Calculations Using Born-Haber Cycles (OCR A Level Chemistry)

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Born-Haber Cycles - 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

Given the data below, calculate the ΔHlatt of potassium chloride (KCl)  Worked example_Calculating the lattice energy of KCl, downloadable AS & A Level Chemistry revision notes

Answer

Step 1: The corresponding Born-Haber cycle is:

 

Chemical Energetics - Constructing a Born-Haber cycle for KCl Cycle 1, downloadable AS & A Level Chemistry revision notes

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

Given the data below, calculate the of ΔHlattmagnesium oxide of magnesium oxide (MgO)Worked example_Calculating the lattice energy of MgO, downloadable AS & A Level Chemistry revision notes

Answer

Step 1: The corresponding Born-Haber cycle is:

 

Chemical Energetics - Constructing a Born-Haber cycle for MgO Cycle 2, downloadable AS & A Level Chemistry revision notes

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

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Philippa

Author: Philippa

Expertise: Chemistry

Philippa has worked as a GCSE and A level chemistry teacher and tutor for over thirteen years. She studied chemistry and sport science at Loughborough University graduating in 2007 having also completed her PGCE in science. Throughout her time as a teacher she was incharge of a boarding house for five years and coached many teams in a variety of sports. When not producing resources with the chemistry team, Philippa enjoys being active outside with her young family and is a very keen gardener.