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Using the data provided, calculate the multiple bond energy $\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)$ of a $\mathrm{C} \equiv \mathrm{C}$ bond in $\mathrm{C}_{2} \mathrm{H}_{2}$. That energy is (take the bond energy of a $\mathrm{C}-\mathrm{H}$ bond as $350 \mathrm{~kJ} \mathrm{~mol}^{-1}$ ) $2 \mathrm{C}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{HC}=\mathrm{CH}(\mathrm{g}) ; \Delta \mathrm{H}=225 \mathrm{~kJ} \mathrm{~mol}^{-1}$ $2 \mathrm{C}(\mathrm{s}) \longrightarrow 2 \mathrm{C}(\mathrm{g}) ; \Delta \mathrm{H}=1410 \mathrm{~kJ} \mathrm{~mol}^{-1}$ $\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}(\mathrm{g}) ; \Delta \mathrm{H}=330 \mathrm{~kJ} \mathrm{~mol}^{-1}$
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The correct answer is:
815
(i) $2 \mathrm{C}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{H}-\mathrm{C} \equiv \mathrm{C}-\mathrm{H}(\mathrm{g})$
$\Delta \mathrm{H}=225 \mathrm{~kJ} \mathrm{~mol}^{-1}$
(ii) $2 \mathrm{C}(\mathrm{s}) \longrightarrow 2 \mathrm{C}(\mathrm{g}) \Delta \mathrm{H}=1410 \mathrm{~kJ} \mathrm{~mol}^{-1}$
(iii) $\mathrm{H}_{2}$ (g) $\longrightarrow 2 \mathrm{H}$ (g) $\Delta \mathrm{H}=330 \mathrm{~kJ} \mathrm{~mol}^{-1}$
From equation (i) :
$\begin{array}{l}
225=\left[2 \times \Delta \mathrm{H}_{\mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{C}(\mathrm{g})}+1 \times \mathrm{BE}_{\mathrm{H}-\mathrm{H}}\right] \\
-\left[2 \times \mathrm{BE}_{\mathrm{C}-\mathrm{H}}+1 \times \mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\
225=[1410+1 \times 330]-\left[2 \times 350+1 \times \mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\
225=[1410+330]-\left[700+\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\
225=1740-700-\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}} \\
\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}=815 \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{array}$
$\Delta \mathrm{H}=225 \mathrm{~kJ} \mathrm{~mol}^{-1}$
(ii) $2 \mathrm{C}(\mathrm{s}) \longrightarrow 2 \mathrm{C}(\mathrm{g}) \Delta \mathrm{H}=1410 \mathrm{~kJ} \mathrm{~mol}^{-1}$
(iii) $\mathrm{H}_{2}$ (g) $\longrightarrow 2 \mathrm{H}$ (g) $\Delta \mathrm{H}=330 \mathrm{~kJ} \mathrm{~mol}^{-1}$
From equation (i) :
$\begin{array}{l}
225=\left[2 \times \Delta \mathrm{H}_{\mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{C}(\mathrm{g})}+1 \times \mathrm{BE}_{\mathrm{H}-\mathrm{H}}\right] \\
-\left[2 \times \mathrm{BE}_{\mathrm{C}-\mathrm{H}}+1 \times \mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\
225=[1410+1 \times 330]-\left[2 \times 350+1 \times \mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\
225=[1410+330]-\left[700+\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\
225=1740-700-\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}} \\
\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}=815 \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{array}$
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