WBCHSE HS Chemistry cheat sheet

Bohr model: angular momentum quantised as mvr = nh/2π; energy of H-like atom Eₙ = −13.6 Z²/n² eV; radius rₙ = 0.529 n²/Z Å.

de Broglie: λ = h/mv = h/p; Heisenberg uncertainty: Δx·Δp ≥ h/4π, so trajectory and simultaneous position-momentum are incompatible.

Quantum numbers: n = 1,2,3…; l = 0 to n−1 (s,p,d,f); mₗ = −l to +l; mₛ = ±½; orbitals in a shell = n², electrons = 2n².

Aufbau order by (n+l) rule; for equal (n+l) the lower n fills first: 4s before 3d, 6s before 4d before 5d before 4f.

Hund's rule: degenerate orbitals are singly occupied with parallel spins before pairing; explains paramagnetism of O₂ and exchange-energy stability of half-filled shells.

Bond order = ½(N_bonding − N_antibonding); O₂ has bond order 2 yet is paramagnetic because the two π* electrons are unpaired.

VSEPR: lone-pair–lone-pair > lone-pair–bond-pair > bond-pair–bond-pair repulsion; CH₄ 109.5°, NH₃ 107°, H₂O 104.5°, SF₄ see-saw, ClF₃ T-shaped.

Hybridisation from steric number: 2 → sp (linear, 180°), 3 → sp² (120°), 4 → sp³ (109.5°), 5 → sp³d, 6 → sp³d²; multiple bonds count as one electron domain.

Polarity: μ = q × d (1 D = 3.336 × 10⁻³⁰ C m); CO₂ μ = 0 (linear, cancels) while H₂O μ ≈ 1.85 D; bond enthalpy rises with bond order (C–C 348, C=C 614, C≡C 839 kJ/mol).

Ideal gas: PV = nRT with R = 8.314 J K⁻¹ mol⁻¹ = 0.0821 L atm K⁻¹ mol⁻¹; Dalton's law P_total = ΣPᵢ; Graham's law r₁/r₂ = √(M₂/M₁).

van der Waals equation: (P + an²/V²)(V − nb) = nRT; 'a' measures attractive forces, 'b' the excluded volume; Z = PV/nRT < 1 below Boyle temperature.

Critical constants: T_c = 8a/27Rb, P_c = a/27b², V_c = 3b; compressibility factor at critical point Z_c = 3/8 = 0.375.

First law: ΔU = q + w; work done on the system w = −P_extΔV; for reversible isothermal expansion w = −nRT ln(V₂/V₁); ΔH = ΔU + Δn_gRT.

Enthalpy of reaction from Hess's law: ΔH = ΣΔH_f(products) − ΣΔH_f(reactants); bond-dissociation route gives the same value.

Entropy: ΔS = q_rev/T; ΔS_fusion and ΔS_vaporisation positive; ΔS_universe = ΔS_system + ΔS_surroundings ≥ 0 for a spontaneous change.

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

Kirchhoff: ΔH(T₂) = ΔH(T₁) + ΔC_p(T₂ − T₁); Cp − Cv = R for an ideal gas; for solids and liquids Cp ≈ Cv.

Maxwell distribution: fraction of molecules with speed v given by f(v) ∝ v² exp(−Mv²/2RT); most probable speed √(2RT/M) < average √(8RT/πM) < rms √(3RT/M).

Law of mass action: for aA + bB ⇌ cC + dD, K_c = [C]^c[D]^d / [A]^a[B]^b; K_p = K_c(RT)^Δn, Δn = moles gaseous products − reactants.

Reaction quotient Q compared with K: Q < K forward shift, Q > K reverse shift, Q = K at equilibrium; K depends only on temperature.

Le Chatelier: raising pressure shifts toward fewer gas moles; raising temperature favours the endothermic direction; a catalyst changes rate only, never K.

Exothermic synthesis (N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ/mol): high pressure and moderate temperature (~700 K) with Fe catalyst give good yield.

Degree of dissociation α and K for a weak electrolyte: K = Cα²/(1 − α); for α ≪ 1, α = √(K/C).

K_p for dissociation of PCl₅: with initial pressure P and degree α, K_p = α²P/(1 − α²); Δn = +1 so K_p > K_c.

