Advanced chemistry: colligative properties, Raoult's law, electrochemistry, kinetics, and organic conversions. Essential for JEE/NEET and board exams.
P_A = χ_A × P°_AP_A = partial pressure of A, χ_A = mole fraction, P°_A = vapour pressure of pure AΔP/P° = χ_solute = n_solute / (n_solute + n_solvent)Independent of identity of solute (colligative); for non-volatile solutesΔTb = Kb × mKb = molal boiling point elevation constant (°C·kg/mol), m = molalityΔTf = Kf × mKf = molal freezing point depression constant (°C·kg/mol), m = molalityπ = CRT = (n/V)RTC = molarity, R = 0.0821 L·atm/(mol·K), T in Kelvin; most direct colligative propertyi = observed colligative effect / expected effect for 1 mol solutei ≈ 1 for nonelectrolytes, i > 1 for electrolytes (ions); ΔTb = i·Kb·mα = (initial moles − final moles) / initial molesi = 1 + (n−1)α where n = number of ions per formula unitc = Kₕ × P_gasc = concentration (mol/L), Kₕ = Henry's law constant, P in atms = √(Ksp) (pure water); Ksp = [A⁺]^a × [B⁻]^b for ABAdding common ion decreases solubility; Ksp independent of concentrationE_cell = E°_cell − (0.059/n) × log Q (at 25°C)Q = reaction quotient, n = moles of e⁻ transferred, all E in voltsE_cell = E°_cell − (RT/nF) × ln QR = 8.314 J/(mol·K), T in Kelvin, F = 96,500 C/mol, E in volts0 = E°_cell − (0.059/n) × log Kₑq → Kₑq = 10^(n×E°/0.059)When E_cell = 0, system is at equilibriumE°_cell = E°_cathode − E°_anodeBoth E° from standard reduction potential tablesW = (M/nF) × Q = (M × I × t) / (nF)W = mass deposited (g), Q = charge (coulombs), I = current (A), t = time (s)Λm = κ / cκ = conductivity (S/cm), c = concentration (mol/L), Λm in S·cm²/molκ = (l/A) × Gl = length between electrodes, A = cross-sectional area, G = conductanceΛm = Λ°m − K√cΛ°m = limiting molar conductivity, K = Kohlrausch constantΛm = F(u⁺ + u⁻)u = mobility (cm²/(V·s)), sum of cation and anion mobilityRate = −d[A]/dt = +d[C]/dt (for aA → cC)Negative for reactants (consumed), positive for products (formed)Rate = k[A]^m[B]^nk = rate constant, m & n = order (determined from experiment); overall order = m + n[A] = [A]₀ − kt; t₁/₂ = [A]₀/(2k)Half-life depends on initial concentration; straight line on [A] vs tln[A] = ln[A]₀ − kt; t₁/₂ = 0.693/kHalf-life constant; ln[A] vs t is linear; k in s⁻¹ typically1/[A] = 1/[A]₀ + kt; t₁/₂ = 1/(k[A]₀)Half-life depends on initial concentration; 1/[A] vs t is lineark = A·e^(−Ea/RT); ln(k₂/k₁) = (Ea/R)(T₂−T₁)/(T₁T₂)A = frequency factor, Ea = activation energy (J/mol), R = 8.314 J/(mol·K)Rate doubles for every ~10°C rise (rough estimate)Exact value from Arrhenius; depends on EaRate-determining step controls overall rate lawElementary steps must sum to give overall equationRate = Z·p·e^(−Ea/RT)Z = collision frequency, p = steric factor (orientation), Ea = activation energyRCOOH + R'OH → RCOOR' + H₂O (acid catalyst H₂SO₄, heat)Reversible; equilibrium favors products if water removedRCOOR' + NaOH → RCOONa + R'OH (ester + strong base)Irreversible soap formation; R can be long chain alkyl2 CH₃CHO → CH₃CH(OH)CH₂CHO (base catalyst) → CH₃CH=CHCHO + H₂O (heat)Enolate attacks