CHSE Odisha Elective Chemistry cheat sheet

Bragg's law: nλ = 2d sin θ; first-order diffraction uses n = 1 and gives interplanar spacing d from the glancing angle θ.

Unit-cell contents: primitive cubic Z = 1, body-centred cubic Z = 2, face-centred cubic Z = 4; packing efficiencies are 52.4%, 68% and 74% respectively.

Radius–edge relations: simple cubic r = a/2; bcc r = √3a/4; fcc r = a/(2√2).

Density relation: ρ = ZM/(a³N_A), with a in cm and M in g mol⁻¹ when ρ is in g cm⁻³.

Close-packed structures provide two tetrahedral voids and one octahedral void per constituent atom; octahedral voids are larger.

Schottky defect removes one cation and one anion, decreasing density; Frenkel defect moves a cation to an interstitial site without changing density.

Raoult's law for a two-component solution: p_total = p°_A x_A + p°_B x_B; ideal solutions have ΔH_mix = 0 and ΔV_mix = 0.

Colligative relations: ΔTb = iKb m, ΔTf = iKf m, π = iCRT; i > 1 for dissociation and i < 1 for association.

Henry's law: p = K_H x; lower K_H means higher solubility of a gas at a given partial pressure.

Nernst equation at 298 K: E = E° − (0.0591/n) log Q; Q uses products over reactants, each raised to its stoichiometric coefficient.

Thermodynamic links: ΔG = −nFE and ΔG° = −nFE° = −RT ln K.

Conductivity κ = G(l/A); molar conductivity Λm = 1000κ/M, with κ in S cm⁻¹ and M in mol cm⁻³ or consistent units.

Kohlrausch law: Λ°m = ν₊λ°₊ + ν₋λ°₋; it allows Λ°m of weak electrolytes to be found from strong-electrolyte data.

Faraday's laws: charge Q = It and mass deposited m = (QM)/(zF), where z is the number of electrons per ion.

In a galvanic cell, oxidation occurs at the anode (negative electrode) and reduction at the cathode (positive electrode); E_cell = E_cathode − E_anode.

Lead–acid cell discharge: anode Pb + SO4²⁻ → PbSO4 + 2e⁻; cathode PbO2 + 4H⁺ + SO4²⁻ + 2e⁻ → PbSO4 + 2H2O.

Sacrificial protection uses a metal with more negative reduction potential, such as zinc or magnesium, which oxidises in place of iron.

Standard hydrogen electrode is assigned E° = 0.00 V at 298 K, 1 bar H2 and unit H⁺ activity.

Rate law: rate = k[A]^m[B]^n; m and n are experimental orders, not necessarily the stoichiometric coefficients.

Zero order: [A] = [A]0 − kt and t½ = [A]0/(2k); first order: ln[A] = ln[A]0 − kt and t½ = 0.693/k.

Second order with equal concentrations: 1/[A] = 1/[A]0 + kt and t½ = 1/(k[A]0).

First-order integrated form: k = (2.303/t) log([A]0/[A]).

Arrhenius: k = A e^(−Ea/RT); log(k2/k1) = Ea(T2 − T1)/[2.303R T1T2].

A catalyst lowers Ea and increases k but does not alter ΔH, ΔG° or the equilibrium constant.

For an elementary step, molecularity equals the reaction order; for a complex reaction they may differ.

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

Physisorption is reversible, multilayer and has low enthalpy (about 20–40 kJ mol⁻¹); chemisorption is irreversible, monolayer and has high enthalpy (about 80–240 kJ mol⁻¹).

Freundlich isotherm: x/m = kp^(1/n), with 1/n between 0 and 1; a log–log plot is linear with slope 1/n.

Langmuir isotherm: θ/(1 − θ) = Kp; it assumes monolayer adsorption on equivalent sites with no interaction between adsorbed molecules.

Colloidal particles show Brownian motion, Tyndall scattering and electrophoresis; the charge on a sol is indicated by its direction of movement.

