The proposed mechanism for a reaction is - (1) `A+BhArrD("fast") " " (2) A+Drarr2C ("slow")` . The observed rate for reaction is, rate = `k[A]^(2)[B]`. Write the balanced equation of the reaction. Identify the reaction intermediate, if any forms during the reaction. Does the observed reaction-rate support the above mechanism ?

Explanation

The balanced equation of the reaction is obtained by adding the steps (1) and (2).
`{:(A+BhArrD),(A+Drarr2C),(bar(2A+Brarr2C)):}`
The overall balanced equation does not contain D. So , D is the intermediate in the reaction.
If K is the equilibrium constant of step (1), then-
`K=([D])/([A][B])" or, "[D]=k[A][B]" " .....[1]`
The rate of the step (2) `k_(1)[A][D]" "...[2]`
Putting the value of [D] obtained from equation (1) into equation (2), We get
The rate of the step (2) `=k_(1)k[A]^(2)[B]=k[A]^(2)[B](k=k_(1)K)`
If `k_(1)K=k` then the rate of the step (2) = observed reaction- rate `=k[A]^(2)[B]` .
Therefore , the observed reaction -rate supports the given mechanism.