Enthalpy of reaction and Hess's law

The standard enthalpy of reaction, ∆rH⊖, is the enthalpy change when all the substances are in their standard states: pure, at 1 bar pressure, usually at 298 K.

Phase changes also have enthalpies. For water: melting (fusion) needs 6.00 kJ mol⁻¹ at 273 K, and boiling (vaporisation) needs 40.79 kJ mol⁻¹ at 373 K (44.01 kJ mol⁻¹ at 298 K). Reversing a change reverses the sign: condensing water vapour gives out the heat that boiling took in.

The standard enthalpy of formation, ∆fH⊖, is the enthalpy change when one mole of a compound is formed from its elements in their reference states: their most stable forms at 1 bar and 298 K, such as H₂ gas, carbon as graphite, sulphur as rhombic sulphur. By definition, the ∆fH⊖ of an element in its reference state is zero.

With formation enthalpies, any reaction enthalpy can be worked out:

∆rH⊖ = Σ ∆fH⊖ (products) – Σ ∆fH⊖ (reactants), each multiplied by its coefficient in the equation.

A thermochemical equation gives the balanced equation, the states of all substances, and ∆H. If you multiply the equation by a number, multiply ∆H by the same number; if you reverse it, change the sign of ∆H.

Hess's law of constant heat summation: the enthalpy change of a reaction is the same whether it takes place in one step or in several. It is like climbing to the top floor of a building: whether you take the stairs or the lift, your gain in height is the same. So equations can be added and subtracted like algebra, and their ∆H values added and subtracted in the same way. This lets us find enthalpies that cannot be measured directly.