Topic 15 – Born-Haber cycles
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Born-Haber cycles
Born-Haber cycles are enthalpy cycles that show how ionic compounds are formed from
their elements.
Some important definitions:
Lattice enthalpy (ΔHƟlat) - the enthalpy change when one mole of a solid ionic compound
is separated into gaseous ions under standard conditions (endothermic).
Example: NaCl(s) → Na+(g) + Cl-(g)
Enthalpy of atomisation (ΔHƟatom) – the enthalpy change when one mole of gaseous
atoms is formed from an element in its standard state (endothermic).
Example: Na(s) → Na(g) (+107 kJmol-1)
First ionisation energy (ΔHƟi) – the energy required to remove one mole of electrons
from one mole of gaseous atoms (endothermic)
Example: Na(g) → Na+(g) + e- (+496 kJmol-1)
Bond dissociation enthalpy (E) – the enthalpy change when one mole of bonds is broken
in the gaseous state (endothermic).
Example: Cl2(g) → 2Cl(g) (+242 kJmol-1)
First electron affinity (ΔHƟe) – the enthalpy change when one mole of electrons are
added to mole of gaseous atoms (exothermic).
Example: Cl(g) + e- → Cl-(g) (-349 kJmol-1)
Standard enthalpy change of formation (ΔHƟf) - The enthalpy change when one mole of a
compound is formed from it elements in their standard states under standard conditions.
Example: Na(s) + ½ Cl2(g) → NaCl(s) (-411 kJmol-1)
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Topic 15 – Born-Haber cycles
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1) Using the values given above, construct a Born-Haber cycle using the template
below, and calculate the ΔHƟlat for NaCl.
2) Using the values given in the table below, construct a Born-Haber cycle and calculate
the ΔHƟlat for CaF2
ΔHat Ca(s) (enthalpy of atomization)
+179 kJ mol–1
E F2(g) (bond dissociation enthalpy)
+158 kJ mol–1
ΔHƟi Ca(g) (1st ionisation energy)
+590 kJ mol–1
ΔHƟi Ca+(g) (2nd ionisation energy)
+1150 kJ mol–1
ΔHƟe F(g) (first electron affinity)
–348 kJ mol–1
ΔHf CaF2(s) (enthalpy of formation)
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–1220 kJ mol–1
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Topic 15 – Born-Haber cycles
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Answers:
1) Born-Haber cycle for NaCl
Na+(g) + Cl(g)
½ E Cl2(g) ½(+242kJ)
Na+(g) + ½ Cl2(g)
ΔHƟe Cl (-349kJ)
Na+(g) + Cl-(g)
ΔHƟi Na(g) (+496
kJ)
Na(g) + ½ Cl2(g)
ΔHƟatom Na(s) (+107 kJ)
ΔHƟf NaCl (-411 kJmol-1)
Na(s) + ½ Cl2(g)
ΔHƟlat NaCl
NaCl(s)
ΔHƟlat = (ΔHƟatom Na(s)) + (ΔHƟi Na(g)) + (½ E Cl2(g)) + (ΔHƟe Cl) – (ΔHƟf NaCl)
ΔHƟlat = (+107) + (+496) + (+121) + (-349) - (-411)
ΔHƟlat = +786 kJmol-1
2) Born-Haber cycle for CaF2
Ca2+(g) + 2F(g)
E F2(g) (+158kJ)
Ca2+(g) + F2(g)
Ca2+(g) + 2F-(g)
ΔHƟi Ca+(g) (+1150 kJ)
ΔHƟi Ca(g) (+590 kJ)
Ca(g) + F2(g)
ΔHƟatom Ca(s) (+179 kJ)
Ca(s) + F2(g)
ΔHƟf CaF2 (-1220 kJmol-1)
ΔHƟe F (-348kJ) x2
ΔHƟlat CaF2
CaF2(s)
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Topic 15 – Born-Haber cycles
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ΔHƟlat = (ΔHƟatom Ca(s)) + (ΔHƟi Ca(g)) + (ΔHƟi Ca+(g)) + (E F2(g)) + 2(ΔHƟe F2) – (ΔHƟf CaF2)
ΔHƟlat = (+193) + (+590) + (+1150) + (+158) + 2(-348) - (-1220)
ΔHƟlat = +2615 kJmol-1
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