Question

A reaction : $A_2+B\to$ Products, involves the following mechanism :
$A_2\rightleftharpoons 2A\left(fast\right)$ (A being the intermediate)
$A+B\underset{k_2}{\to }\left(slow\right)$.The rate law consistent to this mechanism is :

• A. $rate=k\left[A_2\right]\left[B\right]$
• B. $rate=k\left[A_2{]}^2\right[B]$
• C. $rate=k\left[A_2{]}^{\frac{1}{2}}\right[B]$
• D. $rate=k\left[A_2\right][B{]}^2$

Answer 1

The correct option is C

$rate=k\left[A_2{]}^{\frac{1}{2}}\right[B]$

From the slow step : rate $=k_2\left[A\right]\left[B\right]$ ...............(i)

From fast step : $K_e=\frac{[A{]}^2}{\left[A_2\right]}or\left[A\right]=K_e^{\frac{1}{2}}{A}^{\frac{1}{2}}$ ..............(ii)

From (i) and (ii) rate $=k_2{k}_e^{\frac{1}{2}}\left[A_2{]}^{\frac{1}{2}}\right[B]=k[A_2{]}^{\frac{1}{2}}\left[B\right]$