Relationship of related equilibria: reversing gives 1/K; halving coefficients gives √K; adding two reactions multiplies their K values.

Le Chatelier and inert gas: adding inert gas at constant volume has no effect; at constant pressure it dilutes and shifts toward more gas moles.

K_w = [H⁺][OH⁻] = 10⁻¹⁴ at 298 K; pH + pOH = 14; pH = −log[H⁺]; for a strong acid pH = −log C, for a strong base pH = 14 + log C.

Weak acid: [H⁺] = √(K_a·C); pH = ½(pK_a − log C); weak base [OH⁻] = √(K_b·C); degree of hydrolysis h = √(K_w/K_a·C) for salt of weak acid and strong base.

Buffer (Henderson–Hasselbalch): pH = pK_a + log([salt]/[acid]); basic buffer pOH = pK_b + log([salt]/[base]); maximum buffering at pH = pK_a.

Solubility product: for AₓB_y, K_sp = xˣyʸ s^(x+y); e.g. AgCl K_sp = s², Ag₂CrO₄ K_sp = 4s³; precipitation when ionic product exceeds K_sp.

Titration curves: strong acid–strong base equivalence pH = 7; weak acid–strong base > 7; weak base–strong acid < 7; indicator range must straddle the steep part (phenolphthalein 8.3–10, methyl orange 3.1–4.4).

Oxidation number rules: free element 0; O usually −2 (peroxide −1); H usually +1 (hydride −1); sum equals charge; Mn in KMnO₄ is +7, Cr in K₂Cr₂O₇ is +6.

Balancing in acidic medium: add H₂O to balance O, then H⁺ to balance H, then electrons; in basic medium add OH⁻ and H₂O instead of H⁺.

Equivalent mass: oxidising/reducing agent = molar mass / number of electrons transferred per formula unit; KMnO₄ in acid = M/5, in neutral = M/3, in alkaline = M/1.

Rate law: rate = k[A]^m[B]^n; order = m + n (experimental), molecularity is a whole number from the mechanism; order may be zero or fractional.

First order: k = (2.303/t) log(a/(a − x)); t₁/₂ = 0.693/k independent of initial concentration; zero order t₁/₂ = a/2k.

Arrhenius: k = A e^(−Ea/RT); log(k₂/k₁) = (Ea/2.303R)(1/T₁ − 1/T₂); a 10 K rise roughly doubles rate for Ea ≈ 50 kJ/mol.

Collision theory: rate ∝ Z·e^(−Ea/RT); only molecules with energy ≥ Ea and proper orientation react; catalyst lowers Ea, raising the fraction of effective collisions.

Half-life and fraction remaining: after n half-lives, fraction left = (½)ⁿ; for first order, time to 99.9% completion is ~10 t₁/₂.

Physisorption: van der Waals forces, ΔH ≈ −20 kJ/mol, multilayer, reversible, no activation energy; chemisorption: covalent bonds, ΔH ≈ −200 kJ/mol, monolayer, often irreversible.

Freundlich isotherm: x/m = k·P^(1/n), 0 < 1/n < 1; log(x/m) = log k + (1/n) log P gives a straight line; Langmuir gives a limiting monolayer.

Colloids: Tyndall scattering, Brownian motion, electrophoresis; lyophilic sols are reversible and stabilised by solvation; lyophobic sols need electrolytes and coagulate by Hardy–Schulze rule (higher charge, more effective).

Raoult's law: P_solution = x_solvent·P°_solvent; relative lowering ΔP/P° = x_solute; positive deviation when solute–solvent forces are weaker (ethanol + acetone).

Elevation of boiling point: ΔT_b = K_b·m; depression of freezing point: ΔT_f = K_f·m; m = molality = moles solute per kg solvent; K_f water = 1.86 K kg mol⁻¹.

Osmotic pressure: π = CRT = (n/V)RT; for electrolytes multiply by van 't Hoff factor i; isotonic solutions have equal π at the same temperature.

van 't Hoff factor i = observed colligative effect / calculated; i > 1 for dissociation (NaCl i ≈ 2), i < 1 for association (benzoic acid in benzene i ≈ ½).

Molar mass from colligative data: M = K_f·w_solute·1000 / (ΔT_f·w_solvent); this method suits non-volatile solutes and gives number-average molar mass for polymers.

