STPM Chemistry 962 cheat sheet

Atomic number Z = protons; mass number A = protons + neutrons; isotopes differ in neutron count only.

Relative atomic mass Ar = Σ(abundance × isotope mass) / Σabundance; use fractional abundances that sum to 1.

Mass spectrometry: m/z peaks give isotope masses; peak heights give relative abundances used in Ar calculation.

Bohr energy levels: E = −RH/n²; photon energy ΔE = hf = hc/λ; RH = 2.18 × 10⁻¹⁸ J per atom.

Ionisation energy decreases down a group (larger radius, shielding) and generally increases across a period (higher Zeff).

Successive ionisation energies jump sharply when a new noble-gas core is breached, revealing group number.

Quantum numbers: n (shell), l = 0…n−1 (s,p,d,f), m = −l…+l, ms = ±½; Pauli forbids identical sets.

Orbitals hold max 2 electrons; s=1 orbital, p=3, d=5, f=7; each orbital fills singly (Hund) before pairing.

Aufbau order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p (4s fills before 3d).

Cr = [Ar]3d⁵4s¹ and Cu = [Ar]3d¹⁰4s¹ are exceptions; half-filled and full d subshells favoured.

Ions: remove 4s electrons before 3d when forming cations (e.g. Fe²⁺ = [Ar]3d⁶).

Blocks: s (groups 1–2), p (13–18), d (transition metals), f (lanthanides/actinides).

Atomic radius decreases across a period (rising Zeff) and increases down a group (extra shells, shielding).

Electronegativity rises across a period and falls down a group; F is highest on the Pauling scale.

First ionisation energy trend mirrors electronegativity but has dips at group 13 (np¹) and group 16 (np⁴).

Metallic character decreases left to right; oxides shift from basic (Na₂O) to amphoteric (Al₂O₃) to acidic (SO₃).

Ionic bonding: electron transfer, lattice energy ∝ (q₁q₂)/r; higher charges and smaller ions give stronger lattices.

Covalent bond strength rises with bond order (triple > double > single) and falls with bond length.

VSEPR: electron pairs repel; lone pairs repel more, compressing bond angles (CH₄ 109.5°, NH₃ 107°, H₂O 104.5°).

Hybridisation: steric number 2 = sp, 3 = sp², 4 = sp³; multiple bonds count as one region.

Polarity: bond dipoles cancel in symmetric shapes (CO₂ linear, CCl₄ tetrahedral) giving non-polar molecules.

Hydrogen bonding requires H bonded to N, O or F; explains high boiling points of H₂O, HF, NH₃.

London dispersion forces increase with electron count/surface area; stronger than dipole forces for large molecules.

Ideal gas assumptions: negligible particle volume and no intermolecular forces; real gases deviate at high pressure and low temperature.

Mole: n = m/M; Avogadro constant NA = 6.02 × 10²³ mol⁻¹; molar gas volume 24 dm³ mol⁻¹ at r.t.p.

Empirical formula from mass or percentage composition; molecular formula = empirical × n where n = M/empirical mass.

Balanced equation gives mole ratio; convert masses to moles, apply ratio, convert back.

Limiting reagent: divide moles of each reactant by its coefficient; smallest quotient limits.

Percentage yield = (actual/theoretical) × 100; atom economy = (M of desired product / ΣM reactants) × 100.

Concentration c = n/V (mol dm⁻³); dilution: c₁V₁ = c₂V₂.

Titration: n(acid)/n(base) from equation; use c × V in dm³ consistently.

Combustion analysis: mass CO₂ → moles C; mass H₂O → 2 × moles H; remainder is oxygen.

Ideal gas equation: pV = nRT; R = 8.31 J K⁻¹ mol⁻¹; T in kelvin (K = °C + 273).

Combined gas law: p₁V₁/T₁ = p₂V₂/T₂ for a fixed mass of gas.

Kinetic theory: average KE ∝ T; pV = ⅓Nm⟨c²⟩; mean speed increases with √(T/M).

Graham's law: rate of effusion/diffusion ∝ 1/√M (lighter gas diffuses faster).

Dalton's law: total pressure = sum of partial pressures; pᵢ = mole fraction × P_total.

Real gas deviation: attractive forces lower pressure; finite volume raises it; greatest at high p and low T.

Phase changes: melting/boiling absorb energy (latent heat) without temperature change at constant pressure.

Critical temperature: above it a gas cannot be liquefied by pressure alone.

Exothermic: ΔH negative (heat released); endothermic: ΔH positive (heat absorbed).

q = mcΔT; ΔH = −q/n (per mole) with correct sign convention.

Hess's law: ΔH is path-independent; sum enthalpy steps to get the target reaction.

Bond enthalpy method: ΔH = Σ(bonds broken) − Σ(bonds formed).

Standard enthalpy of formation ΔHf°: ΔHr = ΣΔHf°(products) − ΣΔHf°(reactants).

Calorimetry: bomb calorimetry gives ΔU; constant-pressure gives ΔH; ΔH = ΔU + ΔnRT for gases.

Entropy: ΔS positive on increasing disorder (gas > liquid > solid; more moles of gas).

Gibbs free energy: ΔG = ΔH − TΔS; spontaneous when ΔG < 0; at equilibrium ΔG = 0 and ΔG° = −RT ln K.

Kc = [products]^x/[reactants]^y using coefficients as powers; Kp uses partial pressures.

Le Chatelier: system shifts to oppose change in concentration, pressure or temperature.

