Thermodynamics and Thermochemistry 2 Question 7
7. Using the data provided, calculate the multiple bond energy $\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)$ of a $\mathrm{C} \equiv \equiv \mathrm{C}$ bond $\mathrm{C}{2} \mathrm{H}{2}$. That energy is (take the bond energy of a $\mathrm{C}-\mathrm{H}$ bond as $350 \mathrm{~kJ} \mathrm{~mol}^{-1}$ )
(2012)
$$ \begin{array}{rlr} 2 \mathrm{C}(s)+\mathrm{H}{2}(g) & \longrightarrow \mathrm{C}{2} \mathrm{H}{2}(g) ; & \Delta H=225 \mathrm{~kJ} \mathrm{~mol}^{-1} \ 2 \mathrm{C}(s) & \longrightarrow 2 \mathrm{C}(g) ; & \Delta H=1410 \mathrm{~kJ} \mathrm{~mol}^{-1} \ \mathrm{H}{2}(g) & \longrightarrow 2 \mathrm{H}(g) ; & \Delta H=330 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{array} $$
(a) 1165
(b) 837
(c) 865
(d) 815
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Solution:
- For calculation of $\mathrm{C} \equiv \mathrm{C}$ bond energy, we must first calculate dissociation energy of $\mathrm{C}{2} \mathrm{H}{2}$ as
$$ \mathrm{C}{2} \mathrm{H}{2}(g) \longrightarrow 2 \mathrm{C}(g)+2 \mathrm{H}(g) $$
Using the given bond energies and enthalpies :
$$ \begin{aligned} \mathrm{C}{2} \mathrm{H}{2}(g) & \longrightarrow 2 \mathrm{C}(g)+2 \mathrm{H}(g) ; & \Delta H=-225 \mathrm{~kJ} \ 2 \mathrm{C}(s) & \longrightarrow 2 \mathrm{C}(g) ; & \Delta H=1410 \mathrm{~kJ} \ \mathrm{H}_{2}(g) & \longrightarrow 2 \mathrm{H}(g) ; & \Delta H=330 \mathrm{~kJ} \end{aligned} $$
Adding Eqs. (ii), (iii) and (iv) gives Eq. (i).
$$ \begin{array}{cc} \Rightarrow & \mathrm{C}{2} \mathrm{H}{2}(g) \longrightarrow 2 \mathrm{C}(g)+2 \mathrm{H}(g) ; \quad \Delta H=1515 \mathrm{~kJ} \ \Rightarrow & 1515 \mathrm{~kJ}=2 \times(\mathrm{C}-\mathrm{H}) \mathrm{BE}+(\mathrm{C} \equiv \mathrm{C}) \mathrm{BE} \ & =2 \times 350+(\mathrm{C} \equiv \mathrm{C}) \mathrm{BE} \ \Rightarrow & (\mathrm{C} \equiv \mathrm{C}) \mathrm{BE}=1515-700=815 \mathrm{~kJ} / \mathrm{mol} \end{array} $$