Henry's law: p = K_H·x; solubility of gas falls as temperature rises and rises with pressure; explains why CO₂ escapes from warm soft drinks.

Azeotropes: minimum-boiling (ethanol–water, positive deviation) and maximum-boiling (HNO₃–water, negative deviation); neither can be separated by simple distillation.

Colligative properties depend on particle number, not identity: 0.1 m NaCl gives nearly twice the ΔT_f of 0.1 m glucose.

Nernst equation: E = E° − (0.0591/n) log Q at 298 K; for a cell E_cell = E_cathode − E_anode; E°_cell = (0.0591/n) log K.

Standard hydrogen electrode has E° = 0.00 V by convention; species with higher E° is reduced (cathode), the other is oxidised (anode).

ΔG° = −nFE° and ΔG° = −RT ln K; 1 F = 96500 C/mol; maximum electrical work = −ΔG.

Conductance: Λ = κ/c; molar conductivity Λ_m = 1000κ/M; for strong electrolytes Λ_m = Λ°_m − A√c (Debye–Hückel–Onsager); for weak electrolytes α = Λ_m/Λ°_m and K_a = cα²/(1 − α).

Kohlrausch's law: Λ°_m for an electrolyte is the sum of limiting ionic conductivities; used to find Λ°_m of weak electrolytes such as acetic acid.

Faraday's laws: mass deposited m = (Q/F)(M/z) = (It/F)(M/z); 1 mol electrons deposits 1 mol Ag but only ½ mol Cu.

Galvanic cell: anode oxidation (negative electrode), cathode reduction (positive electrode); electrons flow through the external wire from anode to cathode.

Electrolysis: products depend on discharge potentials; concentrated NaCl brine gives Cl₂ at the anode and H₂ + NaOH at the cathode; CuSO₄ with inert electrodes gives O₂ and Cu.

Corrosion: rusting requires both O₂ and moisture; sacrificial anodes (Zn, Mg) protect iron because they are more easily oxidised.

Group 15: N₂ inert due to triple bond; NH₃ is a Lewis base; HNO₃ is a strong oxidiser; P shows +3 and +5; white P is more reactive than red P.

Group 16: O, S, Se, Te, Po; H₂O has high b.p. from hydrogen bonding; H₂S is a weak acid; SO₂ bleaches by reduction, Cl₂ by oxidation.

Group 17: F₂, Cl₂, Br₂, I₂; oxidising power F₂ > Cl₂ > Br₂ > I₂; bond dissociation energy of F₂ is anomalously low; HF is a weak acid, HCl strong.

Group 18: noble gases are monatomic with very high ionisation energy; Xe forms XeF₂, XeF₄, XeF₆ with F₂ under specific conditions; He has the lowest boiling point.

Interhalogens and pseudohalides: ClF₃ (T-shaped), BrF₅ (square pyramidal), ICl (polar); pseudohalide ions CN⁻, SCN⁻, N₃⁻ behave like halides.

Oxoacids of chlorine: HClO < HClO₂ < HClO₃ < HClO₄ in acid strength; oxidising power falls as oxygen count rises (HClO strongest oxidiser).

Inert-pair effect: heavier p-block elements show oxidation state n − 2 more readily; e.g. Pb(II) more stable than Pb(IV), Bi(III) more stable than Bi(V).

Allotropes: diamond, graphite, fullerenes, graphene for carbon; rhombic and monoclinic sulphur; graphite conducts because of delocalised π electrons, diamond does not.

3d series: Sc to Zn; variable oxidation states arise from similar 3d and 4s energies; Mn shows +2 to +7, Cr shows +2, +3, +6, Fe +2 and +3.

Colour of transition-metal ions arises from d–d transitions; requires partly filled d orbitals, so Zn²⁺ and Cu⁺ are colourless (Cu²⁺ is blue).

Magnetic moment μ = √(n(n+2)) BM where n = unpaired electrons; Fe³⁺ (d⁵) has 5 unpaired spins, μ ≈ 5.92 BM.

Lanthanoid contraction: ionic radius decreases from La to Lu because 4f electrons poorly shield the nucleus; causes Zr/Hf similarity and Y³⁺ ≈ Ho³⁺.

