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Using the data (all values are in kiloca...

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`

Text Solution

Verified by Experts

We are giving (i)`C_(2)H_(6)(g)+(7)/(2) O_(2)(g) rarr 2CO_(2)(g)+H_(2)O(l),DeltaH^(@) =- 372.0 kcal`
(ii) `C_(3)H_(8) +5O_(2)(g) rarr 3CO_(2)(g)+4H_(2)O(l),DeltaH^(@) = - 530.0 kcal`
(iii) `C(s) rarr C(g), DeltaH^(@) =172.0kcal`
(iv) `H_(2)(g) rarr 2H(g) , DeltaH^(@) = 104.0kcal`
(vi)` C(g)+ O_(2)(g) rarr CO_(2)(g) , DeltaH^(@) = - 94.0 kcal`
Suppose the bond energy of`C-C` bond `=x kcal ` mol`e^(-1)` and thatof`C-H` bond `=y` kcal` mol e^(-1)`. Then for `C_(2)H_(6)(g), i.e.,H- underset(H) underset(|) overset(H) overset(|) (C) - underset( H ) underset(|) overset(H) overset(|) (C)-H rarr C(g) + H(g),DeltaH = x+6y` ....(vii)
andfor `C_(3)H_(8) (g)`, i.e., `H-underset(H) underset(|) overset(H) overset(|)(C) - underset(H) underset(|) overset(H) overset(|) (C) - underset(H) underset(|) overset(H) overset(|) (C) - H rarr 3C(g) +8 H(g), DeltaH = 2x + 8 y ` .....(viii)
To get Eqn. (vii) , operate Eqn. (i) `+ 2 xx `Eqn. (iii) ` + 3 xx ` Eqn. (iv) `- 3 xx` Eqn. (v) `- 2 xx` Eqn. (vi).
This gives`DetlaH = 676 kcal`
To get Eqn. (viii) , operateEqn. `+` Eqn. (iii) `+`Eqn. (iii) `+ 4 xx` Eqn. (vi)` - 4 xx` Eqn. (v) `- 3 xx `Eqn. (vi).
This gives `DeltaH = 956kcal`
Thus, `x + 6y= 676 `
`2x + 8y=956`
On solving these equations, we get `x= 82,y = 99`
Hence, `C-C` bond energy `= 83 kcal mol^(-1)` and `C-H` bond energy `= 99` kcal `mol^(-1)`
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