NZ Scholarship Chemistry cheat sheet

Amount relation: n = m/M, n = cV (V in L), n = V/22.4 L mol⁻¹ for gases at STP; Avogadro constant N_A = 6.022 × 10²³ mol⁻¹, so N = nN_A.

Ideal gas law pV = nRT with R = 8.314 J K⁻¹ mol⁻¹; for fixed amount, p₁V₁/T₁ = p₂V₂/T₂ (T in kelvin). Limiting reagent: compare n/stoichiometric coefficient for each reactant.

Equilibrium: K_c expression uses only species with variable concentration (pure solids/liquids omitted); reaction quotient Q compared with K predicts direction - Q < K forward, Q > K reverse, Q = K at equilibrium.

Le Chatelier rules: adding reactant shifts forward; increasing pressure shifts toward fewer gas moles; raising temperature shifts in the endothermic direction and changes K itself; a catalyst changes rate only, never K or position.

Acids/bases: pH = −log₁₀[H₃O⁺]; K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 298 K; weak acid K_a = [H₃O⁺][A⁻]/[HA], with approximations valid only when dissociation is small (<5%).

Buffer decision rule: pH = pK_a + log([A⁻]/[HA]); buffer capacity is maximal when [A⁻] ≈ [HA], i.e. pH ≈ pK_a; a buffer resists pH change by consuming added acid or base.

Thermochemistry: q = mcΔT; ΔH°_rxn = ΣΔH°_f(products) − ΣΔH°_f(reactants); Hess's law allows summing step enthalpies; ΔG° = ΔH° − TΔS° and spontaneity requires ΔG < 0.

Electrochemistry: E°_cell = E°_cathode − E°_anode (reduction potentials); ΔG° = −nFE°_cell with F = 96 485 C mol⁻¹; oxidation occurs at the anode in every cell type (sign conventions differ between galvanic and electrolytic cells).

Redox/stoichiometry discipline: balance atoms then charge (half-reaction method in acid or base), identify oxidation-number changes to locate oxidant and reductant, and check significant figures against the least precise given datum.

VSEPR decision rule: count electron domains (lone pairs included) to assign shape; lone-pair repulsion order lp–lp > lp–bp > bp–bp, so NH₃ is trigonal pyramidal and H₂O bent, not tetrahedral.

Intermolecular forces ranked for boiling point: ion–dipole > hydrogen bonding (H bonded to N, O, F) > dipole–dipole > London dispersion (increases with electron count and surface area); branching lowers boiling point by reducing surface contact.

Hybridisation from steric number: 2 = sp (linear, 180°), 3 = sp² (trigonal planar, 120°), 4 = sp³ (tetrahedral, 109.5°); delocalised π systems (benzene) require sp² carbons and resonance description.

Organic functional-group reactivity: alkenes undergo electrophilic addition; alcohols oxidise to aldehydes/ketones then carboxylic acids; carboxylic acids + alcohols give esters (acid catalyst, reversible); amines act as bases/nucleophiles; acyl chlorides react faster than carboxylic acids.

Isomer counting: structural isomers differ in connectivity; stereoisomers divide into enantiomers (non-superimposable mirror images, chiral centre with four different groups) and diastereomers including E/Z geometric isomers about C=C.

Reaction-mechanism conventions: curly arrows show electron-pair movement from electron-rich to electron-poor site; primary haloalkanes favour S_N2 (one step, inversion), tertiary favour S_N1 (carbocation intermediate); rate laws follow the slow step.

Titration/analysis calculations: at equivalence n(acid)/n(base) equals the stoichiometric ratio; use c₁V₁/coefficient₁ = c₂V₂/coefficient₂; back-titration subtracts unreacted excess from initial amount.

Spectroscopy use: IR identifies functional groups (broad O–H ~3300 cm⁻¹, C=O ~1700 cm⁻¹), ¹³C NMR counts distinct carbon environments, ¹H NMR gives integration (H ratio), chemical shift (environment) and splitting n+1 (neighbouring H); mass spectra give molecular ion and fragmentation.

Error and data handling: distinguish random from systematic error; report uncertainty to one significant figure and match decimal places; percentage yield = actual/theoretical × 100; purity from melting-point range or titration data.

Quantitative justification standard: derive the expression symbolically before substituting numbers, state assumptions (ideal behaviour, complete dissociation, closed system, standard conditions) and show that the approximation is valid.

Multi-step problem chain: convert mass → amount → limiting reagent → equilibrium or enthalpy/electrochemistry quantity → final answer with units; carry unrounded values through intermediate steps and round only at the end.

Compare-and-contrast prompts require a criterion: rank species by a stated property (e.g. acidity by conjugate-base stability, boiling point by intermolecular force strength) and justify each rank with structural evidence.

Equilibrium shifts vs K changes: only temperature alters K; concentration, pressure and volume changes alter Q or partial pressures and hence position, not K - an explicit distinction examiners reward.

Thermodynamic vs kinetic control: a reaction may be thermodynamically favourable (ΔG < 0) yet slow if E_a is high; catalysts lower E_a without changing ΔG or K, and enzymes show specificity and saturation.

Solubility and precipitation: K_sp = [cation]^a[anion]^b; a precipitate forms when the ion product exceeds K_sp; the common-ion effect suppresses solubility and is predicted by Q vs K_sp comparison.

Redox feasibility: a reaction is spontaneous when E°_cell > 0; under non-standard conditions use the Nernst equation E = E° − (RT/nF)ln Q, and note that changing concentrations can reverse the predicted direction.

Structure–property argumentation: link bonding (covalent network, ionic lattice, metallic, molecular) to melting point, conductivity (mobile charge carriers required) and solubility ('like dissolves like', plus lattice-energy vs hydration-energy competition).

Answer quality in extended responses: define terms precisely, quote data with units and uncertainties, address the question's command word (explain, justify, evaluate, compare), and evaluate limitations of a model or method rather than only describing it.