Physical Chemistry: Where Physics Meets Chemistry

Chemical Thermodynamics

First law: energy is conserved — ΔU = q + w. Enthalpy: H = U + PV, ΔH = qp (heat at constant pressure). Exothermic (ΔH < 0): combustion, neutralization. Endothermic (ΔH > 0): melting, dissolution of NH₄NO₃. Hess's law: ΔH is path-independent — calculate from standard enthalpies of formation. Second law: entropy of an isolated system always increases — ΔS_universe > 0 for spontaneous processes. Entropy: S = k_B ln W (Boltzmann) — disorder, number of microstates. Third law: S → 0 as T → 0 K for a perfect crystal. Gibbs free energy: G = H − TS, ΔG < 0 for spontaneous processes at constant T, P. Chemical potential: μᵢ = (∂G/∂nᵢ)T,P — equilibrium when μᵢ equal in all phases. Equilibrium constant: ΔG° = −RT ln K — connects thermodynamics to chemical equilibrium. Phase diagrams: pressure-temperature maps showing solid/liquid/gas regions, triple point, critical point. Clausius-Clapeyron equation: dP/dT = ΔH/(TΔV) — relates phase boundary slope to enthalpy of transition.

Chemical Kinetics

Reaction rate: change in concentration per unit time — rate = −d[A]/dt = k[A]ⁿ (rate law). Rate constant k: depends on temperature (Arrhenius equation: k = Ae^(−Eₐ/RT)). Activation energy (Eₐ): energy barrier that must be overcome — determines temperature sensitivity. Reaction order: zeroth (constant rate), first (exponential decay, t½ = ln2/k), second (1/[A] linear in t). Reaction mechanisms: series of elementary steps — rate law comes from rate-determining step (RDS). Steady-state approximation: d[intermediate]/dt ≈ 0 — simplifies complex mechanisms. Catalysis: lowers activation energy without being consumed. Homogeneous (same phase) vs. heterogeneous (different phases). Enzyme kinetics: Michaelis-Menten — v = V_max[S]/(K_M + [S]). Lineweaver-Burk plot: 1/v vs. 1/[S] for parameter determination. Transition state theory (Eyring): k = (k_BT/h)e^(−ΔG‡/RT) — relates rate to activation free energy. Collision theory: rate depends on collision frequency, orientation factor, and energy factor. Marcus theory: electron transfer rates — Nobel Prize 1992 (Rudolph Marcus).

Quantum Chemistry

Schrödinger equation: Ĥψ = Eψ — the fundamental equation of quantum chemistry. Hydrogen atom: exact solution — energy levels Eₙ = −13.6/n² eV, atomic orbitals (s, p, d, f). Multi-electron atoms: no exact solution — approximation methods required. Hartree-Fock (HF): self-consistent field method — each electron moves in the average field of all others. Electron correlation: HF misses instantaneous electron-electron interactions. Post-HF methods: MP2 (perturbation theory), CCSD(T) ("gold standard" of quantum chemistry — chemical accuracy ~1 kcal/mol). Density Functional Theory (DFT): Hohenberg-Kohn theorems — energy is a functional of electron density. Kohn-Sham DFT (Nobel 1998): practical implementation — B3LYP functional most widely used. Basis sets: mathematical functions representing orbitals — STO-3G, 6-31G*, cc-pVTZ, plane waves. Molecular orbital theory: LCAO (Linear Combination of Atomic Orbitals) — bonding and antibonding orbitals. Computational chemistry software: Gaussian, ORCA, VASP, Quantum ESPRESSO, PySCF.

Spectroscopy

Spectroscopy: study of interaction between matter and electromagnetic radiation — the primary tool of physical chemistry. UV-Vis spectroscopy: electronic transitions (π→π*, n→π*) — Beer-Lambert law: A = εbc. Conjugation shifts absorption to longer wavelengths (lower energy). IR spectroscopy: vibrational modes (stretching, bending) — molecular fingerprint. Key peaks: O-H (3200-3600 cm⁻¹), C=O (1680-1750 cm⁻¹), C-H (2850-2960 cm⁻¹). Raman spectroscopy: complementary to IR — measures inelastic scattering, different selection rules (polarizability change). NMR spectroscopy: nuclear spin transitions in magnetic field — chemical shifts, coupling constants, 2D techniques (COSY, NOESY). ¹H and ¹³C NMR: structure determination workhorses in organic chemistry. Mass spectrometry: molecular weight and fragmentation pattern — ESI, MALDI, EI ionization. Tandem MS (MS/MS) for protein sequencing. X-ray crystallography: diffraction pattern → electron density map → 3D molecular structure. Bragg's law: nλ = 2d sinθ. Cryo-EM (electron microscopy): near-atomic resolution of large complexes without crystallization — Nobel 2017 (Henderson, Frank, Dubochet). Spectroscopy + computation: DFT-calculated spectra compared with experimental — aids assignment and interpretation.

❓ Frequently Asked Questions

First law: energy is conserved — ΔU = q + w. Enthalpy: H = U + PV, ΔH = qp (heat at constant pressure). Exothermic (ΔH < 0): combustion, neutralization. Endothermic (ΔH > 0): melting, dissolution of N...

Reaction rate: change in concentration per unit time — rate = −d[A]/dt = k[A]ⁿ (rate law). Rate constant k: depends on temperature (Arrhenius equation: k = Ae^(−Eₐ/RT)). Activation energy (Eₐ): energy...

Schrödinger equation: Ĥψ = Eψ — the fundamental equation of quantum chemistry. Hydrogen atom: exact solution — energy levels Eₙ = −13.6/n² eV, atomic orbitals (s, p, d, f). Multi-electron atoms: no ex...

Spectroscopy: study of interaction between matter and electromagnetic radiation — the primary tool of physical chemistry. UV-Vis spectroscopy: electronic transitions (π→π*, n→π*) — Beer-Lambert law: A...

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