BSEH SS Chemistry cheat sheet

Unit-cell contents: simple cubic 1 atom (r = a/2, CN 6), bcc 2 atoms (r = √3a/4, CN 8), fcc 4 atoms (r = √2a/4, CN 12); packing efficiencies 52.4 %, 68 % and 74 % respectively.

Density from cell: ρ = Z·M/(a³·N_A), with a in cm and N_A = 6.022 × 10²³; Z is the number of atoms per unit cell.

Bragg law: nλ = 2d sin θ; X-ray diffraction gives interplanar spacing d and hence the lattice type.

Schottky defect: equal cation and anion vacancies, density decreases, shown by NaCl; Frenkel defect: ion displaced to an interstitial site, density unchanged, shown by AgCl.

Raoult's law for two volatile liquids: p = p°_A x_A + p°_B x_B; for a non-volatile solute the relative lowering Δp/p°_A = x_B.

Colligative relations: ΔTb = i·Kb·m, ΔTf = i·Kf·m, π = i·C·R·T with C in mol L⁻¹ and R = 0.0821 L atm K⁻¹ mol⁻¹.

Van't Hoff factor i = observed/calculated value: i = 2 for KCl, 3 for K₂SO₄, and i < 1 for association such as benzoic acid dimerising in benzene.

Henry's law: p = K_H·x; gas solubility falls as temperature rises and rises with increasing partial pressure.

Conductance relations: G = 1/R and κ = G·(l/A); the cell constant l/A is found using 0.1 M KCl of known conductivity.

Λm = 1000κ/M (κ in S cm⁻¹, M in mol L⁻¹); for strong electrolytes Λm = Λ°m − A√C (Debye–Hückel–Onsager).

Kohlrausch's law: Λ°m of a weak electrolyte equals the sum of limiting ionic conductivities; degree of dissociation α = Λm/Λ°m.

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

Thermodynamics: ΔG° = −nFE° and ΔG° = −2.303RT log K, so E° = (0.0591/n) log K at 298 K.

Faraday: 1 F = 96500 C mol⁻¹; moles deposited = It/(nF), with charge Q = I × t in coulombs.

Lead storage battery: Pb | PbO₂ in about 38 % H₂SO₄; discharge forms PbSO₄ at both electrodes and the cell is rechargeable.

Rusting is electrochemical and needs both O₂ and moisture; zinc coating protects iron by sacrificial cathodic protection.

Rate law: rate = k[A]^x[B]^y; the order x + y is found experimentally and is not taken from the balanced equation.

Zero order: [A] = [A]₀ − kt, t½ = [A]₀/2k, units of k are mol L⁻¹ s⁻¹.

First order: k = (2.303/t) log([A]₀/[A]), t½ = 0.693/k, units of k are s⁻¹.

Second order: 1/[A] = 1/[A]₀ + kt, t½ = 1/(k[A]₀), units of k are L mol⁻¹ s⁻¹.

Arrhenius: k = A e^(−Ea/RT) and log(k₂/k₁) = Ea(1/T₁ − 1/T₂)/2.303R.

A catalyst lowers Ea and speeds the forward and backward reactions equally; it changes neither ΔH, ΔG° nor the equilibrium constant.

The rate-determining step is the slowest elementary step, and the overall rate law follows that step.

Collision theory: rate = P·Z·e^(−Ea/RT), where P is the steric factor and Z the collision frequency.

Physisorption: van der Waals forces, ΔH about 20–40 kJ mol⁻¹, reversible, multilayer, decreases with temperature; chemisorption: 80–240 kJ mol⁻¹, irreversible, monolayer.

Freundlich isotherm: x/m = k·p^(1/n) with 0 < 1/n < 1; the log–log plot is linear with slope 1/n and fails at high pressure.

Langmuir isotherm assumes monolayer coverage, equivalent adsorption sites and no interaction between adsorbed molecules.

Hardy–Schulze rule: coagulating power increases with ionic charge, Al³⁺ > Ca²⁺ > Na⁺; the ion of charge opposite to the sol is effective.

