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Thermodynamics

Question
CBSEENCH11006214

Calculate the standard enthalpy of formation of CH3OH(l) from the following data:

left parenthesis straight i right parenthesis space CH subscript 3 OH left parenthesis straight l right parenthesis space plus space 3 over 2 straight O subscript 2 left parenthesis straight g right parenthesis space space space rightwards arrow space space CO subscript 2 left parenthesis straight g right parenthesis space plus space 2 straight H subscript 2 straight O left parenthesis straight l right parenthesis semicolon space
increment subscript straight r straight H to the power of 0 space equals space minus 726 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 space rightwards arrow space space space CO subscript 2 left parenthesis straight g right parenthesis semicolon increment straight H to the power of 0 space equals space minus 393 space kJ space mol to the power of negative 1 end exponent
space left parenthesis iii right parenthesis space straight H subscript 2 left parenthesis straight g right parenthesis space plus space 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 increment subscript straight f straight H to the power of 0 space equals space minus 286 space kJ space mol to the power of negative 1 end exponent
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


Solution

We have equation,
           straight C left parenthesis straight s right parenthesis space plus space 2 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 CH subscript 3 OH left parenthesis straight l right parenthesis semicolon space increment subscript straight r straight H to the power of 0 space equals space ?
Multiplying equation (iii) by 2,
space 2 straight H subscript 2 left parenthesis straight g right parenthesis space plus straight O subscript 2 left parenthesis straight g right parenthesis space space space rightwards arrow space space 2 straight H subscript 2 straight O left parenthesis straight l right parenthesis semicolon space space space increment subscript straight f straight H to the power of 0 space equals space minus 572 space kJ
Adding equations (ii) and (iii),
 space straight C left parenthesis straight s right parenthesis space plus space 2 straight H subscript 2 left parenthesis straight g right parenthesis space plus space 2 straight O subscript 2 left parenthesis straight g right parenthesis space space space rightwards arrow space C O subscript 2 left parenthesis straight g right parenthesis space plus 2 straight H subscript 2 straight O left parenthesis straight l right parenthesis semicolon space
space space space space space space space space space increment subscript straight r straight H to the power of 0 space equals space minus 393 space k J space minus space 572 space k J space equals space minus 965 space k J
Subtracting equation (i) from equation (ii), 
       straight C left parenthesis straight s right parenthesis space plus space 2 straight H subscript 2 left parenthesis straight g right parenthesis space plus space 1 half straight O subscript 2 space minus space CH subscript 3 OH left parenthesis straight l right parenthesis space space space
space space space space space space space space space space space space space space space rightwards arrow space space CO subscript 2 left parenthesis straight g right parenthesis space plus space 2 straight H subscript 2 straight O left parenthesis straight l right parenthesis space minus space CO subscript 2 left parenthesis straight g right parenthesis space minus space 2 straight H subscript 2 straight O left parenthesis straight l right parenthesis
                         increment subscript straight r straight H to the power of 0 space equals space minus 965 space k J space plus space 726 space straight k space equals space minus 239 space straight k
or space space straight C left parenthesis straight s right parenthesis space plus space 2 straight H subscript 2 left parenthesis straight g right parenthesis space plus space 1 half straight O subscript 2 left parenthesis straight s right parenthesis space minus space CH subscript 3 OH left parenthesis straight l right parenthesis
space space space space space space space space increment subscript straight r straight H to the power of 0 space equals space minus 239 space kJ space mol to the power of negative 1 end exponent