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23 Chemical energetics

23.1 Lattice energy and Born-Haber cycles 23.2 Enthalpies of solution and hydration 23.3 Entropy change, ΔS 23.4 Gibbs free energy change, ΔG

Enthalpies of solution and hydration

Specification Reference Physical Chemistry, Chemical energetics 23.2

Quick Notes

  • Enthalpy change of solution (ΔHsol):
    • The energy change when 1 mole of an ionic solid dissolves in water (to form an infinitely dilute solution).
  • Enthalpy change of hydration (ΔHhyd):
    • the energy released when 1 mole of gaseous ions dissolves in water (to form an infinitely dilute solution).
  • We can construct energy cycles using enthalpies of solution, lattice energy and enthalpies of hydration for an ionic compound.
CIE A-Level Chemistry energy cycle diagram linking enthalpy of solution, lattice enthalpy, and hydration enthalpies.
  • Higher ionic charge and smaller ionic radius gives a more exothermic enthalpy of hydration (ΔHhyd).

Full Notes

Enthalpies of solution and hydration have been outlined in more detail here.
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Key Definitions

Enthalpy of solution (ΔHsol):
The enthalpy change when 1 mole of an ionic compound dissolves in enough water to form an infinitely dilute solution.

CIE A-Level Chemistry diagram of ionic solid dissolving in water to form aqueous ions.

Example NaCl(s) → Na⁺(aq) + Cl⁻(aq)

Enthalpy of hydration (ΔHhyd):
The enthalpy change when 1 mole of gaseous ions dissolves in water to form aqueous ions.

CIE A-Level Chemistry diagram showing hydration of Na⁺ and Cl⁻ ions forming aqueous ions.

Example

Na⁺(g) → Na⁺(aq)
Cl⁻(g) → Cl⁻(aq)

Energy Cycle for Solution Enthalpy

An energy cycle can be constructed that links enthalpy of solution (ΔHsol), hydration enthalpies (ΔHhyd) and lattice energy (ΔHlatt):

CIE A-Level Chemistry Born–Haber type cycle linking solution enthalpy, lattice enthalpy, and hydration enthalpies.
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For these energy cycles, the lattice energy is given as a positive value as the arrow direction is going from the ionic solid to the gaseous ions, this is breaking apart the lattice. This is the exact same value as lattice energy however it has a positive sign (+ΔH) rather than negative as it is an endothermic process.

Energy cycle equation:

CIE A-Level Chemistry equation showing ΔHsol = ΔHlatt + ΣΔHhyd.

Worked Example Calculation

Worked Example: Enthalpy of solution

Calculate ΔHsol, given:

  • ΔHlatt (NaCl) = +769 kJ mol⁻¹
  • ΔHhyd (Na⁺) = –406 kJ mol⁻¹
  • ΔHhyd (Cl⁻) = –364 kJ mol⁻¹

Calculate ΔHsol: ΔHsol = +769 + (–406) + (–364)
ΔHsol = –1 kJ mol⁻¹
So, dissolving NaCl is slightly exothermic.

Factors Affecting Enthalpy of Hydration

The magnitude of ΔHhyd depends on:

So, small, highly charged ions have more exothermic hydration enthalpies.

Summary