Question

Mechanism of a hypothetical reaction
$X_2+Y_2\to 2XY$ is given below
$(1)$ $X_2\to X+X$ (fast)
$(2)$ $X+Y_2\rightleftharpoons XY+Y$ (slow)
$(3)$ $X+Y\to XY$ (fast)
The overall order of the reaction will be:

• A. $2$
• B. $0$
• C. $1.5$
• D. $1$

Answer 1

Answer: (C)

$X_2\to X+X$ (Fast)
$X+Y_2\rightleftharpoons XY+Y$ (Slow)
As we know that slow step is
Rate determine step
$\therefore$ Rate$=K\left[X\right][Y_2]$ (i)
From first step
$K_1=\frac{{\left[X\right]}^2}{\left[X_2\right]}$
${\left[X\right]}^2=K_1[X_2]$ (ii)
From equation (i)&(ii)
Rate $=K\sqrt{K_1}{\left[X_2\right]}^{\frac{1}{2}}\left[Y_2\right]$
Rate $=K^{{}^{\prime }}{\left[X_2\right]}^{\frac{1}{2}}\left[Y_2\right]$
Order $=\frac{1}{2}+1=1.5$