Question

Using the data (all values are in kilo calorie per mole at ${25}^{o}C$) given below, calculate the bond energy of $C-C$ and $C-H$ bonds.
$\Delta H_{combustionofethane}^o=-372.0$
$\Delta H_{combustionofpropane}^o=-530.0$
$\Delta H^{}$ for $C_{graphite}\to C\left(g\right)=+172.0$
Bond energy of $H-H$ bond $=+104.0$
$\Delta H_f$ of $H_{2}O\left(l\right)=-68.0$
$\Delta H_f$ of ${CO}_2\left(g\right)=-94.0$

Answer 1

$C_2{H}_6\left(g\right)+\frac{7}{2}{O}_2\to 2{CO}_2\left(g\right)+3H_{2}O\left(l\right);\Delta H=-372.0$
$\Delta H_{{f(C}_2{H}_6)}^o=2\times (-94.0)+3\times (-68.0)+372.0=-20kcal$
$C_2{H}_8\left(g\right)+5O_2\to 3{CO}_2+4H_{2}O\left(l\right);\Delta H=-530.0$
$\Delta H_{f\left(C_3{H}_8\right)}^o=2\times (-94.0)+4\times (-68.0)+530.0=-24kcal$
$2C\left(s\right)+3H_2\left(g\right)\to C_2{H}_6\left(g\right);\Delta H=-20.0$
$2C\left(g\right)\to 2C\left(s\right);\Delta H=-344.0$
$6H\left(g\right)\to 3H_2;\Delta H=-312.0$
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Adding:$2C\left(g\right)+6H\left(g\right)\to C_2{H}_6\left(g\right);\Delta H=-676kcal$
So enthalpy of formation of $6C-H$ bonds and one $C-C$ bond is $-676.0kcal$
$3C\left(s\right)+4H_2\left(g\right)\to C_3{H}_8\left(g\right);\Delta H=-24.0$
$3C\left(g\right)\to 3C\left(s\right);\Delta H=-516.0$
$8H\left(g\right)\to 4H_2\left(g\right);\Delta H=-416.0$
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Adding: $3C\left(g\right)+8H\left(g\right)\to C_3{H}_8\left(g\right);\Delta H=-956.0kcal$
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 $C-H=99kcal$