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5.4.1Physical Chemistry and Transition Elements

Lattice Enthalpy

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Section 1 of 5Lattice Enthalpy

5.4.1 Lattice Enthalpy

Lattice enthalpy measures the strength of the electrostatic attraction in an ionic solid.

Definition
  • The enthalpy change when one mole of an ionic lattice is formed from its gaseous ions under standard conditions.
Equation
  • Na⁺(g) + Cl⁻(g) → NaCl(s) is the lattice enthalpy equation, and it is always exothermic.
Sign
  • Because the lattice is formed, ΔH(LE) is negative; a larger negative value means a stronger ionic lattice.
Why it matters
  • It cannot be measured directly, so it is found indirectly using a Born–Haber cycle and Hess's law.

Section 2 of 5Enthalpy Changes in the Cycle

Each step in the formation of an ionic compound from its elements has a defined enthalpy change.

1
Enthalpy change of formation, ΔHf: one mole of the compound forms from its elements in their standard states, for example Na(s) + ½Cl₂(g) → NaCl(s).
2
Enthalpy change of atomisation, ΔHat: one mole of gaseous atoms forms from the element in its standard state, for example Na(s) → Na(g).
3
First ionisation energy: one mole of gaseous atoms loses one mole of electrons to form 1+ ions, for example Na(g) → Na⁺(g) + e⁻.
4
First electron affinity: one mole of gaseous atoms gains one mole of electrons to form 1− ions, for example Cl(g) + e⁻ → Cl⁻(g), which is exothermic.
5
Second electron affinity, for forming O²⁻, is endothermic because the electron is added to an ion that already carries a negative charge.

Section 3 of 5Strength of Ionic Lattices

Strength of Ionic Lattices
Charge
  • Ions with greater charges attract more strongly, so MgO has a much more exothermic lattice enthalpy than NaCl.
Radius
  • Smaller ions can approach each other more closely, so the attraction is stronger and the lattice enthalpy more exothermic.
Charge density
  • The ratio of charge to size controls both how tightly the lattice is held and how strongly ions are hydrated.
Melting point
  • A more exothermic lattice enthalpy generally corresponds to a higher melting point and a harder crystal.

Section 4 of 5Worked Example

Question Write the equation, with state symbols, that defines the lattice enthalpy of magnesium chloride, and state its sign.

  1. The lattice is formed from gaseous ions, so the ions on the left are Mg²⁺(g) and Cl⁻(g).
  2. One mole of MgCl₂(s) requires one mole of Mg²⁺ and two moles of Cl⁻.
  3. Forming a lattice releases energy, so the value is negative.

Answer

  • Mg²⁺(g) + 2Cl⁻(g) → MgCl₂(s);
    • ΔH(LE) is negative.

Section 5 of 5Exam Checklist & Tips

5.4.1 – Key Points for the Exam

  • Lattice enthalpy The enthalpy change when one mole of an ionic lattice forms from its gaseous ions.
  • Enthalpy of atomisation The enthalpy change when one mole of gaseous atoms is formed from an element in its standard state.
  • Electron affinity The enthalpy change when one mole of gaseous atoms gains one mole of electrons.
  • First ionisation energy The energy needed to remove one electron from each atom in one mole of gaseous atoms.

Common Mistakes

  • Writing lattice enthalpy as the energy to break the lattice, when this course defines it for lattice formation.
  • Omitting state symbols such as (g) and (s), which are essential to the definition.
  • Giving the first electron affinity of oxygen as endothermic, when only the second one is endothermic.
  • Using the enthalpy of formation of an element, which is zero, as if it were a step in a cycle.
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