##### J. W. Hill, R. H. Petrucci, T. W. McCreary, & S. S. Perry General Chemistry, 4th edition.

Problem 13.47.

The following data were obtained in two separate experiments in the reaction: A products. Determine the rate law for this reaction, including the value of k.
 Experiment 1 Experiment 2 [A], M Time, s [A], M Time, s 0.800 0 0.400 0 0.775 40 0.390 64 0.750 83 0.380 132 0.725 129 0.370 203 0.700 179 0.360 278

The general rate law is Rate = –k[A]m; the method of initial rates can be used to establish the order of reaction and give an estimate of the rate constant.

The initial rate are found from the first two data points in each experiment:

Using the initial concentrations with the initial rates:

So this is a second order reaction. The rate constant can estimated from k = –Rate/[A]2 for each experiment: k(exp. 1) = –(–6.25×10–4)/[0.800]2 = 9.8×10–4 M–1 s–1 and k(exp. 2) = –(–1.56×10–4)/[0.400]2 = 9.8×10–4 M–1 s–1.

k = 9.8×10–4 M–1 s–1

To confirm this and get a better value for the rate constant, a plot of [A]–1 vs. t should be linear with a slope equal to the rate constant:

The slopes of these plots show that a better value for the rate constant is k = 1.0×10–3 M–1 s–1.