Cambridge IAL Chemistry cheat sheet

ΔH(solution) = ΔH(lattice) + ΔH(hydration of cation) + ΔH(hydration of anion); use Born–Haber cycles to link lattice enthalpy, ionisation, electron affinity and atomisation.

Lattice enthalpy magnitude rises with higher ionic charge and smaller ionic radius; compare MgO with NaCl accordingly.

Entropy change: ΔS(total) = ΔS(system) − ΔH(system)/T; a reaction is feasible when ΔG = ΔH − TΔS < 0.

Rate equation is determined experimentally: rate = k[A]^m[B]^n, where m and n are orders, not stoichiometric coefficients.

Arrhenius: k = Ae^(−Ea/RT); ln k = ln A − Ea/(RT), so a plot of ln k against 1/T has gradient −Ea/R.

Kc uses equilibrium concentrations with powers from the balanced equation; Kp uses partial pressures p_i = mole fraction × total pressure.

Le Chatelier: raising pressure shifts equilibrium toward the side with fewer moles of gas; a catalyst changes rate but not Kc or Kp.

Brønsted–Lowry acid donates H⁺; conjugate base differs by one H⁺. pH = −log[H⁺]; for a weak acid Ka = [H⁺]²/[HA].

Buffer pH: pH = pKa + log([salt]/[acid]); buffer capacity is greatest when [salt] ≈ [acid], i.e. pH ≈ pKa.

Period 3 oxides: Na2O and MgO are basic, Al2O3 is amphoteric, SiO2 is acidic (giant covalent), P4O10, SO3 and Cl2O7 are acidic molecular oxides.

Reaction with water: Na2O gives NaOH, MgO is sparingly soluble giving Mg(OH)2, P4O10 gives H3PO4, SO3 gives H2SO4, Cl2O7 gives HClO4.

Group 2: thermal stability of carbonates and nitrates increases down the group as cation charge density falls; solubility of hydroxides increases down the group.

Group 2 sulfates become less soluble down the group (MgSO4 soluble, BaSO4 insoluble); BaCl2 solution tests for sulfate ions.

Group 17: oxidising power decreases down the group; reducing power of halide ions increases down the group.

Displacement: a halogen oxidises halide ions below it in the group, e.g. Cl2 + 2Br⁻ → 2Cl⁻ + Br2.

Silver halide precipitates: AgCl white, AgBr cream, AgI yellow; each is soluble in dilute ammonia in the order Cl > Br > I.

Transition metals: variable oxidation states, coloured complex ions, catalytic activity and paramagnetism arise from partially filled 3d orbitals.

Ligand substitution: [Cu(H2O)6]²⁺ (blue) + excess NH3 gives [Cu(NH3)4(H2O)2]²⁺ (deep blue); excess Cl⁻ gives green [CuCl4]²⁻.

Homologous series members share a general formula and similar reactions but show a gradual trend in physical properties as chain length grows.

Free-radical substitution of alkanes: initiation (UV splits Cl2), propagation (Cl• + CH4 → CH3• + HCl), termination (radicals combine).

Electrophilic addition to alkenes: the π bond attacks an electrophile; Markovnikov's rule places H on the carbon with more hydrogens.

Nucleophilic substitution: primary halogenoalkanes favour SN2, tertiary favour SN1; hydroxide in aqueous ethanol gives an alcohol.

Elimination with ethanolic KOH gives an alkene; substitution with aqueous KOH gives an alcohol from the same halogenoalkane.

Oxidation: primary alcohols give aldehydes then carboxylic acids, secondary give ketones, tertiary resist oxidation; acidified K2Cr2O7 turns orange to green.

Aldehydes reduce Tollens' reagent to a silver mirror and Fehling's solution to a red precipitate; ketones do neither.

Esterification: carboxylic acid + alcohol ⇌ ester + water, acid-catalysed and reversible; esters hydrolyse under acid or alkali.

Acyl chlorides react vigorously with alcohols, water and amines, releasing HCl; they are more reactive than carboxylic acids.

Titration: rinse burette with the titrant, pipette with the solution being measured; read the burette to the bottom of the meniscus at eye level.

Concordant titres agree within about 0.10 cm³; use the mean of concordant values for the calculation.

Moles = concentration (mol dm⁻³) × volume (dm³); convert cm³ to dm³ by dividing by 1000.

Percentage yield = (actual moles / theoretical moles) × 100; atom economy = (Mr of desired product / sum of Mr of reactants) × 100.

Uncertainty of a single reading is ± half the smallest scale division; percentage uncertainty = (uncertainty / measured value) × 100.

Qualitative tests: flame tests identify cations; adding dilute acid then BaCl2 confirms sulfate; AgNO3 with dilute HNO3 confirms halide.

Recrystallisation: dissolve in minimum hot solvent, cool to crystallise, filter under reduced pressure, wash with cold solvent.

Melting point comparison with literature values indicates purity; an impure solid melts over a range and below the true value.

When plotting graphs, label axes with quantity and unit, use a suitable scale, draw a line of best fit and read gradients over the largest interval.