Final answer:
The order of the reaction is third-order with respect to the reagent in question, as the rate increases by a factor of eight when the concentration of the reagent is doubled.
Step-by-step explanation:
The question pertains to the determination of the order of a chemical reaction with respect to a specific reactant based on how changes in its concentration affect the reaction rate. In the case described, when the concentration of the reactant is doubled, the initial rate of the reaction increases by a factor of eight. This is indicative of the reaction being third-order with respect to that reactant, as the change in rate is the cube of the change in concentration.
In first-order reactions, doubling the concentration doubles the rate, and in second-order reactions, it quadruples the rate, hence the rate being proportional to the concentration squared. As per the problem given, since the rate becomes eight times greater, which is 23, the reaction must be third-order with respect to that one reagent.