Question

If the bond dissociation energies of $XY,X_2$ and $Y_2$ (all diatomic molecules) are in the ratio of 1 : 1 : 0.5 and ${\Delta }_{f}H$ for the formation of $XY$ is $-200\text{kJ/mol}$, the bond dissociation energy of $X_2$ will be:

• A. $\text{100 kJ/mol}$
• B. $\text{200 kJ/mol}$
• C. $\text{800 kJ/mol}$
• D. $\text{400 kJ/mol}$

Answer 1

The correct option is C $\text{800 kJ/mol}$

Let the bond dissociation energies of $XY,X_2$ and $Y_2$ be $x,x$ and $0.5x\text{kJ/mol}$ respectively.
$\frac{1}{2}{X}_2+\frac{1}{2}{Y}_2\to XY;\Delta H_f=-200\text{kJ/mol}$
$\Delta H=\frac{1}{2}\Delta H\left(X_2\right)+\frac{1}{2}\Delta H\left(Y_2\right)-\Delta H\left(XY\right)\Rightarrow -200=\frac{1}{2}x+\frac{0.5x}{2}-x$
$\Rightarrow -0.25x=-200$
$\Rightarrow x=\frac{200}{0.25}=800\text{kJ/mol}$