Deriving a Rate Law from a Multistep Mechanism

Deriving a rate law from a multistep mechanism means writing the rate law for the rate-determining step, then, if that step's rate law contains an intermediate's concentration, using an earlier fast, reversible step at equilibrium to re-express that intermediate in terms of the original reactants.

For NO + Cl2 proceeding through a fast reversible first step forming intermediate NOCl2, followed by a slow second step where NOCl2 reacts with a second NO, the second step's rate law contains [NOCl2]. Setting the first step's forward and reverse rates equal at equilibrium expresses [NOCl2] in terms of [NO] and [Cl2], substituting this back into the rate-determining step's rate law and simplifying yields the overall rate law rate = k[NO]²[Cl2], matching the reaction's experimentally measured second-order dependence on NO.