Answer : The rate law for the overall reaction is, ![R=\frac{K[A]^2[D]}{[C]}](https://tex.z-dn.net/?f=R%3D%5Cfrac%7BK%5BA%5D%5E2%5BD%5D%7D%7B%5BC%5D%7D)
Explanation :
As we are given the mechanism for the reaction :
Step 1 :
(equilibrium)
Step 2 :
(slow)
Overall reaction : 
First we have to determine the equilibrium constant from step 1.
The expression for equilibrium constant will be,
![K'=\frac{[B][C]}{[A]^2}](https://tex.z-dn.net/?f=K%27%3D%5Cfrac%7B%5BB%5D%5BC%5D%7D%7B%5BA%5D%5E2%7D)
Form this, the value of [B] is,
............(1)
Now we have to determine the rate law from the slow step 2.
The expression for law will be,
.............(2)
Now put equation 1 in 2, we get:
![Rate=K''\frac{K'[A]^2}{[C]}[D]](https://tex.z-dn.net/?f=Rate%3DK%27%27%5Cfrac%7BK%27%5BA%5D%5E2%7D%7B%5BC%5D%7D%5BD%5D)
![Rate=\frac{K[A]^2[D]}{[C]}](https://tex.z-dn.net/?f=Rate%3D%5Cfrac%7BK%5BA%5D%5E2%5BD%5D%7D%7B%5BC%5D%7D)
Therefore, the rate law for the overall reaction is, ![R=\frac{K[A]^2[D]}{[C]}](https://tex.z-dn.net/?f=R%3D%5Cfrac%7BK%5BA%5D%5E2%5BD%5D%7D%7B%5BC%5D%7D)