States of matter and properties of substances
This domain combines gas calculations with phase behaviour and solution properties. The exam typically supplies a set of conditions and asks for one derived quantity, so unit discipline matters more than memorising formulas.
The ideal gas law and mixtures
pV = nRT with R = 0.0821 atm·L·mol⁻¹·K⁻¹ or 8.314 J·mol⁻¹·K⁻¹. Convert to kelvin and match the pressure and volume units to the R you choose. Dalton's law: p_total = Σp_i with p_i = x_i·p_total. Graham's law gives effusion rates inversely proportional to √M.
Real gases
The van der Waals equation (p + an²/V²)(V − nb) = nRT corrects a for attraction and b for molecular volume. Real gases approach ideality at high temperature and low pressure; deviation is largest near condensation.
Phase changes and phase diagrams
Heating curves show latent-heat plateaus: q = m·c·ΔT within one phase, q = m·ΔH_fus or m·ΔH_vap at a transition. On a p–T diagram the triple point is where all three phases coexist, the critical point terminates the liquid–vapour line, and the slope of the solid–liquid line shows whether the solid or the liquid is denser (negative for water). Sublimation occurs below the triple-point pressure.
Solubility and colligative properties
Like dissolves like: polar solutes in polar solvents. Colligative properties depend only on the number of dissolved particles: ΔTb = Kb·m, ΔTf = −Kf·m (water: Kb = 0.512, Kf = 1.86 °C·kg·mol⁻¹), π = MRT, and Raoult's law p = x_solvent·p°. Electrolytes need the van 't Hoff factor i.
Worked example
18.0 g of glucose (M = 180 g/mol, so 0.100 mol) in 500 g of water gives molality 0.100/0.500 = 0.200 mol/kg. ΔTb = 0.512 × 0.200 = 0.102 °C, so it boils at 100.10 °C. ΔTf = 1.86 × 0.200 = 0.372 °C, so it freezes at −0.372 °C. Glucose is a non-electrolyte, so i = 1.
Traps
- Adding the solute mass to the solvent mass when computing molality.
- Using i = 1 for NaCl (i = 2) or CaCl₂ (i = 3).
- Assuming complete dissociation at every concentration.
- Reading a phase diagram with the axes swapped.