RBSE SS Chemistry cheat sheet

For a cubic unit cell, atoms per cell: primitive = 1, body-centred = 2, face-centred = 4; packing efficiency = 52.4%, 68.0% and 74.0% respectively.

Density relation: ρ = (Z × M)/(a³ × N_A), where Z = atoms per unit cell, M = molar mass, a = edge length in cm and N_A = 6.022×10²³ mol⁻¹.

Edge–radius relations: simple cubic a = 2r; BCC √3a = 4r; FCC √2a = 4r.

Bragg equation: nλ = 2d sin θ, used to determine interplanar spacing d from X-ray diffraction.

Schottky defect: equal cation and anion vacancies, lowering density. Frenkel defect: an ion moves to an interstitial site, so density is unchanged.

Physisorption: van der Waals forces, low enthalpy, reversible, multilayer. Chemisorption: chemical bonds, high enthalpy, irreversible, monolayer.

Freundlich isotherm: x/m = k·P^(1/n), with 1/n between 0 and 1; a log–log plot gives slope 1/n and intercept log k.

Langmuir adsorption isotherm assumes monolayer coverage on identical sites with no interaction between adsorbed molecules.

Catalyst promoters increase activity and poisons reduce it. A homogeneous catalyst is in the same phase as reactants; a heterogeneous catalyst is in a different phase.

Raoult's law for a volatile solute: p_A = x_A p°_A. Ideal solutions obey it with ΔH_mix = 0 and ΔV_mix = 0.

Relative lowering of vapour pressure: (p° − p)/p° = x_B = n_B/(n_A + n_B).

Elevation of boiling point: ΔT_b = K_b·m; depression of freezing point: ΔT_f = K_f·m, where m is molality.

For water, K_f = 1.86 K kg mol⁻¹ and K_b = 0.52 K kg mol⁻¹.

Osmotic pressure: π = CRT, where C is molarity and R = 0.0821 L atm K⁻¹ mol⁻¹; for electrolytes π = iCRT.

van't Hoff factor i = observed colligative value ÷ calculated value; i > 1 for dissociation and i < 1 for association.

Henry's law: p = K_H·x; the solubility of a gas in a liquid decreases as temperature rises.

Minimum-boiling azeotrope: ethanol–water, showing positive deviation from Raoult's law. Maximum-boiling azeotrope: nitric acid–water, showing negative deviation.

Colligative properties depend on the number of solute particles, not their nature; molality is temperature-independent.

Nernst equation at 298 K: E = E° − (0.0591/n) log Q.

Standard cell potential: E°cell = E°cathode − E°anode; a positive E°cell means ΔG° < 0 and a spontaneous reaction.

ΔG° = −nFE° and ΔG° = −RT ln K; F = 96485 C mol⁻¹.

Molar conductivity Λm = κ × 1000/M, with κ in S cm⁻¹ and M in mol L⁻¹; Λm increases with dilution.

Kohlrausch law: Λ°m = ν₊λ°₊ + ν₋λ°₋; it is used to calculate Λ°m for weak electrolytes.

Lead storage battery: anode Pb + SO₄²⁻ → PbSO₄ + 2e⁻; cathode PbO₂ + 4H⁺ + SO₄²⁻ + 2e⁻ → PbSO₄ + 2H₂O.

Dry cell: zinc anode, MnO₂–carbon cathode, NH₄Cl–ZnCl₂ paste; it is not rechargeable. The H₂–O₂ fuel cell produces only water.

Rusting requires both oxygen and water and is electrochemical; iron acts as the anode and is oxidised to Fe²⁺.

In acidic medium: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O; Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O.

Rate law: rate = k[A]^m[B]^n; overall order is m + n and is determined experimentally, not from the balanced equation.

Zero-order reaction: [A] = [A]₀ − kt; t₁/₂ = [A]₀/(2k); units of k are mol L⁻¹ s⁻¹.

