Calculations using Born-Haber Cycles (CIE A Level Chemistry)

• Once a Born-Haber cycle has been constructed, it is possible to calculate the lattice energy (ΔH_latt^ꝋ) by applying Hess’s law and rearranging:

ΔH_f^θ = ΔH_at^θ + ΔH_at^θ + IE + EA + ΔH_latt^θ

If we simplify this into three terms, this makes the equation easier to see:

• ΔH_latt^θ
• ΔH_f^θ
• ΔH₁^θ (the sum of all of the various enthalpy changes necessary to convert the elements in their standard states to gaseous ions)
• The simplified equation becomes

ΔH_f^θ = ΔH₁^θ + ΔH_latt^θ

So, if we rearrange to calculate the lattice energy, the equation becomes

ΔH_latt^θ = ΔH_f^θ - ΔH₁^θ

• When calculating the ΔH_latt^θ, all other necessary values will be given in the question
• A Born-Haber cycle could be used to calculate any stage in the cycle
  • For example, you could be given the lattice energy and asked to calculate the enthalpy change of formation of the ionic compound
  • The principle would be exactly the same
  • Work out the direct and indirect route of the cycle (the stage that you are being asked to calculate will always be the direct route)
  • Write out the equation in terms of enthalpy changes and rearrange if necessary to calculate the required value

• Remember: sometimes a value may need to be doubled or halved, depending on the ionic solid involved
  • For example, with MgCl₂ the value for the first electron affinity of chlorine would need to be doubled in the calculation, because there are two moles of chlorine atoms
  • Therefore, you are adding 2 moles of electrons to 2 moles of chlorine atoms, to form 2 moles of Cl^- ions