Final answer:
The order of the reaction with respect to A is first-order since the log of the concentration of A versus time is a straight line. This straight line indicates that the rate is directly proportional to the concentration of A.
Step-by-step explanation:
The order of a reaction with respect to a reactant indicates the power to which the concentration of that reactant is raised in the rate law. If the log of the concentration of reactant A versus time is a straight line, this suggests a first-order reaction with respect to A. In a first-order reaction, the rate at which A reacts is directly proportional to its concentration. An expression for a first-order reaction is [A] = [A]oe-kt, where [A]o is the initial concentration, k is the rate constant, and t is the time.
Since plotting the natural logarithm ln[A] versus time yields a straight line, the equation can be expressed as ln[A] = -kt + ln[A]o, which parallels the algebraic form of a straight line, y = mx + b. Thus, when a plot of the log of the concentration against time for reactant A creates a straight line, it indicates that the reaction is first-order in A because the slope of this line is equal to the negative of the rate constant k.
The fact that the initial concentration of B is much larger (10 M) than that of A (0.01 M) and that B remains virtually unchanged during the reaction suggests that the order of the reaction with respect to B cannot be determined without additional data.