First-order reaction: k = (2.303/t) log([A]₀/[A]); t₁/₂ = 0.693/k, independent of initial concentration.

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

A catalyst lowers activation energy and increases k; it does not change ΔH or the equilibrium constant.

Molecularity is the number of species colliding in an elementary step; order is experimental and can be zero or fractional.

Units of k: zero order mol L⁻¹ s⁻¹; first order s⁻¹; second order L mol⁻¹ s⁻¹.

Half-life of a first-order reaction is constant; for a second-order reaction t₁/₂ = 1/(k[A]₀).

Rate of reaction is the change in concentration of a reactant or product per unit time; average rate uses a finite interval, instantaneous rate uses a tangent.

Group 15 elements: N, P, As, Sb, Bi; N₂ is inert because of its strong N≡N triple bond.

Group 16: O, S, Se, Te, Po; oxygen shows −2 and −1 oxidation states, while sulphur shows +4 and +6.

Group 17 halogens: oxidising power F₂ > Cl₂ > Br₂ > I₂; fluorine is the strongest oxidising agent.

Noble gases: He, Ne, Ar, Kr, Xe, Rn; xenon forms XeF₂, XeF₄ and XeF₆ with fluorine.

Inert-pair effect: heavier p-block elements show an oxidation state two units lower, e.g. Tl⁺, Pb²⁺ and Bi³⁺ are more stable than +3, +4 and +5.

Allotropes include white, red and black phosphorus, and rhombic and monoclinic sulphur.

Acid strength of oxoacids of chlorine: HClO < HClO₂ < HClO₃ < HClO₄.

Contact process for H₂SO₄: S → SO₂; 2SO₂ + O₂ ⇌ 2SO₃ with V₂O₅ catalyst; SO₃ is absorbed in concentrated H₂SO₄.

Ozone is a bent molecule; it is a powerful oxidising agent and absorbs ultraviolet radiation.

First transition series: Sc to Zn; general configuration (n−1)d¹⁻¹⁰ ns¹⁻²; Cr = 3d⁵4s¹ and Cu = 3d¹⁰4s¹.

Transition metals show variable oxidation states, complex formation, catalytic activity, paramagnetism and coloured ions.

Mn shows the highest oxidation state +7 in KMnO₄; Sc shows only +3.

Lanthanoid contraction: gradual decrease in atomic and ionic radii across the 4f series due to poor shielding by 4f electrons.

Lanthanoids commonly show +3; Ce⁴⁺ and Eu²⁺ are important exceptions. Actinoids are radioactive and fill 5f orbitals.

KMnO₄ in acidic medium: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O, giving a colourless solution.

K₂Cr₂O₇ in acidic medium: Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O, giving a green solution.

Spin-only magnetic moment: μ = √(n(n+2)) BM, where n is the number of unpaired electrons.

Colour of transition-metal ions arises from d–d transitions; ions with d⁰ or d¹⁰ configurations are colourless.

Coordination number is the number of ligand donor atoms bonded to the central metal ion; common values are 2, 4 and 6.

IUPAC naming: ligands are named alphabetically before the metal; an anionic complex ends in -ate; the metal oxidation state is given in Roman numerals in parentheses.

Geometrical isomerism in square planar [MA₂B₂] gives cis and trans; octahedral [MA₄B₂] also gives cis and trans.

Optical isomerism occurs in octahedral complexes with bidentate ligands, e.g. [Co(en)₃]³⁺.

Linkage isomerism arises with ambidentate ligands such as NO₂⁻ (nitro/nitrito) and SCN⁻ (thiocyanato/isothiocyanato).

Crystal field theory: Δo is the energy gap between t₂g and e_g sets; strong-field ligands give low-spin complexes.

Spectrochemical series: I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO.

Chelate effect: complexes with bidentate or polydentate ligands are more stable than similar complexes with monodentate ligands.

