$\Delta\text{H}^\circ$ combustion (ethane) = -372.0
$\Delta\text{H}^\circ$ combustion (propane) = -530.0 $\Delta\text{H}^\circ$ for C(graphite) → C(g)= 172.0 Bond energy of H-H = 104.0 $\Delta_\text{f}\text{H}^\circ$ of H2O(l) = -68.0 $\Delta\text{H}^\circ$ for CO2(g) = -94.0$\text{C}_2\text{H}_6(\text{g})+\frac{7}{2}\text{O}_2(\text{g})\overrightarrow{\ \ \ \ \ }\ 2\text{CO}_2(\text{g})+\text{H}_2\text{O};$ $\Delta\text{H}^\circ=-372.0\text{kcal}$
$\text{C}_3\text{H}_8(\text{g})+5\text{O}_2(\text{g})\overrightarrow{\ \ \ \ \ \ }\ 3\text{CO}_2(\text{g})+4\text{H}_2\text{O};$ $\Delta\text{H}^\circ=-530.0\text{kcal}$
$\text{C(s)}\overrightarrow{\ \ \ \ \ }\ \text{C(g)};$ $\Delta\text{H}^\circ=172.0\text{kcal}$
$\text{H}_2(\text{g})\overrightarrow{\ \ \ \ \ }\ 2\text{H(g)};$ $\Delta\text{H}^\circ=104.0\text{kcal}$
$\text{H}_2(\text{g})+\frac{1}{2}\text{O}_2(\text{g})\overrightarrow{\ \ \ \ \ \ }\ \text{H}_2\text{O(l)};$ $\Delta\text{H}^\circ=-68.0\text{kcal}$
$\text{C(g)}+\text{C}_2(\text{g})\overrightarrow{\ \ \ \ \ }\ \text{CO}_2(\text{g});$ $\Delta\text{H}^\circ=-94.0\text{kcal}$
Suppose the bond energy of C-C bond = xkcal mol-1 and that of C-H bond = ykcal mol-1. Then for C2H6 (g),
$\ \ \ \ \ \ \ \ \text{H} \ \ \ \ \ \text{H}\\ \ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ |\\\text{H}-\text{C}-\text{C}-\text{H}\overrightarrow{\ \ \ \ \ }\ 2\text{C(g)}+6\text{H};\\ \ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ |\\ \ \ \ \ \ \ \ \ \text{H}\ \ \ \ \text{H}$ $\Delta\text{H}=\text{x}+6\text{y}\dots(\text{vii})$
and for C3H8(g); i.e.,
$\ \ \ \ \ \ \ \ \text{H} \ \ \ \ \ \text{H} \ \ \ \ \ \text{H}\\ \ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ \ |\ \ \ \ \ \ |\\\text{H}-\text{C}-\text{C}-\text{C}-\text{H}\overrightarrow{\ \ \ \ \ }\ 3\text{C(g)}+8\text{H(g)};\\ \ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ \ |\ \ \ \ \ \ |\\ \ \ \ \ \ \ \ \ \text{H} \ \ \ \ \ \text{H}\ \ \ \ \text{H}$ $\Delta\text{H}=2\text{x}+8\text{y}\dots(\text{viii})$
To get eq. (vii), operate eq. (i) + 2 × eq. (iii) + 3 × eq. (iv) - 3 × eq. (v) - 2 × eq. (vi).
It gives $\Delta\text{H}=676\text{kcal}$
It get eq. (viii) operate eq. (ii) + eq. (iii) + 4 × eq. (iv) - 4 × eq. (v) - 3 × eq. (vi)
It gives $\Delta\text{H}=956\text{kcal}$
Thus, x + 6y = 676, 2x + 8y = 956
On solving these equations, we get x = 82, y = 99
Hence, C-C bond energy = 82kcal mol-1 and C-H bond energy = 99kcal mol-1.
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