Constructing Energy Cycles (CIE A Level Chemistry)

• The standard enthalpy change of hydration (ΔH_hyd^θ) can be calculated by constructing energy cycles and applying Hess’s law

Example energy cycle

Energy cycle involving enthalpy change of solution, lattice energy, and enthalpy change of hydration

• The energy cycle shows that there are two routes to go from the ionic lattice to the hydrated ions in an aqueous solution:
  • Route 1: going from ionic solid → ions in aqueous solution (this is the direct route)

ΔH_sol^θ = Enthalpy of solution

• Route 2: going from ionic lattice →  gaseous ions  →  ions in aqueous solution (this is the indirect route)

-ΔH_latt^θ + ΔH_hyd^θ = reverse lattice enthalpy + hydration enthalpies

Lattice enthalpy usually means Lattice formation enthalpy, in other words bond forming. If we are breaking the lattice then this is reversing the enthalpy change so a negative sign is added in front of the term (alternatively it is called lattice dissociation enthalpy)

• According to Hess’s law, the enthalpy change for both routes is the same, such that:

ΔH_sol^θ = -ΔH_latt^θ + ΔH_hyd^θ

ΔH_hyd^θ = ΔH_sol^θ + ΔH_latt^θ 

• Each ion will have its own enthalpy change of hydration, ΔH_hyd^θ, which will need to be taken into account during calculations
  • The total ΔH_hyd^θ is found by adding the  ΔH_hyd^θ values of both anions and cations together