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

Born–Haber Cycles

• A Born-Haber cycle is a specific application of Hess's Law

  • It applies to ionic compounds

• A Born-Haber cycle allows us to calculate lattice enthalpy which cannot be found by experiment

  • These calculations require the use of several different enthalpies

Enthalpy of formation, ΔH_f^Ꝋ

• The enthalpy change when one mole of substance is formed from its constituent elements, under standard conditions with all reactants and products in their standard states

O₂ (g) + H₂ (g) H₂O (l) ΔH_f^Ꝋ = -286 kJ mol^-1

• The reactions to form substances can be:

  • Exothermic - with a negative enthalpy change

  • Endothermic - with a positive enthalpy change

• The standard enthalpy of formation for elements is 0 kJ mol^-1

• The enthalpy of formation can be calculated using mean bond enthalpies

Enthalpy of combustion, ΔH_c^Ꝋ

• The enthalpy change when one mole of substance is completely burned in oxygen, under standard conditions with all reactants and products in their standard states

CH₄ (g) + 2O₂ (g) CO₂ (g) + 2H₂O (l) ΔH_c^Ꝋ = -890 kJ mol^-1

• Combustion releases energy from fuels

• This means combustion is an exothermic process

  • So, the enthalpy change of combustion will always be negative

Enthalpy of atomisation, ΔH_at^Ꝋ

• The enthalpy change which accompanies the formation of one mole of gaseous atoms from the element in its standard state under standard conditions

Mg (s) Mg (g) ΔH_at^Ꝋ = +148 kJ mol^-1

• Atomisation requires energy to change the physical state of an element

• This means atomisation is an endothermic process

  • So, the enthalpy change of atomisation will always be positive

First ionisation energy, ΔH_ie^Ꝋ

• The standard enthalpy change when one mole of gaseous atoms is converted into one mole of gaseous ions each with a single positive charge

Mg (g) Mg⁺ (g) + e^- ΔH_ie^Ꝋ = +738 kJ mol^-1

• First ionisation requires energy to remove an electron from an atom

• This means that ionisation is an endothermic process

  • So, the enthalpy change of ionisation will always be positive

Second ionisation energy, ΔH_ie^Ꝋ

• The standard enthalpy change one mole of gaseous 1+ ions is converted into one mole of gaseous 2+ ions

Mg⁺ (g) Mg²⁺ (g) + e^- ΔH_ie^Ꝋ = +1451 kJ mol^-1

• Second ionisation requires energy to remove an electron from a 1+ ion

  • This requires more energy than first ionisation as there is a stronger attraction between the nucleus of the 1+ ion and the outer electron

• This means that second ionisation is an endothermic process

  • So, the enthalpy change of second ionisation will always be positive

First electron affinity, ΔH_ea^Ꝋ

• The standard enthalpy change when one mole of gaseous atoms is converted to one mole of gaseous ions, each with a single negative charge

O (g) + e^- O^- (g) ΔH_ea^Ꝋ = -141 kJ mol^-1

• First electron affinity can require energy, release energy or be energetically neutral

• So, first electron affinity can be:

  • Exothermic - with a negative enthalpy change

  • Endothermic - with a positive enthalpy change

  • Neutral - with no enthalpy change

Second electron affinity, ΔH_ea^Ꝋ

• The standard enthalpy change when one mole of gaseous 1- ions is converted to one mole of gaseous 2- ions

O^- (g) + e^- O^2- (g) ΔH_ea^Ꝋ = +798 kJ mol^-1

• Second electron affinity requires energy to overcome the repulsion between the negative 1- ion and the negative electron

• This means that second electron affinity is an endothermic process

  • So, the enthalpy change of second electron affinity will always be positive

Enthalpy of lattice formation, ΔH_latt^Ꝋ

• The standard enthalpy change when one mole of solid ionic compound is formed from its gaseous ions

Na⁺ (g) + Cl^- (g) NaCl (s) ΔH_latt^Ꝋ = -788 kJ mol^-1

• This cannot be measured directly

• Lattice formation creates new bonds which means that energy is released

• This means that lattice formation is an exothermic process

  • So, the enthalpy change of lattice formation will always be negative

Lattice enthalpy of dissociation

• The standard enthalpy change when one mole of solid ionic compound dissociates into its gaseous ions

NaCl (s) Na⁺ (g) + Cl^- (g) ΔH_latt^Ꝋ = +788 kJ mol^-1

• This cannot be measured directly

• Lattice dissociation breaks bonds which means that energy is required

• This means that lattice dissociation is an endothermic process

  • So, the enthalpy change of lattice dissociation will always be positive