Enthalpy

When you light a match, energy is released — heat, light, the small mechanical work of expanding gases. Where does the energy come from? Not from creation; the first law of thermodynamics forbids that. The energy was stored in the chemical bonds of the match-head materials and released when those bonds were broken and re-formed into more thermodynamically stable products. Chemists keep a particular kind of energy ledger — enthalpy — that tracks the heat content of substances at constant pressure; reaction enthalpy, the difference between the enthalpy of products and reactants, tells you whether a reaction releases heat (exothermic, like the match) or absorbs it (endothermic, like an instant cold pack). The book-keeping that lets us predict, design, and optimize chemical reactions runs on enthalpy.

Enthalpy (denoted H) is a thermodynamic state function defined as H = U + PV — internal energy plus pressure times volume — and at constant pressure the change in enthalpy ΔH equals the heat absorbed or released by the system: ΔH = q_p, with negative ΔH exothermic and positive ΔH endothermic. The reason chemists track enthalpy rather than just internal energy is that at constant pressure when a reaction changes the volume, some energy goes into work against atmospheric pressure, and enthalpy automatically accounts for this PV work. Hess's law (Germain Hess, 1840) — that enthalpy is a state function whose change depends only on initial and final states, not on the path between — lets chemists compute reaction enthalpies for reactions never measured directly. The standard enthalpy of formation (ΔH_f°, the enthalpy change when one mole of a compound forms from its elements in standard states at 25 °C and 1 atm) is tabulated for thousands of compounds. Bond enthalpies (the average energy required to break a particular type of bond — C-H ≈ 414 kJ/mol, O-H ≈ 463, C=C ≈ 614) let reaction enthalpies be estimated by summing broken-bond enthalpies and formed-bond enthalpies. Calorimetry measures these heats directly at either constant volume or constant pressure, and combustion enthalpies are particularly well tabulated for fuels (gasoline ~47 MJ/kg, ethanol ~30, hydrogen ~142). Crucially, exothermic does not mean spontaneous — the Gibbs free energy G = H − TS governs spontaneity at constant T, P, so a reaction is spontaneous when ΔG = ΔH − TΔS < 0, and an endothermic reaction can still be spontaneous if the entropy increase is large enough. Phase changes have characteristic enthalpies (ΔH_fusion, ΔH_vaporization, ΔH_sublimation), and water's anomalously large vaporization enthalpy (~40.7 kJ/mol) due to hydrogen bonding is the reason sweat cools the body so effectively.