Born-Haber Cycle
Born-Haber Cycles
The BornHaber cycle is an approach to analyzing reaction energies. It was named after and developed by the two German scientists Max Born and Fritz Haber. BornHaber cycles are used primarily for calculating lattice enthalpies which cannot otherwise be measured directly. The lattice enthalpy is the enthalpy change involved in the formation of an ionic compound from gaseous ions.
What do we mean by lattice enthalpy?
For an ionic compound the lattice enthalpy is the enthalpy change when one mole of solid in its standard state is formed from its ions in the gaseous state.
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+
-
+
-
+
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-
+
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The lattice enthalpy cannot be measured directly and so we make use of other known enthalpies and link them together with an enthalpy cycle. This enthalpy cycle is the Born-Haber cycle.
http://www.tes.co.uk/teaching-resource/Lattice-Enthalpy-6354465/
kJmol-1
+800
+700 +600
Born-Haber Cycle for Sodium Chloride 1 Sublimation of Sodium
+500
+400 +300 +200 +100 0 -100 -200 -300 -400
Na(g) + 1/2 Cl2(g)
Na(s) + 1/2 Cl2(g)
HS = +107kJmol-1
kJmol-1
+800
+700 +600
Born-Haber Cycle for Sodium Chloride
+500
+400 +300
Na(g) + Cl(g)
2 Bond Dissociation of Chlorine
+200 +100 0 -100 -200 -300 -400
Na(g) + 1/2 Cl2(g)
-1 = +121kJmol H D
Na(s) + 1/2 Cl2(g)
kJmol-1
+800
+700 +600
Born-Haber Cycle for Sodium Chloride
Na+(g) + Cl(g)
e-
+500
+400 +300
3 First Ionisation of Sodium
HI =
e-
+502kJmol-1
eee-
Na(g) + Cl(g)
+200 +100 0 -100 -200 -300 -400
Na(g) + 1/2 Cl2(g)
Na(s) + 1/2 Cl2(g)
kJmol-1
+800
+700 +600
Born-Haber Cycle for Sodium Chloride
Na+(g) + Cl(g)
4 Electron Affinity of Chlorine
HE= -355kJmol-1
Na+(g) + Cl-(g) Na(g) + Cl(g)
+500
+400 +300 +200 +100 0 -100 -200 -300 -400
Na(g) + 1/2 Cl2(g)
Na(s) + 1/2 Cl2(g)
kJmol-1
+800
+700 +600
Born-Haber Cycle for Sodium Chloride
Na+(g) + Cl(g)
+500
+400 +300
Na(g) + Cl(g) Na+(g) + Cl-(g)
+
-
+200 +100 0 -100 -200 -300 -400 NaCl(s)
Na(g) + 1/2 Cl2(g)
+
-
+
-
Na(s) + 1/2 Cl2(g)
HF = -411kJmol-1
5 Formation of Sodium Chloride
kJmol-1
+800
+700 +600
Born-Haber Cycle for Sodium Chloride
Na+(g) + Cl(g)
+500
+400 +300
Na(g) + Cl(g) Na+(g) + Cl-(g)
+200 +100 0 -100 -200 -300 -400 NaCl(s)
Na(g) + 1/2 Cl2(g)
Lattice Enthalpy for Sodium Chloride
H L = -786 kJmol-1
Na(s) + 1/2 Cl2(g)
+
-
+
-
+
-
kJmol-1
+800
+700 +600
Born-Haber Cycle for Sodium Chloride
Na+(g) + Cl(g)
+500
+400 +300
H=
+502kJmol-1
HE= -355kJmol-1
Na+(g) + Cl-(g) Na(g) + Cl(g)
+200 +100 0 -100 -200 -300 -400 NaCl(s)
HF = Na(g) + 1/2 Cl2(g)
H = +121kJmol-1 = +107kJmol-1
= -1141kJmol-1
-
Na(s) + 1/2 Cl2(g) H
+
-
-411kJmol-1
H L = -786 kJmol-1
+
-
+
-
Born-Haber Cycle
Max Born 1882-1970
German physicist and mathematician who was
Fritz Haber 1868-1934
German chemist. Nobel Prize winner in Chemistry in 1918 for
Born-Haber Cycle - NaCl
1
Enthalpy of formation of NaCl
Na(s) + Cl2(g) >
2
NaCl(s)
Na+(g) + Cl(g)
Enthalpy of sublimation of sodium
Na(s)
3
>
Na(g)
5
4
Na+(g) + Cl(g) Na(g) + Cl(g)
Enthalpy of atomisation of chlorine
Cl2(g) >
4
Cl(g)
Ist Ionisation Energy of sodium
Na(g) > Na+(g) + e
5
3
Na(g) + Cl2(g)
Electron Affinity of chlorine
Cl(g) + e
6
>
Cl(g)
Na(s) + Cl2(g)
Lattice Enthalpy of NaCl
Na+(g) + Cl(g) > NaCl(s)
1
NaCl(s)
Lattice Enthalpy is exothermic. Oppositely charged ions are attracted to each other.
