Born-Haber Cycles (AQA A Level Chemistry): Revision Note

Constructing Born-Haber Cycles

• A Born–Haber cycle is a specific application of Hess’s Law used for ionic compounds. It allows the calculation of lattice enthalpy, which cannot be measured directly by experiment

• The basic principle of constructing the cycle is to draw a diagram in which energy increases upwards

• The cycle shows all the enthalpy changes required to convert elements into gaseous ions and then form the ionic lattice from those ions

• The alternative route to the ionic lattice starts from the enthalpy of formation of the compound from its elements in their standard states

Drawing the cycle for sodium chloride

• A good starting point is to draw the elements, with their state symbols, about one-third of the way up the diagram

• These appear on the left-hand side of the equation for the process being represented

• This position is marked by a horizontal line, which represents the starting energy level

• Next, the gaseous ions must be formed

• This occurs in two steps: first, gaseous atoms are produced, and then these atoms are converted into ions

• The formation of gaseous atoms involves bond breaking, so these steps are represented by arrows drawn upwards on the diagram

• It does not matter whether sodium or chlorine is considered first

• 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

• The products of each step are shown on horizontal lines, with the enthalpy change written next to the vertical arrow connecting the energy levels

• Next, the gaseous ions are formed

• The sodium atom loses an electron, so this energy change corresponds to the first ionisation energy of sodium:

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

• This process is endothermic, so the arrow is drawn upwards on the diagram

• The chlorine atom gains an electron, which is the electron affinity of chlorine:

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

• This change is exothermic, so the arrow is drawn downwards

• The electron affinity step is often displaced to the right on the diagram to improve clarity and avoid overlapping arrows

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

• The enthalpy of formation of sodium chloride is added 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 is drawn downwards

• Enthalpy of formation can be either exothermic or endothermic. If it is endothermic, the arrow must be drawn upwards and is often displaced to the right of the diagram for clarity

• The final step is the lattice enthalpy, which can be shown as the enthalpy change for lattice formation or dissociation

  • For sodium chloride, the formation equation is:

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

• The cycle is now complete

• It is most commonly used to calculate the lattice enthalpy of an ionic solid, but it can also be used to determine other enthalpy changes if the lattice enthalpy is known