Chemistry / Unit 9 Chem 1721 worked example, 60 to 90 seconds
Deriving a Rate Law from a Multistep Mechanism
The idea
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.
In practice
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.
Where people slip
Leaving an intermediate's concentration in a final rate law is an incomplete derivation — a correct rate law names only species present in the overall balanced equation.
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