Born-Haber Cycles

Full Notes

Born-Haber cycles and Lattice Enthalpies are covered in more detail here.
This page is just what you need to know for AQA A-level Chemistry :)

Lattice Enthalpy: Definition and Types

Lattice enthalpy refers to the energy change associated with the formation or dissociation of an ionic solid. It can be defined in two ways:

• Lattice enthalpy of formation (ΔH_LE^f):
• The energy released when one mole of an ionic solid is formed from its gaseous ions.
• Always exothermic (negative value).
  

  Example: Na⁺(g) + Cl⁻(g) → NaCl(s)

• Lattice enthalpy of dissociation (ΔH_LE^d):
• The energy absorbed to break one mole of an ionic solid into its gaseous ions.
• Always endothermic (positive value).

Example: NaCl(s) → Na⁺(g) + Cl ^-(g)

Note: Magnitude of both values is the same, but their signs differ.
Lattice enthalpies can’t be measured directly, however they can be found indirectly using experimental data and Born-Haber cycles.

Key Enthalpy Changes in a Born-Haber Cycle

A Born-Haber cycle is an energy cycle that applies Hess’s Law to determine lattice enthalpy. Standard Born-Haber cycles often include:

• Enthalpy of Formation (ΔH_f)
  Energy change when 1 mole of an ionic compound forms from its elements in standard states.
  

  Example: Na(s) + ½Cl₂(g) → NaCl(s)

• Enthalpy of Atomisation (ΔH_atom)
  Energy change when 1 mole of gaseous atoms forms from an element.
  

  Example: Na(s) → Na(g) and ½Cl₂(g) → Cl(g)

• 1st Ionisation Energy (IE)
  Energy required to remove 1 mole of electrons from 1 mole of gaseous atoms of an element (to form 1 mole worth of ions with a 1+ charge).
  

  Example: Na(g) → Na⁺(g) + e⁻

• Bond Enthalpy
  Energy required to break one mole worth of a covalent bond in gaseous molecules.
  

  Example: Cl₂(g) → 2Cl(g)

• 1st Electron Affinity (EA)
  Energy change when 1 mole of gaseous atoms gains electrons to form 1 mole worth of ions with a 1− charge.
  

  Example: Cl(g) + e⁻ → Cl⁻(g)

• Lattice Enthalpy (ΔH_LE)
  Energy change when 1 mole of an ionic lattice forms or dissociates from gaseous ions.
  This is often the unknown value we solve for.

Matt’s exam tip

Make sure you know and can recall each of the above definitions - they are easy marks when they come up and are vital in order to understand how Born-Haber cycles work (see below).

Constructing a Born-Haber Cycle

Steps:

1. Write the enthalpy of formation equation (solid compound from elements).
2. Convert elements to gaseous atoms (atomisation enthalpy).
3. Remove electrons from metal atoms (ionisation energy).
4. Add electrons to non-metal atoms (electron affinity).
5. Combine gaseous ions to form lattice (lattice enthalpy).

Example: Born-Haber Cycle for NaCl

Step 1: Formation of NaCl (ΔH_f)
Na(s) + ½Cl₂(g) → NaCl(s)

Step 2: Atomisation of Na (ΔH_atom)
Na(s) → Na(g)

Step 3: Atomisation of Cl₂ (ΔH_atom)
½Cl₂(g) → Cl(g)

Step 4: Ionisation Energy of Na (IE₁)
Na(g) → Na⁺(g) + e⁻

Step 5: Electron Affinity of Cl (EA₁)
Cl(g) + e⁻ → Cl⁻(g)

Step 6: Lattice Enthalpy (ΔH_LE)
Na⁺(g) + Cl⁻(g) → NaCl(s)

Ex

Worked Example

Born-Haber Cycle for NaCl with values:

Comparing Lattice Enthalpy Values: Experimental vs. Theoretical

Born-Haber cycle values (experimental lattice enthalpy) come from experimental data.
Theoretical lattice enthalpy assumes purely ionic bonding based on perfectly spherical ions with a uniform charge.

If experimental values differ from theoretical values, the compound has some covalent character due to polarisation of the anion by the cation.
The greater the difference between experimental and theoretical values, the greater the degree of covalent character in the compound.

Example:
NaCl is nearly purely ionic (experimental ≈ theoretical).
AgCl has a higher experimental lattice enthalpy than theoretical, indicating covalent character.

Enthalpy Changes of Solution and Hydration

Born-Haber cycles can also be used to calculate enthalpy changes of solution and hydration:

• Enthalpy of solution (ΔH_sol):
  Energy change when 1 mole of an ionic compound dissolves in water.

  Example:NaCl(s) → Na⁺(aq) + Cl ^-(aq)

• Enthalpy of hydration (ΔH_hyd):
  Energy released when 1 mole of gaseous ions dissolves in water.

  Example:Na⁺(g) → Na⁺(aq)

Equation for enthalpy of solution:
ΔH_sol = -ΔH_LE + ΣΔH_hyd