IIT JAM CY cheat sheet

First law: ΔU = q + w, with w = −P_extΔV for work done on the system; enthalpy H = U + PV and ΔH = q_p at constant pressure.

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

Clausius–Clapeyron: ln(P₂/P₁) = −(ΔH_vap/R)(1/T₂ − 1/T₁), so ln P is linear in 1/T with slope −ΔH_vap/R.

Arrhenius: k = A e^(−Ea/RT); ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂); a larger Ea gives a stronger temperature dependence of k.

First-order kinetics: [A] = [A]₀e^(−kt) and t½ = 0.693/k; second order in one reactant: 1/[A] = 1/[A]₀ + kt.

Particle in a 1D box: E_n = n²h²/(8mL²); level spacing decreases as L increases and the zero-point energy is h²/(8mL²) at n = 1.

Harmonic oscillator: E_v = (v + ½)hν with ν = (1/2π)√(k/μ), IR selection rule Δv = ±1; rigid rotor E_J = hcBJ(J+1) with ΔJ = ±1.

Nernst equation: E = E° − (0.0592/n) log Q at 298 K; at equilibrium E_cell = 0, so E° = (0.0592/n) log K.

Beer–Lambert: A = εcl = −log T; linearity holds only for dilute solutions, monochromatic light and non-interacting absorbing species.

Spectrochemical series: I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO; strong-field ligands give large Δo and favour low-spin configurations.

Octahedral CFSE = (−0.4 n_t2g + 0.6 n_eg)Δo plus pairing energy; tetrahedral splitting Δt ≈ (4/9)Δo and tetrahedral complexes are always high-spin.

Spin-only moment μ = √(n(n+2)) BM: high-spin d⁵ Fe³⁺ (n = 5) gives 5.92 BM, d³ Cr³⁺ (n = 3) gives 3.87 BM.

High-spin state occurs when Δo < pairing energy (weak field, 3d ions); low-spin when Δo > pairing energy (4d/5d ions, strong-field ligands such as CN⁻).

18-electron rule counts the metal d electrons plus two electrons per two-electron donor ligand; Ni(CO)₄, Fe(CO)₅ and Cr(CO)₆ obey it.

Jahn–Teller distortion is pronounced for octahedral d⁹ (Cu²⁺) and high-spin d⁴ (Cr²⁺, Mn³⁺) because the eg set is unequally occupied.

HSAB: hard acids (Al³⁺, Fe³⁺, Ti⁴⁺) bind F⁻ and O donors; soft acids (Ag⁺, Hg²⁺, Pt²⁺) bind S donors, I⁻ and CN⁻.

Lanthanide contraction arises from poor shielding by 4f electrons, making Zr/Hf and Nb/Ta nearly identical in radius and hard to separate.

Chelate effect: polydentate ligands give larger formation constants than analogous monodentate ligands because chelation releases more solvent molecules, increasing ΔS.

SN2: rate = k[RX][Nu], concerted backside attack with inversion; favoured for CH₃ and primary halides with a strong nucleophile in polar aprotic solvent (DMSO, DMF, acetone).

SN1: rate = k[RX]; carbocation stability 3° > 2° > 1° > CH₃; polar protic solvents and weak nucleophiles favour it, and racemisation with inversion bias results.

E2 requires an anti-periplanar β-H and leaving group, rate = k[RX][base]; bulky bases such as t-BuOK and tertiary halides favour elimination over substitution.

Markovnikov addition: H adds to the carbon bearing more hydrogens; peroxides reverse regiochemistry for HBr only, through a bromine radical chain.

Aromaticity requires a cyclic, planar, fully conjugated system with 4n+2 π electrons; 4n systems are antiaromatic and non-planar conjugated rings are non-aromatic.

EAS substituents: activating o/p - NH₂, OH, OR, NHCOR, R; deactivating m - NO₂, CN, COR, COOH, SO₃H; halogens are deactivating but o/p directing.

Cannizzaro: non-enolizable aldehydes (HCHO, PhCHO) with concentrated NaOH give alcohol plus carboxylate; enolizable aldehydes instead undergo aldol condensation.

Grignard reagents are destroyed by acidic hydrogens in H₂O, ROH, RNH₂ and terminal alkynes; they add to aldehydes, ketones, esters and CO₂.

Baeyer–Villiger migration aptitude: tertiary > secondary > primary > methyl, and the migrating group retains its configuration.

EDTA forms 1:1 complexes with most metal ions regardless of charge; the conditional constant K′ = α_Y⁴⁻ × K_f depends on pH, so titrations are buffered (e.g. pH 10 NH₃/NH₄Cl).

Mohr method: Cl⁻ titrated with AgNO₃ using K₂CrO₄ indicator, brick-red Ag₂CrO₄ marks the end point; the solution must be neutral to slightly alkaline.

Iodometry: oxidant plus excess KI liberates I₂, titrated with Na₂S₂O₃ (1 mol I₂ ≡ 2 mol S₂O₃²⁻); starch indicator is added near the end point.

Chromatography: k = (t_R − t₀)/t₀; resolution R = 2(t_R2 − t_R1)/(w₁ + w₂); plate number N = 16(t_R/w)².

Confidence interval: x̄ ± ts/√n with t for n − 1 degrees of freedom; a paired t-test compares two methods applied to the same samples.

Standard addition compensates for matrix effects; the calibration line is extrapolated to zero signal to obtain the original analyte concentration.

AAS uses a hollow cathode lamp emitting the analyte's sharp resonance lines, with flame or graphite-furnace atomisation; absorbance follows Beer's law.

Solvent extraction: D = [S]_org/[S]_aq and fraction extracted = D/(D + V_aq/V_org); several small portions extract more than one large portion.

Potentiometry: E = E° − (0.0592/n) log a; the glass electrode responds to H⁺ with a Nernstian slope of about 59 mV per decade at 25 °C.