4.1 Gases: ideal, real and pV = nRT

Gas pressure is produced by gas particles colliding with the walls of their container. Each collision transfers momentum to the wall; the combined effect of many collisions over an area gives the measured pressure.

At constant temperature, reducing the container volume packs the particles into a smaller space. Wall collisions become more frequent, so pressure increases: pressure is inversely related to volume under this condition.

At constant volume, increasing temperature raises the particles' average kinetic energy. They move faster and collide with the walls more frequently and with greater effect, so pressure increases: pressure is directly related to temperature under this condition.

State the controlled variable with every relationship: the volume–pressure relationship requires constant temperature, while the temperature–pressure relationship requires constant volume. Do not treat either proportionality as an unrestricted rule when the condition changes.

An ideal gas is a model whose particles move rapidly and randomly, occupy negligible volume, exert no intermolecular attraction or repulsion, and collide elastically. Its temperature is linked to the particles' average kinetic energy.

Because the particles are treated as point-like and non-attracting, the model predicts gas behaviour using only measurable pressure, volume, temperature and amount. At constant pressure, heating gives the particles more kinetic energy and the volume increases so the collision effect on the walls remains consistent.

Real gases approach the model under suitable conditions but deviate at very high pressure or low temperature. Particles are then closer: attractions can pull particles inward and lower the measured wall pressure, while the particles' own volume reduces the free space available for movement.

Do not treat ‘ideal’ as the description of every real gas or forget which assumptions fail. Keep this card on model assumptions and their limits; the numerical use of pV = nRT, unit conversion and Mr calculations belong to the neighbouring quantitative objective.

Use the ideal-gas equation pV = nRT to connect pressure, volume, amount of gas and temperature. Identify the unknown and keep pressure, volume, amount and temperature consistent with the units required by the chosen gas constant.

Before substituting, convert pressure to Pa, volume to m³ and temperature to kelvin; keep the amount in mol. A value in kPa, cm³ or dm³ is not ready for direct use with the SI value of R, and Celsius must not be used as an absolute temperature.

Use an ordered calculation: write pV = nRT, rearrange for the unknown, audit units, substitute, calculate, and convert the final output only when needed. For molar mass, first find the amount from n = pV/RT, then divide mass by amount in moles.

Do not mix pressure, volume or temperature units, confuse mass with amount of substance, or use the wrong amount of gas. Keep this card on quantitative use of the ideal-gas equation; deviations from ideal behaviour belong to the neighbouring model-and-limitations objective.