Boyle's law states that, at constant temperature:

P ∝ 1/V. Pressure is inversely proportional to volume at fixed temperature — squeeze the gas and pressure rises.

In PV = nRT, the temperature T must be in:

kelvin. The gas laws use absolute temperature; kelvin (K = °C + 273) is required.

A gas at constant pressure is heated from 300 K to 600 K. Its volume:

doubles. V ∝ T at constant pressure (Charles), so doubling the absolute temperature doubles the volume.

Which is an assumption of kinetic molecular theory?

Collisions are elastic (no energy lost). Ideal-gas particles collide elastically, have negligible volume and no intermolecular forces, with KE ∝ temperature.

Real gases deviate most from ideal behaviour at:

high pressure, low temperature. When compressed and cold, particle volume and attractions become significant, breaking the ideal assumptions.

Using PV = nRT, if you know P, V and T you can find:

the number of moles of gas. Rearranging gives n = PV/RT — and from moles you can get mass or molar mass.

A container holds nitrogen at 60 kPa and oxygen at 20 kPa. The total pressure is:

80 kPa. By Dalton's law the total pressure is the sum of the partial pressures: 60 + 20 = 80 kPa.

Gas X has four times the molar mass of gas Y. Compared with Y, gas X diffuses:

half as fast. Rate ∝ 1/√M; √4 = 2, so X diffuses at half the rate of Y.

Gases

The gas laws, the ideal gas equation, and why real gases misbehave

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Practise the full question bank:

The gas laws

A gas responds to pressure, volume and temperature in fixed ways, each captured by a law (temperature always in kelvin, K = °C + 273).

Boyle's law: at constant temperature, pressure is inversely proportional to volume (P ∝ 1/V) — squeeze a gas and its pressure rises. Charles's law: at constant pressure, volume is proportional to temperature (V ∝ T) — heat a gas and it expands. Pressure (Gay-Lussac) law: at constant volume, pressure ∝ T. Together they give the combined gas law, P₁V₁/T₁ = P₂V₂/T₂.

The ideal gas equation

All the laws roll into one: PV = nRT, where n is the moles of gas and R the gas constant (8.31 J K⁻¹ mol⁻¹). It links all four quantities, so given any three you can find the fourth — including the moles (and hence mass or molar mass) of a gas from measurements you can take in a lab.

PV = nRT(T in kelvin, R = 8.31 J K⁻¹ mol⁻¹)the equation of state for an ideal gas

Kinetic molecular theory

The gas laws are explained by picturing a gas as tiny particles in constant random motion. The kinetic molecular theory assumes the particles have negligible volume, exert no forces on each other, collide elastically (no energy lost), and have an average kinetic energy proportional to the temperature.

From those assumptions the behaviour falls out: pressure is just particles hitting the walls, and raising temperature raises their speed, which is why hot gases push harder.

Why real gases deviate

No gas is truly ideal. Real gas particles do take up space and do attract one another, so real gases deviate from PV = nRT most at high pressure and low temperature — exactly where the particles are forced close together and moving slowly enough for attractions to matter. Under everyday conditions the ideal equation is an excellent approximation.

When "ideal" breaks down

A gas behaves most ideally when it is hot and at low pressure (particles far apart, fast, attractions negligible). It behaves least ideally when cold and compressed — near the point where it would condense to a liquid.

A worked example

Worked example

A gas occupies 2.0 L at 300 K and 100 kPa. What volume does it occupy at 400 K and the same pressure?

Pressure is constant, so use Charles's law: V₁/T₁ = V₂/T₂.Only volume and temperature change.
V₂ = V₁ × T₂/T₁ = 2.0 × 400/300.Rearrange for the new volume; temperatures already in kelvin.
V₂ = 2.67 L.Heating at constant pressure expands the gas in proportion to absolute temperature.

About 2.67 L — the gas expands as V ∝ T at constant pressure.

Dalton's law of partial pressures

In a mixture of gases that do not react, each gas exerts the pressure it would if it were alone — its partial pressure — and the total pressure is simply the sum of them. A gas's partial pressure is its mole fraction (its share of the total moles) multiplied by the total pressure.

This is why, in the Haber process or in the air you breathe, each component pushes independently, and why collecting a gas over water means correcting for the water vapour's own partial pressure.

