm3 at 100 kPa and 298 K. Treat it as ideal. Find its molar mass.
- Convert V to 2.50 × 10-4 m3 and p to 1.00 × 105 Pa.
- n = pV/RT = (1.00 × 105 × 2.50 × 10-4)/(8.31 × 298) = 0.0101 mol.
- M = m/n = 0.444/0.0101, retaining unrounded n during calculation.
M = 44.0 g mol-1 to three significant figures. The corresponding relative molecular mass Mr is 44.0 and has no units.
Combining n = m/M with the gas equation gives M = mRT/pV. Alternatively, with density ρ = m/V, M = ρRT/p. If density is in kg m-3 with SI R, the resulting molar mass is in kg mol-1; multiply by 1000 to obtain g mol-1.
A fixed gas sample also obeys p1V1/T1 = p2V2/T2, provided the amount is unchanged and the ideal approximation is suitable. Do not use a memorised room-temperature molar volume when the stated pressure or temperature differs.