R1.2.5 Born-Haber Cycle (Higher Level Only) Notes

Application of Hess’s Law: Born-Haber Cycles and Lattice Enthalpy

What is a Born-Haber Cycle?

1. It connects the energy changes from individual steps involved in forming an ionic lattice from its elements in their standard states.
2. These steps include:
   1. Enthalpy of atomization – converting elements into gaseous atoms.
   2. Ionization energy – removing electrons from metal atoms to form cations.
   3. Electron affinity – adding electrons to non-metal atoms to form anions.
   4. Lattice enthalpy – forming the ionic lattice from gaseous ions.
3. Hess’s Law states that the total enthalpy change for a reaction is the same, regardless of the pathway taken.
4. This principle allows us to construct the Born-Haber cycle, where the sum of all energy changes equals the enthalpy of formation of the ionic compound.

Key Components of a Born-Haber Cycle

Let’s break down each step of the Born-Haber cycle using sodium chloride $NaCl$ as an example.

1. Enthalpy of Atomization ($ΔH_\text{at}$)

1. The enthalpy of atomization is the energy required to convert one mole of an element in its standard state into gaseous atoms.
2. For sodium, this involves sublimation: $$
   \text{Na(s)} \rightarrow \text{Na(g)} \quad \Delta H_{\text{atomization}} = +107 \, \text{kJ mol}^{-1}
   $$
3. For chlorine, the process involves bond dissociation, as chlorine exists as diatomic molecules: $$
   \frac{1}{2} \text{Cl}_2(g) \rightarrow \text{Cl(g)} \quad \Delta H_{\text{dissociation}} = +122 \, \text{kJ mol}^{-1}
   $$

2. Ionization Energy (IE)

Ionization energy is the energy required to remove an electron from a gaseous atom to form a cation. For sodium:

$$
\text{Na(g)} \rightarrow \text{Na}^+(g) + e^- \quad \text{IE} = +496 \, \text{kJ mol}^{-1}
$$

3. Electron Affinity (EA)

Electron affinity is the energy change when an electron is added to a gaseous atom to form an anion. For chlorine: