• Once a Born-Haber cycle has been constructed, it is possible to calculate the lattice energy (ΔHlatt?) by applying Hess’s law and rearranging:

ΔHf??= ΔHat??+ ΔHat??+?IE?+?EA?+ ΔHlatt?

• If we simplify this into three terms, this makes the equation easier to see:
  • ΔHlatt?
  • ΔHf?
  • ΔH1??(the sum of all of the various enthalpy changes necessary to convert the elements in their standard states to gaseous ions)

   

• The simplified equation becomes

ΔHf??= ΔH1??+ ΔHlatt?

So, if we rearrange to calculate the lattice energy, the equation becomes

ΔHlatt??= ΔHf??- ΔH1?

• When calculating the ΔHlatt?, all other necessary values will be given in the question
• A Born-Haber cycle could be used to calculate any stage in the cycle
  • For example, you could be given the lattice energy and asked to calculate the enthalpy change of formation of the ionic compound
  • The principle would be exactly the same
  • Work out the?direct?and?indirect route?of the cycle (the stage that you are being asked to calculate will always be the direct route)
  • Write out the equation in terms of enthalpy changes and rearrange if necessary to calculate the required value

   

• Remember:?sometimes a value may need to be doubled or halved, depending on the ionic solid involved
  • For example, with MgCl2?the value for the first electron affinity of chlorine would need to be doubled in the calculation, because there are two moles of chlorine atoms
  • Therefore, you are adding?2 moles?of electrons to?2 moles?of chlorine atoms, to form?2 moles?of Cl-?ions

   

Answer

Step 1:?The corresponding Born-Haber cycle is:

Step 2:?Applying Hess’ law, the lattice energy of KCl?is:

ΔHlatt??= ΔHf??- ΔH1?

ΔHlatt??= ΔHf??- [(ΔHat??K) + (ΔHat??Cl) + (IE1?K) + (EA1?Cl)]

Step 3:?Substitute in the numbers:

ΔHlatt??= (-437) - [(+90) + (+122) + (+418) + (-349)]?= -718 kJ mol-1

Answer

Step 1:?The corresponding Born-Haber cycle is:

Step 2:?Applying Hess’ law, the lattice energy of MgO is:

ΔHlatt??= ΔHf??- ΔH1?

ΔHlatt??= ΔHf??- [(ΔHat??Mg) + (ΔHat??O) + (IE1?Mg) + (IE2?Mg) + (EA1?O) + (EA2?O)]

Step 3:?Substitute in the numbers:

ΔHlatt??= (-602) - [(+148) + (+248) + (+736) + (+1450) + (-142) + (+770)]

= -3812 kJ mol-1