BornHaber Cycle

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Born-Haber Cycle

• The process of ionic bond formation can be broken
  down into stages.
• At each stage the enthalpy changes are considered
• The Born Haber cycle is often used to calculate
  the lattice energy of an ionic compound
• - Consider the enthalpy changes in the formation
• of sodium chloride, NaCl

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• -The Born-Haber cycle is useful for predicting
  the stability or existence of ionic compounds.
• The more negative the lattice energy the stable
  the compounds

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?411.3 kJ
Na(s) ½Cl2(g)
NaCl(s)
107.8 kJ
121.3 kJ
Na(g)
Cl(g)
?
495.4 kJ
?348.8 kJ
Na(g)
Cl?(g)

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Enthalpy of formation NaCl
Enthalpy of atomization of Na
First ionization energy of Na
Enthalpy of atomization of Cl
Electron affinity of Cl
Lattice energy of NaCl
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?411.3 107.8 495.4 121.3 (?348.3)
?H6o
?787 kJ mol?1
Example VIDEO 1
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• In the presentation of Born-Haber cycle by energy
  diagram, by convention, positive values are
  denoted as going upwards, negative values as
  going downwards.

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Example Born-Haber Cycle
Figure below shows Born-Haber Cycle for sodium
bromide. Calculate the lattice energy for sodium?
? H1
Na (s) ½ Br2 (g)
NaBr (s)
?H2
?H4
Na(g)
Br (g)

?H3
?H6
?H5
Na(g)
Br (g)

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? H1 - 411 kJmol-1
Enthalpy formation NaBr
?H2 108 kJmol-1
Na Atomization
?H4 500 kJmol-1
Br Atomization
?H3 121 kJmol-1
Ionization energy
?H5 - 364 kJmol-1
Br electron affinity
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• ?H1 ?H2 ?H3 ?H4 ?H5 ?H6
• - 411 108 121 500 (-364) ?H6
• - 411 365 ?H6
• ?H6 - 776 kJ/mol

More example in VIDEO6
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Example
?H1 - 436kJmol-1 Enthalphy of formation KCl
?H2 90 kJmol-1 Enthalpy of atomization of K
?H4 90 kJmol-1 Ionization energy of K
?H5 - 364 kJmol-1 Electron affinity of Cl
?H6 - 373 kJmol-1 Lattice energy of KCl

Calculate the value of ?H3 in the Born-Haber
cycle and determine the types of enthalpy
involved.
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?H1 ?H2 ?H3 ?H4 ?H5 ?H6 - 436 90
?H3 90 (-364) (-373) ?H2 557 - 436
?H2 121 kJ/mol
?H3 Enthalpy of atomization of Cl
More example in VIDEO5
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• Construct the Born-Haber cycle for calcium
  bromide, CaBr2 and find the enthalpy of
  atomisation for calcium.
• Given
• First ionization energy of Ca 590
  kJ/mol
• Second ionization energy Ca 1137 kJ/mol
• Enthalpy of vaporisation of Br 31
  kJ/mol
• Enthalpy of atomisation of Br 112 kJ/mol
• Electron affinity - 325 kJ/mol
• Lattice energy -2176 kJ/mol
• Enthalpy of formation - 666 kJ/mol

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• THE BORN-HABER CYCLE IS USEFUL FOR PREDICTING THE
  STABILITY OR EXISTENCE OF IONIC COMPOUNDS.

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Example

• Magnesium normally forms simple ionic compounds
  in which magnesium exists as Mg2 cations.
  Construct a Born-Haber cycle for MgCl and predict
  the stability.
• Given
• Enthalpy of sublimation of Mg 149 kJ/mol
• First ionization energy of Mg 740
  kJ/mol
• Enthalpy of atomization of Cl 121 kJ/mol
• Electron affinity of Cl - 364 kJ/mol
• Lattice energy of MgCl - 776 kJ/mol

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Mg(g) Cl(g)
?HoEA
?HoIE
Mg(g) Cl?(g)
Energy
Mg(g) Cl(g)
?Hoa
Mg(g) ½Cl2(g)
?HLattice
?Hoa
Mg(s) ½Cl2(g)
MgCl(s)
?Hof
Born-Haber Cycle for the formation of MgCl
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?Hfo 149 121 740 (- 364) (-776)
- 130 kJ mol-1
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• The standard enthalpy of MgCl is negative. The
  compound exists and is stable under standard
  conditions.

VIDEO2
Explanation in
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• Construct a Born-Haber cycle to explain why ionic
  compound NaCl2 cannot form under standard
  conditions. Given
• Enthalpy of sublimation of Na 108 kJ/mol
• First ionization energy of Na 500
  kJ/mol
• Second ionization energy Na 4562 kJ/mol
• Enthalpy of atomization of Cl 121 kJ/mol
• Electron affinity of Cl - 364 kJ/mol
• Lattice energy of NaCl2 - 2489 kJ/mol

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Na2(g) 2Cl(g)
?HIE2o
?HEAo
Na(g) 2Cl (g)
Na2(g) 2Cl?(g)
Energy
?HIE1o
Na(g) 2Cl (g)
?Hao
Na(g) Cl2(g)
?HLattice
?Hso
Na(s) Cl2(g)
?Hfo
NaCl2(s)
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?Hfo ?Hso 2?Hao ?HIE1o ?HIE2o
2?HEAo ?Hlatticeo 108 2(121)
500 4562 (2x (- 364))
(-2489) 2195 kJ/mol The standard
enthalpy of formation of NaCl2 is highly
endothermic. Thus, this compound is unstable with
respect to its elements, and cannot exist under
standard conditions.
Explanation in VIDEO3
Solution with graph in VIDEO7