Born-Haber Cycles (DP IB Chemistry: HL)

Drawing the cycle for sodium chloride

• A good starting point is to draw the elements with their state symbols about a third of the way up the diagram
• This is shown as the left hand side of the equation for the process indicated
• The location is marked by drawing a horizontal bar or line which represents the starting energy level

Drawing a Born-Haber cycle step 1

• Next, we need to create the gaseous ions
• This is a two step process of first creating the gaseous atoms and then turning them into ions
• Creating gaseous atoms 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

Drawing a Born-Haber cycle step 2 – creating the gaseous atoms

• Now that the ions are created:
• 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

Drawing a Born-Haber cycle step 3 – creating the gaseous ions

• 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 points downwards
• Enthalpy of formation can be exothermic or endothermic, so you may need to show it above the elements (and displaced to the right) for a endothermic change
• The final change is lattice enthalpy, which is shown as the change from solid to gaseous ions. This means the arrow must point upwards. For sodium chloride, the equation is

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

 

Drawing a Born-Haber cycle step 4 – completing the cycle

• The cycle is now complete
• The cycle is usually used to calculate the lattice enthalpy of an ionic solid, but can be used to find other enthalpy changes if you are given the lattice enthalpy