S1.5
Ideal gases
3 SL (SL 1.5.1-1.5.4)
Unverified
← View on the mapParent topic: Models of the particulate nature of matter
Guiding question
Guiding questionHow does the model of ideal gas behaviour help us to predict the behaviour of real gases?
The one big idea
The ideal gas model assumes particles of negligible volume with no intermolecular forces and perfectly elastic collisions. PV = nRT quantifies the relationship between pressure, volume, temperature and amount for gases that approximate this model.
What this rests on
Our editorial judgement.The dependencies in this section are this site’s own assessment of what a sub-topic rests on. They have notbeen verified by a chemistry teacher and are not part of the official IB guide. By contrast, section 8 (Linking questions) reproduces the IB’s own wording verbatim.
- EditorialS1.1 Introduction to the particulate nature of matterThe ideal gas model is kinetic molecular theory made quantitative.
- EditorialS1.4 Counting particles by mass: The molePV = nRT contains n, the mole.
What rests on this
Core concepts that must be mastered
- The ideal gas model(1.5.1)An ideal gas consists of particles of negligible volume with no intermolecular forces, undergoing perfectly elastic collisions. These are assumptions — no real gas is truly ideal — but they are a good approximation under many conditions. The three assumptions let you derive a simple equation of state: if particles have no volume, the container volume is all free space; if there are no intermolecular forces, the particles do not attract or repel each other between collisions; if collisions are elastic, no kinetic energy is lost. Temperature is the measure of average kinetic energy, so a higher temperature means faster particles and more frequent, harder collisions with the walls — which is pressure.
- Real gas deviations(1.5.2)Real gases deviate from ideality, particularly at low temperature and high pressure. At low temperature, the particles are moving slowly enough that intermolecular forces have time to act — the "no forces" assumption breaks down, and particles attract each other, reducing the pressure below the ideal prediction (the gas occupies less volume than PV = nRT predicts). At high pressure, the particles are forced so close together that their own volume becomes a non-negligible fraction of the container volume — the "negligible volume" assumption breaks down, and the gas takes up more space than the ideal model predicts (the gas occupies more volume than PV = nRT predicts). No mathematical treatment of deviations is required, but you must be able to explain qualitatively which assumption fails and why, and in which direction the real gas deviates from ideality. Helium and hydrogen deviate least because they have the weakest intermolecular forces and the smallest particles.
- Molar volume(1.5.3)The molar volume of an ideal gas is constant at a specified temperature and pressure: one mole of any ideal gas occupies the same volume under the same conditions. The data booklet gives the molar volume at STP. This follows directly from Avogadro's law (S1.4): if equal volumes contain equal numbers of molecules, then one mole of molecules always occupies the same volume at a given T and P. This is a powerful simplification — it means that at STP, 1 mol of H₂ gas and 1 mol of CO₂ gas occupy the same volume despite having very different molecular masses. You should be able to investigate the temperature–pressure–volume relationship for a fixed mass of gas and analyse the resulting graphs (e.g. plotting P vs V at constant T gives a curve, while P vs 1/V gives a straight line). The names of the individual gas laws (Boyle's law, Charles's law) are not assessed — only the combined relationship matters.
- The ideal gas equation(1.5.4)The equation of state PV = nRT and the combined gas law P₁V₁/T₁ = P₂V₂/T₂ let you solve quantitative problems. In PV = nRT, P is pressure in Pa, V is volume in m³, n is amount in mol, R is the ideal gas constant (in the data booklet), and T is temperature in kelvin. Use SI units for volume and pressure — this is the most common source of calculation errors. If a question gives volume in dm³, convert to m³ (1 dm³ = 10⁻³ m³); if pressure is in kPa, convert to Pa (1 kPa = 10³ Pa). The combined gas law applies when the amount of gas is fixed and only T, P, and V change. You can also use PV = nRT to find the molar mass of a gas from experimental data: if you measure the mass, pressure, volume, and temperature of a gas sample, you can calculate n from PV = nRT, and then M = m/n. This is a powerful technique for identifying an unknown gas.
- How this sub-topic connectsIdeal gases connect to intermolecular forces (S2.2): the deviation of real gases from ideality is explained by the same London forces, dipole–dipole forces, and hydrogen bonding that determine boiling points and solubility. The gas equation connects to stoichiometry (R2.1) when gas volumes are involved in reacting ratio calculations, and to equilibrium (R2.3) when Kc expressions involve gaseous species. There is no HL extension — the ideal gas model is shared SL and HL ground.
Quantitative non-negotiables
- Apply PV = nRT and the combined gas law P₁V₁/T₁ = P₂V₂/T₂ using SI units for volume (m³) and pressure (Pa).
- Convert between Celsius and kelvin.
- Explain when and why real gases deviate from ideal behaviour.
Common failure modes
M-24 — One mole of any gas is 24 dm³.
Confidence: verified
Why it’s wrong: Only at RTP (~298 K, 100 kPa).
Correction: Use PV = nRT, or the molar volume specified in the data booklet for the stated conditions.
What "HL standard" actually looks like
No HL extension. Ideal gases are shared SL and HL. The names of individual gas laws (Boyle's, Charles's) are not assessed — only the combined relationship and PV = nRT.
Linking questions
Official IB.The questions in this section are the IB’s own linking questions, reproduced verbatim from the guide. They are not this site’s editorial judgement — see section 3 for that distinction.
- Official IB
Avogadro's law applies to ideal gases. Under what conditions might the behaviour of a real gas deviate most from an ideal gas?
- Official IB
Under comparable conditions, why do some gases deviate more from ideal behaviour than others?
- Official IBwording unverified against the guide
Graphs can be presented as sketches or as accurately plotted data points. What are the advantages and limitations of each representation?
- Official IB
To what extent can intermolecular forces explain the deviation of real gases from ideal behaviour?
- Official IB
How does the molar volume of a gas vary with changes in temperature and pressure?
1 further official linking question target a Tool, Inquiry or Nature of Science strand and are not drawn as edges on the map:
Editorial The decision to surface these off-graph questions here is our editorial judgement — the IB does not prescribe where they should appear.
- Official IB
How can the ideal gas law be used to calculate the molar mass of a gas from experimental data?
Bridge: GCSE → IB HL
Derived. These are the bridge items tagged to this sub-topic— places where the GCSE model gets redefined, genuinely new territory, or carry-over strengths. The tagging is this site’s editorial judgement.