Kaplan MCAT General Chemistry Review

Fortunately there are very few—almost zero—reactions in which a single-reaction step involves a termolecular process; in other words, there are almost no elementary processes whose rate is third-order with respect to a single reactant. This is because it is almost impossible to get three particles to collide simultaneously. Any order higher than 3 is virtually unknown.

Mixed-Order Reactions

Mixed-order reactions sometimes refer to noninteger orders (fractions) and in other cases to reactions whose order varies over the course of the reaction. Fractions are more specifically described as broken-order, and in recent times, the term mixed-order has come to refer solely to reactions whose order changes over time. Knowing those two definitions will probably be enough for you on Test Day.

An example of a mixed-order reaction is a catalyzed reaction whose rate law is given by

where A is the single reactant and E the catalyst. (The overall reaction and its mechanism are beyond the relevance and scope of the MCAT, and the derivation of this rate law is even more unnecessary!) The result of the large value for [A] at the beginning of the reaction is that k₃[A] >> k₂, and the reaction will appear to be first-order; at the end of the reaction, k₂ >> k₃[A] because [A] will have a low value, making the reaction appear to be second-order. While the MCAT will not ask you to derive a rate expression for a mixed-order reaction, you are responsible for being able to recognize how the rate order changes as the specific reactant concentration changes.

THEORIES OF THE MOLECULAR BASIS OF CHEMICAL REACTIONS

It’s one thing to say “A₂ reacts with B₂ to form 2AB”; it’s quite another to be able to describe, as precisely as possible, the actual interactions that occur between A₂ and B₂ to produce AB at some rate. Various theories have been proposed to explain the events that are taking place at the atomic level through the process of a reaction.

Collision Theory of Chemical Kinetics

For a reaction to occur, molecules must collide with each other in much the same way that for children to enjoy themselves, there usually must be some rough physical contact involved; that is, of course, until someone’s eye gets poked out. The collision theory of chemical kinetics states that the rate of a reaction is proportional to the number of collisions per second between the reacting molecules.

The theory suggests, however, that not all collisions result in a chemical reaction. An effective collision (that is, one that leads to the formation of products) occurs only if the molecules collide with each other in correct orientation and sufficient energy to break the existing bonds and form new ones. Not every punch that a professional boxer throws is going to result in a knockout, only the ones that have the right angle and energy. The minimum energy of collision necessary for a reaction to take place is called the activation energy, E_a or the energy barrier. Only a fraction of colliding particles have enough kinetic energy to exceed the activation energy. This means that only a fraction of all collisions are effective. The rate of a reaction can therefore be expressed as follows:

rate = fZ

where Z is the total number of collisions occurring per second and f is the fraction of collisions that are effective.

Transition State Theory

The discussion of this theory introduces us to some terms that will be more fully defined and explored in the next chapter, Thermochemistry, so if some of these concepts are not clear to you, be patient, because you’ll have another opportunity to consider them more carefully soon enough.

When molecules collide with sufficient energy at least equal to the activation energy, they form a transition state in which the old bonds are weakened and the new bonds begin to form. The transition state then dissociates into products, and the new bonds are fully formed. For the reaction A₂ + B₂ = 2AB, the change along the reaction coordinate, which is a measure of the extent to which the reaction has progressed from reactants to products, can be represented as shown in Figure 5.1.

Figure 5.1

Key Concept

Relative to reactants and products, transition states have the highest energy. So they are only theoretical structures and cannot be isolated. Nevertheless, we can still use the proposed structures to understand better the reactions in which they are involved.