5.1.7 Constructing Energy Cycles using Enthalpy Changes & Lattice Energy

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

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^ꝋ= Enthalpy of solution

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

-ΔH_latt^ꝋ + ΔH_hyd^ꝋ = 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^ꝋ = -ΔH_latt^ꝋ + ΔH_hyd^ꝋ

ΔH_hyd^ꝋ = ΔH_sol^ꝋ + ΔH_latt^ꝋ 

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

Worked example: Constructing an energy cycle and energy level diagram of KCl

Answer

Energy cycle:

Energy level diagram:

Worked example: Constructing an energy cycle and energy level diagram of MgCl₂

Answer

Energy cycle:

Energy level diagram: