Textbook Problem Section 7A Question 17A

[Amber Shanks 2K]

I am confused on a kinetics textbook problem where you have to find the order for the concentration for [B] in order to write the rate law for the reaction. It says in the solution that "increasing the concentration of B by the ratio 3.02/1.25 (experiments 2 & 3) increases by the rate (3.02/1.25)^2 which makes the reaction second order for B". I am confused about the logic behind this part of the problem and how the answer key derives this answer.

[Erika Patel 3I]

When you are looking to find the order with respect to each species, you need to isolate where only that species has concentration changing. For B, you would use experiments 2 and 3 since only its concentrations are changing. When you divide the rate of experiment 3 by experiment 2, you get 5.84... and this will be equal to (3.02/1.25)^b since you are finding the order. This comes out to about 2.416...^b and b will equal 2.