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The rate law is an expression for the reaction rate in terms of concentrations of chemical species involved in the reaction. For example, Rate = k [A]m [B]n. where k is a rate constant, m is reaction order with respect to A, n is the reaction order with respect to B, and m+n is the overall reaction order. The rate constant is independent of the concentrations of the chemical species involved in the reaction.
The rate of an overall reaction is NOT the product of the concentrations of the reactants raised to their stoichiometric powers. The rate law for the first elementary step in the is rate = k [O3]. Because this step is the rate determining step, the rate law is also the rate law for the overall reaction. Using similar techniques we can calculate the rate law predicted by any mechanism.