A reaction is assumed to have a rate expression of the form v = k[A]2[B]. Which set of data below is consistent with this rate expression?

Question

A reaction is assumed to have a rate expression of the form v = k[A]2[B], where A and B are the reactants. Which set of data below is consistent with this rate expression?

Answer 1

You might get a better response if you post this in Chemistry instead of Mathematics. Also, if 2 is an exponent (and can't type a superscript), use ^ before it.

v = k[A]²[B]

or

v = k[A]^2[B]

I believe the question is saying which pair of reactions would have the same constant of proportionality (k).

UPDATE:

Try solving in terms of k:

k = v / (A²B)

Let's check the first pair:

From the first reaction, we have A=1, B=1, v=10

k = 10/(1²*1) = 10/1 = 10

From the second reaction, we have A=2, B=2, v=40

k = 40/(2²*2) = 40/8 = 5

Clearly we get different values of k, so those aren't consistent.

Let's check the second pair:

From the first reaction, we have A=1, B=2, v=10:

k = 10/(1²*2) = 10/2 = 5

From the second reaction, we have A=0.5, B=4, v=5

k = 5/(0.5²*4) = 5/1 = 5

What conclusion can you draw?