Final answer:
To find the values of m and n in the rate law equation, we use the provided experimental data to see how varying one reactant's concentration while holding the other constant affects the rate. For this scenario, both m and n are found to be 1, making the reaction first-order with respect to both NO and O3.
Step-by-step explanation:
When determining the reaction orders (m and n) using rate law, we observe how changes in reactant concentrations affect the reaction rate. The rate law equation in this scenario is rate = k[NO]^m [O3]^n, and we are provided with experimental data to deduce the values of m and n.
Step 1: Determining m
When [NO] concentration changes and [O3] remains constant, if the rate changes in direct proportion to [NO], then m equals the factor by which the rate changes. For instance, if the rate doubles when [NO] concentration doubles, m is 1, indicating a first-order reaction with respect to NO.
Step 2: Determining n
Similarly, when [O3] concentration changes and [NO] stays constant, the same direct proportionality can be used to determine n. If the rate triples when [O3] concentration triples, n is also 1, revealing a first-order reaction with respect to O3.
In the given experiments, when [NO] is doubled, the rate doubles, and when tripled, the rate triples, indicating m=1. When [O3] is doubled or tripled, the rate exhibits the same change, indicating n=1.
Thus the rate law is rate = k[NO] [O3], and the overall reaction order is m + n = 2. Determination of the rate constant k would require additional data showing the actual rates of the reaction for known concentrations of the reactants.