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Thermodynamics

Question
CBSEENCH11006231

Calculate the lattice enthalpy of KCl crystal from the following data:

Sublimation enthalpy of pottasium (K) = +89 kJ mol-1
Dissociation enthalpy of 1 half Cl subscript 2 left parenthesis straight g right parenthesis
                                          = +122 kJ mol-1
Ionisation enthalpy of K(g) +425 kJ mol-1
Electron gain enthalpy of Cl(g) = -355 kJ mol-1
Enthalpy of formation of KCl left parenthesis increment subscript straight r straight H degree right parenthesis space equals space minus 438 space kJ space mol to the power of negative 1 end exponent



Solution

Using Born-Haber cycle for KCl,
increment subscript straight f straight H to the power of circled dash space equals space increment straight H subscript 1 superscript 0 plus increment straight H subscript 2 superscript 0 space plus space increment straight H subscript 3 superscript 0 space plus space increment straight H subscript 4 superscript 0 space plus space increment straight H subscript 5 superscript 0
or space space space increment straight H subscript 5 superscript 0 space equals space increment subscript straight f straight H to the power of 0 space minus space increment straight H subscript 1 superscript 0 space minus increment straight H subscript 2 superscript 0 space minus space increment straight H subscript 3 superscript 0 space minus space increment straight H subscript 4 superscript 0
Substituting the values we have,
    increment straight H subscript 5 superscript 0 space equals space minus 438 minus 89 minus 122 minus 425 plus 355
space space space space space space space space equals negative 719 space kJ space mol to the power of negative 1 end exponent
increment straight H subscript 5 superscript 0 space equals space minus 438 minus 89 minus 122 minus 425 plus 355
space space space space space space space equals negative 719 space kJ space mol to the power of negative 1 end exponent
increment straight H subscript 5 superscript 0 space equals space minus 438 minus 89 minus 122 minus 425 plus 355
space space space space space space space equals negative 719 space kJ space mol to the power of negative 1 end exponent
increment straight H subscript 5 superscript 0 space equals space Enthalpy space change space for space lattice space formation space from
space straight K to the power of plus left parenthesis straight g right parenthesis space plus space Cl to the power of minus left parenthesis straight g right parenthesis space space rightwards arrow space space KCl left parenthesis straight s right parenthesis
The reverse of the above equation i.e.
KCl left parenthesis straight s right parenthesis space rightwards arrow space space space straight K to the power of plus left parenthesis straight g right parenthesis space plus space Cl to the power of minus left parenthesis straight g right parenthesis space defines space the space enthalpy space of space KCl
Hence the lattice enthalpy of KCl = +719 kJ mol-1