Common oxidising agents: KMnO₄ (purple, Mn +7), K₂Cr₂O₇ (orange, Cr +6); Cr₂O₇²⁻ in acid turns green Cr³⁺ with reducing agents.

Lanthanoids show mainly +3 state; Ce⁴⁺ and Eu²⁺ are exceptions; actinoids show wider range of oxidation states and greater radioactivity.

Catalytic uses: Fe in Haber process, V₂O₅ in contact process, Ni in hydrogenation, Pt/Rh in catalytic converters; transition metals adsorb reactants and provide variable oxidation states.

Alloy and colour: alloying changes properties (steel, brass); interstitial alloys form when small atoms occupy holes in the metal lattice.

Coordination number is the number of donor atoms bonded to the central metal ion; common values 2 (linear), 4 (tetrahedral or square planar), 6 (octahedral).

Nomenclature: name ligands alphabetically with prefixes di, tri, tetra, bis; anionic complex ends in -ate; charge of complex = oxidation state of metal + ligand charges.

Isomerism: geometrical (cis/trans in square planar and octahedral), optical (chiral complexes), ionisation, hydrate, linkage and coordination isomerism.

Crystal field splitting: Δ_o = 10Dq; strong-field ligands (CN⁻, CO) give low-spin, weak-field (I⁻, Br⁻, H₂O) give high-spin; spectrochemical series: I⁻ < Br⁻ < Cl⁻ < F⁻ < H₂O < NH₃ < en < CN⁻ < CO.

CFSE and colour: absorption of light excites electrons across Δ_o; [Cu(H₂O)₆]²⁺ is blue, [Cu(NH₃)₄]²⁺ deep blue because Δ changes with ligand.

EAN rule (18-electron rule): stable complexes have metal electrons + ligand donations = 18; [Fe(CN)₆]⁴⁻ has Fe²⁺ (6) + 12 = 18.

Chelation: polydentate ligands such as EDTA (hexadentate) and oxalate (bidentate) form more stable complexes than comparable monodentate ligands.

Werner's theory: primary (ionisable) and secondary (non-ionisable) valencies; AgNO₃ precipitation gives the number of free chloride ions, e.g. CoCl₃·5NH₃ gives 3 AgCl.

SN1 vs SN2: SN2 is one-step, second order, favoured by primary halides and strong nucleophiles, gives inversion; SN1 is two-step, first order, favoured by tertiary halides and polar protic solvents, gives racemisation.

Haloarenes are unreactive toward nucleophilic substitution because of partial double-bond character of C–X and sp² hybridisation; they react under drastic conditions (Dow process) or via benzyne.

Elimination: alcoholic KOH gives alkene (Saytzeff, more substituted alkene), alcoholic KOH with bulky base gives Hofmann product; aqueous KOH gives substitution to alcohol.

Finkelstein reaction (NaI in acetone) and Swarts reaction (AgF, Hg₂F₂) convert alkyl halides to alkyl iodides and fluorides; Finkelstein works because NaI is soluble in acetone.

Alcohols: Lucas test distinguishes 3° (immediate turbidity), 2° (5 min) and 1° (on heating); Victor Meyer test also distinguishes classes; oxidation of 1° gives aldehyde then acid, 2° gives ketone, 3° resists.

Phenols are more acidic than alcohols (pK_a phenol ≈ 10, ethanol ≈ 16) because phenoxide is resonance-stabilised; electron-withdrawing groups increase acidity (p-nitrophenol pK_a ≈ 7.2).

Phenol reactions: with FeCl₃ gives violet colour, with Br₂ water gives 2,4,6-tribromophenol, with NaOH gives sodium phenoxide, with CHCl₃/NaOH gives salicylaldehyde (Reimer–Tiemann).

Williamson synthesis: alkoxide + primary alkyl halide gives ether; tertiary halide gives elimination instead; ethers are cleaved by HI, giving alkyl iodide and alcohol (Zeisel determination of methoxy groups).

Aldehydes are oxidised by Tollens' reagent (silver mirror), Fehling's solution (red Cu₂O) and Benedict's solution; ketones give no reaction except methyl ketones in the iodoform test.

Nucleophilic addition: HCN gives cyanohydrin, NaHSO₃ gives bisulphite adduct (used for purification), Grignard reagent gives alcohol; aldehydes react faster than ketones because of less steric hindrance and less electron donation.

