Mechanism of a hypothetical reaction $\mathrm{X}{}_2+\mathrm{Y}{}_2\to 2\mathrm{XY}$ is given below: (i) $\mathrm{X}{}_2\rightleftharpoons \mathrm{X}+\mathrm{X}$ (fast) (ii) $\mathrm{X}+\mathrm{Y}{}_2\rightleftharpoons \mathrm{XY}+\mathrm{Y}$ (slow) (iii) $\mathrm{X}+\mathrm{Y}\to \mathrm{XY}$ (fast) The overall order of the reaction will be

Solution & Explanation

\textbf{Answer:} (D) 1.5 \textbf{Solution:} The rate is governed by the slow (rate-determining) step (ii): $\text{Rate}=k[\mathrm{X}][\mathrm{Y}{}_2]$ The intermediate $[\mathrm{X}]$ comes from the fast pre-equilibrium step (i), $\mathrm{X}{}_2\rightleftharpoons 2\mathrm{X}$, for which $K_{eq}=\frac{[\mathrm{X}{]}^2}{[\mathrm{X}{}_2]}⟹[\mathrm{X}]=K_{eq}^{1/2}[\mathrm{X}{}_2{]}^{1/2}$ Substituting: $\text{Rate}=k{K}_{eq}^{1/2}[\mathrm{X}{}_2{]}^{1/2}[\mathrm{Y}{}_2]$ Overall order $=\frac{1}{2}+1=\frac{3}{2}=1.5$.