DP IB Chemistry: HL

Revision Notes

Syllabus Edition

First teaching 2014

Last exams 2024

|

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 (ΔHlat) 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

ΔHlat= 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 chloride ions, i.e. 2Cl-

Worked example

Calculating the lattice energy of KCl

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: Construct the Born-Haber cycle

15-1-2-born-haber-cycles-we-kcl-cycle-1-new

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)Worked example_Calculating the lattice energy of MgO, downloadable AS & A Level Chemistry revision notes

Answer

Step 1: Construct the Born-Haber cycle

15-1-2-born-haber-cycles-we-mgo-cycle-2-nnew

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

Factors affecting lattice enthalpy

  • The two key factors which affect lattice energy, ΔHlat, are the ionic charge and ionic radii of the ions that make up the crystalline lattice

Ionic Radius

  • The radius of the anion increases as you move down a group
  • As the distance between the bonded ions increases, the strength of the electrostatic attraction decreases
  • This is reflected by a decrease in the lattice enthalpy
  • The lattice enthalpy becomes less positive or less endothermic as the ionic radius of the ions increases
  • This is because the charge on the ions is more spread out over the ion when the ions are larger
  • The ions are also further apart from each other in the lattice
    • The attraction between ions is between the centres of the ions involved, so the bigger the ions the bigger the distance between the centre of the ions

  • Therefore, the electrostatic forces of attraction between the oppositely charged ions in the lattice are weaker
  • For example, down group 17, the ionic radii increases which directly influences the lattice enthalpy

Lattice enthalpies of sodium halides

Lattice Enthalpies of Sodium Halides, downloadable IB Chemistry revision notes

Ionic Charge

  • Increasing the ionic charge will result in an increased attraction between oppositely charged ions
  • This will increase the energy required to break the lattice apart, and therefore increase the lattice enthalpy (becomes more positive or more endothermic)
  • The greater the ionic charge, the higher the charge density
  • This results in stronger electrostatic attraction between the oppositely charged ions in the lattice
  • As a result, the lattice enthalpy is more endothermic
    • For example, the lattice energy of calcium oxide (CaO) is more endothermic than the lattice energy of potassium chloride (KCl)

Lattice enthalpies with varying ionic charges and radii

Variations in Lattice Enthalpy, downloadable IB Chemistry revision notes

You've read 0 of your 0 free revision notes

Get unlimited access

to absolutely everything:

  • Downloadable PDFs
  • Unlimited Revision Notes
  • Topic Questions
  • Past Papers
  • Model Answers
  • Videos (Maths and Science)

Join the 80,663 Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Stewart

Author: Stewart

Stewart has been an enthusiastic GCSE, IGCSE, A Level and IB teacher for more than 30 years in the UK as well as overseas, and has also been an examiner for IB and A Level. As a long-standing Head of Science, Stewart brings a wealth of experience to creating Topic Questions and revision materials for Save My Exams. Stewart specialises in Chemistry, but has also taught Physics and Environmental Systems and Societies.