Catalysts do not change K or position of equilibrium; they only speed attainment.

Temperature change alters K: exothermic reactions have K decreasing as T rises; endothermic K rises with T.

Reaction quotient Q: if Q < K reaction goes forward; Q > K goes backward; Q = K at equilibrium.

Kp = Kc(RT)^Δn where Δn = moles gaseous products − reactants.

For a reversed reaction K' = 1/K; for a doubled equation K'' = K².

Haber process: N₂ + 3H₂ ⇌ 2NH₃ exothermic and fewer moles gas; high p and moderate T favour yield.

pH = −log[H⁺]; pOH = −log[OH⁻]; pH + pOH = 14 at 25 °C; Kw = 1 × 10⁻¹⁴.

Strong acid: [H⁺] = c × (number of ionisable H); weak acid: Ka = [H⁺]²/c so [H⁺] = √(Ka·c).

pKa = −log Ka; smaller pKa = stronger acid; conjugate base strength inversely related.

Buffer (weak acid + salt): pH = pKa + log([salt]/[acid]) (Henderson–Hasselbalch).

Buffer capacity is greatest when [acid] ≈ [salt]; resists pH change on adding small acid or base.

Solubility product Ksp = [cation]^a[anion]^b; precipitation occurs when ionic product Q > Ksp.

Common-ion effect lowers solubility of a sparingly soluble salt.

Titration curves: strong–strong equivalence pH 7; weak acid–strong base >7; indicator pKa near equivalence pH.

Rate = change in concentration per unit time; units mol dm⁻³ s⁻¹.

Rate law rate = k[A]^m[B]^n; orders determined experimentally, not from stoichiometry.

Zero order: rate independent of [A]; first order: rate ∝ [A]; half-life first order t½ = ln2/k.

Arrhenius: k = Ae^(−Ea/RT); ln k = ln A − Ea/RT; plot ln k vs 1/T gives slope −Ea/R.

Collision theory: reaction requires sufficient energy (≥ Ea) and correct orientation.

Catalyst lowers Ea, increasing fraction of successful collisions; homogeneous vs heterogeneous.

Rate-determining step: slowest elementary step governs overall rate law.

Increasing temperature raises both collision frequency and fraction with E ≥ Ea; effect is dominated by the latter.

Oxidation = loss of electrons (OIL); reduction = gain (RIG); oxidation numbers track electron transfer.

Standard electrode potential E°: more positive = stronger oxidising agent; Ecell° = E°cathode − E°anode.

Spontaneity: ΔG° = −nFE°; positive E°cell gives negative ΔG° and a feasible reaction.

Electrolysis: cathode attracts cations (reduction); anode attracts anions (oxidation); Faraday's law n(e⁻) = It/F.

Electrolytic vs galvanic: electrolysis uses external supply; galvanic cells generate current.

Transition metals: variable oxidation states, coloured ions, catalytic activity, complex formation.

Ligand substitution and complex geometry (octahedral, tetrahedral, square planar); coordination number.

d–d transitions give colour; splitting of d orbitals in ligand field; colour depends on ligand and oxidation state.

Homologous series: same functional group, differ by CH₂; general formula and similar chemical properties.

Isomerism: structural (chain, position, functional) and stereoisomerism (geometric, optical).

Alkanes: free-radical substitution with halogens (initiation, propagation, termination).

Alkenes: electrophilic addition (HBr, Br₂, H₂O); Markovnikov's rule for unsymmetrical addition.

Alcohols: oxidation to aldehyde (primary, mild) or carboxylic acid (strong oxidant); secondary to ketone; tertiary resistant.

Nucleophilic substitution: haloalkanes with OH⁻/CN⁻/NH₃; SN1 vs SN2 depends on substrate and conditions.

Acyl chlorides, esters, amides: nucleophilic acyl substitution; esterification is reversible with acid catalyst.

Aromatic: electrophilic substitution; benzene stability from delocalised π system (resonance).

Chromatography: separation by differential affinity between mobile and stationary phases; Rf = distance spot / distance solvent front.

TLC/paper: identify by Rf and visualisation (UV, iodine, ninhydrin for amino acids).

Gas chromatography: retention time identifies components; peak area quantifies.

Infrared: functional-group identification; O–H broad ~3300, C=O ~1700, C–H ~2900 cm⁻¹.

Mass spectrometry: molecular ion M⁺ gives molar mass; fragmentation pattern aids structure.

NMR: chemical shift (environment), integration (number of H), splitting (neighbouring H, n+1 rule).

Atomic absorption/emission: quantitative metal analysis via characteristic wavelengths and calibration.

Titration and gravimetric analysis: quantitative methods; use standard solutions and indicators or precipitation.

Record raw data to instrument precision; do not round intermediate values; report to correct significant figures.

Plot graphs with labelled axes, units and line of best fit; gradient gives derived constants (e.g. k, Ea).

Calibration curves: plot known standards, interpolate unknowns; check linearity range.

Safety: risk assessment identifies hazards (corrosive, flammable, toxic) and controls (fume hood, goggles, gloves).

Waste disposal: segregate halogenated organics, heavy metals, acids/bases; never pour down sink without neutralisation.

Heating flammable liquids: use water bath, not open flame; keep away from ignition sources.

Reproducibility: repeat measurements, average concordant results, identify and exclude outliers.

Uncertainty: combine as percentage errors; final result uncertainty from smallest scale division and instrument error.