Final answer:
The rate-determining step in the mechanism for the given rate law rate = k[NO]² [H₂] must involve an intermediate species formed from the dimerization of NO, which then reacts with H₂. The intermediate concentration can be expressed as a function of [NO], yielding a rate law that matches the overall rate law.
Step-by-step explanation:
The question asks about the rate-determining step (RDS) for a reaction with a given rate law:
rate = k[NO]² [H₂]
The RDS is the slowest step in a reaction mechanism that determines the reaction rate. Based on the given rate law, it indicates that the step involves the collision of two NO molecules and one H₂ molecule. A reaction mechanism consistent with this rate law would likely involve an intermediate species formed from NO that goes on to react with H₂ in the rate-determining step. To definitively determine the RDS, one would look at the steps proposed in the mechanism and compare their rate laws with the experimentally determined rate law. The proposed step with a matching rate law would then be considered the RDS. For instance, if one step yields a rate law of rate = k[Intermediate][H₂], and the intermediate is formed by the dimerization of NO ([Intermediate] = k[NO]²), this would be consistent with the given rate law when the concentrations are substituted.