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Thermodynamics

Question
CBSEENCH11006193

The combustion of one mole of benzene takes place at 298K and 1 atm. After combustion, CO2(g) and H2O(l) are produced and 3267.0 kJ of heat is liberated. Calculate the standard enthalpy of formation of ∆fH° benzene, given that standard enthalpy of formation of CO2(g) and H2O(l) are –393.5 kJ mol–1 and –285.83 kJ mol–1respectively.

Solution
The thermochemical equation for the combustion of one mole of benzene is as follows:
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space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space increment subscript straight c straight H to the power of 0 space equals space minus 3267.0 space kJ space mol to the power of negative 1 end exponent
We space know comma space
space space space space space increment subscript straight r straight H to the power of 0 space equals space increment subscript straight c straight H to the power of 0 space equals space sum from blank to blank of increment subscript straight f straight H to the power of 0 space left parenthesis Products right parenthesis
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   space equals space open square brackets 6 space cross times space increment subscript straight f straight H to the power of 0 space left parenthesis CO subscript 2 right parenthesis space plus 3 space cross times space increment subscript straight f straight H to the power of 0 left parenthesis straight H subscript 2 straight O right parenthesis close square brackets
space space space space space space space space space minus open square brackets increment subscript straight f straight H to the power of 0 left parenthesis straight C subscript 6 straight H subscript 6 right parenthesis space plus space 15 over 2 increment subscript straight f straight H to the power of 0 left parenthesis straight g right parenthesis close square brackets
or space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space minus 3267.0 space kJ space mol to the power of negative 1 end exponent
            equals open square brackets 6 space cross times space left parenthesis negative 393.5 space kJ space mol to the power of negative 1 end exponent right parenthesis close square brackets
plus space 3 left parenthesis negative 285. space 83 space kJ space mol to the power of negative 1 end exponent right parenthesis space minus space open square brackets increment subscript straight f straight H to the power of 0 left parenthesis straight C subscript 6 straight H subscript 6 right parenthesis minus 0 close square brackets
or space space minus 3267.0 space kJ space mol to the power of negative 1 end exponent
space space space space space space space space space space equals space open square brackets negative 2361 space kJ space mol to the power of negative 1 end exponent space minus space 857.49 space kJ space mol to the power of negative 1 end exponent close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space minus open square brackets increment subscript straight f straight H to the power of 0 left parenthesis straight C subscript 6 straight H subscript 6 right parenthesis close square brackets
space space space space space equals space minus 3218.49 space kJ space mol to the power of negative 1 end exponent space minus space increment subscript straight f straight H to the power of 0 left parenthesis straight C subscript 6 straight H subscript 6 right parenthesis
or space space
increment subscript straight f straight H to the power of 0 left parenthesis straight C subscript 6 straight H subscript 6 right parenthesis space equals space minus 3218.49 space kJ space mol to the power of negative 1 end exponent space plus space 3267.0 space kJ space mol to the power of negative 1 end exponent space
equals space 48.51 space kJ space mol to the power of negative 1 end exponent