6.5 Born Haber Cycle

This topic explains the Born Haber cycle, a special application of Hess's Law used to calculate the lattice energy of ionic compounds.

Definition

Born Haber Cycle: A special application of Hess's Law to binary ionic compounds. It helps us calculate lattice energies of binary ionic compounds (M⁺X⁻).

Lattice Energy: The change in energy that takes place when separated gaseous ions are packed together to form one mole of an ionic solid.

Main Idea

Lattice energy cannot be determined directly. However, it can be determined indirectly by means of the Born Haber cycle. Consider the case of NaCl. Its standard enthalpy of formation (ΔH°_f) is −411 kJ mol⁻¹. The formation reaction can be considered as taking place in several steps, one of which is the formation of the lattice. This complete sequence of reactions is called a cycle.

Core Concept

• Sublimation of solid sodium
• Ionization of Na(g) to form Na⁺(g)
• Dissociation of Cl₂ molecules
• Electron affinity of Cl(g)
• Lattice formation of NaCl(s)

The sum of these five steps gives the overall reaction, and the sum of the individual energy changes gives the overall energy change.

Detailed Explanation

What is Lattice Energy?

- The change in energy that takes place when separated gaseous ions are packed together to form one mole of an ionic solid is called lattice energy.

M⁺_(g) + X^-_(g) → MX_(s)

• Lattice energy cannot be determined directly.
• However, it can be determined indirectly by means of the Born Haber cycle.

Born Haber Cycle for NaCl

Step I: Sublimation of solid sodium The energy of sublimation for Na(s) is 108 kJ/mole. Na_(s) → Na_(g) Δ H^° = +108 kJ/mole

Step II: Ionization of Na(g) atom to form Na⁺(g) ion This process corresponds to the first ionization energy for Na. Na_(g) → Na⁺_(g) + 1e^- Δ H^° = +496 kJ/mole

Step III: Dissociation of Cl₂ molecules We need to form one mole of Cl atoms by breaking the Cl−Cl bond in ½ mole of Cl₂ molecules. The energy required to break this bond is 121 kJ/mole and is known as enthalpy of atomization for Cl₂. 12Cl_2(g) → Cl_(g) Δ H^° = +121 kJ/mole

All these three steps are endothermic and are drawn upward in the figure.

Step IV: Formation of Cl⁻(g) ion Energy is released in this step equal to the electron affinity for Cl. Cl_(g) + 1e^- → Cl^-_(g) Δ H^°_EA = -349 kJ/mole

Step V: Formation of solid NaCl from gaseous Na⁺ and Cl⁻ ions This corresponds to the lattice energy (ΔH_l) for NaCl(s), which is to be calculated. Na⁺_(g) + Cl^-_(g) → NaCl_(s) Δ H^°_l = ?

Calculation

Since the sum of these five steps gives the overall reaction and the sum of the individual energy changes gives the overall energy change:

Δ H^°_f = Δ H^°_sub + Δ H^°_IE + Δ H^°_diss + Δ H^°_EA + Δ H^°_lattice

-411 kJ = +108 kJ + 496 kJ + 121 kJ + (-349 kJ) + Δ H^°_lattice

Δ H^°_lattice = -411 kJ - (108 kJ + 496 kJ + 121 kJ - 349 kJ)

Δ H^°_lattice = -411 kJ - (376 kJ)

Δ H^°_lattice = -787 kJ mol^-1

Thus, the lattice energy of NaCl is 787 kJ/mole.

Why This Matters

• Understanding ionic compounds: Explains the stability of ionic solids.
• Calculations: Used to determine lattice energies indirectly.
• Periodic trends: Explains trends in ionic compound properties.
• Science: Foundation of thermochemistry.

Important Points

• 1. Born Haber cycle is a special application of Hess's Law.
• 2. Lattice energy: Energy released when gaseous ions form a solid.
• 3. Steps for NaCl: Sublimation, ionization, dissociation, electron affinity, lattice formation.
• 4. Calculation: ΔH°_f = sum of all steps.
• 5. Lattice energy of NaCl = 787 kJ/mol.
• 6. Electrons are released in electron affinity step.

Remember

• - Born Haber Cycle: Special application of Hess's Law
• - Lattice Energy: Energy released when gaseous ions form solid
• - Steps for NaCl: Sublimation, ionization, dissociation, electron affinity, lattice formation
• - **ΔH°_f = sum of all steps**
• - Lattice energy of NaCl: 787 kJ/mol

Common Mistakes

• 1. Forgetting the signs of ΔH values: Sublimation, ionization, dissociation are positive; electron affinity is negative; lattice energy is negative.
• 2. Mixing up ionization energy and electron affinity: Ionization = removing electron; Electron affinity = adding electron.
• 3. Forgetting the factor of ½ for Cl₂: Only ½ mole of Cl₂ is needed for 1 mole of Cl atoms.
• 4. Confusing lattice energy with enthalpy of formation: Lattice energy is one step in the cycle.

Quick Revision

• Born Haber cycle is a special application of Hess's Law.
• Lattice energy: Energy released when gaseous ions form a solid.
• Steps for NaCl: Sublimation, ionization, dissociation, electron affinity, lattice formation.
• Calculation: ΔH°_f = sum of all steps.
• Lattice energy of NaCl = 787 kJ/mol.

60-Second Revision

• Born Haber Cycle: Special application of Hess's Law
• Lattice Energy: Energy released when gaseous ions form solid
• Steps for NaCl: Sublimation, ionization, dissociation, electron affinity, lattice formation
• **ΔH°_f = sum of all steps**
• Lattice energy of NaCl: 787 kJ/mol

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