Final answer:
The student's question pertains to chemical kinetics and involves determining the rate law of a reaction by understanding how reaction rates vary with reactant concentrations. The rate constant k and the exponents m and n in the rate law expression can be evaluated using proportional changes in reaction rates obtained from experimental data. The concepts of rate law, stoichiometry, and relationships between different scientific quantities are central to the question.
Step-by-step explanation:
The question relates to chemical kinetics and the determination of the rate law for a chemical reaction. The use of a rate law expression rate = k[NO]"[O3]" suggests that the student is asked to deduce the values of m, n, and the rate constant k from given experimental data. When it is observed that changing the concentration of NO changes the rate of reaction in a directly proportional manner, this indicates that the exponent m in the rate law equals 1. Similarly, other variables such as n and k can be evaluated using experimental data where the concentration of the other reactants is varied.
Another aspect of the question seems to involve a stoichiometry problem, relating the total mass M of a substance to the number of unit cells N, their individual mass m, and molar mass. Various mathematical relationships, including those between pressure P and amount of substance n, and n versus temperature T, are hinted at also being relevant to the discussion. The particular details of these relationships would depend on additional context not provided in the question.