P_total = P₁ + P₂ + P₃ + …Pₐ = xₐ × P_totalPₐ = partial pressure of gas A · xₐ = mole fraction of A

Graham's law of diffusion

Lighter gas molecules move faster, so they diffuse and effuse more quickly. Graham's law states that the rate of diffusion is inversely proportional to the square root of the molar mass — so a gas four times heavier diffuses half as fast. It is the reason ammonia (light) meets hydrogen chloride (heavier) nearer the HCl end of a tube.

rate ∝ 1 / √Mrate₁ / rate₂ = √(M₂ / M₁)M = molar mass; lighter gases diffuse faster

Practice questions

6 questions · 20 marks · full working on every one

Try each one on paper first, then open the working. The marks are shown where they are actually awarded, because that is where they are actually lost.

Short questions

4 · 9 marks

Two marks each, in the style of the short-question section of the paper. Answer in two or three lines.

SQ1[2 marks]

State Boyle's law and give its equation.

Model answer

At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure: PV = constant (P₁V₁ = P₂V₂).

Examiner tip. Boyle's law: pressure up, volume down, at constant temperature.

SQ2[3 marks]

A gas occupies 500 cm³ at a pressure of 100 kPa. Calculate its volume at 250 kPa, at constant temperature.

Model answer

P₁V₁ = P₂V₂ → 100 × 500 = 250 × V₂ → V₂ = 50000 ÷ 250 = 200 cm³.

Examiner tip. Rearrange P₁V₁ = P₂V₂ for the unknown; higher pressure gives a smaller volume.

SQ3[2 marks]

State the assumptions of the ideal gas model (any two).

Model answer

Gas particles have negligible volume; there are no forces between them; collisions are perfectly elastic; they move randomly (any two).

Examiner tip. Real gases deviate most at high pressure and low temperature, where these assumptions fail.

SQ4[2 marks]

A gas mixture contains 0.25 mol of helium and 0.75 mol of argon at a total pressure of 200 kPa. Calculate the partial pressure of helium.

Model answer

Mole fraction of He = 0.25 ÷ (0.25 + 0.75) = 0.25. Partial pressure = 0.25 × 200 = 50 kPa.

Examiner tip. Partial pressure = mole fraction × total pressure.

Long questions

2 · 11 marks

Theory and numerical together, as they appear in the long-question section.

LQ1[6 marks]

The ideal gas equation is PV = nRT (R = 8.31 J K⁻¹ mol⁻¹).

State what each symbol represents. [2]
Calculate the volume occupied by 0.50 mol of an ideal gas at 300 K and a pressure of 100 000 Pa. [3]
State one condition under which a real gas behaves most like an ideal gas. [1]

Mark scheme

P = pressure, V = volume, n = number of moles[1]
R = gas constant, T = temperature in kelvin[1]
V = nRT ÷ P = (0.50 × 8.31 × 300) ÷ 100000[1]
= 1246.5 ÷ 100000[1]
V = 0.0125 m³ (12.5 dm³)[1]
Low pressure (and/or high temperature)[1]

P,V,n,R,T defined; V ≈ 0.0125 m³; ideal behaviour at low pressure / high temperature.

Examiner tip. Always use temperature in kelvin (°C + 273) and SI units in PV = nRT.

LQ2[5 marks]

This question is about gases and their behaviour.

State Graham's law of diffusion. [1]
Oxygen (M = 32) and hydrogen (M = 2) diffuse from the same point. Calculate how many times faster hydrogen diffuses. [2]
Explain why real gases deviate most from ideal behaviour at high pressure and low temperature. [2]

Mark scheme

Rate of diffusion is inversely proportional to the square root of the molar mass[1]
rate(H₂)/rate(O₂) = √(32/2) = √16[1]
= 4 times faster[1]
At high pressure the molecules are close, so their own volume and the forces between them matter[1]
at low temperature they move slowly, so intermolecular attractions have a bigger effect — both break the ideal assumptions[1]

Graham's law: rate ∝ 1/√M; hydrogen diffuses 4× faster; real gases deviate at high P/low T where molecular volume and intermolecular forces matter.

Examiner tip. Ideal-gas assumptions (no volume, no forces) fail when molecules are crowded or slow.