15.1.3 Born-Haber Cycle Calculations

Born-Haber Cycle Calculations

• 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

Worked Example

Calculating the lattice energy of KCl

Given the data below, calculate the ΔHlatt of potassium chloride (KCl) 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

Worked Example

Calculating the lattice energy of MgO

Given the data below, calculate the of ΔHlattmagnesium oxide of magnesium oxide (MgO) 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

Size & Charge of Ions & Lattice Enthalpy

Size & Charge of Ions & Lattice Enthalpy

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