# 5.1.2 Born-Haber Cycles

### Constructing Born-Haber Cycles

• A Born-Haber cycle is a specific application of Hess's Law for ionic compounds and enable us to calculate lattice enthalpy which cannot be found by experiment
• The basic principle of drawing the cycle is to construct a diagram in which energy increases going up the diagram The basic principle of a Born-Haber cycle

• The cycle shows all the steps need to turn atoms into gaseous ions and from gaseous ions into the ionic lattice
• The alternative route to the ionic lattice begins from the enthalpy of formation of the 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 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
• The enthalpy of atomisation of sodium is

Na (s) → Na (g)           ΔHat = +108 kJ mol -1

• The enthalpy of atomisation of chlorine is

½Cl2 (g) → Cl (g)       ΔHat= +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 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          ΔHie= +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)           ΔHeaꝋ = -364 kJ mol-1

• The exothermic change means this is downwards
• The change is displace 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)            ΔHfꝋ = -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 usually shown a formation. For sodium chloride the equation is

#### Na+(g) + Cl–(g) → NaCl (s)  ΔHlattꝋ 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

#### Constructing a Born-Haber cycle for KCl

Construct a Born-Haber Cycle which can be used to calculate the lattice energy of potassium chloride.  #### Constructing a Born-Haber cycle for MgO

Construct a Born-Haber Cycle which can be used to calculate the lattice energy of magnesium oxide. #### Exam Tip

When constructing Born-Haber cycles, the direction of the changes is important, but the relative size of the steps does not matter so don’t worry if the steps don’t correspond to the magnitude of the energy changes.

You don’t need to show the energy axis in a Born-Haber cycle, but you do need to show the electron(s) in the ionisation step otherwise you might lose marks in an exam.

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