The following questions refer to the hypothetical reaction A + B → products. The kinetics data given can be analyzed to answer the questions.
-The rate law for the reaction is Rate = k[A]^x[B]^y. What are the values of x and y?

Question

The following questions refer to the hypothetical reaction A + B → products. The kinetics data given can be analyzed to answer the questions.

-The rate law for the reaction is Rate = k[A]^x[B]^y. What are the values of x and y?

Quizplus · Accepted Answer

The rate law for the reaction is Rate = k[A]^x[B]^y. 
Since A is a reactant and B is also a reactant, their exponents must be positive integers. The overall order of the reaction is the sum of the exponents, which is (x + y). 
Using the given data, the initial rate of the reaction is measured at different concentrations of A and B:

Experiment #  [A]  [B]  Initial rate (M/s) 
1           0.10  0.20  4.0 x 10^-4 
2           0.20  0.20  8.0 x 10^-4 
3           0.20  0.40  1.6 x 10^-3

When [A] is doubled in experiment 2, the rate also doubles, indicating a first order dependence on [A]. Therefore, x = 1. 
When [B] is doubled in experiment 3, the rate quadruples, indicating a second order dependence on [B]. Therefore, y = 2. 
The rate law for the reaction is Rate = k[A]^1[B]^2, which is equivalent to Rate = k[A][B]^2. Therefore, the best choice is B.

The Following Questions Refer to the Hypothetical Reaction a