The overall rate of a complex reaction is governed by the slowest step, which is the rate-determining step (RDS). From the given mechanism, the slowest step is: $X + Y_2 \rightarrow XY + Y$ Therefore, the rate law based on the slowest step is: $\text{Rate} = k[X][Y_2]$ Since $X$ is an intermediate formed in a fast equilibrium step, its concentration must be expressed in terms of the reactants using the equilibrium step: $X_2 \rightleftharpoons 2X$ The equilibrium constant $K_c$ is: $K_c = \frac{[X]^2}{[X_2]}$ $\Rightarrow [X]^2 = K_c[X_2]$ $\Rightarrow [X] = K_c^{1/2}[X_2]^{1/2}$ Substituting $[X]$ back into the rate equation gives: $\text{Rate} = k \cdot (K_c^{1/2}[X_2]^{1/2}) \cdot [Y_2]$ $\text{Rate} = k' [X_2]^{1/2}[Y_2]^1$ (where $k' = k \cdot K_c^{1/2}$) The overall order of the reaction is the sum of the powers of the concentration terms in the rate law: $\text{Overall order} = \frac{1}{2} + 1 = 1.5$