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Learn9701Paper 2 · AS Level Structured QuestionsStates of matterIdeal gases and lattices
States of matter · Subtopic 1 of 1

Ideal Gases and Lattices

An ideal gas has particles of negligible volume, no intermolecular forces and perfectly elastic collisions. It obeys pV=nRTpV=nRT with pp in Pa, VV in m³, TT in K and R=8.31 J K−1mol−1R=8.31\ \text{J K}^{-1}\text{mol}^{-1}. Real gases deviate at high pressure (particle volume matters) and low temperature (intermolecular forces matter); they behave most ideally at high temperature and low pressure. Solids can be giant ionic, giant molecular (covalent), simple molecular or metallic lattices.

Cambridge 9701 Paper 1Cambridge 9701 Paper 2Edexcel YCH11 WCH11AQA 7405 Paper 1≈ 40 minRevision 1 · updated 2026-10-30
Section 1 of 14

Learning objectives

  • State the assumptions of the kinetic theory for an ideal gas.
  • Use pV=nRTpV=nRT, including to find MrM_r.
  • Explain when real gases deviate from ideal behaviour.
  • Describe the four lattice types and their properties.
Pause and think

Why does a bicycle tyre feel harder on a hot day?

Section 2 of 14

Core idea

Start hereOne equation for every gas

Hydrogen, oxygen, steam, even a volatile liquid's vapour: at moderate conditions they all obey the same equation, whatever the molecules are.

The big idea

An ideal gas has no intermolecular forces and negligible particle volume, so pV=nRTpV=nRT. Real gases approach this at high temperature and low pressure.

1. Finding MrM_r from a gas

MrM_r from the ideal gas equation
  1. pV=nRTpV=nRT
    Ideal gas equation.
  2. n=mMrn=\frac{m}{M_r}
    Moles from mass.
  3. pV=mMrRTpV=\frac{m}{M_r}RT
    Substitute.
  4. Mr=mRTpVM_r=\frac{mRT}{pV}
    Rearrange.
Worked exampleVolatile liquid

0.150 g of liquid vaporises to 52.0 cm³ at 101 kPa and 100 °C.

Goal
MrM_r.
Strategy
Convert units, then substitute.
  1. V=5.20×10−5 m3, T=373 K, p=1.01×105 PaV=5.20\times10^{-5}\ \text{m}^3,\ T=373\ \text{K},\ p=1.01\times10^5\ \text{Pa}
    SI units.
  2. Mr=0.150×8.31×3731.01×105×5.20×10−5M_r=\frac{0.150\times8.31\times373}{1.01\times10^5\times5.20\times10^{-5}}
    Substitute.
  3. =88.5=88.5
    Evaluate.
AnswerMr≈88M_r\approx88.
✓ CheckCould be ethyl ethanoate, Mr=88M_r=88 ✓.
Key takeawayWhen gases misbehave High pressure: particle volume matters. Low temperature: attractions matter. Polar or large molecules deviate most.
Pause and think

Why does the gas syringe method give a slightly high MrM_r if some liquid doesn't vaporise?

Summary

  • pV=nRTpV=nRT in SI.
  • Mr=mRT/pVM_r=mRT/pV.
  • Ideal at high TT, low pp.
Key words
Ideal gas
A model gas with no intermolecular forces and negligible particle volume.
Kelvin
Absolute temperature: °C + 273.
Lattice
A regular 3D arrangement of particles.
HistoryBoyle and Charles. Robert Boyle (1662) found pVpV is constant at fixed temperature; Jacques Charles (1787) found V∝TV\propto T. The ideal gas equation combines them with Avogadro's law.
Fun factHot-air balloons. Heating the air in a balloon by about 100 °C lowers its density by around a quarter, enough to lift a basket and passengers.
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