Tamil Nadu HSE First Year Chemistry cheat sheet

Mole: 1 mol = 6.022×10^23 entities; molar mass in g mol^-1 equals formula mass in u.

Number of moles n = given mass / molar mass = N / 6.022×10^23 = V at STP / 22.4 L (gases at 273.15 K, 1 atm).

Molarity M = moles of solute / volume of solution in litres; molality m = moles of solute / kg of solvent.

Empirical formula from % composition: divide each % by atomic mass, then divide by the smallest quotient; multiply to reach whole numbers.

Limiting reagent: divide moles of each reactant by its stoichiometric coefficient; the smallest ratio is limiting.

Significant figures: addition/subtraction keeps the least number of decimal places; multiplication/division keeps the least number of significant figures.

Equivalent mass of an acid = molar mass / basicity; of a base = molar mass / acidity; of a salt = molar mass / total charge.

Oxidation number rules: free element 0; O usually -2 (peroxide -1); H usually +1 (hydride -1); sum equals overall charge.

Bohr energy: E_n = -13.6 Z^2/n^2 eV; radius r_n = 0.529 n^2/Z Å; for hydrogen-like species replace Z accordingly.

Rydberg: 1/λ = R_H Z^2 (1/n1^2 - 1/n2^2), R_H = 1.097×10^7 m^-1; Lyman n1=1 (UV), Balmer n1=2 (visible), Paschen n1=3 (IR).

de Broglie: λ = h/mv = h/p; h = 6.626×10^-34 J s.

Heisenberg uncertainty: Δx·Δp ≥ h/4π; consequence is that trajectory and simultaneous position-momentum are undefined.

Allowed quantum numbers: n = 1,2,3...; l = 0 to n-1; m_l = -l to +l; m_s = +1/2 or -1/2.

Orbital labels: l = 0,1,2,3 correspond to s, p, d, f; number of orbitals in a subshell = 2l+1; maximum electrons = 2(2l+1).

Aufbau order follows (n+l) rule; when (n+l) ties, the lower n fills first: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p.

Hund's rule: degenerate orbitals are singly occupied with parallel spins before pairing; half-filled and fully filled subshells have extra stability.

Radial probability: number of radial nodes = n - l - 1; number of angular nodes = l; total nodes = n - 1.

Modern periodic law: properties are periodic functions of atomic number; periods 1-7 contain 2, 8, 8, 18, 18, 32, 32 elements.

Groups: 1 alkali, 2 alkaline earth, 16 chalcogens, 17 halogens, 18 noble gases; d-block groups 3-12, f-block lanthanoids and actinoids.

Atomic radius decreases across a period (increasing Z_eff) and increases down a group (new shells).

Ionisation enthalpy increases across a period and decreases down a group; exceptions arise from stable half-filled/filled configurations (e.g. N > O, Be > B).

Electron gain enthalpy is most negative for Cl, not F, because of the small size and electron repulsion in F.

Electronegativity: Pauling scale, F = 4.0 highest; increases across a period, decreases down a group.

Metallic character decreases across a period and increases down a group; non-metallic character shows the reverse trend.

Diagonal relationship examples: Li-Mg, Be-Al, B-Si; caused by similar charge/radius ratio.

Octet rule exceptions: BeCl2 (4 e), BF3 (6 e), PCl5 (10 e), SF6 (12 e); odd-electron species include NO and NO2.

VSEPR: electron-pair repulsion order lone pair-lone pair > lone pair-bond pair > bond pair-bond pair; count electron domains to fix geometry.

Shapes: 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral; lone pairs give bent, trigonal pyramidal, seesaw, square pyramidal, T-shaped.

Hybridisation from steric number: 2 sp, 3 sp2, 4 sp3, 5 sp3d, 6 sp3d2; bond angle order sp > sp2 > sp3.

Bond order = (bonding electrons - antibonding electrons)/2; use MO theory for O2 (paramagnetic, bond order 2) and N2 (bond order 3).

