Question

Calculate the lattice enthalpy of MgBr₂ from the given data. The enthalpy of formation of MgBr₂ according to the reaction

$Mg left parenthesis straight s right parenthesis space plus space Br subscript 2 left parenthesis straight l right parenthesis space space space rightwards arrow space space MgBr subscript 2 left parenthesis straight s right parenthesis semicolon space increment subscript straight f straight H to the power of 0 space equals space minus 524 space kJ space mol to the power of negative 1 end exponent CH subscript 1 superscript 0 space for space Mg left parenthesis straight s right parenthesis space space rightwards arrow space space Mg to the power of 2 plus end exponent left parenthesis straight g right parenthesis space plus space 2 straight e to the power of minus space equals space plus 2187 space kJ space mol to the power of negative 1 end exponent$
$increment straight H subscript 3 superscript 0 space for space Br subscript 2 left parenthesis straight l right parenthesis space space rightwards arrow space space space space Br subscript 2 left parenthesis straight g right parenthesis space equals space 31 space kJ space mol to the power of negative 1 end exponent increment straight H subscript 4 superscript 0 space for space Br subscript 2 left parenthesis straight g right parenthesis space equals space 2 space Br left parenthesis straight g right parenthesis space equals space 193 space kJ space mol to the power of negative 1 end exponent increment straight H subscript 5 superscript 0 space for space Br left parenthesis straight g right parenthesis space plus space straight e to the power of minus left parenthesis straight g right parenthesis space space rightwards arrow space space Br to the power of minus space equals space minus 331 space kJ space mol to the power of negative 1 end exponent increment straight H subscript 6 superscript 0 space for space Mg to the power of 2 plus end exponent left parenthesis straight g right parenthesis space plus 2 Br to the power of minus left parenthesis straight g right parenthesis space space rightwards arrow space space space MgBr subscript 2 left parenthesis straight s right parenthesis space equals space ?$

Solution

Using Born-Haber cycle of MgBr₂,
$increment subscript straight f straight H to the power of 0 space equals space increment straight H subscript 1 superscript 0 space plus space increment straight H subscript 2 superscript 0 space plus space increment straight H subscript 3 superscript 0 space plus space increment straight H subscript 4 superscript 0 space plus space increment straight H subscript 5 superscript 0 space plus space increment straight H subscript 6 superscript 0 or space space space space space increment straight H subscript 6 superscript 0 space equals space increment subscript straight f straight H to the power of 0 space minus space increment straight H subscript 1 superscript 0 space minus space increment straight H subscript 2 superscript 0 space minus space increment straight H subscript 3 superscript 0 space minus space increment straight H subscript 4 superscript 0 space minus space increment straight H subscript 5 superscript 0$
Substituting the values, we have,
= -524 - 148 - 2187 - 31 - 193 - 2 (-331)
= -2421 kJ mol^-1Hence lattice enthalpy = $negative increment straight H subscript 6 superscript 0 space equals space 2421 space kJ space mol to the power of negative 1 end exponent$

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Thermodynamics

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