Unit 5: Topic 8 - Reaction Mechanism and Rate Law Flashcards
What determines the rate of a reaction in which the first step is the slowest?
A reaction mechanism is composed of a series of elementary reactions. If the first step, or first elementary reaction, is the slowest, then it is known as the rate-determining step. To think of it more intuitively, because the first step is the slowest, it will limit the speed of the overall reaction, making this step rate-determining. As a result, the rate law of the overall reaction is equal to that of the first step.
For instance, in this example, the first step is the slowest and is thus the rate-determining step. Using the rate law, we know that this elementary reaction has a rate of k1[NO2]^1[NO2]^1, which simplifies to k1[NO2]^2, due to the two reactants being NO2 with coefficients of 1. The overall reaction will also then have a rate of k1[NO2]^2.
As shown by the chart, the rate doubled from experiment 1 to experiment 2 when [X] remained constant and [Y] doubled. Therefore, in the rate law, [Y] will have an exponent of 1. However, when comparing experiments 2 and 3, we observed that the rate stayed the same when [Y] remained constant and [X] doubled. Since the change in the concentration of X had no effect on the rate, [X] would have an exponent of 0. Thus, rate = k[X]^0[Y]^1, which simplifies to k[Y]. To find the value of k, we can plug in 7.0x10^-4 for the rate and 0.10 for [Y]. As a result, we find that k = 7.0x10^-3 s^-1 (units determined by reaction order). Therefore, rate = 7.0x10^-3[Y].
To answer part two, we should first look at mechanism I. Since the first step is slow, the rate of the overall reaction will be k[X][Y], which is inconsistent with our rate of k[Y] in part one. For mechanism II, the rate is k[Y], but the overall reaction would be X + Y –> Z, so it is incorrect. Finally, for mechanism III, the rate is k[Y], and the overall reaction is 2X + Y –> Z, which is the same as the reaction in part one. Hence, the correct answer is mechanism III.