EAN rule: the effective atomic number of the metal equals that of the next noble gas; [Co(NH₃)₆]³⁺ satisfies EAN.

SN2: one step, bimolecular, inversion of configuration, favoured by primary halides and strong nucleophiles.

SN1: two steps via a carbocation, racemisation, favoured by tertiary halides and polar protic solvents.

Reactivity toward SN1: 3° > 2° > 1°; toward SN2: 1° > 2° > 3°.

Haloarenes are less reactive toward nucleophilic substitution because the C–X bond has partial double-bond character and the ring is electron-rich.

Finkelstein reaction: R–X + NaI → R–I + NaX in dry acetone. Swarts reaction: R–X + AgF → R–F + AgX.

Wurtz reaction: 2R–X + 2Na → R–R + 2NaX in dry ether. Wurtz–Fittig: aryl halide + alkyl halide + Na → alkylarene.

Sandmeyer reaction: ArN₂⁺Cl⁻ + CuCl/HCl → ArCl + N₂. Gattermann reaction: ArN₂⁺ + Cu/HCl → ArCl.

Balz–Schiemann reaction: ArN₂⁺BF₄⁻ → ArF + N₂ + BF₃ on heating.

Saytzeff rule: dehydrohalogenation of alkyl halides gives the more substituted, more stable alkene as the major product.

Lucas test: with concentrated HCl/ZnCl₂, a 3° alcohol turns cloudy immediately, a 2° alcohol in about five minutes and a 1° alcohol only on heating.

Dehydration of alcohols with concentrated H₂SO₄: ease 3° > 2° > 1°; alkenes follow Saytzeff rule.

Oxidation: 1° alcohol → aldehyde → carboxylic acid; 2° alcohol → ketone; 3° alcohol is resistant to oxidation.

Phenol is acidic because the phenoxide ion is resonance-stabilised; electron-withdrawing groups increase acidity and electron-donating groups decrease it.

Reimer–Tiemann: phenol + CHCl₃ + NaOH → salicylaldehyde. Kolbe: sodium phenoxide + CO₂ then H⁺ → salicylic acid.

Williamson ether synthesis: R–O⁻Na⁺ + R'–X → R–O–R' + NaX; it works best with primary alkyl halides.

Cleavage of ethers with HI: cold dilute HI gives an alcohol and an alkyl iodide; excess hot HI converts both alkyl groups to alkyl iodides.

Haloform reaction: ethanol and methyl ketones give a yellow precipitate of CHI₃ with I₂ and NaOH.

Boiling points: alcohols > ethers > alkanes of comparable mass because alcohols form intermolecular hydrogen bonds.

Aldehydes are more reactive than ketones toward nucleophilic addition because of less steric hindrance and less electron donation by alkyl groups.

Tollens' test: aldehydes give a silver mirror with ammoniacal AgNO₃; ketones do not.

Fehling's and Benedict's tests: aliphatic aldehydes give a red precipitate of Cu₂O; aromatic aldehydes and ketones do not.

Iodoform test: acetaldehyde and methyl ketones give yellow CHI₃ with I₂/NaOH.

Aldol condensation: two carbonyl compounds with α-hydrogens form a β-hydroxy aldehyde or ketone, which may dehydrate to an α,β-unsaturated carbonyl.

Cannizzaro reaction: aldehydes without α-hydrogens undergo disproportionation with concentrated NaOH to give an alcohol and a carboxylate salt.

Clemmensen reduction: C=O → CH₂ with Zn(Hg)/HCl. Wolff–Kishner reduction: C=O → CH₂ with NH₂NH₂/KOH.

Carboxylic acid acidity increases with electron-withdrawing groups: CCl₃COOH > CHCl₂COOH > CH₂ClCOOH > CH₃COOH.

Hell–Volhard–Zelinsky reaction: carboxylic acids with α-hydrogens are brominated with Br₂/P.

