Thermochemistry

The heat content of a system at constant pressure is its enthalpy, H. We never measure H itself, only the change, ΔH, during a reaction. Exothermic reactions release heat, so ΔH is negative; endothermic reactions absorb it, so ΔH is positive — the deeper, quantitative version of the energetics you met earlier.

Enthalpy changes are quoted per mole under standard conditions (298 K, 1 atm), written ΔH°.

A few named enthalpy changes come up constantly. Enthalpy of formation (ΔHf°): forming one mole of a compound from its elements. Enthalpy of combustion (ΔHc°): burning one mole completely in oxygen. Enthalpy of reaction: for the reaction as written. Elements in their standard state have ΔHf° = 0 by definition.

Enthalpy is a state function — it depends only on the start and end states, not the route between them. That is Hess's law: the total enthalpy change is the same whether a reaction happens in one step or several.

It is enormously useful because it lets you calculate a ΔH you cannot measure directly, by adding known steps in an energy cycle. Reverse a step and you flip the sign of its ΔH; multiply a step and you multiply its ΔH.

You find an enthalpy change experimentally with a calorimeter: carry out the reaction and measure the temperature change of a known mass of water (or solution). The heat transferred is q = mcΔT — mass × specific heat capacity × temperature change — and dividing by the moles reacted gives ΔH per mole.

Every bond stores energy: breaking a bond absorbs energy (endothermic) and making one releases energy (exothermic). The average bond enthalpy is the mean energy to break one mole of a given bond, averaged over many molecules. You can estimate a reaction's enthalpy change by totalling the bonds broken in the reactants and subtracting the bonds made in the products.

Because the values are averages, bond-enthalpy calculations give an approximation, not the exact figure a calorimeter or Hess cycle would.

For an ionic compound, the lattice energy is the energy released when gaseous ions come together to form one mole of the solid lattice — a measure of how strongly the ions are held. It cannot be measured directly, so a Born–Haber cycle uses Hess's law to find it from steps that can be measured (atomisation, ionisation, electron affinity and formation).

Lattice energy is larger (more exothermic) for ions with higher charges and smaller radii, because the electrostatic attraction is stronger — which is why magnesium oxide melts far higher than sodium chloride.