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Thermodynamics

Question
CBSEENCH11006215

The combustion of one mole of benzne 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, ∆fH° of benzene. Standard enthalpies of formation of CO2(g) and H2O(l) are – 393.5 kJ mol–1 and –285.83 kJ mor–1respectively. 

Solution

We just aim at the equation
6 straight C left parenthesis straight s right parenthesis space plus space 3 straight H subscript 2 left parenthesis straight g right parenthesis space space space rightwards arrow space space straight C subscript 6 straight H subscript 6 left parenthesis straight l right parenthesis space plus space increment subscript straight r straight H to the power of 0 space equals space ?
Here,
    left parenthesis straight i right parenthesis space straight C subscript 6 straight H subscript 6 left parenthesis straight l right parenthesis space plus space 15 over 2 straight O subscript 2 left parenthesis straight g right parenthesis space space rightwards arrow space space 6 CO subscript 2 left parenthesis straight g right parenthesis space plus space 3 straight H subscript 2 straight O left parenthesis straight l right parenthesis semicolon
increment subscript straight c straight H to the power of 0 space equals space 3267.0 space kJ space mol to the power of negative 1 end exponent
   left parenthesis ii right parenthesis space straight C left parenthesis straight s right parenthesis space plus space straight O subscript 2 left parenthesis straight g right parenthesis space rightwards arrow space space CO subscript 2 left parenthesis straight g right parenthesis semicolon
space increment subscript straight f straight H to the power of 0 left parenthesis CO subscript 2 right parenthesis space equals space minus 393.5 space kJ space mol to the power of negative 1 end exponent
   left parenthesis iii right parenthesis space straight H subscript 2 left parenthesis straight g right parenthesis space plus space 1 half straight O subscript 2 left parenthesis straight g right parenthesis space space rightwards arrow space space space straight H subscript 2 straight O left parenthesis straight l right parenthesis semicolon
space space space space space space space space space space space increment subscript straight f straight H to the power of 0 left parenthesis straight H subscript 2 straight O right parenthesis space equals space minus 285.83 space kJ space mol to the power of negative 1 end exponent
6 space cross times space Equation space left parenthesis ii right parenthesis space plus space 3 space cross times space Equation space left parenthesis iii right parenthesis
minus Equation space left parenthesis straight i right parenthesis space gives space the space required space equation space with
increment straight H to the power of 0 space equals space 6 left parenthesis negative 393.5 right parenthesis space plus space 3 left parenthesis negative 285.83 right parenthesis minus left parenthesis negative 3267.0 right parenthesis
space space space space space space space space space space equals space plus 48.51 space kJ space mol to the power of negative 1 end exponent