Question

Mechanism of a hypothetical reaction
$X_{2}+Y_{2}\rightarrow 2XY$ is given below
$\left(\right.1\left.\right)$ $X_{2} \rightarrow X+X$ (fast)
$\left(\right.2\left.\right)$ $X+Y_{2}\rightleftharpoons XY+Y$ (slow)
$\left(\right.3\left.\right)$ $X+Y \rightarrow XY$ (fast)
The overall order of the reaction will be:

• A. $2$
• B. $0$
• C. $1.5$
• D. $1$

Answer 1

Answer: (C)

$X_{2} \rightarrow X+X$ (Fast)
$X+Y_{2}\rightleftharpoons XY+Y$ (Slow)
As we know that slow step is
Rate determine step
$\therefore $ Rate$=K\left[X\right]\left[\right.Y_{2}\left]\right.$ (i)
From first step
$K_{1}=\frac{\left[X\right]^{2}}{\left[X_{2}\right]}$
$\left[X\right]^{2}=K_{1}\left[\right.X_{2}\left]\right.$ (ii)
From equation (i)&(ii)
Rate $=K\sqrt{K_{1}}\left[X_{2}\right]^{\frac{1}{2}}\left[Y_{2}\right]$
Rate $=K^{'}\left[X_{2}\right]^{\frac{1}{2}}\left[Y_{2}\right]$
Order $=\frac{1}{2}+1=1.5$