AB, ${\mathrm{A}}_2 \mathrm{and} {\mathrm{B}}_2$ are diatomic molecules, if the bond enthalpies of ${\mathrm{A}}_2, \mathrm{AB} \mathrm{and} {\mathrm{B}}_2$ are in the ratio of 1 : 1 : 0.5 and the enthalpy of formation of AB from ${\mathrm{A}}_2 \mathrm{and} {\mathrm{B}}_2$ is $-100 \mathrm{kJ} {\mathrm{mol}}^{-1}, \mathrm{combustion} \mathrm{of} {\mathrm{A}}_2 \mathrm{gives} \mathrm{AO} \mathrm{and} ∆{\mathrm{H}}_{\mathrm{C}}=-1200 \mathrm{kJ} {\mathrm{mol}}^{-1}.$ Bond energy of $\left(\mathrm{O}=\mathrm{O}\right) \mathrm{bond} \mathrm{is} 500 \mathrm{kJ} {\mathrm{mol}}^{-1}.$ What is the bond enthalpy of (A - O) bond ?

Bond enthalpy (BE) of ${\mathrm{A}}_2 = \mathrm{x}, \mathrm{AB} = \mathrm{x} \mathrm{and} {\mathrm{B}}_2 = \frac{\mathrm{x}}{2}$

$$\begin{gathered} \frac{1}{2}{\mathrm{A}}_2+\frac{1}{2}{\mathrm{B}}_2 \stackrel{ }{\to }\mathrm{AB} -100 \mathrm{kJ}/{\mathrm{mol}}^{-1} .....\left(\mathrm{i}\right) \\ \frac{1}{2}{\mathrm{A}}_2+\frac{1}{2}{\mathrm{O}}_2 \stackrel{ }{\to }\mathrm{AO} -1200 \mathrm{kJ}/\mathrm{mol} \left(\mathrm{given}\right) \\ {\mathrm{A}}_2+{\mathrm{O}}_2 \stackrel{ }{\to }2\mathrm{AO} -2400 \mathrm{kJ}/\mathrm{mol} ....\left(\mathrm{ii}\right) \\ \mathrm{O}=\mathrm{O}\stackrel{ }{\to }500 \mathrm{kJ}/\mathrm{mol} \\ \mathrm{From} \mathrm{eq}. \left(\mathrm{i}\right) \\ \frac{1}{2} \mathrm{B}.{\mathrm{E}}_{{\mathrm{A}}_2} + \frac{1}{2} \mathrm{B}.{\mathrm{E}}_{{\mathrm{B}}_2}- \mathrm{B}.{\mathrm{E}}_{\mathrm{AB}}=-100 \\ \frac{1}{2}\mathrm{x} + \frac{\mathrm{x}}{4}-\mathrm{x}=-100 \\ -\frac{\mathrm{x}}{4}=-100 \\ \mathrm{x}= 400 \mathrm{kJ}/\mathrm{mol} \\ \mathrm{Now}, \mathrm{from} \mathrm{eq}. \left(\mathrm{ii}\right) \\ \mathrm{B}.{\mathrm{E}}_{{\mathrm{A}}_2} + \mathrm{B}.{\mathrm{E}}_{{\mathrm{O}}_2}-2 \mathrm{B}.{\mathrm{E}}_{\mathrm{AO}}=-2400 \\ \mathrm{x}+\left(+500\right)-2 \mathrm{B}.{\mathrm{E}}_{\mathrm{AO}}=-2400 \\ 400 + 500 - 2 \mathrm{B}.{\mathrm{E}}_{\mathrm{AO}}=-2400 \\ - \mathrm{B}.{\mathrm{E}}_{\mathrm{A}-\mathrm{O}}=-3300 \\ \mathrm{B}.{\mathrm{E}}_{\mathrm{A}-\mathrm{O}}=1650 \mathrm{kJ}/\mathrm{mol}. \end{gathered}$$