Constructing Born–Haber Cycles (Oxford AQA International A Level Chemistry)

Constructing Born–Haber Cycles

• The basic principle of drawing a Born-Haber cycle is to construct a diagram in which energy increases going up the diagram

• The cycle shows all the steps needed to turn atoms into gaseous ions and from gaseous ions into the ionic lattice

• The alternative route to the ionic lattice is the enthalpy of formation of the elements in their standard states

Drawing the cycle for sodium chloride

Step 1 - starting elements

• A good starting point is to write the elements required to form the ionic compound

• This should be placed:

  • On the left hand side of the diagram

  • About a third of the way up the diagram

• The elements required should:

  • Be written on their own energy level, shown by a horizontal line

  • Include state symbols

Step 2 - gaseous atoms

• The second step is to create the gaseous atoms

• Creating gaseous ions is a bond breaking process, so arrows must be drawn upwards

• It doesn't matter whether you start with sodium or chlorine

• The enthalpy of atomisation of sodium is:

Na (s) → Na (g)           ΔH_at^ꝋ = +108 kJ mol ^-1

• The enthalpy of atomisation of chlorine is:

½Cl₂ (g) → Cl (g)       ΔH_at^ꝋ = +121 kJ mol ^-1

• We can show the products of the process on the horizontal lines and the energy value against a vertical arrow connecting the energy levels

Step 3 - gaseous ions

• The third step is to create the gaseous ions

• The sodium ion loses an electron, so this energy change is the first ionisation energy for sodium:

Na (g) → Na⁺ (g) + e^–          ΔH_ie^ꝋ = +500 kJ mol^-1

• The change is endothermic so the direction continues upwards

• The chlorine atom gains an electron, so this is electron affinity:

Cl (g) + e^– → Cl^- (g)           ΔH_ea^ꝋ = -364 kJ mol^-1

• The exothermic change means this is downwards

• The change is displaced to the right to make the diagram easier to read

Step 4 - forming the ionic lattice

• The two remaining parts of the cycle can now be completed:

  • Enthalpy of formation

  • Lattice enthalpy

• The enthalpy of formation of sodium chloride is added:

  • On the left hand side of the diagram

  • At the bottom of the diagram

Na (s) + ½Cl₂ (g) → NaCl (s)            ΔH_f^ꝋ = -411 kJ mol ^-1

• This is an exothermic change for sodium chloride so the arrow points downwards

• The lattice enthalpy is usually the enthalpy of lattice formation

• The lattice enthalpy is added:

  • On the right hand side of the diagram

  • At the bottom of the diagram

    • This is usually shown as lattice formation

• For sodium chloride the equation is:

Na⁺(g) + Cl^-(g) → NaCl (s)  ΔH_latt^ꝋ 

• This is an exothermic change for sodium chloride so the arrow points downwards

• The cycle is now complete and can be used to calculate the lattice enthalpy of an ionic solid

  • It can also be used to find other enthalpy changes if you are given the lattice enthalpy