Final answer:
The order of the reaction with respect to the reactant is second-order since tripling the concentration of the reactant leads to a nine-fold increase in rate, indicating a direct squared relationship between reactant concentration and rate.
Step-by-step explanation:
If increasing the concentration of a different reactant by a factor of three increases the rate of a reaction nine times, we need to determine the order of the reaction with respect to that reactant. To find the reaction order, we look at the relationship between the concentration changes and the rate changes. In this case, since tripling the concentration increases the rate by a factor of nine, we can use the rate laws concept to deduce the reaction order.
For a reaction where the rate is directly proportional to the concentration of a reactant raised to some power, the rate equation can be written as rate = k[Reactant]^n. Here, k is the rate constant, and n is the order of the reaction with respect to the reactant in question. Given that tripling the concentration (an increase by a factor of 3^n equals 3) leads to a nine-fold increase in the rate (which can be expressed as 3^2), we can solve for n by setting 3^n equal to 9 (or 3^2).
Thus, by comparing the increase in rate to the increase in concentration, we conclude that n = 2, which means the