Calculations Using Born-Haber Cycles (OCR A Level Chemistry A): Revision Note

Born-Haber Cycles - Calculations

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

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

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

  • ΔH_latt^ꝋ

  • ΔH_f^ꝋ

  • ΔH₁^ꝋ (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^ꝋ = ΔH₁^ꝋ + ΔH_latt^ꝋ

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

ΔH_latt^ꝋ = ΔH_f^ꝋ - ΔH₁^ꝋ

• When calculating the ΔH_latt^ꝋ, 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 enthalpy 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 two routes start and end at the same points, so their enthalpy changes are equal)

  • 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