The complete lecture — gases come alive in the live panel as you read. Scroll down; the animation keeps pace, and you can drive the gas simulator yourself.
1 — The gaseous state
Gas particles are far apart and move freely, so a gas has no fixed shape or volume, is highly compressible, has low density, and exerts pressure in all directions.
A gas's state is fixed by P, V, T and n.
2 — Pressure of a gas
- Pressure — force per unit area from molecules hitting the walls.
Units1 atm = 760 mmHg = 101325 Pa = 1.013 bar
3 — Boyle's law
Boyle's law (constant T)V ∝ 1/P · PV = constant · P₁V₁ = P₂V₂
worked
2 dm³ at 1 atm → at 4 atm: (1)(2)=(4)V → 0.5 dm³
4 — Charles's law
Charles's law (constant P)V ∝ T · V/T = constant · V₁/T₁ = V₂/T₂ (T in K)
Absolute zero = −273 °C = 0 K. Always use kelvin.
5 — Gay-Lussac's & Avogadro's laws
- Gay-Lussac — constant V: P ∝ T.
- Avogadro — constant T,P: V ∝ n; 1 mole gas = 22.4 dm³ at STP.
6 — The ideal-gas equation
Ideal gas equationPV = nRT · R = 0.0821 dm³·atm·K⁻¹·mol⁻¹
All the gas laws combine here. Move the sliders in the live panel: shrink the box (lower V) or heat it (higher T) and watch the pressure climb.
7 — Dalton's law of partial pressures
Dalton's lawP_total = P₁ + P₂ + … · Pᵢ = xᵢ · P_total
8 — Graham's law of diffusion
Graham's lawrate ∝ 1/√M · r₁/r₂ = √(M₂/M₁)
9 — Kinetic Molecular Theory
- Random, continuous, straight-line motion.
- Negligible molecular volume; no intermolecular forces.
- Elastic collisions; average K.E. ∝ absolute temperature.
10 — Temperature & molecular speed
RMS speedc_rms = √(3RT / M)
11 — Real gases
van der Waals(P + an²/V²)(V − nb) = nRT
12 — Liquefaction of gases
- Critical temperature — above it a gas can't be liquefied by pressure alone.
13 — Worked numericals
combined
2 dm³, 1 atm, 273 K → 2 atm, 546 K: V₂ = 2 × ½ × 2 = 2 dm³
partial pressure
2 mol N₂ + 3 mol O₂, total 5 atm → P_O₂ = (3/5)(5) = 3 atm
14 — Exam recap
- Gas properties; pressure & units; STP.
- Boyle, Charles, Gay-Lussac, Avogadro.
- PV = nRT & the combined gas law.
- Dalton's & Graham's laws.
- KMT postulates; K.E. ∝ T.
- Real gases & van der Waals.