Born-Haber Cycle Calculations (HL) (DP IB Chemistry: HL): Revision Note

Born-Haber cycle calculations

• Once a Born–Haber cycle is set up, you can use Hess’s Law to calculate the lattice enthalpy (ΔH^ꝋ_latt) by rearranging the following expression:

ΔH^ꝋ_f = ΔH^ꝋ_at + ΔH^ꝋ_at + ΔH^ꝋ_ie + ΔH^ꝋ_ea - ΔH^ꝋ_latt

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

  • ΔH^ꝋ_latt

  • ΔH^ꝋ_f

  • ΔH^ꝋ₁ (the sum of all the various enthalpy changes necessary to convert the elements in their standard states to gaseous ions)

• The simplified equation becomes:

ΔH^ꝋ_f = ΔH^ꝋ₁ - ΔH^ꝋ_latt

• Rearranging to calculate lattice enthalpy gives:

ΔH^ꝋ_latt = - ΔH^ꝋ_f + ΔH^ꝋ₁

• A Born-Haber cycle could be used to calculate any stage in the cycle

  • You might be given ΔH^ꝋ_latt and asked to work out ΔH^ꝋ_f 

  • The process remains the same; apply Hess’s Law

  • Identify the direct and indirect routes in the cycle

  • Write an equation linking all relevant enthalpy changes, then rearrange to isolate the unknown value

• Always consider the stoichiometry of the ions involved:

  • If you are dealing with ions like MgCl₂, remember that values (e.g., for electron affinity) may need to be multiplied to reflect the number of moles involved

  • For example:

    • MgCl₂ forms 2 Cl⁻ ions, so the electron affinity of chlorine must be doubled

    • You’re effectively adding 2 moles of electrons to 2 moles of chlorine atoms, forming 2 moles of Cl⁻