Dipole moment is a vector sum; CO2 and CCl4 have zero net moment despite polar bonds; NH3 has a net moment, BF3 does not.

Hydrogen bond strength is roughly 10-40 kJ mol^-1; it explains the high boiling point of H2O, HF and NH3 and the dimer of carboxylic acids.

Fajans' rules: small highly charged cations polarise anions; increased covalent character raises melting point of ionic solids.

Ideal gas equation: PV = nRT; R = 8.314 J K^-1 mol^-1 = 0.0821 L atm K^-1 mol^-1.

Combined gas law: P1V1/T1 = P2V2/T2; at STP 1 mol of ideal gas occupies 22.4 L.

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

Graham's law: rate of diffusion ∝ 1/√M; ratio of rates r1/r2 = √(M2/M1).

van der Waals equation: (P + an^2/V^2)(V - nb) = nRT; 'a' measures attraction, 'b' measures excluded volume.

Critical temperature: above Tc a gas cannot be liquefied by pressure; ease of liquefaction rises with stronger intermolecular forces.

Kinetic molecular theory: average kinetic energy per molecule = (3/2)kT; root mean square speed = √(3RT/M).

Boyle temperature: at T = 2a/Rb, a real gas behaves ideally over a range of pressures.

First law: ΔU = q + w; with work done by the system w = -PΔV, so at constant volume q_v = ΔU.

Enthalpy: H = U + PV; at constant pressure q_p = ΔH = ΔU + Δn_g RT.

Standard enthalpy of formation of an element in its standard state is zero; ΔH°reaction = ΣΔH°f(products) - ΣΔH°f(reactants).

Hess's law: enthalpy change is path-independent; add or reverse thermochemical equations with sign changes.

Bond enthalpy: ΔH = Σ(bonds broken) - Σ(bonds formed); bond breaking is endothermic.

Entropy: ΔS = q_rev/T; ΔS_universe = ΔS_system + ΔS_surroundings > 0 for a spontaneous change.

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

Calorimetry: q = mcΔT; heat capacity of a bomb calorimeter gives q_v = ΔU.

State functions: U, H, S, G, P, V, T; q and w are path functions.

Law of mass action: for aA + bB ⇌ cC + dD, Kc = [C]^c[D]^d / [A]^a[B]^b; Kp = Kc(RT)^Δn.

Reaction quotient Q compared with K: Q < K forward, Q > K reverse, Q = K equilibrium.

Le Chatelier: raising pressure shifts toward fewer moles of gas; raising temperature shifts in the endothermic direction.

Adding an inert gas at constant volume does not change partial pressures and does not shift the equilibrium.

A catalyst changes neither K nor position of equilibrium; only the rate at which equilibrium is reached.

For a reversed reaction K' = 1/K; for an equation multiplied by n, K' = K^n; adding reactions multiplies their K values.

Degree of dissociation α and Kp for A ⇌ 2B at pressure P: Kp = 4α^2P/(1-α^2).

Equilibrium is dynamic: both forward and reverse reactions continue at equal rates.

Water: Kw = [H+][OH-] = 1×10^-14 at 298 K; pH + pOH = 14; pH = -log[H+].

Strong acid/base fully dissociates; weak acid Ka = [H+][A-]/[HA] and [H+] = √(Ka·C).

Henderson-Hasselbalch: pH = pKa + log([salt]/[acid]); pOH = pKb + log([salt]/[base]).

Buffer capacity is greatest when pH = pKa, i.e. salt/acid ratio near 1.

Salt hydrolysis: salt of weak acid and strong base gives pH > 7; weak base and strong acid gives pH < 7; weak-weak depends on Ka and Kb.

Solubility product Ksp for AB2 is 4s^3; precipitation occurs when the ionic product exceeds Ksp.

Common ion effect suppresses ionisation of a weak electrolyte and lowers solubility of a sparingly soluble salt.

