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

The following are the given thermochemical reactions:
(i) `C_(2)H_(6)(g)+3(1)/(2)O_(2)(g) to 2CO_(2)(g)+3H_(2)O(l),DeltaH^(0)=-372`
(ii) `C_(3)H_(8)(g)+5O_(2)(g) to 3CO_(2)(g)+4H_(2)O(l), DeltaH^(0)=-530`
(iii) `H_(2)(g)+(1)/(2)O_(2)(g) to H_(2)O(l), DeltaH^(0)=-68`
(iv) `C(s)+O_(2)(g) to CO_(2)(g), DeltaH^(0)=-94`
Let us first calculate the heat of formation of `C_(2)H_(6)` and `C_(3)H_(8)` from which we shall calculate the bond energy of C-C and C-H bonds.
`2C(s)+3H_(2)(g) to C_(2)H_(6)(g), DeltaH^(0)=?`
and `3C(s)+4H_(2)(g) to C_(3)H_(8)(g), DeltaH^(0)=?`
Appling the enspection method, i.e.,
[- Eqn. (i)+3xxEqn. (iii) +3xxEqn. (iv)], we get,
`3C(s)+4H_(2)(g) to C_(3)H_(8)(g), DeltaH^(0)=-24`
`[DeltaH^(0)=-(-530)+4(-68)+3(-94)=-24]`
Calculation of bond energy:
Now we have,
`2C(s)+3H_(2)(g) to C_(2)H_(6)(g), DeltaH^(0)=-20`
For reactants :
Heat of atomisation of 2 moles of C atoms `=2xx172`
Heat of dissociation of 3 moles of H-H bonds `=3xx104`
For products :
Heat of formation of 1 mole of C-C bonds `=x("say")`
Heat of formation of 6 moles of C-H bonds `=6y("say")`
On adding, we get `DeltaH^(0)` of formation of `C_(2)H_(6)` .
`2xx172+3xx104+x+6y=-20`
or `x+6y=-676` ....(1)
Again, we have,
`3C(s)+4H_(2)(g) to C_(3)H_(8)(g),DeltaH^(0)=-24`
For reactants :
Heat of atomisation of 3 moles of C atoms `=3xx172`
Heat of dissociation of 4 moles of H-H bonds `=4xx104`
For products :
Heat of formation of 2 moles of C-C bonds `=2x`
Heat of formation of 8 moles of C-H bonds `=8y`
On adding, we get,
`3xx172+4xx104+2x+8y=-24`
or `2x+8y=-956` ....(2)
From eqns. (1) and (2), we get, `x=-82` and `y=-99`
`:. C-C bond energy =82 "kcal"`
`C-H bond energy `=99 "kcal"`