20.1    Born-Haber Cycles

What are Born-Haber cycles?

• Lattice energy cannot be determined experimentally, however, it can be calculated using a special type of Hess’ cycle, this is called the Born-Haber cycle.

• It assumes that the final product is the solid ionic compound. To make this compound, we start with its elements in their standard states, and convert them to ions in gaseous state. These ions are then converted to the solid lattice. Lattice energy can be obtained by considering the energetics of the entire process.
• A typical Born-Haber cycle looks like this, take sodium chloride, NaCl as an example:Here, the final product is NaCl(s). To make this, we begin with Na(s) + ½Cl2(g). This is then converted step-by-step into Na⁺(g) + Cl⁻(g). This is done using atomisation energy, ionisation energy and electron  affinity.
  The energy released when the gaseous ions join to form the lattice is the lattice  energy.
  By Hess’ Law,
  -411 = +107 + 496 + 122 – 349 + LE
  LE = -411 – 107 – 496 – 122 + 349
  LE = -787 kJ mol⁻¹

  -411 is the enthalpy change of
  +107 is the enthalpy change of atomisation of Na.
  +496 is the first ionisation energy of Na.
  +122 is the enthalpy change of atomisation of ½Cl2.
  -349 is the first electron affinity of

Note:

1) Each level should only indicate one type of enthalpy change.

• Another example, Born-Haber cycle of magnesium chloride, MgCl2.