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For an ionic compound the lattice enthalpy is the heat energy released when one mole of solid in its standard state is formed from its ions in the gaseous state. This value cannot be determined directly and so we make use of changes for which data are available and link them together with an enthalpy cycle. This enthalpy cycle is based on the formation of the compound from its elements in their standard states. From John Slater From John Slater :
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BORN-HABER CYCLE FOR SODIUM CHLORIDE
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Atomisation of sodium Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) 0 +100 +200 +300 +400 +500 +600 +700 +800 kJ -400 -300 -200 -100 H= +107kJmol -1
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Atomisation of chlorine Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ H = +121kJmol -1
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+ First Ionisation of sodium e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ Na + (g) + Cl(g) H = +502kJmol -1
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First electron affinity of chlorine e-e- - Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ Na + (g) + Cl(g) Na + (g) + Cl - (g ) H = -355kJmol -1
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-- - -- + ++ + Formation of sodium chloride Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ Na + (g) + Cl(g) Na + (g) + Cl - (g) NaCl(s) H = -411kJmol -1
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-- - -- ++++ Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ Na (s) + 1/2 Cl 2 (g) Na(g) + 1/2 Cl 2 (g) Na(g) + Cl(g) 0 +100 +200 +300 +400 +500 +600 +700 +800 -400 -300 -200 -100 kJ Na + (g) + Cl(g) Na + (g) + Cl - (g) NaCl(s) Lattice enthalpy for sodium chloride H = -786 kJmol - 1
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