Born haber cycle

Born-Haber Cycle

The Born-Haber cycle is a thermodynamic process used to determine the lattice energy of an ionic compound through a stepwise energy analysis. Named after German scientists Max Born and Fritz Haber, it is based on Hess's Law, which states that the total enthalpy change for a chemical reaction is the same, no matter the pathway taken.

Purpose of the Born-Haber Cycle

The primary goal of the Born-Haber cycle is to determine the lattice enthalpy (or lattice energy) of an ionic solid, which is difficult to measure directly. This energy plays a crucial role in analyzing the formation and stability of ionic substances.

Steps in the Born-Haber Cycle

The Born-Haber cycle involves the following sequential stages:

1. Sublimation Energy (ΔH_sub): Energy required to convert one mole of solid metal to gaseous atoms.
2. Ionization Energy (IE): Energy needed to remove electrons from the gaseous atoms to form cations.
3. Bond Dissociation Energy (ΔH_diss): Energy required to break the bond in a diatomic molecule to form individual atoms (for nonmetals).
4. Electron Affinity (EA): Energy released when electrons are added to nonmetal atoms to form anions.
5. Lattice Energy (U or ΔH_latt): Energy released when gaseous ions combine to form the ionic solid.
6. Enthalpy of Formation (ΔH_f): The total heat change when one mole of an ionic compound is produced from its constituent elements in their standard forms.

Mathematical Expression

Based on Hess’s law, the lattice energy can be calculated as:

ΔH_f = ΔH_sub + IE + ½ΔH_diss + EA + (–U)

Rearranging the equation to find lattice energy (U):

U = ΔH_sub + IE + ½ΔH_diss + EA – ΔH_f

Example: Born-Haber Cycle for NaCl

• Sublimation of Na: Na(s) → Na(g)   ΔH_sub = +108 kJ/mol
• Ionization of Na: Na(g) → Na⁺(g) + e⁻  IE = +496 kJ/mol
• Dissociation of Cl₂: ½Cl₂(g) → Cl(g)  ΔH_diss = +122 kJ/mol
• Electron affinity of Cl: Cl(g) + e⁻ → Cl⁻(g) EA = –349 kJ/mol
• Enthalpy of formation: Na(s) + ½Cl₂(g) → NaCl(s) ΔH_f = –411 kJ/mol

Now apply the formula to find lattice energy:

U = 108 + 496 + 122 – 349 – (–411) = 788 kJ/mol

So, lattice energy of NaCl = –788 kJ/mol (negative because it's exothermic).

Applications

• Calculation of lattice energies of ionic solids.
• Helps explain why ionic compounds are stable.
• Comparison of ionic character between different compounds.
• Determining if a compound is likely to be formed under standard conditions.

The Born-Haber cycle is a useful thermodynamic tool in chemistry that provides insight into the energetics of ionic compound formation. It helps chemists understand bond strengths, stability, and how much energy is involved in forming a compound from its constituent elements.