A proposed mechanism for a reaction `ArarrB` is
`A underset(k_(2))overset(k_(1))hArr C " " C underset(k_(4))overset(k_(3))hArr B`
Determine the expresison for the equilibrium constant for the overall reaction in terms of the rate constants.

Explanation

At equilibrium, for each step:
`k=([C ])/([A])=(k_(1))/(k_(2)) ,k'=([B])/([C ])=(k_(3))/(k_(4))`
Solving first equation and substituting into the second equation gives:
`'([B])/([A]((k_(1))/(k_(2))))=(k_(3))/(k_(4))`
Overall equilibrium constant is given by:
`([B])/([A])=((k_(3))/(k_(4)))((k_(1))/(k_(2)))`