Enthalpies of combustion, atomisation, bonds and solution

Several special enthalpies are used often:

• Enthalpy of combustion, ∆cH⊖: when one mole of a substance burns completely in oxygen. Methane: –890.3, carbon: –393.5, hydrogen: –285.8 kJ mol⁻¹. Combustion enthalpies are easy to measure, and through Hess's law they give formation enthalpies that are hard to measure.
• Enthalpy of atomisation, ∆aH⊖: when one mole of a substance is broken completely into gaseous atoms. For H₂ it is 435.0 kJ mol⁻¹; for CH₄, 1665 kJ mol⁻¹. For a diatomic molecule, this is the same as its bond dissociation enthalpy. Breaking a bond always needs energy, like pulling two close friends apart.

In a molecule with several bonds of the same kind, we use the mean bond enthalpy: the atomisation enthalpy divided by the number of bonds. For water, ∆aH ≈ 929 kJ mol⁻¹ for two O–H bonds, so the mean O–H bond enthalpy is 929 ÷ 2 ≈ 464.5 kJ mol⁻¹.

Bond enthalpies give an estimate of a reaction's enthalpy, for reactions in the gas phase:

∆rH ≈ Σ bond enthalpies of bonds broken – Σ bond enthalpies of bonds formed.

Breaking bonds costs energy; forming bonds releases it. If the new bonds are stronger, the reaction is exothermic.

Lattice enthalpy (for NaCl, +788 kJ mol⁻¹) cannot be measured directly. It is found indirectly using a Born-Haber cycle: a Hess's law cycle that builds the solid from its elements step by step (atomising the metal, ionising it, breaking the non-metal molecule into atoms, adding electrons to them, and finally forming the lattice).

When a salt dissolves, the lattice must be broken (costing the lattice enthalpy) and the ions are surrounded by water (releasing the hydration enthalpy): ∆solH = ∆latticeH + ∆hydH. For most salts, the result is positive, so they dissolve endothermically. Salts with a very large lattice enthalpy, such as many fluorides, dissolve only a little.