Question

Bond dissociation energy of $XY,X_2$, and $Y_2$ (all diatomic molecules) are in the ratio of $1:1:0.5$ and $\mathrm{\Delta }{H}_f$ of $XY$ is $-100kJ{mol}^{-1}$. The bond dissociation energy of $X_2$ is $100x.$ The value of $x$ is

Answer 1

Correct Answer: 4

Explanation:
Given:Bond dissociation energy of $XY,X_2$ and $Y_2$ are in the ratio $1:1:0.5$$\mathrm{\Delta }{H}_f$ of $XY=-100kJ{mol}^{-1}$Let the bond dissociation energy for $XY$ be 'a'.Therefore, for $X_2$ it is 'a' and for $Y_2$ it is $\frac{\mathit{a}}{2}$Now,$\frac{1}{2}{X}_2+\frac{1}{2}{Y}_2\to XY;\mathrm{\Delta }{H}_f=-100kJmo{l}^{-1}$One $X-X$ and one $Y-Y$ are broken and one $X-Y$ is formed:$\therefore \frac{1}{2}a+\frac{1}{2}\left(\frac{a}{2}\right)-a=-100{kJmol}^{-1}$$\Rightarrow \frac{a}{2}+\frac{a}{4}-a=-100$$\Rightarrow \frac{2a+a-4a}{4}=-100$$\Rightarrow a=-400$$\therefore a=400$Here, 'a' is the bond dissociation energy of $X_2=100x$$100x=400$$x=4$Hence, the correct answer is 4.