Lattice energy and Born-Haber cycles
Lattice energy and Born–Haber cycles
- Forming an ionic solid involves several enthalpy steps.
- The lattice energy is the big energy release.
- A Born–Haber cycle ties them all together.
The key enthalpy changes
- atomisation $\Delta H_{\text{at}}$: energy to make one mole of gaseous atoms (always positive).
- lattice energy $\Delta H_{\text{latt}}$: change when one mole of solid lattice forms from gaseous ions (always negative).
- first electron affinity: change when gaseous atoms each gain an electron (usually negative); going down a group it gets less exothermic (larger atom).
Practice
The lattice energy is:
Strong ionic bonds form, so lattice energy is exothermic (negative).
Practice
Going down Group 17, the first electron affinity becomes:
A bigger atom pulls the incoming electron in less strongly, so EA is less exothermic.
Born–Haber cycle and lattice strength
- A Born–Haber cycle links the formation of an ionic solid with atomisation, ionisation energy, electron affinity and lattice energy. Use Hess's law to find any unknown step.
- The lattice energy is more negative (stronger) when:
- the ionic charge is higher ($\text{Mg}^{2+}$ beats $\text{Na}^{+}$), and
- the ionic radius is smaller.
Practice
A Born–Haber cycle lets you find an unknown enthalpy step by using:
Because enthalpy is conserved, going round the cycle relates all the steps, so any one can be found.
Practice
Lattice energy is most negative (strongest) for ions with:
Higher charge and smaller radius both increase the attraction between the ions.
You've got it
Key idea
- atomisation (+, makes gaseous atoms); lattice energy (−, lattice forms from gaseous ions); electron affinity (usually −)
- a Born–Haber cycle uses Hess's law to find any unknown enthalpy step
- lattice energy is stronger (more negative) for higher charge and smaller radius