The rate law for the proposed mechanism can be determined by examining the rate-determining step, which is the slowest step in the mechanism. In this case, the slowest step is step 1, which involves the collision of N2O and H2 to form N2 and H2O. Therefore, the rate law for the overall reaction can be written as:
Rate = k[N2O][H2]
where k is the rate constant and [N2O] and [H2] are the concentrations of the reactants.
It is important to note that the coefficients in the balanced equation do not necessarily correspond to the stoichiometric coefficients in the rate law. This is because the rate law depends on the specific mechanism of the reaction, which may involve multiple steps with different stoichiometries.
Additionally, the rate law only includes the reactants that are involved in the rate-determining step. In this case, N2 and H2O are not included in the rate law because they are not involved in the slowest step.
Overall, understanding the rate law for a reaction is important for predicting how changing the concentration of reactants will affect the rate of the reaction. It also provides insight into the specific mechanism of the reaction and how different steps may contribute to the overall rate.