Suppose you have measured the kinetics of the reaction, 2 A + B → C + 2 D at room temperature using the method of initial rates.

Question

A table summarizing the results of four different experimental trials is shown below:

Experimental	Initial A	Initial B	Initial rate
Trial	(M)	(M)	(M s-1)
1	0.15	0.30	0.000476
2	0.30	0.30	0.000953
3	0.15	0.15	0.000119
4	0.45	0.45	0.003215

You conclude that the reaction is first order in [A] and second order in [B].



Based on these data, what is the value of the rate constant k (in units of  M^-2 s^-1).

{Enter your value with three significant figures.}

Answer 1

First order in A and 2nd order in B allows us to write the rate law as ...

Rate = k[A][B]²

Use the data from any trial and solve for k. I will use trial 1:

Rate = k[A][B]²

0.000476 M/s = k[0.15 M][0.3 M]²

0.000476 M/s = 0.0135 M³ k

k = 0.000476 M/s ÷ 0.0135 M³

k = 0.0135 M^-2s^-1 (3 sig. figs.)