Basicity in aqueous solution: 2° > 1° > 3° for methylamines; aromatic amines are much weaker bases than aliphatic amines.

Hinsberg test: 1° amines react with benzenesulphonyl chloride to give an alkali-soluble product; 2° give an insoluble sulphonamide; 3° do not react.

Gabriel phthalimide synthesis gives pure primary amines; it fails for aromatic amines.

Hofmann bromamide degradation: an amide + Br₂/NaOH gives a primary amine with one carbon fewer.

Carbylamine test: primary amines + CHCl₃ + KOH give foul-smelling isocyanides.

Aromatic amines undergo diazotisation with NaNO₂/HCl at 0–5 °C to give diazonium salts.

Coupling reaction: a diazonium salt + phenol in alkaline medium gives an orange azo dye.

Basicity of substituted anilines: electron-donating groups increase basicity; electron-withdrawing groups decrease it.

Amines are more basic than ammonia in aqueous solution because of the +I effect of alkyl groups and solvation of the conjugate acid.

Monosaccharides: glucose and fructose are reducing sugars; sucrose is a non-reducing disaccharide of glucose and fructose.

Starch is a polymer of α-glucose; cellulose is a polymer of β-glucose and cannot be digested by humans.

Proteins are polymers of α-amino acids linked by peptide bonds; primary structure is the amino acid sequence.

Denaturation destroys the secondary and tertiary structure of a protein without breaking peptide bonds.

DNA contains deoxyribose and bases A, T, G, C; RNA contains ribose and uracil instead of thymine.

DNA double helix: A pairs with T by two hydrogen bonds; G pairs with C by three hydrogen bonds.

Enzymes are biological catalysts; the lock-and-key model explains their high specificity.

Fat-soluble vitamins: A, D, E, K; water-soluble vitamins: B group and C.

Essential amino acids cannot be synthesised by the human body and must be supplied in the diet.

Addition polymerisation: monomers with C=C join without losing small molecules, e.g. polyethylene, PVC and polystyrene.

Condensation polymerisation: monomers join with loss of a small molecule such as water, e.g. nylon 6,6 and terylene.

Bakelite is a thermosetting phenol–formaldehyde resin; it cannot be softened again on heating.

Natural rubber is cis-polyisoprene; vulcanisation with sulphur forms cross-links and increases strength.

Ziegler–Natta catalyst, TiCl₄ + Al(C₂H₅)₃, polymerises ethene to high-density polyethylene.

Copolymers: Buna-S is butadiene–styrene; Buna-N is butadiene–acrylonitrile; neoprene is polychloroprene.

Nylon 6,6 is a polyamide of adipic acid and hexamethylenediamine; terylene is a polyester of ethylene glycol and terephthalic acid.

Thermoplastics soften on heating and can be remoulded; thermosetting polymers become infusible cross-linked networks.

Degree of polymerisation is the number of monomer units in a polymer molecule.

Antacids neutralise excess stomach acid; examples include sodium bicarbonate, magnesium hydroxide and aluminium hydroxide.

Antihistamines block histamine receptors and reduce allergy symptoms; ranitidine is an antiulcer drug.

Analgesics: aspirin is a non-narcotic analgesic; morphine is a narcotic analgesic.

Antibiotics: penicillin is a narrow-spectrum antibiotic; tetracycline and chloramphenicol are broad-spectrum.

Antiseptics are applied to living tissue, e.g. Dettol and iodine; disinfectants are used on non-living objects, e.g. phenol.

Soap is a sodium or potassium salt of a long-chain fatty acid; it forms micelles and works poorly in hard water.

Detergents are synthetic surfactants; sodium alkyl sulphate is anionic and does not form scum with hard water.

Food preservatives include sodium benzoate, table salt and sugar; artificial sweeteners include saccharin, aspartame and sucralose.

Antioxidants such as BHA and BHT prevent oxidation of fats and oils in food.