Born-Haber Cycle - NaCl
CALCULATING THE LATTICE ENTHALPY Apply Hesss Law 6
Na+(g) + Cl(g)
= -
2 + 1
5
4
Na+(g) + Cl(g) Na(g) + Cl(g)
The minus shows you are going in the opposite direction to the definition
= - (-355) - (+502) - (+121) - (+107) + (-411) = - 786 kJ mol-1
3
Na(g) + Cl2(g)
2
Na(s) + Cl2(g)
1
NaCl(s)
Born-Haber Cycle - NaCl
CALCULATING THE LATTICE ENTHALPY Apply Hesss Law 6
Na+(g) + Cl(g)
= -
2 + 1
5
4
Na+(g) + Cl(g) Na(g) + Cl(g)
The minus shows you are going in the opposite direction to the definition
= - (-364) - (+500) - (+121) - (+108) + (-411) = - 786 kJ mol-1
OR Ignore the signs and just use the values;
3
Na(g) + Cl2(g)
2
Na(s) + Cl2(g)
If you go up you add, if you come down you subtract the value
6
1
NaCl(s)
= (355) - (502) - (121) - (107) - (411) = - 786 kJ mol-1
Your Task: Draw the Born-Haber cycle for - MgCl2
Enthalpy of formation of MgCl2 Mg(s) + Cl2(g) > MgCl2(s) Enthalpy of sublimation of magnesium Mg(s) > Mg(g)
Enthalpy of atomisation of chlorine Cl2(g) > Cl(g) x2 Ist Ionisation Energy of magnesium Mg(g) > Mg+(g) + e 2nd Ionisation Energy of magnesium Mg+(g) > Mg2+(g) + e Electron Affinity of chlorine Cl(g) + e > Cl(g)
x2
Lattice Enthalpy of MgCl2 Mg2+(g) + 2Cl(g) > MgCl2(s)
Born-Haber Cycle - MgCl2
1
Enthalpy of formation of MgCl2 Mg(s) + Cl2(g) > MgCl2(s) Enthalpy of sublimation of magnesium Mg(s) > Mg(g) Enthalpy of atomisation of chlorine Cl2(g) > Cl(g)
Mg2+(g) + 2Cl(g)
5 6
Mg+(g) + 2Cl(g)
x2
4
Mg2+(g) + 2Cl(g) Mg(g) + 2Cl(g)
Ist Ionisation Energy of magnesium Mg(g) > Mg+(g) + e 2nd Ionisation Energy of magnesium Mg+(g) > Mg2+(g) + e Electron Affinity of chlorine
3
Mg(g) + Cl2(g)
Cl(g) + e
7
>
Cl(g)
x2
Mg(s) + Cl2(g)
Lattice Enthalpy of MgCl2 Mg2+(g) + 2Cl(g) > MgCl2(s)
1
MgCl2(s)
Value
Enthalpy of sublimation of Magnesium
Ho (kJmol-1)
148
Ist Ionisation energy of magnesium
2nd Ionisation energy of magnesium Enthalpy of atomisation of chlorine gas 1st electron affinity of chlorine Lattice energy of MgCl2
738
1451 244 -364 -2526
Determine the enthalpy of formation of MgCl2
Born-Haber Cycle - MgCl2
1
Enthalpy of formation of MgCl2 Mg(s) + Cl2(g) > MgCl2(s) Enthalpy of sublimation of magnesium Mg(s) > Mg(g) Enthalpy of atomisation of chlorine Cl2(g) > Cl(g)
Mg2+(g) + 2Cl(g)
1451
Mg+(g) + 2Cl(g)
-364 x 2
6
x2?
738
Mg(g) + 2Cl(g)
4
Mg2+(g) + 2Cl(g)
Ist Ionisation Energy of magnesium Mg(g) > Mg+(g) + e 2nd Ionisation Energy of magnesium Mg+(g) > Mg2+(g) + e Electron Affinity of chlorine
244
Mg(g) + Cl2(g)
3 2
148
1
Cl(g) + e
7
>
Cl(g)
x2
Mg(s) + Cl2(g)
-2526
MgCl2(s)
Lattice Enthalpy of MgCl2 Mg2+(g) + 2Cl(g) > MgCl2(s)
-673
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