Enthalpy of solution and hydrationAQA A-Level Chemistry: Revision notes

When an ionic solid dissolves, the lattice breaks up and the ions become surrounded by water molecules. The enthalpy of solution (ΔHsol) is the enthalpy change when one mole of an ionic solid dissolves in water to form a solution so dilute that further dilution gives no further enthalpy change.

For sodium chloride: NaCl(s) + aq → Na⁺(aq) + Cl⁻(aq). The value can be exothermic or endothermic, and cannot be found by simply adding up the ion energies, so an enthalpy cycle is used.

The enthalpy of hydration (ΔHhyd) is the enthalpy change when one mole of gaseous ions dissolves in water to form one mole of aqueous ions, e.g. Na⁺(g) + aq → Na⁺(aq) or Cl⁻(g) + aq → Cl⁻(aq).

Hydration is always exothermic. Water is polar, so the δ− oxygen atoms are attracted to cations and the δ+ hydrogen atoms to anions. These ion–dipole attractions release energy as they form.

Dissolving can be imagined in two stages:

1. the lattice is broken into gaseous ions, costing the enthalpy of lattice dissociation: MX(s) → M⁺(g) + X⁻(g)
2. the gaseous ions are hydrated, releasing the enthalpies of hydration of each ion.

By Hess's law: ΔHsol = ΔH(lattice dissociation) + ΣΔH(hydration)

Since the enthalpy of lattice formation is the reverse of lattice dissociation, ΔHsol = −ΔH(lattice formation) + ΣΔH(hydration). Count the ions: for MgCl₂ the chloride hydration enthalpy must be counted twice.

Find ΔHsol for sodium bromide. Lattice formation = −751; hydration of Na⁺ = −406; hydration of Br⁻ = −335 (kJ mol⁻¹).

Lattice dissociation = +751. ΔHsol = +751 + (−406) + (−335) = +10 kJ mol⁻¹

So the dissolving of NaBr is slightly endothermic. For 0.50 mol the energy change is 0.50 × 10 = +5.0 kJ, absorbed from the surroundings.

The cycle can be rearranged to find any unknown term. If ΔHsol and the other terms are known, an unknown hydration enthalpy is found by subtraction.

How exothermic the hydration of an ion is depends on its charge density, the charge divided by the ionic radius.

• A higher charge attracts water molecules more strongly: Mg²⁺ (−1920) is far more exothermic than Na⁺ (−406).
• A smaller radius brings water molecules closer: F⁻ (−506) is more exothermic than Cl⁻ (−364).

Whether a compound dissolves exothermically depends on the balance between lattice dissociation and hydration. Smaller or more highly charged ions raise both terms, so the net ΔHsol can go either way.