Question

For a given reaction 2A + B --> C, if the concentration of A doubles, then the reaction rate doubles. If the concentration of both A and B doubles, then the reaction rate increases by a factor of eight. What is the order of the reaction with respect to B?

Answer 1

Doubling both reactants A and B increases the reaction rate by a factor of eight, which indicates that the reaction is first-order with respect to both A and B. Thus, the reaction is second-order overall, and B must be first-order because the reaction rate increases by the concentration factor.

Step-by-step explanation:

To determine the order of a reaction with respect to a reactant, we analyze how changes in concentration affect the rate of the reaction. In this case, when the concentration of A is doubled, the reaction rate doubles, indicating a first-order dependence on A. The question further states that doubling both A and B increases the reaction rate by a factor of eight. Since doubling A alone doubles the rate, the additional fourfold increase (from 2 to 8) must be due to the doubling of B's concentration. This implies that the reaction's rate is also first-order with respect to B, as the rate increases by the same factor as the concentration of B. Therefore, the reaction is first-order in both A and B, making it a second-order reaction overall with a rate equation of rate = k [A] [B].