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(C) The rate of the reaction is determined by the slow step $(ii)$: $r = k[X][Y_2]$ $---$ $(1)$ From the fast equilibrium step $(i)$,we have: $K_{eq}

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$1.5$

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(C) The rate of the reaction is determined by the slow step $(ii)$: $r = k[X][Y_2]$ $---$ $(1)$ From the fast equilibrium step $(i)$,we have: $K_{eq} = \frac{[X]^2}{[X_2]}$ $[X]^2 = K_{eq}[X_2]$ $[X] = K_{eq}^{1/2}[X_2]^{1/2}$ $---$ $(2)$ Substituting equation $(2)$ into equation $(1)$: $r = k \cdot K_{eq}^{1/2}[X_2]^{1/2}[Y_2]^1$ $r = k'[X_2]^{1/2}[Y_2]^1$ The overall order of the reaction is the sum of the exponents of the concentration terms in the rate law: Order $= 0.5 + 1 = 1.5$

Mechanism of a hypothetical reaction $X_2 + Y_2 \rightarrow 2XY$ is given below:
$(i)$ $X_2 \rightarrow X + X$ (fast)
$(ii)$ $X + Y_2 \rightleftharpoons XY + Y$ (slow)
$(iii)$ $X + Y \rightarrow XY$ (fast)
The overall order of the reaction will be

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Mechanism of a hypothetical reaction $X_2 + Y_2 \rightarrow 2XY$ is given below: $(i)$ $X_2 \rightarrow X + X$ (fast) $(ii)$ $X + Y_2 \rightleftharpoons XY + Y$ (slow) $(iii)$ $X + Y \rightarrow XY$ (fast) The overall order of the reaction will be