Q70 / 180 · JIPMER 2015 · Chemistry

A hypothetical reaction, $X_2+Y_2 \longrightarrow 2 X Y$ follows the following mechanism $X_2 \rightleftharpoons X+X \ldots . . . . . .$. fast $X+Y_2 \longrightarrow X Y+Y \ldots \ldots$ slow $X+Y \longrightarrow X Y$.......... fast The order of the overall reaction is

  • A
    $2$
  • Correct answer
    B
    $3 / 2$
  • C
    $1$
  • D
    $0$

Solution

Rate $=k[X]\left[Y_2\right]$ But, $k=\frac{[X]^2}{\left[X_2\right]}$ or, $[X]=\sqrt{k \cdot\left[X_2\right]}$ Rate $=k \cdot \sqrt{k} \sqrt{\left[X_2\right]}\left[Y_2\right]=k^{\prime}\left[X_2\right]^{1 / 2}\left[Y_2\right]$ Thus, order, $=1+\frac{1}{2}=\frac{3}{2}$

Hence, the correct answer is option: 'B'.

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