Hardy–Schulze rule: coagulation power increases sharply with coagulating ion charge; Al³⁺ > Ca²⁺ > Na⁺ for a negative sol.

Emulsions are liquid-in-liquid colloids; oil-in-water and water-in-oil types are stabilised by emulsifiers that lower interfacial tension.

Heterogeneous catalysts act through adsorption and provide a lower-energy path; promoters increase activity and poisons reduce it.

Isoelectric point: pH at which a colloidal particle has zero net charge, so coagulation is favoured and electrophoresis stops.

Froth flotation concentrates sulphide ores: collectors such as xanthates make ore particles hydrophobic, frothers stabilise bubbles, and depressants suppress gangue.

Roasting heats a sulphide ore in excess air to give an oxide and SO2; calcination heats a carbonate or hydroxide in limited air to give an oxide.

Ellingham diagram plots ΔG° of oxide formation against temperature; a metal can reduce the oxide of any metal whose curve lies above its own.

Carbon reduces zinc oxide above about 1180 K, while aluminium reduces Cr2O3 or Fe2O3 in the thermite process because Al2O3 is more stable.

Leaching of bauxite with hot NaOH dissolves alumina as aluminate; gold is leached with dilute NaCN in the presence of air.

Mond process refines nickel through volatile Ni(CO)4; van Arkel–de Boer process refines titanium through volatile TiI4.

Zone refining moves a molten zone along a rod and concentrates impurities at the end; it is used for silicon and germanium.

Electrolytic refining uses impure metal as anode and pure metal as cathode; copper and aluminium are refined this way.

Borax is Na2B4O7·10H2O; its aqueous solution is alkaline because B4O7²⁻ hydrolyses, and boric acid is a weak Lewis acid.

Diborane B2H6 has two B–H–B three-centre two-electron bonds and four terminal B–H bonds; AlCl3 is dimeric with bridging chlorines.

Nitrogen is unreactive because of its strong N≡N triple bond; ammonia is pyramidal and basic, while nitric acid is a strong oxidising acid.

Ozone is bent with bond angle about 117°; it is a powerful oxidiser and its bleaching action is due to oxidation, unlike SO2 bleaching which is reduction.

Sulphuric acid manufacture by the contact process uses V2O5 catalyst and SO3 absorption in concentrated H2SO4.

Fluorine is the strongest oxidising halogen; chlorine disproportionates in cold dilute alkali to chloride and hypochlorite, and in hot alkali to chloride and chlorate.

Interhalogens such as ClF3, BrF5 and IF7 have the more electronegative halogen at the terminal positions.

XeF2 is linear, XeF4 square planar and XeF6 distorted octahedral; xenon fluorides form when xenon reacts with excess fluorine under controlled conditions.

Acid strength of oxoacids of chlorine increases with oxygen number: HClO < HClO2 < HClO3 < HClO4.

Transition metals show variable oxidation states, coloured ions, paramagnetism, catalytic activity and complex formation because of partly filled d orbitals.

Octahedral crystal field splitting Δo: strong-field ligands such as CN⁻ and CO give low-spin complexes; weak-field ligands such as Cl⁻ and H2O give high-spin complexes.

Spectrochemical series: CO > CN⁻ > NH3 > H2O > F⁻ > Cl⁻ > Br⁻ > I⁻; stronger ligands produce larger Δ.

Lanthanoid contraction arises from poor shielding by 4f electrons; it makes Zr and Hf, and Nb and Ta, similar in size and chemistry.

Common lanthanoid oxidation state is +3; Ce⁴⁺ is a strong oxidiser and Eu²⁺ is a reducing agent.

Coordination number is the number of donor atoms bonded to the central metal; EDTA is hexadentate and forms chelate complexes.

IUPAC naming lists ligands alphabetically, then the metal with oxidation state in Roman numerals; anionic complexes end in -ate.

