Chemistry: Physical Chemistry

Chemistry: Physical Chemistry

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Physical Chemistry links physics to chemical change: it quantifies states of matter, thermodynamics, equilibrium, kinetics, electrochemistry, and solutions. The single most-tested equation is the ideal gas law, PV = nRT, where P is pressure (atm), V is volume (L), n is moles, R = 0.0821 L·atm·mol⁻¹·K⁻¹, and T is temperature (K). Spontaneity of any reaction at constant T and P is decided by Gibbs free energy, ΔG = ΔH − TΔS; ΔG < 0 means the reaction proceeds on its own. Reaction speed follows the rate law, rate = k[A]ᵐ[B]ⁿ, where k is the rate constant and the exponents m, n are reaction orders found by experiment, never from stoichiometry. For acid–base questions, always remember pH = −log[H⁺] and Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. In NAT-I, expect one or two MCQs drawn from these clusters; the trap answers usually confuse ΔG sign with K or mix up order vs. molecularity.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Atomic Structure and Bonding

The Bohr model restricts electrons to fixed orbits with quantized angular momentum mvr = nh/2π; transitions between levels n₁ and n₂ emit/absorb photons of energy ΔE = −13.6 Z²(1/n₁² − 1/n₂²) eV. Four quantum numbers (n, l, mₗ, mₛ) describe each electron uniquely, and the Aufbau, Hund, and Pauli principles build the electronic configuration. Bonding spans ionic (electron transfer, lattice energy driven), covalent (shared pairs, directional), coordinate (one atom donates both electrons), and hydrogen bonding (special dipole–dipole, responsible for water’s high boiling point). VSEPR theory predicts molecular shape from lone-pair repulsion, and hybridization (sp, sp², sp³, sp³d, sp³d²) explains observed geometries.

Gases and Solutions

Beyond PV = nRT, the combined gas law P₁V₁/T₁ = P₂V₂/T₂ handles constant-mole problems; Dalton’s law says total pressure = sum of partial pressures; Graham’s law relates diffusion rate to 1/√M. Solutions are quantified by molarity (mol/L), molality (mol/kg solvent), normality, mass %, and mole fraction x. Raoult’s law: P_solution = x_solvent · P°_solvent; positive/negative deviations mark non-ideal behaviour.

Colligative Properties

Properties depending only on particle count, not identity: relative lowering of vapour pressure (ΔP/P° = x_solute), boiling-point elevation ΔT_b = i K_b m, freezing-point depression ΔT_f = i K_f m, and osmotic pressure π = iMRT, where i is the van’t Hoff factor.

Thermodynamics

First law: ΔE = q + w. Hess’s law lets you sum reaction enthalpies to get an unknown ΔH. Entropy ΔS measures disorder; the second law requires ΔS_universe > 0 for a spontaneous process. Combining gives ΔG = ΔH − TΔS and the link ΔG° = −RT ln K.

Equilibrium and Kinetics

At equilibrium, rates of forward and reverse reactions are equal; K_c = [products]^coeff / [reactants]^coeff. Le Chatelier’s principle predicts shifts when concentration, temperature, or pressure changes. For kinetics, the Arrhenius equation k = A e^(−Ea/RT) shows that a small temperature rise sharply increases k. Catalysts lower Eₐ without being consumed.

Electrochemistry and Ionic Equilibria

In a galvanic cell, electrons flow from anode (oxidation) to cathode (reduction); E°cell = E°cathode − E°anode. The Nernst equation at 25 °C: E = E° − (0.0591/n) log Q. Faraday’s first law states m = (E·I·t)/96500. For weak acids, [H⁺] = √(Kₐ·C); for salts of weak acid + strong base, hydrolysis makes the solution basic.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge Cases and Connections

Thermodynamics vs. kinetics: a reaction with ΔG < 0 is thermodynamically spontaneous but may be kinetically frozen (diamond → graphite). Heterogeneous equilibria (e.g., CaCO₃(s) ⇌ CaO(s) + CO₂(g)) omit pure solids/liquids from K expressions. In electrolysis, the product at an electrode depends on overpotential, not just standard potential — water is oxidised before F⁻ or SO₄²⁻. Activity vs. concentration: at high ionic strength, replace [X] with aₓ = γₓ[X]; for the Nernst equation, use activities for accurate cell potentials.

Worked Example — Buffer pH

A buffer contains 0.20 mol/L acetic acid (Kₐ = 1.8 × 10⁻⁵) and 0.30 mol/L sodium acetate. Using the Henderson–Hasselbalch equation: pH = pKₐ + log([A⁻]/[HA]) = −log(1.8 × 10⁻⁵) + log(0.30/0.20) pH = 4.74 + 0.176 ≈ 4.92.

Common Traps in NAT-I

• Confusing order (experimental, in rate law) with molecularity (theoretical, in elementary step).
• Forgetting the sign of w: expansion work is w = −PΔV, so w is negative when gas expands.
• Treating K_p and K_c as interchangeable; K_p = K_c(RT)^Δn.
• Assuming catalysts shift equilibrium — they only speed the approach.

Practice Prompts

1. For the reaction 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), ΔH = −198 kJ/mol. Predict how (a) increasing pressure and (b) raising temperature will shift equilibrium. Justify using Le Chatelier’s principle and the sign of ΔH.
2. A first-order reaction has k = 2.5 × 10⁻³ s⁻¹. Calculate the half-life t₁/₂ and the time for 80% completion. (Hint: use ln(2)/k and ln([A]₀/[A]) = kt.)

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