Thermodynamics And Thermochemistry Result Question 7
7. Using the data provided, calculate the multiple bond energy $(\mathrm{kJ}$ $ \mathrm{mol}^{-1}$ ) of a $\mathrm{C} \equiv \mathrm{C}$ 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)
$\begin{aligned} 2 \mathrm{C}(s)+\mathrm{H}_2(g) & \longrightarrow \mathrm{C}_2 \mathrm{H}_2(g) ; \quad \Delta H=225 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ 2 \mathrm{C}(s) & \longrightarrow 2 \mathrm{C}(g) ; \quad \Delta H=1410 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ \mathrm{H}_2(g) & \longrightarrow 2 \mathrm{H}(g) ; \quad \Delta H=330 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned}$
(a) $1165$
(b) $837$
(c) $865$
(d) $815$
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Answer:
Correct Answer: 7. ( d )
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
$\mathrm{C}_2 \mathrm{H}_2(\mathrm{~g}) \longrightarrow 2 \mathrm{C}(\mathrm{g})+2 \mathrm{H}(\mathrm{g})$ …(i)
Using the given bond energies and enthalpies :
$\mathrm{C}_2 \mathrm{H}_2(g) \longrightarrow 2 \mathrm{C}(g)+2 \mathrm{H}(\mathrm{g}) ; \quad \Delta H=-225 \mathrm{~kJ}$ …(ii)
$2 \mathrm{C}(s) \longrightarrow 2 \mathrm{C}(\mathrm{g}) ; \quad \Delta H=1410 \mathrm{~kJ} $ …(iii)
$\mathrm{H}_2(g) \longrightarrow 2 \mathrm{H}(\mathrm{g}) ; \quad \Delta H=330 \mathrm{~kJ}$ …(iv)
Adding Eqs. (ii), (iii) and (iv) gives Eq. (i).
$\Rightarrow \mathrm{C}_2 \mathrm{H}_2(\mathrm{~g}) \longrightarrow 2 \mathrm{C}(\mathrm{g})+2 \mathrm{H}(\mathrm{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} $
$\Rightarrow (\mathrm{C} \equiv \mathrm{C}) \mathrm{BE}=1515-700=815 \mathrm{~kJ} / \mathrm{mol}$
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