States of Matter
Unit 5 tests gas laws, the ideal gas equation, kinetic molecular theory, deviations of real gases, and the properties of liquids.
Core rules
- Boyle's law (PV constant at fixed T), Charles's law (V/T constant at fixed P), Avogadro's law (V/n constant) and Dalton's law of partial pressures apply to non-reacting gases.
- Ideal gas equation: PV = nRT, with R = 0.0821 L atm K⁻¹ mol⁻¹ or 8.314 J K⁻¹ mol⁻¹.
- Graham's law: r₁/r₂ = √(M₂/M₁).
- Kinetic molecular theory assumes negligible molecular volume and no intermolecular forces; real gases deviate at high pressure and low temperature.
- Van der Waals equation: (P + an²/V²)(V − nb) = nRT; a measures attraction, b measures excluded volume.
- Liquids show vapour pressure (dependent on temperature), surface tension and viscosity.
Worked example
2 L of O₂ at 1 atm and 3 L of N₂ at 2 atm are transferred at constant temperature into a 5 L vessel. Using P₁V₁ = P₂V₂: p(O₂) = 1 × 2/5 = 0.4 atm; p(N₂) = 2 × 3/5 = 1.2 atm. By Dalton's law, total pressure = 0.4 + 1.2 = 1.6 atm.
Traps
- Always convert temperature to kelvin.
- Graham's law compares rates, not times; the lighter gas effuses faster.
- At the Boyle temperature, Z = 1 over a range of pressures, but the gas is still not ideal.
- Vapour pressure depends only on temperature for a given liquid, not on the liquid's surface area.
- Critical temperature is the highest temperature above which a gas cannot be liquefied by pressure alone.