Aldol condensation needs α-hydrogen and dilute base; Cannizzaro reaction needs no α-hydrogen and concentrated base, giving alcohol and carboxylate (disproportionation).

Carboxylic acids: acidity order HCOOH > CH₃COOH > CH₃CH₂COOH; electron-withdrawing groups raise acidity (ClCH₂COOH > CH₃COOH); resonance stabilises the carboxylate ion.

Acid derivatives reactivity: acid chloride > anhydride > ester > amide; hydrolysis of esters (saponification with NaOH) gives soap plus alcohol; HVZ reaction gives α-halogenated acid.

Amines: basicity in water 2° > 1° > 3° > NH₃ for methylamines; in gas phase 3° > 2° > 1°; aryl amines are weaker bases because the lone pair is delocalised into the ring.

Amine reactions: Hinsberg test (benzenesulphonyl chloride) distinguishes 1°, 2°, 3°; carbylamine test (CHCl₃ + KOH) is positive only for primary amines; diazotisation at 273–278 K gives diazonium salt.

Biomolecules: glucose is an aldohexose with a pyranose ring, fructose a ketohexose; sucrose is a non-reducing disaccharide; proteins are linked by peptide bonds; DNA has deoxyribose and thymine, RNA ribose and uracil.

Addition polymers: polyethene (ethene), PVC (vinyl chloride), polystyrene (styrene), Teflon (tetrafluoroethylene), Buna-S and Buna-N (copolymers); no small molecule is eliminated.

Condensation polymers: nylon-6,6 from adipic acid + hexamethylenediamine, terylene (PET) from ethylene glycol + terephthalic acid, bakelite from phenol + formaldehyde; water or HCl is eliminated.

Natural polymers: starch and cellulose are polysaccharides of glucose; proteins are polyamides of amino acids; natural rubber is cis-1,4-polyisoprene; vulcanisation cross-links with sulphur.

Degree of polymerisation and molar mass: number-average and weight-average molar masses differ; polydispersity index = M_w/M_n ≥ 1.

Biodegradable polymers: PHBV and nylon-2-nylon-6 are biodegradable; Buna-S is not; recycling codes identify common plastics.

Drugs and targets: analgesics (aspirin, paracetamol), antibiotics (penicillin, chloramphenicol), antacids (Mg(OH)₂, Al(OH)₃), antihistamines (brompheniramine); enzyme inhibition is the usual mechanism.

Antiseptics vs disinfectants: antiseptics are safe on living tissue (dettol, iodine tincture), disinfectants are for non-living surfaces (phenol, formalin, bleaching powder).

Food additives: preservatives (sodium benzoate, salt, sugar), artificial sweeteners (saccharin, aspartame), antioxidants (BHA, BHT); artificial sweeteners are not metabolised and are calorie-free.

Qualitative analysis: group I cations Pb²⁺, Ag⁺, Hg₂²⁺ precipitate with dilute HCl; group II with H₂S in acidic medium; group III with NH₄OH/NH₄Cl; group IV with H₂S in basic medium; group V with (NH₄)₂CO₃.

Anion tests: carbonate gives effervescence with acid, sulphate gives white BaSO₄ insoluble in acid, chloride gives white AgCl soluble in NH₄OH, nitrate gives brown ring with FeSO₄ and conc. H₂SO₄.

Flame tests: Na golden yellow, K lilac, Ca brick red, Sr crimson, Ba apple green, Cu blue-green; use a clean platinum or nichrome wire.

Titration technique: rinse burette with the titrant, use a white tile, read the meniscus at eye level, take at least three concordant readings; phenolphthalein for strong base–weak acid, methyl orange for strong acid–weak base.

Salt analysis logic: cation tests require a clear solution, so insoluble salts are first converted to soluble chlorides or nitrates; interfering ions are removed by group separation.

Detection of functional groups: unsaturation decolourises Br₂ water, phenol gives violet with FeCl₃, aldehydes give silver mirror, carboxylic acids effervesce with NaHCO₃, amines turn red litmus blue.

Practical error: percentage error = |true − measured|/true × 100; report mean, standard deviation or range for repeated measurements; significant figures must match the instrument.

Project work: state aim, hypothesis, materials, method, observations table, and conclusion; cite data sources and record safety precautions for reagents used.