0.19 Reaction kinetics  (Page 6/7)

The key assumption of the collision model is that the reaction occurs by a single collision. Since this assumption leads to incorrect predictions of rate laws in some cases, the assumption must be invalid in at least those cases. It may well be that reactions require more than a single collision to occur, even in reactions involving just two types of molecules as in Equation (10).

Moreover, if more than two molecules are involved as in Equation (8), the chance of a single collision involving all of the reactive molecules becomes very small. It is hard enough to get two particles to collide and react. It is much less probable that three particles will collide simultaneously to react in a single step.

We conclude that many reactions, including those in Equations (8) and (10), must occur as a result of several collisions occurring in sequence, rather than a single collision. The rate of the chemical reaction must be determined by the rates of the individual steps in the reaction.

Each step in a complex reaction is a single collision, often referred to as an “elementary process.” In a single collision process step, our collision model should correctly predict the rate of that step. The sequence of such elementary processes leading to the overall reaction is referred to as the “reaction mechanism.” Determining the mechanism for a reaction can require gaining substantially more information than simply the rate data we have considered here. However, we can gain some progress just from the rate law.

Consider, for example, the reaction in Equation (10) described by the rate law in Equation (11). Since the rate law involved [NO ₂ ] ² , one step in the reaction mechanism must involve the collision of two NO ₂ molecules since the probability of such a collision would be proportional to [NO ₂ ] ² .

Eventually, the CO reactant molecule must come into play in the reaction, so we would think that [CO] would have to be included in the rate law. But this is not the experimental result. This means that the rate of the reaction depends only on how fast the reaction between the two NO ₂ molecules occurs. That one step must determine the rate of the overall reaction. Why would that be?

In any multi-step process, if one step is considerably slower than all of the other steps, the rate of the multi-step process is determined entirely by that slowest step, because the overall process cannot go any faster than the slowest step. It does not matter how rapidly the rapid steps occur. Therefore, the slowest step in a multi-step process is called the “rate determining” or “rate limiting” step.

This argument suggests that the reaction in Equation (10) proceeds via a slow step in which two NO ₂ molecules collide, followed by at least one other rapid step leading to the products. A possible mechanism is therefore

Step 1: NO ₂ + NO ₂ → NO ₃ + NO slow

Step 2: NO ₃ + CO → NO ₂ + CO ₂ fast

If Step 1 is much slower than Step 2, the rate of the reaction is entirely determined by the rate of Step 1. From our collision model, the rate law for Step 1 must be Rate = k[NO ₂ ] ² , which is consistent with the experimentally observed rate law for the overall reaction. This suggests that the mechanism in Equations (12a) and (12b) is the correct description of the reaction process for Reaction (10), with the first step as the rate determining step.