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.
BORN-HABER CYCLE FOR SODIUM CHLORIDE
kJ H= +107kJmol-1 Atomisation of sodium +800 +700 +600 +500 +400 +300 +200 Na(g) + 1/2 Cl2(g) +100 H= +107kJmol-1 Na(s) + 1/2 Cl2(g) -400 -300 -200 -100 Atomisation of sodium
kJ H = +121kJmol-1 Atomisation of chlorine +800 +700 +600 +500 +400 +300 Na(g) + Cl(g) +200 H = +121kJmol-1 Na(g) + 1/2 Cl2(g) +100 Na(s) + 1/2 Cl2(g) -400 -300 -200 -100 Atomisation of chlorine
kJ e- e- e- e- e- e- e- e- e- e- e- + H = +502kJmol-1 +800 Na+(g) + Cl(g) +700 e- e- e- e- +600 e- e- +500 e- e- +400 e- H = +502kJmol-1 e- e- +300 Na(g) + Cl(g) +200 + Na(g) + 1/2 Cl2(g) +100 Na(s) + 1/2 Cl2(g) -400 -300 -200 -100 First Ionisation of sodium
First electron affinity of chlorine kJ kJ kJ +800 +800 +800 Na+(g) + Cl(g) +700 +700 +700 +600 +600 +600 H = -355kJmol-1 +500 +500 +500 +400 +400 +400 Na+(g) + Cl-(g) +300 +300 +300 Na(g) + Cl(g) Na(g) + Cl(g) Na(g) + Cl(g) +200 +200 +200 - e- Na(g) + 1/2 Cl2(g) Na(g) + 1/2 Cl2(g) Na(g) + 1/2 Cl2(g) +100 +100 +100 Na(s) + 1/2 Cl2(g) Na(s) + 1/2 Cl2(g) Na(s) + 1/2 Cl2(g) -400 -300 -200 -100 -400 -300 -200 -100 -400 -300 -200 -100 First electron affinity of chlorine
kJ kJ kJ - + H = -411kJmol-1 +800 +800 +800 +700 +700 +700 +600 +600 Na+(g) + Cl(g) +700 +700 +700 +600 +600 +600 +500 +500 +500 +400 +400 +400 Na+(g) + Cl-(g) +300 +300 +300 - + Na(g) + Cl(g) Na(g) + Cl(g) Na(g) + Cl(g) +200 +200 +200 Na(g) + 1/2 Cl2(g) Na(g) + 1/2 Cl2(g) Na(g) + 1/2 Cl2(g) +100 +100 +100 Na(s) + 1/2 Cl2(g) Na(s) + 1/2 Cl2(g) Na(s) + 1/2 Cl2(g) -400 -300 -200 -100 -400 -300 -200 -100 -400 -300 -200 -100 H = -411kJmol-1 Formation of sodium chloride NaCl(s)
kJ kJ kJ - - - - - + + + + H = -786 kJmol-1 +800 +800 +800 +700 +700 Na+(g) + Cl(g) +700 +700 +700 +600 +600 +600 +500 +500 +500 +400 +400 +400 Na+(g) + Cl-(g) +300 +300 +300 Na(g) + Cl(g) Na(g) + Cl(g) Na(g) + Cl(g) +200 +200 +200 - - Na(g) + 1/2 Cl2(g) Na(g) + 1/2 Cl2(g) Na(g) + 1/2 Cl2(g) + +100 +100 +100 + - + Na(s) + 1/2 Cl2(g) Na(s) + 1/2 Cl2(g) Na(s) + 1/2 Cl2(g) - + - -400 -300 -200 -100 -400 -300 -200 -100 -400 -300 -200 -100 H = -786 kJmol-1 Lattice enthalpy for sodium chloride NaCl(s)