Use the information below to determine the rate law for the hypothetical reactio

Question

Use the information below to determine the rate law
for the hypothetical reaction: A + B P

Exp. #                    [A] (M)             [B] (M)                         Initial Rate (M/s)
1                           0.600                0.500                            0.040
2                           0.300                0.500                            0.040
3                           0.600                1.500                            0.360

Why is the answer: Rate = k[B]^2 ? Please show work on how to get the answer

Explanation / Answer

To calculate the order of the reaction for A, notice that experiments 1 and 2 hold the concentration of B constant while doubling the concentration of A. The initial rate of the reaction is unaffected by the decrease in A concentration, so the reaction is zero order in A. We can prove this mathematically by taking the ratio of the rates from experiments 1 and two:

rate2/rate1= k*[A]2^p*[B]2^q/k*[A]1^p*[B]1^q = 0.3^p*0.5^q/0.6^p*0.5^q = 0.3^p/0.6^p = 0.040/0.040 = 1

2^p=1 then, p must equal to 0.

As you can see in the above equations, by holding the concentrations of all but one species constant between two experiments, you can calculate the order of the reaction in a single reactant at a time. By similar reasoning, we can conclude that because the rate of reaction doubled when the concentration of A was doubled the reaction must be first order in A.

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