Chemistry: Physical Chemistry

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your HAT-UG Subject Knowledge paper.

Physical Chemistry applies physics-based laws to atomic structure, bonding, energetics, and reaction rates. For HAT-UG, the heaviest-yield units are gas laws, stoichiometry, equilibrium, electrochemistry, and kinetics. Master the six formulas below and you can attempt roughly 70% of the numerical items in the 3% chemistry block.

Ideal gas law: PV = nRT (R = 8.314 J·mol⁻¹·K⁻¹ or 0.0821 L·atm·mol⁻¹·K⁻¹; T in Kelvin).
Mole bridge: n = mass / molar mass (g·mol⁻¹).
Spontaneity: ΔG = ΔH − TΔS — negative ΔG means a spontaneous process.
Acidity: pH = −log₁₀[H⁺].
Rate law: Rate = k[A]ᵐ[B]ⁿ.
Electrolysis: m = (I × t × M) / (n × F), where F = 96,485 C·mol⁻¹.

Must-know constant	Value	Used in
R (gas constant)	8.314 J·mol⁻¹·K⁻¹	PV = nRT
F (Faraday)	96,485 C·mol⁻¹	Electrolysis
K_w at 25 °C	1.0 × 10⁻¹⁴	pH, pOH

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Atomic structure and bonding

Bohr’s model postulates fixed orbits where angular momentum mvr = nh/2π; modern quantum theory replaces orbits with orbitals defined by four quantum numbers (n, l, mₗ, mₛ). Electronegativity rises across a period and falls down a group, governing bond polarity. Ionic bonds form between metals and non-metals via electron transfer; covalent bonds share electrons; coordinate (dative) bonds share a lone pair from one atom.

States of matter and gas laws

Ideal gases obey PV = nRT, but real gases deviate at high P and low T. The Van der Waals equation corrects this with attraction (a) and volume (b) constants: (P + a n²/V²)(V − nb) = nRT. Always convert Celsius to Kelvin before substituting.

Thermodynamics and equilibrium

Hess’s law states the total enthalpy change is path-independent, so formation, combustion, and neutralisation enthalpies can be combined algebraically. ΔG = ΔH − TΔS predicts spontaneity: spontaneous when ΔG < 0. Equilibrium constants K_c (concentration-based) and K_p (partial-pressure-based) relate through K_p = K_c(RT)^Δn.

Common exam traps

Temperature must be in Kelvin for every gas-law and ΔG calculation.
Only gaseous species appear in K_p expressions — solids and liquids are excluded.
Molecularity equals reaction order only for elementary reactions.

Concept	Key point
K_c vs K_p	K_p = K_c(RT)^Δn
Le Chatelier	Shift opposes the applied change
Arrhenius	k = A·e^(−Eₐ/RT)

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Electrochemistry deep dive

A galvanic cell converts chemical energy to electrical energy spontaneously (ΔG < 0); an electrolytic cell does the reverse using external power. The Nernst equation links cell potential to concentration: E = E° − (RT/nF) ln Q. Faraday’s first law: mass deposited m = (I·t·M)/(n·F), where n is electrons transferred per ion.

Kinetics and mechanism

The rate law Rate = k[A]ᵐ[B]ⁿ is determined experimentally, not from stoichiometry. The Arrhenius equation k = A·e^(−Eₐ/RT) shows a 10 K rise roughly doubles k for many reactions. Catalysts lower Eₐ without altering ΔH.

Solutions and colligative properties

Colligative properties depend only on solute particle count. ΔT_b = K_b·m and ΔT_f = K_f·m describe boiling-point elevation and freezing-point depression respectively. Raoult’s law: P_solution = X_solvent·P°_solvent.

Worked micro-example

What mass of Mg is deposited when 2.0 A passes through molten MgCl₂ for 1 hour? n = (2.0 × 3600)/96485 = 0.0746 mol e⁻; Mg²⁺ needs 2 e⁻, so n(Mg) = 0.0373 mol; mass = 0.0373 × 24.3 = 0.91 g.

Practice prompts

At 25 °C, K_c for N₂ + 3H₂ ⇌ 2NH₃ is 4.0. If [N₂] = 0.10 M and [H₂] = 0.20 M, find [NH₃] at equilibrium.
ΔH = −92 kJ·mol⁻¹, ΔS = −198 J·mol⁻¹·K⁻¹. Is the reaction spontaneous at 298 K? At 500 K?

Advanced formula	Application
Nernst: E = E° − (0.0592/n) log Q	25 °C cell potential
π = MRT	Osmotic pressure
ΔG° = −RT ln K	Link K to free energy

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Chemistry: Physical Chemistry