Born-Haber Calculations (Oxford AQA International A Level Chemistry)

Born-Haber Calculations

• Once a Born-Haber cycle has been constructed, lattice energy (ΔH_latt^ꝋ) can be calculated by applying Hess’s law and rearranging:

ΔH_f^Ꝋ = ΔH_at^Ꝋ + ΔH_at^Ꝋ + ΔH_ie^Ꝋ+ ΔH_ea^Ꝋ + ΔH_latt^Ꝋ

• 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^Ꝋ = ΔH₁^Ꝋ + ΔH_latt^Ꝋ

• So, if we rearrange to calculate the lattice energy, 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 energy and asked to calculate the enthalpy change of formation of the ionic compound

  • 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:

  • To include all the required enthalpies

  • Sometimes an enthalpy value may need to be doubled or halved, depending on the ionic solid involved

• For example, magnesium chloride

  • Magnesium has two ionisation energies:

    • First ionisation energy creating the Mg⁺ ion

    • Second ionisation energy creating the Mg²⁺ ion

  • There are two chlorine atoms required to form magnesium chloride

    • Therefore, you are adding 2 moles of electrons to 2 moles of chlorine atoms, to form 2 moles of Cl^- ions

    • This means that the value for the electron affinity of chlorine is doubled

Comparing Lattice Enthalpies

• It is possible to calculate a theoretical value for the lattice enthalpy of an ionic solid

• To do this you need to know:

  • The geometry of the ionic solid

  • The charge on the ions

  • The distance between the ions

Ionic lattice of sodium chloride

• This has been calculated for a number of ionic solids and allows a comparison between theoretical lattice enthalpies and experimental lattice enthalpies obtained from Born-Haber cycles

• The calculation of the theoretical value assumes that the substance is a highly ionic compound with only electrostatic attraction between cations and anions

Table comparing theoretical and experimental lattice enthalpies

• You can see from the table that there is quite close agreement between the two values for the lattice enthalpy of sodium chloride

• The difference between theoretical and experimental lattice enthalpy increases for zinc sulfide

• This suggests that the bonding is not purely ionic and some covalent character is present

• This can be explained as follows:

  • Zn²⁺ is a smaller ion with a greater charge than Na⁺

  • Zn²⁺ ions attract electron density towards themselves

  • This distorts the electron cloud and makes the bonding slightly covalent

  • S^2- ions are larger ions than chloride ions Cl^- with a greater negative charge

  • The electron cloud around S^2- is more easily distorted than in chloride ions leading to further covalent character

Distortion of electron clouds

• As you move left to right across the period table, the lattices become less ionic and more covalent leading to a discrepancy in the lattice enthalpy values

• The result of these analyses provides strong evidence that supports the ionic model for some compounds like sodium chloride