Geometrical isomerism occurs in square planar and octahedral complexes; optical isomerism occurs when the complex and its mirror image are non-superimposable.

Linkage isomerism arises from ambidentate ligands such as SCN⁻ and NO2⁻; ionisation isomerism arises from different counter ions.

SN1 reactions proceed through a carbocation and are favoured by tertiary substrates and polar protic solvents; SN2 reactions are concerted and favoured by primary substrates and strong nucleophiles.

Aryl halides resist nucleophilic substitution because the C–X bond has partial double-bond character from resonance and the ring repels nucleophiles; they undergo electrophilic substitution.

Grignard reagents R-MgX form in dry ether and react with water, alcohols and acids to give alkanes, so moisture must be excluded.

Lucas test: tertiary alcohol gives cloudiness immediately, secondary on warming, primary only on prolonged heating; it depends on carbocation stability.

Phenols are more acidic than alcohols because the phenoxide ion is resonance-stabilised; electron-withdrawing substituents increase phenol acidity.

Reimer–Tiemann reaction treats phenol with CHCl3 and NaOH to give ortho-hydroxybenzaldehyde; Kolbe reaction with CO2 and NaOH gives salicylic acid.

Williamson ether synthesis uses an alkoxide and a primary alkyl halide; tertiary halides give elimination instead of substitution.

Ether cleavage by HI gives an alcohol and an alkyl iodide; the reaction proceeds by protonation and SN2 attack on the smaller alkyl group.

Haloform reaction: methyl ketones and ethanol react with iodine and alkali to give iodoform, detected as a yellow precipitate.

Aldehydes are oxidised by Tollens' reagent and Fehling's solution; ketones are not, except α-hydroxy ketones which reduce Fehling's.

Nucleophilic addition to carbonyl: HCN gives cyanohydrin, NaHSO3 gives bisulphite adduct, and Grignard reagents give alcohols after hydrolysis.

Aldol condensation requires an α-hydrogen and gives a β-hydroxy carbonyl; Cannizzaro disproportionation occurs for aldehydes without α-hydrogen.

Clemmensen reduction uses Zn-Hg/HCl and Wolff–Kishner uses hydrazine/KOH; both convert C=O to CH2.

Carboxylic acid derivatives reactivity: acid chloride > anhydride > ester > amide toward nucleophilic acyl substitution.

Carboxylic acids with electron-withdrawing substituents are stronger; formic acid is a reducing acid and gives a silver mirror with Tollens' reagent.

Amines in water: basicity order for methylamines is (CH3)2NH > CH3NH2 > (CH3)3N > NH3; aromatic amines are weaker bases because the lone pair is delocalised.

Hinsberg test uses benzenesulphonyl chloride: primary amines give soluble sulphonamide, secondary give insoluble, tertiary do not react.

Diazonium salts undergo coupling with phenol or aniline to give azo dyes; Sandmeyer reaction replaces N2⁺ with Cl, Br or CN.

Glucose is an aldohexose that exists mainly as a cyclic hemiacetal; sucrose is non-reducing because its glycosidic bond links both anomeric carbons.

Starch contains amylose and amylopectin; cellulose is β-1,4-linked glucose and is not digested by humans.

Amino acids are zwitterionic near neutral pH; the peptide bond is a planar amide link, and denaturation disrupts secondary and tertiary structure without breaking primary bonds.

DNA contains deoxyribose and thymine, with A–T and G–C base pairs; RNA contains ribose and uracil.

Addition polymers form from unsaturated monomers without loss of small molecules; condensation polymers form with loss of water or another small molecule.

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

Natural rubber is cis-1,4-polyisoprene; vulcanisation with sulphur introduces cross-links that increase strength and elasticity.

Soaps are salts of long-chain fatty acids and form micelles; detergents are synthetic surfactants and some branched types resist biodegradation.

Drug classes by action include analgesics for pain, antibiotics against bacteria, antacids for excess stomach acid, and antihistamines for allergic responses.