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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
Options:
$X_2 \rightleftharpoons X+X \ldots . . . . . .$. fast
$X+Y_2 \longrightarrow X Y+Y \ldots \ldots$ slow
$X+Y \longrightarrow X Y$.......... fast
The order of the overall reaction is
Solution:
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Verified Answer
The correct answer is:
$3 / 2$
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, $=1+\frac{1}{2}=\frac{3}{2}$
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, $=1+\frac{1}{2}=\frac{3}{2}$
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