Thermodynamic bookkeeping of reactions: enthalpy, Gibbs free energy, Hess's law, and the ΔG < 0 spontaneity criterion. Grounded directly in thermodynamics (L1) and statistical mechanics.
thermochemistry
Enthalpy (H)
Thermodynamic state function H = U + pV. At constant pressure, ΔH equals the heat of reaction: exothermic (ΔH < 0) or endothermic (ΔH > 0).
Gibbs free energy (G)
Thermodynamic potential G = H - TS minimised at constant T and p. ΔG < 0 ⇔ spontaneous forward reaction; ΔG = 0 ⇔ equilibrium.
Hess's law
Enthalpy change for a reaction is independent of the pathway taken: ΔH_total = Σ ΔH_steps. A direct consequence of H being a state function.
Reaction spontaneity criterion
A reaction at constant T, p is spontaneous iff ΔG = ΔH − TΔS < 0. Enthalpy-driven (ΔH < 0, TΔS small), entropy-driven (TΔS > ΔH), or…
Bond dissociation energy
Enthalpy change for homolytic cleavage of a specific bond in the gas phase at 298 K. Bookkeeping value for estimating ΔH_rxn via Hess-like…
Standard enthalpy of formation (Δ_f H°)
Enthalpy change when one mole of a compound is formed from its elements in standard states. Elemental standard states have Δ_f H° ≡ 0 by…
Clausius-Clapeyron equation
Coexistence-curve slope on a (p,T) phase diagram: dp/dT = L / (T Δv). For liquid-gas equilibria, integrates to ln(p) = -ΔH_vap / (RT) + C.
Calorimetry
Experimental measurement of heat flow during a process, typically in a bomb calorimeter (constant V → ΔU) or coffee-cup calorimeter…
State function
A thermodynamic quantity whose value depends only on the current state of the system, not on the path taken to reach it. Internal energy U,…
Van 't Hoff equation
Temperature dependence of the equilibrium constant: d(ln K)/dT = ΔH° / (RT²), where ΔH° is the standard reaction enthalpy. Integrates…
Trouton's rule
ΔS_vap ≈ 85-88 J/(K·mol) for non-H-bonding liquids at normal boiling point. H-bonded liquids exceed (water ~109) due to structured liquid…
Hess's law & thermochemical cycles
ΔH of reaction path-independent; construct Born-Haber cycle for lattice energy; MO for bond dissociation.
Bomb calorimetry
Constant-V combustion in O₂; measures ΔU then converts to ΔH via RTΔn; heat capacity C_cal calibrated with benzoic acid.
DSC and TGA
DSC heat-flow vs T gives melt, glass, crystal, rxn; TGA mass loss quantifies decomposition/desolvation; coupled DSC-TGA.
Atomization and sublimation enthalpies
ΔH_at = Σ BDE for molecule → gaseous atoms; ΔH_sub for solid → gas; bridge MO-derived to experimental energetics.
Lattice energy — Born–Lande / Kapustinskii
U ~ (N_A M z⁺z⁻ e²/4πε₀r₀)(1-1/n); Kapustinskii uses thermochemical radii; predicts ionic solid stabilities.
Hydration enthalpy — Born model
ΔH_hyd = -N_A z²e²/(8πε₀r)(1-1/ε); predicts trends but under-accounts for short-range structure; informs ΔG of ion in solution.
Gibbs–Helmholtz equation
∂(ΔG/T)/∂T = -ΔH/T²; extrapolate ΔG across temperatures; useful for equilibria.
Ellingham diagrams
ΔG°_f vs T for oxide formation; crossing points set reduction thresholds in metallurgy; carbothermic reduction above CO line.
Residual entropy (glass/CO crystal)
S(0) > 0 for frozen disorder; CO crystal has 5.76 J/mol·K; glass entropy in amorphous solids.
Isothermal titration calorimetry (ITC)
Direct measurement of ΔH + K_a for binding in a single experiment; standard for drug-target thermodynamics.