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Thermodynamics

Question
CBSEENCH11006223

Calculate the C – C bond energy from the following data:

left parenthesis straight i right parenthesis space 2 straight C left parenthesis graphite right parenthesis space plus space 3 straight H subscript 2 left parenthesis straight g right parenthesis rightwards arrow space space straight C subscript 2 straight H subscript 6 left parenthesis straight g right parenthesis semicolon space space space increment straight H space equals space minus 84.67 space kJ
left parenthesis ii right parenthesis space straight C left parenthesis graphite right parenthesis space space rightwards arrow space space straight C left parenthesis straight g right parenthesis semicolon space space space increment straight H space equals space 716.7 space kJ
left parenthesis iii right parenthesis space straight H subscript 2 left parenthesis straight g right parenthesis space space space rightwards arrow space space 2 straight H left parenthesis straight g right parenthesis semicolon space space space increment straight H space equals space 435.9 space kJ
Assume 416 kJ as the C - H bond energy, Express it in kJ mol-1.

Solution

We aim at the equation,

Multiplying equation (ii) by 2 and equation (iii) by 3, we have,
  left parenthesis iv right parenthesis space 2 straight C left parenthesis graphite right parenthesis space space rightwards arrow space space 2 straight C left parenthesis straight g right parenthesis semicolon space space increment straight H space equals space plus 1433.4 space kJ
left parenthesis straight v right parenthesis space space 3 straight H subscript 2 left parenthesis straight g right parenthesis space space space rightwards arrow space space 6 straight H left parenthesis straight g right parenthesis semicolon space space space increment straight H space equals space plus 1307.7 space kJ
Adding space equations space left parenthesis iv right parenthesis space and space left parenthesis straight v right parenthesis comma space we space have
left parenthesis vi right parenthesis space 2 straight C left parenthesis graphite right parenthesis space plus space 3 straight H subscript 2 left parenthesis straight g right parenthesis space space rightwards arrow space space space 2 straight C left parenthesis straight g right parenthesis space plus space 6 straight H left parenthesis straight g right parenthesis semicolon
space space space space space space space space space space increment straight H space equals space 1433.4 space plus space 1307.7 space equals space 2741.1 space kJ
Subtracting (i) from (vi), we have, 
     2 straight C left parenthesis graphite right parenthesis space plus space 3 straight H subscript 2 left parenthesis straight g right parenthesis space space rightwards arrow space space 2 straight C left parenthesis graphite right parenthesis space minus space 3 straight H subscript 2 left parenthesis straight g right parenthesis
space space space space space space space space space space space space space space space space rightwards arrow space space space 2 straight C left parenthesis straight g right parenthesis space plus space 6 straight H left parenthesis straight g right parenthesis space space minus space straight C subscript 2 straight H subscript 6 left parenthesis straight g right parenthesis semicolon space space
space space space space space space increment straight H space equals space 2741.1 space plus space 84.67 space kJ
space space space or space space straight C subscript 2 straight H subscript 6 left parenthesis straight g right parenthesis space space space rightwards arrow space space space 2 straight C left parenthesis straight g right parenthesis space plus space 6 straight H left parenthesis straight g right parenthesis semicolon space space increment straight H space equals space 2825.77
space space space
space space space space space space space space space space space space space
Ethane molecule contains one C - C bond and six C - H bonds
     because  Bond dissociation energy of one C - H bond = 416 kJ
     therefore  Bond dissociation energy of six C - H bonds = 6 x 416 = 2496 kJ
space space space therefore space
space Bond space energy space of space straight C space minus space straight C space bond
space space space space equals space Bond space energy space of space straight C subscript 2 straight H subscript 6 space
space space space space space space space space space space space space minus space 6 space left parenthesis Bond space energy space of space straight C space minus space straight H space bonds right parenthesis
space space space space space equals space 2825.77 space minus space 2496 space
space space space space space equals space 329.77 space kJ thin space mol to the power of negative 1 end exponent