Using the data (all values are in kilocalorie per mole at `25^(@)C`) given below, calculate the bond enegry of `C-C` and `C-H` bonds.
`DeltaH^(Theta)` combustion of ethane `=- 372.0`
`DeltaH^(Theta)` combustion of propane `=- 530.0`
`DeltaH^(Theta)` for `C`( garphite) `rarr C(g) =+ 172.0`
Bond enegry of `H-H` bond `=+ 104.0`
`Delta_(f)H^(Theta) of H_(2)O(l) =- 68.0`
`Delta_(f)H^(Theta) of CO_(2)(g) =- 94.0`

Explanation

`C_(2)H_(6)(g)+(7)/(2)O_(2)to2CO_(2)(g)+3H_(2)O(l),DeltaH=-372.0`
`DeltaH_(f(C_(2)H_(6)))^(@)=2xx(-94.0)+3xx(-68.0)+372.0=-20kcal`
`C_(3)H_(8)(g)+5O_(2)to3CO_(2)(g)+4H_(2)O(l),DeltaH=-530.0`
`DeltaH_(f(C_(3)H_(8)))^(@)=2xx(-94.0)+4xx(-68.0)+530.0=-24kcal`
`2C(s)+3H_(2)(g)toC_(2)H_(6)(g)," "DeltaH=-20.0`
`2C(g)to2C(s)," "DeltaH=-344.0`
`6H(g)to3H_(2)(g)," "DeltaH=-312.0`
Adding `overline(2C(g)+6H(g)toC_(2)H_(6)(g)," "DeltaH=-676kcal)`.
so, enthalpy of formation of `6C-H` bonds and one C-C bond is -676.0 kcal
`3C(s)+4H_(2)(g)toC_(3)H_(8)(g)," "DeltaH=-24.0`
`3C(g)to3C(s)," "DeltaH=-516.0`
`8H(g)to4H_(2)(g)," "DeltaH=-416.0`
Adding `overline(3C(g)+8H(g)toC_(3)H_(8)(g),DeltaH=-956.0kcal)`
So, enthalpy of formation of 8C-H and 2C-C bonds is -956kcal.
Let the bond energy of C-C be x and of C-H be y kcal.
In ethane `x+6y=676`
In propane `2x+8y=956`
On, solving, `x=82` and `y=99`
Thus, bond energy of C-C =82kcal and
bond energy of C-H=99kcal.