Lyophilic sols are reversible and need no stabiliser; lyophobic sols are irreversible and coagulate readily on adding electrolyte.

Tests for sols: Tyndall effect (scattering of light), Brownian motion, electrophoresis (charge on particles) and electro-osmosis.

Emulsion types: oil-in-water (milk) and water-in-oil (butter); emulsifiers such as soap or gelatin lower interfacial tension and stabilise the emulsion.

Froth flotation concentrates sulphide ores using collectors such as xanthates and frothers; depressants like NaCN suppress ZnS while PbS floats.

Leaching: bauxite with hot NaOH gives soluble sodium aluminate; gold or silver with dilute NaCN in air gives a soluble cyanide complex.

Calcination heats a carbonate or hydrated ore in limited air; roasting heats a sulphide ore in excess air, giving the oxide plus SO₂.

Ellingham diagram: plot of ΔG° for oxide formation against temperature; a metal whose line lies lower reduces the oxide above it, and carbon becomes effective above about 983 K.

Thermite (aluminothermic) reduction: Fe₂O₃ + 2Al → 2Fe + Al₂O₃; also used for oxides of Mn and Cr.

Refining methods: distillation (Zn, Hg), liquation (Pb, Sn), zone refining (Ge, Si), van Arkel (Ti, Zr) and the Mond process (Ni).

Electrolytic reduction of alumina dissolved in molten cryolite (Na₃AlF₆) near 1200 K deposits aluminium at the cathode.

Group 15 hydrides: NH₃ (bond angle 107°), PH₃ (93.5°), AsH₃, SbH₃; basicity falls down the group.

HNO₃ is a strong oxidiser: dilute acid with Cu gives NO and concentrated acid gives NO₂; it generally does not liberate H₂ from metals.

Aqua regia (3 HCl : 1 HNO₃) dissolves gold and platinum by forming chloro-complexes along with nitrosyl chloride.

Ozone is bent (117°) and diamagnetic; it oxidises iodide to iodine and bleaches by oxidation.

Halogen trend: oxidising power F₂ > Cl₂ > Br₂ > I₂; with alkali cold dilute gives hypohalite and hot concentrated gives halate by disproportionation.

Oxoacid strength for one central atom: HClO₄ > HClO₃ > HClO₂ > HClO, because more oxygen atoms stabilise the conjugate base by resonance.

Noble gases: XeF₂ linear, XeF₄ square planar, XeF₆ distorted octahedral; xenon fluorides are strong fluorinating agents.

Inert pair effect: Bi(III) is more stable than Bi(V), Pb(II) more stable than Pb(IV) and Tl(I) more stable than Tl(III).

An octahedral field splits d orbitals into lower t2g and higher eg with gap Δo; the tetrahedral pattern is inverted with Δt ≈ 4/9 Δo.

Spectrochemical series (increasing field): I⁻ < Br⁻ < Cl⁻ < F⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO.

Spin-only moment μ = √(n(n+2)) BM; d⁰ and d¹⁰ complexes are colourless and diamagnetic.

Low spin versus high spin depends on whether Δo exceeds the pairing energy; strong-field ligands give low-spin configurations.

IUPAC naming: ligands in alphabetical order, anionic ligands end in -o, then the metal with its oxidation state in Roman numerals in parentheses.

Isomerism types: ionisation, hydration, linkage (NO₂⁻ versus ONO⁻), coordination, geometrical (cis/trans) and optical.

VBT: inner-orbital d²sp³ is octahedral low spin, outer-orbital sp³d² is high spin, and tetrahedral is sp³.

Lanthanoids are mainly +3; Ce⁴⁺ (f⁰) and Eu²⁺ (f⁷) are extra stable, and the lanthanoid contraction explains Zr–Hf similarity.

KMnO₄ is made from MnO₂ via manganate; K₂Cr₂O₇ is made from chromite ore via chromate, with acidification giving the dichromate.

