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Using the data ( all vaues in kcal mol^(...

Using the data `(` all vaues in `kcal mol^(-1) at 25^(@)C)` given below, calculate bond energy of `C-C` and `C-H` bonds.
`C_((s))rarr C_((g)), DeltaH=172`
`H_(2) rarr 2H, DeltaH=104`
`H_(2)+(1)/(2)O_(2) rarr H_(2)O_((l)), DeltaH=-68.0`
`C_((s))+O_(2) rarr CO_(2), Delta H=-94.0`
Heat of combustion of `C_(20H_(6)=-372.0`
Heat of combustion of `C_(3)H_(8)=-530.0`

Text Solution

Verified by Experts

For `C_(2)H_(6): 2C+3H_(2) rarr C_(2)H_(6),DeltaH_(1)`
For `C_(3)H_(8): 3C+4H_(2) rarr C_(3)H_(8), DeltaH_(2)`
`:. DeltaH_(1)=-[1-(C-C)+6(C-H)]+[2C_(srarrg)+3(H-C)] ....(1)`
and
`DeltaH_(2)=-[2(C-C)+8(C-H)]+[3(C_(srarr g))+4(H-H)] .....(2)`
Let `C-C` bond energy be `a kcal`
and `C-H` bond energy be `b kcal`.
`:. DeltaH_(1)=-[a+6b]+[2xx172+3xx104] ...(3)`
and `DeltaH_(2)=-[2a+8b]+[3xx172+4xx10.4] ...(4)`
Also from `C+O_(2) rarr CO_(2), DeltaH=-94.0 kcal ...(5)`
`H_(2)+(1)/(2)O_(2) rarr H_(2)O, DeltaH=-68.0kcal ...(6)`
`C_(2)H_(6)+(7)/(2)O_(2) rarr 2CO_(2)+3H_(2)O, DeltaH=-372kcal ...(7)`
`C_(3)H_(8)+5O_(2) rarr 3CO_(2)+4H_(2)O, DeltaH=-530kcal ...(8)`
Multiply `eq. (5)` by 2 and `eq.(6)` by 3, then add
`2C+3H_(2)+(7)/(2)O_(2) rarr 2CO_(2)+3H_(2)O,DeltaH=-392kcal ...(9)`
Subtracting `eq.(7)` from `eq. (9)`
`ul ({:(C_(2)H_(6),+(7)/(2)O_(2),rarr,2CO_(2),+3H_(2)O,,DeltaH=-372kcal),(-,-,,-,-," +"):})`
`2C+3H_(2) rarr C_(2)H_(6), DeltaH=-20kcal ...(10)`
Similarly also from `eq. (5)` multiplying by 3, `eq. (6)` multiplying by 4 and adding both of them, then subtracting `eq.(8)` , we get
`3C+4H_(2) rarr C_(3)H_(8),DeltaH_(2)=-24kcal ...(11)`
By `eqs. (3), (4), (10), ` and `(11)`
`a+6b=676`
`2a+8b=956`
`:. a=82kcal ` and `b=99 kcal`
`:. ` Bond energy of `C-C` bond `=82 kcal`
and `C-H` bond `=99 kcal`
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