Key Points

Ideal gas equation: $PV = nRT$ ; $R = 0.0821$ L·atm/(mol·K); always use Kelvin
Graham's law: $r_1/r_2 = \sqrt{M_2/M_1}$ ; lighter gas diffuses faster; never invert the ratio
Molecular speed order: $v_{mp} < v_{avg} < v_{rms}$ (formulas: $\sqrt{2RT/M} < \sqrt{8RT/\pi M} < \sqrt{3RT/M}$ )
Compressibility factor: $Z < 1$ → attraction dominates; $Z > 1$ → repulsion dominates; $H_{2}$ and He always $Z > 1$
Liquid state with temperature: vapour pressure ↑, surface tension ↓, viscosity ↓