Gas Laws & the Kinetic Molecular Theory
Boyle, Charles, Gay-Lussac, and the ideal gas law — plus the kinetic molecular theory that explains WHY gases behave the way they do.
Kinetic molecular theory — the model behind the laws
The KMT explains gas behavior with five postulates:
- Gas particles are POINT MASSES with negligible volume vs the container.
- No intermolecular attractions or repulsions.
- Random straight-line motion with constant kinetic energy until collision.
- Collisions are ELASTIC — no kinetic energy lost.
- Average kinetic energy is proportional to absolute temperature (Kelvin).
These assumptions describe an ideal gas. Real gases deviate slightly, especially at very high pressure and very low temperature, but at typical lab conditions the ideal model is excellent.
Key consequence: at the same temperature, all gases have the same average kinetic energy. Lighter gas particles must therefore move FASTER (since KE = ½mv²).
The classical gas laws
Each describes the relationship between two variables while holding the others constant. Temperature MUST be in Kelvin: T(K) = T(°C) + 273.
Boyle's Law (constant T, n)
P₁V₁ = P₂V₂
Pressure and volume are inversely proportional. Double the pressure, halve the volume. A balloon shrinks when you squeeze it. A scuba diver's lungs would expand to dangerous size if they held their breath while ascending.
Charles's Law (constant P, n)
V₁/T₁ = V₂/T₂
Volume is directly proportional to absolute temperature. Heat a balloon, it expands. Cool it (with liquid nitrogen, say), it shrinks dramatically. Reminder: KELVIN ONLY.
Gay-Lussac's Law (constant V, n)
P₁/T₁ = P₂/T₂
Pressure proportional to absolute temperature. Heating a sealed can dangerously increases its pressure — risk of explosion.
Combined gas law (constant n)
(P₁V₁)/T₁ = (P₂V₂)/T₂
Combines all three. Use when more than one of P, V, T changes.
Ideal gas law — the master equation
Include moles (n) and you get the most powerful gas equation:
PV = nRT
where R = 0.0821 L·atm/(mol·K). Use:
- P in atm, V in liters, n in moles, T in Kelvin.
- Find any one variable if you know the other three.
Example: 0.500 mol of gas at 273 K in a 10.0 L container has what pressure?
P = nRT/V = (0.500)(0.0821)(273)/10.0 = 1.12 atm.
Standard Temperature and Pressure (STP)
STP is defined as 0 °C (273 K) and 1 atm. At STP, 1 mole of ANY ideal gas occupies exactly 22.4 L. This is the molar volume shortcut.
This is hugely useful. Example: how many liters of CO₂ at STP from 2.0 mol CaCO₃ via CaCO₃ → CaO + CO₂?
Mole ratio 1:1, so 2.0 mol CO₂. Volume = 2.0 × 22.4 = 44.8 L. ✓
Dalton's Law of Partial Pressures
In a mixture of gases, each gas exerts its own pressure (partial pressure) independent of the others. Total pressure = sum of partial pressures:
P_total = P₁ + P₂ + P₃ + …
And each partial pressure relates to mole fraction:
P_i = (mole fraction of i) × P_total
Example: Earth's atmosphere is 78% N₂ by mole at 1.00 atm. So P_N₂ = 0.78 × 1.00 = 0.78 atm. P_O₂ = 0.21 × 1.00 = 0.21 atm.
Graham's Law of Effusion
Lighter gases effuse (escape through a small hole) faster than heavier gases. The rate is inversely proportional to the square root of molar mass:
rate₁ / rate₂ = √(M₂ / M₁)
This is why helium balloons deflate within a day — He (M=4) escapes much faster than the larger N₂ and O₂ molecules in air.