General & Physical Chemistry: Mole Concept to Electrochemistry

Why this topic decides your rank

General and physical chemistry carries the heaviest weight in the MECEE-BL chemistry section, and almost every question is numerical or concept-based rather than memory-based. Master the mole concept, equilibrium and electrochemistry calculations and you convert this into a guaranteed-scoring zone.

Mole concept and stoichiometry

One mole is the amount of substance containing as many elementary entities as there are atoms in 12 g of carbon-12: Avogadro's number, NA = 6.022 x 10^23.

• Limiting reagent: the reactant that is completely consumed; it decides the amount of product. Always divide moles by the stoichiometric coefficient and pick the smallest value.
• Empirical vs molecular formula: molecular formula = (empirical formula) x n, where n = molar mass / empirical formula mass.
• Normality: N = M x n-factor. For acid–base titration, N1V1 = N2V2 is the fastest exam route.
• Laws of chemical combination: conservation of mass (Lavoisier), definite proportions (Proust), multiple proportions (Dalton), Gay-Lussac's law of gaseous volumes and Avogadro's hypothesis.

Atomic structure

• Rutherford established the nucleus; Bohr quantized angular momentum: mvr = nh / 2(pi).
• Bohr radius for hydrogen: r(n) = 0.529 x n^2 / Z angstrom; energy E(n) = -13.6 x Z^2 / n^2 eV per atom.
• Hydrogen spectrum series: Lyman (UV, n1 = 1), Balmer (visible, n1 = 2), Paschen, Brackett, Pfund (IR). Rydberg equation: 1/lambda = R x Z^2 x (1/n1^2 - 1/n2^2), R = 109677 cm^-1.
• de Broglie: lambda = h / mv; Heisenberg: (delta x)(delta p) >= h / 4(pi).
• Quantum numbers: n (shell), l (subshell, 0 to n-1), m (orbital, -l to +l), s (+1/2 or -1/2).
• Filling rules: Aufbau (lowest energy first, by n + l rule), Pauli exclusion (no two electrons with all four quantum numbers identical), Hund's rule (maximum unpaired electrons in degenerate orbitals).
• Exceptional configurations: Cr = [Ar] 3d5 4s1 and Cu = [Ar] 3d10 4s1 (extra stability of half-filled and fully filled subshells).

Chemical bonding

• Ionic bond: complete electron transfer; favoured by low ionization energy of metal, high electron affinity of non-metal, high lattice energy. Fajans' rules: small cation + large anion + high charge increase covalent character.
• Covalent bond: sharing of electrons; described by VSEPR, hybridization and molecular orbital theory.

• Bond order (MOT) = (bonding electrons - antibonding electrons) / 2. O2 has bond order 2 and is paramagnetic (two unpaired electrons) — a classic MCQ.
• Hydrogen bonding explains the high boiling point of water, HF and NH3; intramolecular H-bonding makes o-nitrophenol more volatile than p-nitrophenol.
• Dipole moment: CO2 and BF3 have zero dipole moment (symmetric); H2O and NH3 are polar.

States of matter

• Ideal gas equation: PV = nRT, with R = 0.0821 L atm / (mol K) = 8.314 J / (mol K).
• Boyle's law (PV = constant at fixed T), Charles's law (V/T = constant at fixed P), Dalton's law of partial pressures, Graham's law of diffusion: r1/r2 = sqrt(M2/M1).
• Kinetic energy of one mole of gas: KE = (3/2)RT — depends only on temperature.
• Real gases obey van der Waals equation: (P + a n^2/V^2)(V - nb) = nRT; deviation is maximum at high pressure and low temperature.

Thermodynamics and thermochemistry

• First law: dU = q + w; work of expansion w = -P(delta V).
• Enthalpy: H = U + PV; at constant pressure q(p) = delta H.
• Hess's law: enthalpy change is path-independent — add thermochemical equations like algebra.
• Spontaneity is decided by Gibbs free energy: delta G = delta H - T delta S. Negative delta G means spontaneous; delta G = 0 at equilibrium.
• Relation to equilibrium constant: delta G(standard) = -RT ln K.
• Exothermic reactions have negative delta H; endothermic positive. A reaction with positive delta H and positive delta S becomes spontaneous only at high temperature.

Chemical equilibrium and ionic equilibrium

• For aA + bB = cC + dD: Kc = [C]^c [D]^d / ([A]^a [B]^b) and Kp = Kc (RT)^(delta n).
• Le Chatelier's principle: raising pressure shifts equilibrium toward fewer gas moles; raising temperature favours the endothermic direction; a catalyst changes neither position nor K, only speed.
• Haber process (N2 + 3H2 = 2NH3, exothermic): favoured by high pressure, low temperature (practically ~450 C with Fe catalyst).
• pH = -log[H+]; pH + pOH = 14 at 25 C; Kw = 1 x 10^-14 at 25 C.
• Buffer pH (Henderson–Hasselbalch): pH = pKa + log([salt]/[acid]).
• Common ion effect suppresses ionization of weak electrolytes; solubility product Ksp predicts precipitation when ionic product exceeds Ksp.
• Salt hydrolysis: salt of strong acid + weak base is acidic (NH4Cl); weak acid + strong base is basic (CH3COONa).

Chemical kinetics

• Rate law: rate = k [A]^x [B]^y; order (x + y) is experimental, molecularity is theoretical and never zero or fractional.
• First-order kinetics: k = (2.303/t) log([A]0/[A]); half-life t(1/2) = 0.693/k, independent of initial concentration. Radioactive decay is always first order.
• Zero order: t(1/2) = [A]0 / 2k — half-life proportional to initial concentration.
• Arrhenius equation: k = A e^(-Ea/RT); a catalyst lowers activation energy Ea; roughly, rate doubles for every 10 C rise.

Electrochemistry

• Electrolysis (Faraday's laws): mass deposited W = ZIt = (E x I x t)/96500, where E is equivalent mass and 96500 C is one Faraday.
• Galvanic cell: oxidation at anode (negative), reduction at cathode (positive) — opposite sign convention to electrolytic cells.
• Standard cell EMF: E(cell) = E(cathode) - E(anode); positive EMF means spontaneous.
• Nernst equation (25 C): E = E(standard) - (0.0591/n) log Q.
• Electrochemical series: metals above hydrogen (K, Na, Ca, Mg, Al, Zn, Fe) displace H2 from dilute acids; Cu, Ag, Au do not.
• Daniell cell: Zn anode, Cu cathode, E(standard) = 1.10 V.

Exam tip: MECEE numericals cluster around four formulae — n = m/M, t(1/2) = 0.693/k, pH = -log[H+] and W = EIt/96500. Practise each until a question takes under 45 seconds; the paper rewards speed on these more than on any theory recall.

Quick revision

• 22.4 L of any ideal gas at STP (273 K, 1 atm) contains 1 mole = 6.022 x 10^23 molecules.
• Energy of the H-atom electron: E(n) = -13.6/n^2 eV; Balmer series lies in the visible region.
• Cr and Cu have anomalous configurations because half-filled and fully filled d-subshells are extra stable.
• O2 is paramagnetic with bond order 2 by molecular orbital theory.
• delta G = delta H - T delta S; negative delta G means the process is spontaneous.
• A catalyst speeds attainment of equilibrium but does not change Kc or the equilibrium position.
• First-order half-life is constant (0.693/k); zero-order half-life depends on initial concentration.
• One Faraday = 96500 C deposits one gram-equivalent of any substance during electrolysis.