Summary Cheat Sheet

PV = nRT — applies to ideal gases; T must be in Kelvin.
Boyle: PV = k (const. T, n); Charles: V/T = k (const. P, n); Gay-Lussac: P/T = k (const. V, n).
Avogadro: 1 mol ideal gas = 22.4 L at STP (0°C, 1 atm).
Dalton: P_total = Σp_i; each gas acts independently; p_i = x_i × P_total.
Graham: r_{1}/r_{2} = √( $M_{2}$ / $M_{1}$ ); lighter gas diffuses faster.
Molecular speeds: v_rms > v_avg > v_mp (ratio 1.224 : 1.128 : 1).
v_rms = √(3RT/M); v_avg = √(8RT/πM); v_mp = √(2RT/M); use R = 8.314 J/(mol·K), M in kg/mol.
Average KE = (3/2)RT per mole — depends ONLY on temperature, not on gas type.
Real gas: van der Waals (P + $an^{2}$ / $V^{2}$ )(V − nb) = nRT; 'a' = attraction, 'b' = excluded volume.
Z = PV/nRT; Z = 1 (ideal); Z < 1 (attraction dominates); Z > 1 (repulsion/size dominates).
$H_{2}$ and He: always Z > 1 (negligible 'a' — b correction dominates always).
T_B = a/(Rb) — Boyle temperature; gas behaves ideally over wide pressure range.
T_c = 8a/(27Rb); P_c = a/(27 $b^{2}$ ); V_c = 3b; P_cV_c/T_c = 3R/8.
Liquefaction requires T < T_c; Joule-Thomson effect cools gas below inversion temperature.
Vapour pressure increases with T; surface tension and viscosity (liquid) decrease with T.
Boiling point = T where vapour pressure = external pressure; lower at high altitude.
Intermolecular force strength: London < dipole-dipole < hydrogen bonding.
Density of ideal gas: d = PM/(RT); molar mass: M = dRT/P.