IB Chemistry — Structure 1.5: Ideal Gases

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What temperature unit goes into PV = nRT?

This sub-topic is examined identically at SL and HL. An ideal gas is a simplified model of a gas that obeys PV = nRT exactly. Real gases follow it closely under everyday conditions but deviate when squeezed hard or cooled a lot.

👆 Toggle the gas law · drag the sliders · solve PV = nRT

1. The ideal gas model S1.5.1–2

The model pictures a gas as many tiny particles in constant random motion. Four assumptions make the maths simple:

Gas particles in constant random motion

Negligible volume — the particles themselves take up almost no space compared with the container.

No intermolecular forces — particles don't attract or repel each other.

Elastic collisions — no kinetic energy is lost when particles collide.

Random motion — particles move in straight lines in all directions; average KE ∝ temperature (K).

Real gases deviate most at high pressure (particles are forced close, so their volume and attractions matter) and low temperature (slow particles feel attractions more).

2. The gas laws S1.5.3

For a fixed amount of gas, changing one property changes another. (You don't need the law names for IB — just the relationships and their graphs.) Toggle between them and drag the slider:

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Volume

—

Pressure

—

Boyle: at constant temperature, P × V is constant — halve the volume and the pressure doubles (an inverse curve).

3. The ideal gas equation S1.5.4

PV = nRT, where R = 8.31 J K⁻¹ mol⁻¹ (in the data booklet). Use SI units: P in pascals (Pa), V in cubic metres (m³), T in kelvin (K). Choose what to solve for and type the other three:

PV = nRT solver · R = 8.31 J K⁻¹ mol⁻¹

Solve for

Pressure P (Pa)

Volume V (m³)

Amount n (mol)

Temperature T (K)

Comparing the same gas under two conditions? Use the combined gas law: P₁V₁ / T₁ = P₂V₂ / T₂ (T in kelvin).

Learn Ideal Gases step by step

Free interactive mini-lessons: short screens, worked examples and quick checks. Pick your exam board to open its course map, then tap L on this topic:

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Common mistakes examiners see

What temperature unit goes into PV = nRT?✗ Celsius. ✓ Kelvin. Convert first (K = °C + 273). Using °C is one of the most common errors.

When do real gases deviate most from ideal behaviour?✗ At high temperature and low pressure. ✓ At low temperature and high pressure — particles are close and slow, so their volume and attractions can no longer be ignored.

If you halve the volume of a gas at constant temperature, the pressure…✗ halves. ✓ doubles — P and V are inversely proportional at constant T (PV = constant).

What are the correct SI units for PV = nRT with R = 8.31?✗ kPa, dm³, °C. ✓ P in Pa, V in m³, T in K. (1 kPa = 1000 Pa; 1 dm³ = 1×10⁻³ m³.)

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Ideal Gases