Physical Chemistry
Physical Chemistry items test whether you can move between thermodynamic, kinetic, quantum, and electrochemical descriptions of one system without losing signs, units, or standard-state conventions.
Thermodynamics
- ΔG = ΔH − TΔS governs spontaneity at constant T and P; ΔG < 0 means spontaneous, and ΔG = 0 at equilibrium.
- ΔG° = −RT ln K, while ΔG = ΔG° + RT ln Q describes the actual mixture; use K only at equilibrium.
- dG = V dP − S dT; for an ideal gas, ΔG = nRT ln(P2/P1).
Kinetics
- Arrhenius: k = A exp(−Ea/RT), so ln(k2/k1) = −(Ea/R)(1/T2 − 1/T1). A steep temperature dependence means a large Ea.
- First-order half-life t1/2 = 0.693/k is independent of starting concentration; second-order t1/2 = 1/(k[A]0) is not.
- The rate law is set by the slow step; apply the steady-state approximation to reactive intermediates.
Quantum and spectroscopy
- Particle in a box: E_n = n²h²/(8mL²); longer boxes and heavier particles give smaller spacings.
- Harmonic oscillator: E = (v + ½)hν with Δv = ±1; anharmonicity compresses the upper levels.
- Rigid rotor levels go as J(J + 1) with the selection rule ΔJ = ±1.
Worked example
A reaction has ΔH° = +50.0 kJ/mol and ΔS° = +100 J/(mol·K), both roughly temperature-independent. ΔG° < 0 requires T > ΔH°/ΔS° = 50,000/100 = 500 K. At 298 K, ΔG° = 50,000 − 298(100) = +20.2 kJ/mol, so K = exp(−20,200/(8.314 × 298)) = exp(−8.15) ≈ 2.9 × 10^−4, reactant-favored as expected below the crossover temperature.
Traps
- Mixing kJ and J when ΔS is quoted in J/(mol·K).
- Using ΔG° to decide spontaneity for a nonstandard mixture instead of ΔG.
- Confusing activation energy with the enthalpy of reaction.
- Omitting the RT ln Q term when computing cell potentials.
- Substituting ΔG in kJ into ΔG = −RT ln K without converting to joules.