carbonyl; forms C−C bondRMgX + R'CHO → R−CH(OH)−R' (SN2-like); followed by acid workupHighly nucleophilic; reacts with any C=O or C≡NR−O⁻ + R'−X → R−O−R' + X⁻ (SN2, X = Br, I, Cl)R−O⁻ from alcohol + base (KOH); X on primary/secondary alkyl bestR₃C−H + Base → C=C + alkene (1° substrate poor, 3° excellent)Zaitsev's rule: major product is more substituted (more stable) alkeneAr−NO₂ + Nu⁻ → Ar−Nu + NO₂⁻ (activated by NO₂, CN, F at ortho/para)Requires electron-withdrawing group; rare for Ar−HRCH₂OH → RCHO (primary alcohol to aldehyde); RCHO → RCOOH (aldehyde to carboxylic acid)KMnO₄ strong; Jones quick; final product depends on conditionsRCOOH → RCH₂OH (carboxylic acid to 1° alcohol); RCOR' → RCHOHC'H₃ (ketone to 2° alcohol)LiAlH₄ powerful (all carbonyls); NaBH₄ mild (aldehydes, ketones only)Ar−H + R−CO−Cl → Ar−CO−R (AlCl₃ catalyst)Creates aryl ketone; Lewis acid required; para isomer majorn CH₂=CH₂ → (−CH₂−CH₂−)n (ethylene → polyethylene)Alkene monomers; chain grows by repeated additionn HOOC−R−COOH + n HO−R'−OH → polyester + 2n H₂OBifunctional monomers; water or small molecule eliminated per linkn H₂N−(CH₂)₆−NH₂ + n HOOC−(CH₂)₄−COOH → nylon + 2n H₂OAdipic acid + hexamethylenediamine; amide linkageDegree of polymerization = number of monomer units in chainn in (−C−C−)n formula; typically 100s to 1000sM_polymer = (degree of polymerization) × (molar mass of monomer unit)Approximate for long chains; end groups negligiblex/m = k·P^(1/n) (at constant T)x = mass adsorbed, m = mass adsorbent, P = pressure, k & n constantsx/m = (abP) / (1 + bP)a = monolayer capacity, b = affinity constant; more realistic than FreundlichHigh |ζ| > stability (similar charges repel); low |ζ| → coagulationζ = zeta potential; electrostatic stabilization; salt can cause coagulationCoagulating power of ions ∝ charge; +3 > +2 > +1Higher charge density = faster coagulation of opposite colloidNumber of ligands bonded to central metal ionTypically 4 (square planar, tetrahedral) or 6 (octahedral)Ligands named first (alphabetical) + central metal + oxidation state in ()e.g. [Co(NH₃)₆]³⁺ = hexaamminecobalt(III)d_xy, d_xz, d_yz (lower) | Δ | d_x²−y², d_z² (higher)Δ = Δ₀ (crystal field splitting energy); weak field vs strong field determines spinHigh spin: Δ small → electrons occupy all d orbitals singly first (Hund's rule)Low spin: Δ large → electrons pair in lower orbitals (strong field ligands like CN⁻)μ = √[n(n+2)] B.M. (Bohr magnetons)n = number of unpaired electrons; stronger field → more pairing → lower μ% by mass = (mass of element/total mass) × 100Use molar masses and stoichiometry; sum should = 100%Divide all moles by smallest; multiply by whole number if fractionThis gives the empirical formula subscriptsDivide each reactant moles by its stoichiometric coefficient; smallest = limitingControls theoretical yield; others are in excessN₁V₁ = N₂V₂ (for titrations); relates to concentration for redoxN = equivalents/L; for polyprotic acid, N = M × (number of H⁺/OH⁻)ΔH_rxn = ΔH_reaction per balanced equation (not per mole of single reactant)Always specify 'per mole' or clarify reaction stoichiometry