$\Delta H_f^\circ$ is the enthalpy change when 1 mole of a substance is formed from its constituent elements in their standard states (most stable allotropes at 298 K, 1 bar/1 atm). By convention: $\Delta H_f^\circ$ of any element in its standard state = 0. Examples: $\Delta H_f^\circ[H_2O(l)] = -286$ kJ/mol. $\Delta H_f^\circ[CO_2(g)] = -393.5$ kJ/mol. $\Delta H_f^\circ[NH_3(g)] = -46$ kJ/mol. $\Delta H_f^\circ[C_2H_2(g)] = +227$ kJ/mol (endothermic — less stable than elements). Standard state: gas at 1 bar, liquid or solid in pure form at 1 bar. For ions in solution: reference is $\Delta H_f^\circ[H^+(aq)] = 0$ (arbitrary convention). Standard enthalpy of reaction: $\Delta H_{rxn}^\circ = \sum \Delta H_f^\circ(products) - \sum \Delta H_f^\circ(reactants)$.

Hess law (1840): total enthalpy change for a reaction is independent of the route taken — only depends on initial and final states. This is a consequence of enthalpy being a state function. Applications: (1) Calculating $\Delta H_f^\circ$ for compounds that cannot be directly synthesised. (2) Calculating $\Delta H_{rxn}$ from tabulated $\Delta H_f^\circ$ values. (3) Born-Haber cycle for ionic compounds. (4) Energy of formation of unstable/reactive species. Rules for manipulating equations: reverse reaction → sign of $\Delta H$ changes. Multiply equation by $n$ → multiply $\Delta H$ by $n$. Add equations → add $\Delta H$. Example: $C(s) + O_2(g) \to CO_2(g)$ ($\Delta H_1$) and $CO(g) + \frac{1}{2}O_2(g) \to CO_2(g)$ ($\Delta H_2$) → $C(s) + \frac{1}{2}O_2(g) \to CO(g)$: $\Delta H = \Delta H_1 - \Delta H_2$.

Bond enthalpy (bond dissociation energy): energy required to break 1 mole of bonds in gaseous molecules. Always positive (endothermic). $\Delta H_{rxn} \approx \sum$ (bonds broken) $- \sum$ (bonds formed). Bonds broken: require energy (+ve). Bonds formed: release energy (-ve). Average bond enthalpies (kJ/mol): C-C: 347, C=C: 614, C≡C: 839. C-H: 413, N-H: 391, O-H: 463. C=O: 799, C-N: 305, N=N: 418, N≡N: 945. Cl-Cl: 242, H-H: 436, H-Cl: 431. This method gives approximate $\Delta H$ (uses average values). More accurate: $\Delta H_f^\circ$ method (uses actual experimental values). Bond enthalpy method is useful when $\Delta H_f^\circ$ values are not available.

Born-Haber cycle applies Hess law to ionic compound formation. For NaCl: $\Delta H_f^\circ[NaCl(s)] = \Delta H_{sub}[Na] + IE_1[Na] + \frac{1}{2}\Delta H_{diss}[Cl_2] + EA[Cl] + \Delta H_{lattice}[NaCl]$. All steps: sublimation of Na(s)→Na(g): +108 kJ. Ionisation of Na(g)→Na⁺(g): +496 kJ. Dissociation of Cl2: +121 kJ. Electron affinity of Cl: -349 kJ. Lattice enthalpy of NaCl: -787 kJ. Sum = -411 kJ/mol (matches experimental $\Delta H_f^\circ$). Used to find: lattice enthalpy (not directly measurable), electron affinity of noble gas-like configurations, ionic radii. Lattice enthalpy ∝ charge²/r (Born-Landé/Kapustinski equations).

$\Delta H_c^\circ$ = enthalpy when 1 mole of substance burns completely in excess O2. Always negative (exothermic). Examples: CH4: -890 kJ/mol. C8H18 (octane): -5471 kJ/mol. C6H12O6 (glucose): -2803 kJ/mol. Ethanol: -1367 kJ/mol. Calorific values: coal ~30 MJ/kg, petrol ~44 MJ/kg, natural gas ~50 MJ/kg, hydrogen ~142 MJ/kg (highest). Bomb calorimeter: measures $\Delta U$ (constant volume) → $\Delta H = \Delta U + \Delta n_g RT$. Applications: food energy (kcal/100g from bomb calorimetry), rocket propellant energy density, fuel efficiency comparisons.

Enthalpy of reaction varies with temperature: $\Delta H_{T_2} = \Delta H_{T_1} + \Delta C_p (T_2 - T_1)$ where $\Delta C_p = \sum C_p(products) - \sum C_p(reactants)$. Kirchhoff equation (differential form): $d(\Delta H)/dT = \Delta C_p$. If $\Delta C_p > 0$: $\Delta H$ becomes more positive (less exothermic) at higher $T$. If $\Delta C_p < 0$: $\Delta H$ becomes more negative (more exothermic) at higher $T$. At moderate temperature ranges: $\Delta C_p$ assumed constant. Important for industrial reactions at high temperatures. The standard enthalpy values tabulated at 298 K must be corrected for reactions run at different temperatures.

$\Delta H_{soln}$ = enthalpy change when 1 mole of solute dissolves in large excess of solvent. For ionic salts: $\Delta H_{soln} = \Delta H_{lattice}$(endothermic, breaking lattice) $+ \Delta H_{hydration}$(exothermic, ion-water attraction). If $|\Delta H_{hyd}| > \Delta H_{lattice}$: exothermic dissolution (NaOH, H2SO4). If $|\Delta H_{hyd}| < \Delta H_{lattice}$: endothermic (NH4NO3, KNO3 — used in cold packs). Enthalpy of hydration $\Delta H_{hyd}$ depends on charge density (charge/r): Li⁺ > Na⁺ > K⁺ (smaller ion, more hydration). Mg²⁺ >> Na⁺ (higher charge). Integral vs differential enthalpy of solution: integral = per mole from pure solid to specified concentration. Differential = for dissolving in already-existing solution.

$\Delta G = \Delta H - T\Delta S$. Spontaneous when $\Delta G < 0$. $\Delta G < 0$: $\Delta H < 0, \Delta S > 0$ (always spontaneous). $\Delta H > 0, \Delta S < 0$ (never spontaneous). $\Delta H < 0, \Delta S < 0$: spontaneous at low $T$ (enthalpy driven). $\Delta H > 0, \Delta S > 0$: spontaneous at high $T$ (entropy driven). Transition temperature: $T = \Delta H/\Delta S$ (where $\Delta G = 0$). Standard free energy: $\Delta G^\circ = -RT\ln K$. At equilibrium: $\Delta G = 0$ (not $\Delta G^\circ$). $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$. Electrochemical relation: $\Delta G^\circ = -nFE^\circ$. All three are connected: $\Delta G^\circ = -RT\ln K = -nFE^\circ$.