Hydrogen, oxygen and carbon dioxide are very different molecules, yet at ordinary pressures they all obey one equation. The ideal gas model explains why, and also when the equation stops working.
An ideal gas obeys pV = nRT exactly. The kinetic model assumes the molecules are in rapid random motion, have negligible volume compared with the container, have no intermolecular forces, and collide elastically. Real gases behave most ideally at low pressure and high temperature, where the molecules are far apart and move fast. In pV = nRT use SI units: p in Pa, V in m3, T in K and R = 8.31 J K−1 mol−1. Rearranged with n = m ÷ M, the equation gives M = mRT ÷ pV, a way to find Mr of a gas or volatile liquid.
Change the temperature, volume and amount of gas in the simulator piston and watch the pressure respond. Double the temperature in kelvin at constant volume and the pressure doubles; halve the volume and it doubles again.
| Assumption | Fails when |
|---|---|
| molecules have negligible volume | high pressure: molecules are packed close, so their own volume matters |
| no forces between molecules | low temperature: slow molecules are held back by attractions; also polar or large molecules |
| collisions are elastic | (taken as true) |
| random, rapid motion | (taken as true) |
Almost every error in this section is a unit error. Convert everything to SI before you substitute.
| Quantity | SI unit | Convert |
|---|---|---|
| pressure, p | Pa | kPa × 103 |
| volume, V | m3 | dm3 × 10−3; cm3 × 10−6 |
| temperature, T | K | °C + 273 |
Four quick checks. Each correct answer earns XP and records this skill on your profile.
Which is an assumption of the kinetic theory of an ideal gas?
Under which conditions does a real gas behave most like an ideal gas?
In pV = nRT, what are the units of R?
A volume of 250 cm3 in m3 is:
Inject a known mass of a volatile liquid into a gas syringe held above its boiling point, and measure the volume of vapour. Then M = mRT ÷ pV.
Keep M in g mol−1 by leaving the mass in grams. And check your answer is sensible: an Mr of 0.058 or 58 000 for a simple liquid means a volume or pressure was not converted. A temperature in °C instead of K is the other classic slip.
Unlocks once the four checks above are done. Worth more XP, written to AS Paper 1 and Paper 2 standard.
What volume is occupied by 0.100 mol of an ideal gas at 25 °C and 101 kPa? (R = 8.31 J K−1 mol−1)
0.174 g of a volatile liquid forms 92.0 cm3 of vapour at 100 °C and 101 kPa. What is its Mr? (R = 8.31 J K−1 mol−1)
Ammonia deviates from ideal behaviour more than nitrogen at the same temperature and pressure. Why?
Why does a real gas deviate from ideal behaviour at very high pressure?
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