NCEA L3 Chemistry cheat sheet

Equilibrium constant Kc: for aA + bB ⇌ cC + dD, Kc = [C]^c[D]^d / ([A]^a[B]^b); pure solids and liquids are omitted because their concentration is constant.

Reaction quotient Q compared with Kc predicts direction: Q < Kc shifts right (forward), Q > Kc shifts left (reverse), Q = Kc means the system is at equilibrium.

Le Chatelier's principle: a system at equilibrium opposes change. Adding reactant shifts right; increasing pressure shifts toward the side with fewer gas moles; raising temperature favours the endothermic direction.

A catalyst increases the rates of both forward and reverse reactions equally, so equilibrium position and Kc are unchanged; only the time to reach equilibrium decreases.

Weak acid Ka and pH: Ka = [H3O+][A-]/[HA]; for a weak monoprotic acid, [H3O+] ≈ sqrt(Ka × c), so pH ≈ ½(pKa − log c).

Buffer solutions contain a weak acid and its conjugate base (or weak base and conjugate acid); pH ≈ pKa + log([base]/[acid]) (Henderson–Hasselbalch).

Strong acid–strong base titration equivalence pH = 7 at 25 °C; weak acid–strong base equivalence pH > 7 because the conjugate base hydrolyses; weak base–strong acid equivalence pH < 7.

Solubility product Ks: for AgCl(s) ⇌ Ag+(aq) + Cl-(aq), Ks = [Ag+][Cl-]; a precipitate forms when the ion product exceeds Ks.

Entropy and spontaneity: ΔG = ΔH − TΔS; a reaction is spontaneous when ΔG < 0, so endothermic reactions can be spontaneous if ΔS is sufficiently positive at high temperature.

Oxidation numbers: free element 0; monatomic ion equals its charge; oxygen usually −2 (peroxide −1); hydrogen usually +1 (hydride −1); sum equals overall charge.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons (decrease in oxidation number); oxidant is reduced, reductant is oxidised.

Balancing redox in acid: balance atoms other than O and H, add H2O to balance O, add H+ to balance H, then add electrons and equalise electron loss and gain.

Standard electrode potentials E°: the more positive E° is the stronger oxidant; a spontaneous cell has E°cell = E°cathode − E°anode > 0.

Electrolytic cells use external voltage to drive non-spontaneous reactions; oxidation occurs at the anode and reduction at the cathode in both galvanic and electrolytic cells.

Faraday's law: moles of electrons = Q/F where F = 96 485 C mol-1; mass deposited = (Q × M)/(n × F).

Functional group tests: alkenes decolourise bromine water; aldehydes reduce Tollens' reagent (silver mirror) and Fehling's solution; carboxylic acids liberate CO2 from carbonate.

Amines are basic because the nitrogen lone pair accepts H+; amides are much weaker bases because the lone pair is delocalised into the carbonyl group.

Esterification: carboxylic acid + alcohol ⇌ ester + water, acid-catalysed and reversible; hydrolysis of esters is base-promoted (saponification) or acid-catalysed.

Rate law from data: compare experiments where one reactant concentration changes while others are constant; doubling rate when concentration doubles means first order in that reactant.

Overall order is the sum of individual orders; the rate constant k has units that depend on overall order (e.g. mol-1 L s-1 for second order overall).

Half-life of a first-order reaction is constant: t½ = ln2/k ≈ 0.693/k, independent of initial concentration.

Arrhenius equation k = A e^(−Ea/RT); plotting ln k against 1/T gives a straight line of slope −Ea/R.

Collision theory: reaction requires collisions with sufficient energy (≥ Ea) and correct orientation; a catalyst provides an alternative pathway with lower Ea.

Rate-determining step is the slowest step in a mechanism and controls the overall rate; the rate law reflects only species involved up to and including that step.

Bond enthalpy and ΔH: ΔH = Σ(bonds broken) − Σ(bonds formed); using average bond enthalpies gives an estimate because values are averaged over different molecules.

Hess's law: enthalpy change is independent of route, so ΔH can be found by combining known equations with their ΔH values, reversing signs when equations are reversed.

Structural isomerism includes chain, position, and functional group isomers; stereoisomerism includes geometric (cis/trans about C=C) and optical (chiral carbon with four different groups) isomerism.

Bonding and properties: ionic lattices have high melting points and conduct when molten or aqueous; molecular covalent substances have low melting points and generally do not conduct.

Electronegativity difference guides bond type: roughly < 0.4 nonpolar covalent, 0.4–1.7 polar covalent, > 1.7 largely ionic (a rule of thumb, not a strict boundary).

Polar molecules require polar bonds and an asymmetric shape; CO2 is nonpolar (linear, dipoles cancel) while H2O is polar (bent, dipoles add).

Intermolecular forces increase in the order dispersion < dipole–dipole < hydrogen bonding; hydrogen bonds occur when H is bonded to N, O, or F and interacts with a lone pair on N, O, or F.

Lewis structures: count valence electrons, form single bonds, complete octets, then place remaining electrons as lone pairs; formal charge = valence electrons − nonbonding electrons − ½ bonding electrons.

VSEPR shapes: 2 electron domains linear; 3 trigonal planar; 4 tetrahedral (109.5°); 4 with one lone pair trigonal pyramidal (~107°); 4 with two lone pairs bent (~104.5°).

Periodic trends: atomic radius decreases across a period and increases down a group; ionisation energy generally increases across a period and decreases down a group.

Transition metal ions form coloured complexes because d-orbital splitting causes absorption of visible light; ligands donate electron pairs to form coordinate bonds.

Kc and Kp depend only on temperature; changing concentration or pressure shifts position but leaves Kc unchanged at constant temperature.