H2 Chemistry 7 - Chemical Energetics: Born-Haber Cycle for NaCl

Step 1 - State the problem

Use a Born-Haber cycle to calculate the lattice energy of sodium chloride.

Step 1 - State the problem

You are given the following data: enthalpy of formation of sodium chloride is minus four hundred and eleven kilojoules per mole, enthalpy of atomisation of sodium is plus one hundred and seven kilojoules per mole, first ionisation energy of sodium is plus four hundred and ninety-six kilojoules per mole, enthalpy of atomisation of chlorine is plus one hundred and twenty-two kilojoules per mole, and electron affinity of chlorine is minus three hundred and forty-nine kilojoules per mole.

Step 1 - State the problem

We need to construct the cycle and apply Hess' law.

Step 2 - Draw the cycle pathway from elements to ionic lattice

The Born-Haber cycle has two routes from elements in standard states to the ionic lattice.

Step 2 - Draw the cycle pathway from elements to ionic lattice

Route one is the direct path: the enthalpy of formation of NaCl.

Step 2 - Draw the cycle pathway from elements to ionic lattice

Route two is the indirect path: atomise both elements, ionise sodium, add an electron to chlorine, then bring the ions together to form the lattice.

Step 2 - Draw the cycle pathway from elements to ionic lattice

By Hess' law, both routes have the same total enthalpy change.

Step 3 - Apply Hess' law

By Hess' law, the enthalpy of formation equals the sum of all steps in the indirect route.

Step 3 - Apply Hess' law

So minus four hundred and eleven equals plus one hundred and seven plus four hundred and ninety-six plus one hundred and twenty-two minus three hundred and forty-nine plus the lattice energy.

Step 3 - Apply Hess' law

The sum of the first four steps is plus three hundred and seventy-six.

Step 3 - Apply Hess' law

Rearranging: lattice energy equals minus four hundred and eleven minus three hundred and seventy-six.

Step 4 - Calculate the lattice energy

Lattice energy equals minus four hundred and eleven minus three hundred and seventy-six, which gives minus seven hundred and eighty-seven kilojoules per mole.

Step 4 - Calculate the lattice energy

The large negative value tells us that a lot of energy is released when the gaseous ions come together to form the ionic lattice.

Step 4 - Calculate the lattice energy

This is consistent with the strong electrostatic attraction between the sodium cation and the chloride anion.

Step 5 - Common pitfalls

Common mistake number one: confusing the sign of lattice energy. Lattice energy for formation of the lattice from gaseous ions is exothermic, so it should be negative.

Step 5 - Common pitfalls

Common mistake number two: forgetting that the atomisation of chlorine produces one mole of gaseous chlorine atoms from half a mole of chlorine gas.

Step 5 - Common pitfalls

Common mistake number three: mixing up electron affinity and ionisation energy. Ionisation removes an electron; electron affinity adds one.

Step 5 - Common pitfalls

Always label each arrow in the cycle clearly with the correct enthalpy term.