Acetylsalicylate ion (derived from aspirin and shown as X in the equation below) hydrolyzes in the p — Kinetics Chemistry Question
Problem Context
Acetylsalicylate ion (derived from aspirin and shown as X in the equation below) hydrolyzes in the presence of hydroxide ion:
The reaction was studied at 60 ºC and was found to be first-order in X under all conditions. The amount of X was monitored over time in two different buffer solutions and the following data were obtained:
Time, s
[X], M, pH = 10.10 buffer
[X], M, pH = 10.60 buffer
0 3.61 10 –4 3.59 10 –4
600 1.78 10 –4
740 2.75 10 –4
Since the reaction is first-order in X, and the concentration of hydroxide ion is held constant by the buffer solution, then for each individual run the rate can be written
rate = k'[X]
Determine the value of k' for each of the two runs.
Model Answer
Under these "pseudo" first-order conditions, ln([X]/[X]0) = –k't.
At pH = 10.10, ln([2.75 10 -4]/[3.61 10 -4]) = –k'(740 s), so k' = 3.68 10 -4 s -1.
At pH = 10.60, ln([1.78 10 -4]/[3.59 10 -4]) = –k'(600 s), so k' = 1.17 10 -3 s -1.
What is the reaction order in hydroxide ion? Give your reasoning.
Model Answer
At pH = 10.10, [OH – ] = 10^(10.10-14) = 1.26 10 -4 M
At pH = 10.60, [OH – ] = 10^(10.60-14) = 3.98 10 -4 M
Between the two runs, [OH – ] increases by a factor of 3.16; the pseudo-first-order rate constant k' increases by a factor of 3.18. Thus, k' is directly proportional to [OH – ]. Since
Rate = k'[X] = k[OH – ]^m [X]
where m is the reaction order in hydroxide, we thus have m = 1.
Give the full rate law for the reaction and calculate the rate constant k.
Model Answer
Rate = k[OH – ][X]
Since k[OH – ] = k' for either run, we have k = (3.68 10 -4 s -1 )/(1.26 10 -4 M) = 2.92 M -1 s -1. (Using the data from the second run gives k = 2.94 M -1 s -1 , in good agreement.)
The following mechanism is proposed for this reaction:
Is this mechanism consistent with the observed rate law? If so, state which step(s) could be rate-determining. If not, explain why not.
Model Answer
If the first step of the mechanism were rate-limiting, then Rate = k1[X]. This is inconsistent with the first-order dependence on OH – . If the second step is rate-limiting, then Rate = K1k2[X], also inconsistent with the first-order dependence on OH – . So, regardless of the rate-limiting step this mechanism is predicted to have a zeroth-order dependence on OH – , so it is not consistent with the experimental data. (More generally, if one applies the steady-state approximation to the intermediate, one concludes that Rate = k1k2[X]/(k-1 + k2), which is always zeroth-order in OH – .)