B.3 Gas laws

Amount of gas

• Number of molecules N = n N_A, with N_A = 6.02 × 10²³ mol⁻¹.
• Temperature in kelvin: T / K = θ / °C + 273. Always use kelvin in gas law calculations.

Ideal gas equation

• pV = nRT = NkT, with R = 8.31 J K⁻¹ mol⁻¹ and k = 1.38 × 10⁻²³ J K⁻¹.
• Use SI units: pressure in Pa and volume in m³ (1 dm³ = 10⁻³ m³).

Special cases for a fixed mass of gas

• Constant temperature (Boyle): pV is constant.
• Constant pressure (Charles): V / T is constant.
• Constant volume (pressure law): p / T is constant.

Kinetic model of an ideal gas

• Molecules are in constant random motion and their volume is negligible compared with the volume of the gas.
• There are no intermolecular forces except during collisions, and the collisions are elastic.
• The average kinetic energy of a molecule is proportional to the absolute temperature: Ek = (3/2)kT.
• For a monatomic ideal gas the internal energy is U = (3/2)nRT.

Real gases

A real gas behaves most like an ideal gas at low pressure and high temperature. At high pressure and low temperature the molecular volume and the intermolecular forces matter.