Write a stoichiometric equation for the reaction between `A_(2)` and `C` whose mechanism is given below. Determine the value of equilibrium constant for the first step. Write a rate law equation for the over all reaction in terms of its initial reactants.
(`i`) `A_(2)overset(K_(1))underset(K_(2))hArr2A`
`K_(1)=10^(10)s^(-1)` and `K_(2)=10^(10)M^(-1)s^(-1)`
(`ii`) `A+CtoAC`
`K=10^(-4)M^(-1)S^(-1)`

Explanation

It is apparent from both the steps that step (`ii`) is slowest and thus
`Rate=K[A][C]` ….(`1`)
However overall rate constant `K` can be obtained in terms of `A_(2)` as follows,
`eq.(`i`)+2xxeq.(`ii`)`, `A_(2)+2Cto2AC`
Also for step (`i`),
`K_(c)=(K_(1))/(K_(2))=([A]^(2))/([A_(2)])=(10^(10))/(10^(10))=1`
or `[A_(2)]=[A]^(2)`
or `[A]=[A_(2)]^(1//2)`
Thus by eq. (`1`),
`Rate=K[C][A_(2)]^(1//2)`
`=K[C][A_(2)]^(1//2)`