5.2.1 Lattice Enthalpy

For OCR, learn the formation definition: lattice enthalpy is the enthalpy change when one mole of an ionic solid is formed from its separated gaseous ions.

That direction matters. The oppositely charged gaseous ions come together to form the lattice, so energy is released and the lattice enthalpy is negative.

If you are comparing lattice enthalpies using OCR’s formation convention, the more negative value means stronger electrostatic attraction between the ions in the giant lattice.

For example, a lattice enthalpy of −2500 kJ mol⁻¹ shows stronger ionic bonding than −800 kJ mol⁻¹. I would compare the magnitudes first, then state which lattice has the stronger attraction.

A Born–Haber cycle gives you an indirect route from the elements in their standard states to the ionic solid. Build the gaseous ions one step at a time, then finish by forming the lattice.

I find it safest to write the species after every step. That makes the particle numbers, charges and state symbols much easier to check before you put the enthalpy labels on.

• atomise the elements to gaseous atoms
• remove electrons using the required ionisation energies
• add electrons using the required electron affinities
• form the solid lattice from the gaseous ions

Once the cycle is correct, this is Hess’s law. Add the enthalpy changes along one route and set that total equal to the other route, then solve for the missing term.

For NaCl, we can go from Na(s) + ½Cl₂(g) to NaCl(s) directly using ΔHf, or make gaseous Na⁺ and Cl⁻ first and then form the lattice.

The enthalpy change of solution, ΔHsol, is the enthalpy change when one mole of a solute dissolves in water.

It can be positive or negative. If the solution warms as the solute dissolves, the process is exothermic; if it cools, it is endothermic.

The enthalpy change of hydration, ΔHhyd, is the enthalpy change when one mole of gaseous ions becomes hydrated by water.

Hydration is exothermic because the ion attracts polar water molecules. For example, Na⁺(g) becomes Na⁺(aq) and releases energy.

For a solution cycle, connect the ionic solid to the same aqueous ions by two routes. One route is the enthalpy change of solution. The other breaks the lattice back into gaseous ions, then hydrates those ions.

Because OCR gives lattice enthalpy for formation, you reverse it when you go from solid lattice to gaseous ions. So its sign changes in the solution cycle.

Use the solution cycle exactly like any other Hess cycle: choose two routes between the same start and finish and make their enthalpy totals equal.

For NaCl, you reverse lattice formation first, so that step costs +788 kJ mol⁻¹. Hydrating Na⁺ and Cl⁻ then releases 406 and 364 kJ mol⁻¹ respectively.

When you compare ions, a larger ionic charge gives stronger electrostatic attractions. In a lattice that means stronger attraction between oppositely charged ions; during hydration it means stronger ion–dipole attraction between the ion and water molecules.

Stronger attractions release more energy when they form, so both lattice enthalpy of formation and hydration enthalpy become more negative.

When you compare ions with the same charge, the smaller ion lets opposite charges get closer together, so the electrostatic attraction is stronger.

In the lattice, the ions attract one another more strongly. In hydration, water molecules can get closer to the ion and the ion–dipole attraction is stronger. In both cases, forming those attractions releases more energy, so the enthalpy change is more negative.