Using the data provided, calculate the multiple bond energy $\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)$ of…

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 $350 \mathrm{~kJ} \mathrm{~mol}^{-1}$ ) $2 \mathrm{C}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{HC}=\mathrm{CH}(\mathrm{g}) ; \Delta \mathrm{H}=225 \mathrm{~kJ} \mathrm{~mol}^{-1}$ $2 \mathrm{C}(\mathrm{s}) \longrightarrow 2 \mathrm{C}(\mathrm{g}) ; \Delta \mathrm{H}=1410 \mathrm{~kJ} \mathrm{~mol}^{-1}$ $\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}(\mathrm{g}) ; \Delta \mathrm{H}=330 \mathrm{~kJ} \mathrm{~mol}^{-1}$
  1. 1165
  2. 837
  3. 865
  4. 815

Solution

(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) : $\begin{array}{l} 225=\left[2 \times \Delta \mathrm{H}_{\mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{C}(\mathrm{g})}+1 \times \mathrm{BE}_{\mathrm{H}-\mathrm{H}}\right] \\ -\left[2 \times \mathrm{BE}_{\mathrm{C}-\mathrm{H}}+1 \times \mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\ 225=[1410+1 \times 330]-\left[2 \times 350+1 \times \mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\ 225=[1410+330]-\left[700+\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\ 225=1740-700-\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}} \\ \mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}=815 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{array}$

Asked in: JEE Advanced 2012 (Paper 2)

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