Lewis acid accepts an electron pair; Lewis base donates one; Bronsted acid is a proton donor.

Raoult's law: partial vapour pressure of a component = mole fraction × vapour pressure of the pure component.

Relative lowering of vapour pressure = (p° - p)/p° = mole fraction of solute, for a non-volatile solute.

Ideal solutions show zero enthalpy of mixing and obey Raoult's law; positive deviation gives minimum boiling azeotrope (ethanol-water), negative gives maximum boiling azeotrope (HNO3-water).

Colligative properties: relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure.

ΔTb = Kb·m and ΔTf = Kf·m for non-electrolytes; for electrolytes multiply by the van't Hoff factor i.

Osmotic pressure π = CRT (or iCRT); it is measured at room temperature and suits macromolecules.

Henry's law: solubility of a gas is proportional to its partial pressure; solubility falls as temperature rises.

Molality is preferred over molarity in colligative calculations because it is independent of temperature.

Rate = -Δ[reactant]/Δt = Δ[product]/Δt; average versus instantaneous rate differ unless the rate is constant.

Rate law: rate = k[A]^m[B]^n; order is experimental and need not match stoichiometric coefficients.

Zero order: [A] = [A]0 - kt; first order: k = (2.303/t) log([A]0/[A]); half-life first order = 0.693/k, independent of concentration.

Units of k: mol L^-1 s^-1 (zero), s^-1 (first), L mol^-1 s^-1 (second).

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

Temperature coefficient is about 2-3 per 10 K rise; activation energy is lowered by a catalyst, not by raising temperature.

Collision theory requires proper orientation and energy ≥ threshold; the steric factor accounts for orientation.

Rate-determining step is the slowest elementary step; molecularity applies only to elementary reactions.

Alkanes: C_nH_2n+2, sp3 carbons, substitution by free-radical halogenation; order of reactivity of H is tertiary > secondary > primary.

Markovnikov's rule: in HX addition to an unsymmetrical alkene, H adds to the carbon with more hydrogens; peroxide effect gives anti-Markovnikov with HBr only.

Alkenes: C_nH_2n; test with bromine water (decolourised) and Baeyer's reagent (pink colour discharged).

Alkynes: C_nH_2n-2; terminal alkynes are acidic, react with sodium to give acetylide and give a red precipitate with ammoniacal Cu2Cl2.

Benzene is planar, all C-C bonds 139 pm; undergoes electrophilic substitution (nitration, sulphonation, Friedel-Crafts) rather than addition.

Aromaticity (Huckel): cyclic, planar, fully conjugated, with 4n+2 π electrons.

Ozonolysis of an alkene cleaves the double bond to carbonyl compounds and locates the double bond position.

Conformations: ethane staggered is more stable than eclipsed; cyclohexane chair is more stable than boat.

IUPAC naming: longest chain, lowest locants, suffix for principal functional group; priority order -COOH > -SO3H > ester > acid halide > amide > nitrile > aldehyde > ketone > alcohol > amine > alkene > alkyne.

Hybridisation and shape: sp3 tetrahedral 109.5°, sp2 trigonal planar 120°, sp trigonal linear 180°.

Inductive effect: electron-withdrawing groups (-NO2, -CN, -COOH, -X) stabilise carbanions and increase acidity; alkyl groups are electron-donating.

Resonance requires coplanarity and conjugation; greater number of equivalent resonance structures means greater stability.

Hyperconjugation: more α-hydrogens give greater stability of carbocation and alkene; explains Saytzeff's rule.

Carbocation stability: tertiary > secondary > primary > methyl; carbanion order is reversed.

Optical isomerism requires a chiral centre (four different groups); a racemic mixture is optically inactive.

Purification and testing: crystallisation, distillation, steam distillation, chromatography (adsorption and partition); Lassaigne's test detects N, S, halogens.

Homolytic fission gives radicals; heterolytic fission gives carbocations and carbanions; free-radical substitution is initiated by light or peroxide.