Which of the following is the correct rate law for the reaction?

Question

For the reaction, 2 A(g) + 2 B(g) => C(g) + 3 D(g), the following data were obtained at constant temperature.

Experiment	Initial [A], mol/L	Initial [B], mol/L	Initial Rate, M/min
1	0.11	0.15	2.0 x 10-5
2	0.11	0.30	8.0 x 10-5
3	0.22	0.45	3.6 x 10-4
4	0.22	0.60	6.4 x 10-4

Which of the following is the correct rate law for the reaction?

The answer is: Rate = k[A][B]²

But when I find that B is in SECOND order, and I use experiments 2 and 3, I find that A is in second order but that would be wrong due to the correct answer given.

For experiments 2 and 3, [A] DOUBLES, [B] DOUBLES, and the rate increases by 8. So it would be:

(2)^x + (2)² = 8.

2^x = 4

x = 2

What did I do wrong? How do I find the right answer?

Answer 1

Compare expt 1 and 2. B doubles and rate increases 4x. It is 2nd order in B

Compare expt 2 and 4. You expect the rate to increase by 4x based on B alone but since it increased by 8 x you now know it must be 1st order in A since A doubled. 2 x 4 = 8.

Thus rate = k[A][B]²

Answer 2

B does not double, in experiment 2 and 3, B only goes up by 50%. The question is defective, as B is supposed to have its concentration be the same between 2 experiments when A changes.

You can use 2 and 4 to answer the question. When A and B double what happens to the rate??

This question however, is still misleading as 2 and 4 are changing 2 variables.