Key ideas
The gas laws describe how pressure, volume, temperature and amount of gas depend on each other. For most problems the ideal gas law PV = nRT covers all of them at once.
- With R = 0.08206 L·atm/(mol·K), use pressure in atm, volume in liters and temperature in kelvin. With R = 8.314 J/(mol·K), use pascals and cubic meters.
- Boyle: P₁V₁ = P₂V₂ at constant temperature. Charles: V₁ ÷ T₁ = V₂ ÷ T₂ at constant pressure, with T in kelvin.
- Dalton’s law says a mixture’s pressure is the sum of the partial pressures; each is the mole fraction times the total.
- Graham’s law: lighter gases effuse faster, with rate proportional to 1 ÷ √M.
Key equations
PV = nRTP₁V₁ = P₂V₂ (Boyle)V₁ ÷ T₁ = V₂ ÷ T₂ (Charles)P_total = P₁ + P₂ + …rate₁ ÷ rate₂ = √(M₂ ÷ M₁)
Worked example
What is the pressure of 2.0 mol of gas at 300 K in a 10.0 L vessel? P = nRT ÷ V = 2.0 × 0.08206 × 300 ÷ 10.0 = 4.9 atm. By Graham’s law, hydrogen (2.0 g/mol) effuses √(32 ÷ 2.0) = 4 times faster than oxygen (32 g/mol).
Common mistakes
- Using °C instead of kelvin. Add 273.15 before substituting.
- Mixing the units of R with the units of pressure and volume.
- Applying the ideal gas law without noting that the amount of gas changed between two states.
Practice
Test yourself with practice questions on this topic: Gases