Reactivity of alkyl halides towards nucleophilic substitution: R–I > R–Br > R–Cl > R–F, following C–X bond strength.

SN1: two steps through a carbocation, rate = k[substrate], racemisation, favoured by tertiary carbon and polar protic solvent.

SN2: one step, rate = k[substrate][nucleophile], backside attack with inversion of configuration, favoured by primary carbon and polar aprotic solvent.

Haloarenes resist nucleophilic substitution because the C–X bond has partial double-bond character by resonance and the carbon is sp² hybridised.

Sandmeyer reaction: diazonium salt with CuCl/HCl or CuBr/HBr gives aryl halide; with CuCN/HCN it gives aryl nitrile.

Halogen exchange: Finkelstein (NaI in dry acetone) gives the alkyl iodide; Swarts (AgF or Hg₂F₂) gives the alkyl fluoride.

Addition of HX to an unsymmetrical alkene follows Markownikoff's rule; the peroxide anti-Markownikoff effect applies only to HBr.

Elimination follows Saytzeff's rule giving the more substituted alkene; E2 is concerted while E1 passes through a carbocation.

Acidity order: carboxylic acid > phenol > water > alcohol; phenol is more acidic than water because the phenoxide ion is resonance stabilised.

Lucas test with anhydrous ZnCl₂ in conc. HCl: tertiary alcohol gives turbidity at once, secondary in about five minutes, primary only on heating.

Phenol gives a violet colour with neutral FeCl₃, decolourises bromine water forming 2,4,6-tribromophenol, and undergoes Reimer–Tiemann and Kolbe reactions.

Williamson synthesis: alkoxide plus a primary alkyl halide gives an ether; with tertiary halides elimination dominates.

Ether cleavage with cold HI gives an alcohol and an iodoalkane; excess HI converts both alkyl groups to iodoalkane.

Aldehyde tests: Tollens' silver mirror, Fehling's red Cu₂O and Schiff's pink colour; ketones are negative except α-hydroxy ketones.

Nucleophilic addition reactivity: HCHO > CH₃CHO > other aldehydes > ketones, because alkyl groups donate electron density and hinder the carbonyl carbon.

Named reactions: Cannizzaro (no α-H, conc. alkali), aldol (α-H, dilute alkali), Clemmensen (Zn-Hg/HCl), Wolff–Kishner (N₂H₄/KOH).

HVZ reaction: carboxylic acid with Br₂/P gives the α-bromo acid; acid strength rises with electron-withdrawing substituents, ClCH₂COOH > CH₃COOH.

Basicity of amines in water: (C₂H₅)₂NH > C₂H₅NH₂ > (C₂H₅)₃N > NH₃; in the gas phase the order is 3° > 2° > 1° > NH₃.

Aniline is a weaker base than NH₃ because the nitrogen lone pair is delocalised into the ring; p-nitroaniline < aniline < p-toluidine.

Hinsberg reagent (C₆H₅SO₂Cl): primary amine gives an alkali-soluble sulphonamide, secondary an insoluble one, tertiary no reaction.

Carbylamine test: primary amine with CHCl₃ and KOH gives a foul-smelling isocyanide; with HNO₂ a primary amine gives an alcohol and a secondary gives an N-nitrosamine.

Hofmann bromamide degradation: amide with Br₂/NaOH gives a primary amine containing one carbon less; Gabriel phthalimide synthesis gives only primary amines.

Carbohydrates: glucose and fructose are reducing sugars, sucrose is non-reducing, starch gives a blue colour with iodine; proteins are polypeptides joined by peptide bonds.

Polymers: addition (polyethylene, PVC, Teflon) versus condensation (nylon-6,6, bakelite, PET); vulcanisation cross-links rubber chains with sulphur.

Drug classes: analgesics (aspirin), antibiotics (penicillin), antiseptics (dettol), antacids; soaps are salts of long-chain fatty acids that form micelles.

Detergents are sodium alkyl sulphonates and work in hard water unlike soaps; branched alkyl chains are poorly biodegradable.