Lattice energy and Born-Haber cyclesEdexcel International A Level Chemistry: Revision notes
Section 1
Key definitions
All values are standard enthalpy changes, in kJ mol⁻¹.
- Enthalpy change of atomisation (ΔatH): the enthalpy change when 1 mol of gaseous atoms is formed from the element in its standard state. Always endothermic. Example: ½Cl₂(g) → Cl(g).
- First electron affinity: the enthalpy change when 1 mol of gaseous atoms gains 1 mol of electrons to form 1 mol of gaseous 1− ions. Cl(g) + e⁻ → Cl⁻(g), −349 kJ mol⁻¹ (exothermic).
- Lattice energy: the enthalpy change when 1 mol of an ionic solid is formed from its gaseous ions. Na⁺(g) + Cl⁻(g) → NaCl(s). It is always exothermic.
The second electron affinity of oxygen (O⁻ + e⁻ → O²⁻) is endothermic (+798), because an electron is added to a negative ion and repulsion must be overcome.
Writing lattice energy as the endothermic breakup of the solid. Here it is the exothermic formation, so it has a negative sign.
Section 2
Constructing a Born–Haber cycle
A Born–Haber cycle is a Hess's law cycle that links the enthalpy change of formation of an ionic solid with the gas-phase steps and the lattice energy.
For NaCl, in order:
- Na(s) → Na(g), atomisation, +107
- Na(g) → Na⁺(g) + e⁻, first ionisation energy, +496
- ½Cl₂(g) → Cl(g), atomisation, +122
- Cl(g) + e⁻ → Cl⁻(g), electron affinity, −349
- Na⁺(g) + Cl⁻(g) → NaCl(s), lattice energy, unknown
The formation route Na(s) + ½Cl₂(g) → NaCl(s) has ΔfH = −411. Hess's law gives ΔfH = sum of steps 1 to 4 + lattice energy.
Write each step with state symbols. Check that every species is gaseous until the final lattice step.
Section 3
Calculating a lattice energy
Rearrange: lattice energy = ΔfH − (ΔatH of metal + ionisation energies + ΔatH of non-metal + electron affinities).
NaCl: −411 − (107 + 496 + 122 − 349) = −411 − 376 = −787 kJ mol⁻¹.
For MgCl₂ two Cl atoms and two Cl⁻ ions are needed, so double both chlorine terms, and include both ionisation energies of Mg: −641 − (148 + 738 + 1451 + 2(122) + 2(−349)) = −641 − 1883 = −2524 kJ mol⁻¹.
For oxide, include both electron affinities of oxygen (−141 and +798).
Forgetting to double the chlorine terms for MgCl₂, or leaving out the second ionisation energy.
Section 4
Experimental and theoretical lattice energies
The experimental lattice energy comes from the Born–Haber cycle.
The theoretical value is calculated from electrostatic theory, assuming the compound is 100% ionic: perfectly spherical ions held together only by electrostatic attraction.
Example: NaCl experimental −787, theoretical −770. The values agree closely, so NaCl is very nearly fully ionic.
If the experimental value is more exothermic than the theoretical value, the bonding has extra strength from some covalent character. The larger the difference, the greater the covalent character. AgI: −889 against −778, a difference of 111 kJ mol⁻¹.
Section 5
Polarisation and covalent character
A small, highly charged cation attracts the electron cloud of a nearby anion and distorts it. This is polarisation.
- The anion is more easily polarised if it is large, so its outer electrons are far from the nucleus (I⁻ is polarised more than F⁻).
- The cation polarises more if it has a high charge density.
Polarisation draws some electron density between the nuclei, giving the bond some covalent character. This extra bonding makes the lattice stronger, so the Born–Haber lattice energy is more exothermic than the theoretical ionic value. The difference between the two is the evidence for covalent character.
State the cause (cation polarises anion), the effect (electron density between nuclei) and the evidence (experimental more exothermic than theoretical).
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Lattice energy and Born-Haber cycles
- A student constructs a Born–Haber cycle for sodium chloride using these standard enthalpy changes (kJ mol⁻¹): enthalpy change of formation of NaCl(s) −411; atomisation of sodium +107; first ionisation energy of sodium +496; atomisation of chlorine (per mole of Cl atoms) +122; first electron affinity of chlorine −349.Calculate the lattice energy of sodium chloride.2 marks
- Magnesium chloride is used as a de-icing salt. A Born–Haber cycle is constructed for MgCl₂ using these standard enthalpy changes (kJ mol⁻¹): enthalpy change of formation of MgCl₂(s) −641; atomisation of magnesium +148; first ionisation energy of magnesium +738; second ionisation energy of magnesium +1451; atomisation of chlorine (per mole of Cl atoms) +122; first electron affinity of chlorine −349.Calculate the total enthalpy change for converting 1 mol of Mg(s) and 1 mol of Cl₂(g) into 1 mol of Mg²⁺(g) and 2 mol of Cl⁻(g).2 marks
- A student compares two compounds that each contain a 1+ cation and a 1− anion. Lattice energies (kJ mol⁻¹), defined for formation of the solid from gaseous ions, are: sodium chloride, Born–Haber value −787 and value calculated from a purely ionic model −770; silver iodide, Born–Haber value −889 and value calculated from a purely ionic model −778.Calculate the difference between the Born–Haber and ionic-model lattice energies for each compound, and state which compound has the greater covalent character.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).