Lecture Notes: Calculating Lattice Energies using the Born-Haber Cycle

Introduction to Lattice Energies

• Lattice energy refers to the energy required to form a crystalline solid from its gaseous ions.
• Calculating lattice energy involves complex energy measurements, often simplified using Hess's Law and the Born-Haber cycle.

Born-Haber Cycle

• Concept: A cyclical series of hypothetical steps to calculate lattice energy.
• Purpose: To find unknown energy values by utilizing known values from different reactions.

Example: Formation of CsF (Cesium Fluoride)

• Objective: Determine the ΔH lattice for the formation of CsF.

Steps in the Born-Haber Cycle

1. Formation of CsF

   • Reaction: Cs(s) + ½ F₂(g) → CsF(s)
   • Known ΔH formation: -553.5 kJ/mol
   • Reverse Reaction: CsF(s) → Cs(s) + ½ F₂(g)
     • ΔH: +553.5 kJ/mol (reverse of formation)

2. Heat of Sublimation for Cesium

   • Transition: Cs(s) → Cs(g)
   • Energy required for sublimation is added to the cycle.

3. Ionization Energy of Cesium

   • Concept: Energy required to remove an electron from Cs(g) to form Cs⁺(g).
   • Follows periodic trends for ionization energy.

4. Dissociation of Fluorine Gas

   • Transition: ½ F₂(g) → F(g)
   • Half of the dissociation energy: 79.4 kJ/mol

5. Electron Affinity of Fluorine

   • Process: Energy change when an electron is added to F(g) to form F⁻(g).
   • Electron affinity contributes a negative energy change (decrease).

6. Formation of CsF from Ions

   • Transition: Cs⁺(g) + F⁻(g) → CsF(s)
   • Unknown ΔH lattice calculated by resolving the cycle.

Calculation

• Equation:
  • 553.5 kJ/mol (reverse formation) + Sublimation energy + Ionization energy + 79.4 kJ/mol (½ dissociation) - Electron affinity (328.2 kJ/mol) - ΔH lattice = 0
• Result:
  • ΔH lattice = 756.9 kJ/mol

Conclusion

• The Born-Haber cycle allows calculation of inaccessible energy values by using a cyclical approach.
• It relies on a balance of energy inputs and outputs where the sum total equals zero.
• Useful for predicting properties of ionic compounds like CsF.