2.1.2

# Born-Haber Cycle Calculations (A2 Only)

Test yourself

## Calculations from Born-Haber Cycles

A Born-Haber cycle can be used to calculate any of the enthalpy changes involved in it, as long as you measure the rest.

### Lattice enthalpies

• To calculate a lattice enthalpy from the Born-Haber cycle, you treat it like a large Hess cycle.
• One route to the products is the enthalpy of formation.
• The other route is the sum of every other enthalpy change.
• You can rearrange this to find the lattice enthalpy.

### Theoretical differences

• The calculated lattice enthalpies are rarely correct.
• They’re close, but not exact.
• This is because the ionic model assumes ions are perfect spheres and have even charge distribution.
• This is not the case - ions usually have some degree of covalent bonding.

### Polarisation

• Positive ions can be said to polarise negative ions, if they cause distortion of the charge cloud. They can pull electrons to one side of the ion.
• There is, in fact, a spectrum between ionic and covalent bonding.
• If the lattice enthalpy you calculate is very different from an experimental value, that’s a hint that there is a relatively large degree of covalent bonding.

## Advanced Uses of Born-Haber Cycles

You can use a Born-Haber cycle to calculate enthalpies of hydration or solution.

### Enthalpy of hydration

• The enthalpy change of hydration is the enthalpy change when one mole of gaseous ions dissolves to form one mole of aqueous ions.
• The enthalpy of solution is the enthalpy change when one mole of a solid crystal is dissolved in a large excess of solvent.

### Born-Haber cycles

• You can draw a cycle involving only the enthalpies of hydration, solution, and lattice formation.

### Calculations

• Image: Born-Haber cycle and pictorial calculation.