Lattice energy and Born-Haber cycles

Definitions (spec 12.12)

• Standard enthalpy change of atomisation: the enthalpy change when one mole of gaseous atoms forms from the element in its standard state: ½Cl2(g) -> Cl(g), Na(s) -> Na(g). Always endothermic.
• First electron affinity: the enthalpy change when each atom in one mole of gaseous atoms gains one electron to form one mole of gaseous 1- ions: Cl(g) + e- -> Cl-(g). Usually exothermic.
• Second electron affinity: O-(g) + e- -> O2-(g). Endothermic, because the electron is added to a negative ion, which repels it.
• Lattice energy: the enthalpy change when one mole of an ionic solid forms from its gaseous ions: Na+(g) + Cl-(g) -> NaCl(s). Exothermic.

The cycle (spec 12.13)

Route 1: elements -> compound directly (ΔfH).

Route 2: atomise the metal, atomise the non-metal, ionise the metal (ionisation energies), add electrons to the non-metal (electron affinities), then form the lattice.

By Hess's law: ΔfH = ΔatH(metal) + ΔatH(non-metal) + IE(s) + EA(s) + LE, so LE = ΔfH - (everything else). Multiply each step by the number of atoms or ions, for example 2 x ΔatH(Cl) for MgCl2.

What affects lattice energy

Lattice energy is more exothermic when ions are smaller (closer together) and more highly charged. MgO is far more exothermic than NaCl.

Covalent character (spec 12.14, 12.15)

A theoretical lattice energy is calculated assuming perfect spherical ions (a purely ionic model). If the Born-Haber (experimental) value is close to it, the bonding is almost purely ionic, as in NaCl. If the experimental value is noticeably more exothermic, the bonding has some covalent character: a small, highly charged cation polarises a large, easily distorted anion, pulling electron density between the ions. Silver iodide and zinc sulfide show large differences.

Worked example

Calculate the lattice energy of NaCl. ΔfH(NaCl) = -411, ΔatH(Na) = +107, IE1(Na) = +496, ΔatH(Cl) = +122, EA1(Cl) = -349 (all kJ mol^-1).

1. ΔfH = ΔatH(Na) + ΔatH(Cl) + IE1 + EA1 + LE
2. -411 = 107 + 122 + 496 - 349 + LE
3. LE = -411 - 376

Answer: LE = -787 kJ mol^-1

Check yourself

1. Calculate the lattice energy of potassium chloride. ΔfH(KCl) = -437, ΔatH(K) = +89, IE1(K) = +419, ΔatH(Cl) = +122, EA1(Cl) = -349 (kJ mol^-1).
   Show answer

   -718 kJ mol^-1. LE = -437 - (89 + 419 + 122 - 349) = -718 kJ mol^-1.

2. Calculate the lattice energy of MgCl2. ΔfH(MgCl2) = -641, ΔatH(Mg) = +148, IE1(Mg) = +738, IE2(Mg) = +1451, ΔatH(Cl) = +122, EA1(Cl) = -349 (kJ mol^-1).
   Show answer

   -2524 kJ mol^-1. Other steps: 148 + 738 + 1451 + 2(122) + 2(-349) = 1883; LE = -641 - 1883 = -2524 kJ mol^-1.

3. Which equation represents the lattice energy of magnesium chloride?
   • Mg2+(g) + 2Cl-(g) -> MgCl2(s)
   • Mg(s) + Cl2(g) -> MgCl2(s)
   • MgCl2(s) -> Mg2+(aq) + 2Cl-(aq)
   • Mg(g) + 2Cl(g) -> MgCl2(s)
   Show answer

   Mg2+(g) + 2Cl-(g) -> MgCl2(s). Lattice energy: one mole of solid from its gaseous ions.

4. Why is the second electron affinity of oxygen endothermic?
   • Oxygen has a full outer shell
   • The O2- ion is unstable in water
   • Energy is released when the electron is added
   • The electron is being added to a negative ion, which repels it
   Show answer

   The electron is being added to a negative ion, which repels it. Work must be done to push an electron onto O-.

5. Which equation represents the standard enthalpy change of atomisation of chlorine?
   • Cl2(g) -> 2Cl(g)
   • ½Cl2(g) -> Cl(g)
   • Cl(g) + e- -> Cl-(g)
   • Cl2(g) -> Cl+(g) + Cl-(g)
   Show answer

   ½Cl2(g) -> Cl(g). Atomisation forms one mole of gaseous atoms.

6. The Born-Haber lattice energy of silver iodide is much more exothermic than the theoretical value from the ionic model. What does this show?
   • Silver iodide is purely ionic
   • The theoretical model overestimates ionic bonding
   • Silver iodide has a giant covalent structure only
   • The bonding has significant covalent character
   Show answer

   The bonding has significant covalent character. Polarisation of the large iodide ion adds extra covalent attraction.

7. Which compound has the most exothermic lattice energy?
   • NaCl
   • MgO
   • KBr
   • CaO
   Show answer

   MgO. Mg2+ and O2- are doubly charged and Mg2+ is smaller than Ca2+.

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Sources

• Pearson Edexcel IAL Chemistry (2018) specification
• Pearson Edexcel IAL Chemistry (2018) scheme of work

Last updated 7 November 2026. Spotted a mistake? Tell us.