Kinetics
Kinetics
The process of diamond turning into graphite has a negative ΔG. It happens spontaneously. But, my wife’s wedding ring is not turning into a worthless hunk of graphite any time soon. This process takes eons to occur. It is important for us to understand something about how fast a particular reaction will occur. We need to understand the kinetics of a reaction. Kinetics is the study of the rates of reactions.
The kinetics of a particular reaction is expressed using a rate equation. For a typical reaction, the rate equation takes the following form.
[A] = the concentration of A
[B] = the concentration of B
a = the order of the reaction with respect to A
b = the order of the reaction with respect to B
kr = the rate constant. If kr is high, the reaction is fast, if kr is low, the reaction is slow.
We can know the values for [A] and [B] as we know how much of each reactant we use. But, what about a, b, and kr? The good news is that you will never be asked to predict these. These values can only be discovered experimentally! An experiment needs to be carefully performed to measure how quickly A and B are used up in the reaction. This experiment can give us the values of kr, a, and b. Let’s look at a couple of example reactions to make sense of this.
A one-step reaction
SN2 Backside Attack. A one-step reaction.
In this reaction, hydroxide reacts with bromomethane to make methanol. The rate constant can be measured experimentally, and changes depending on the solvent and the temperature of the reaction. From the rate equation, we see that the superscript for each reactant is 1. The 1 can be written, or like superscripts of 1 in mathematics, they may not be written. We then say that the reaction is first order with respect to hydroxide and first order with respect to bromomethane. Overall, the reaction is a second-order reaction (1+1=2). Let’s start with a concentration of 1 for each reactant.
Now, let’s double the amount of hydroxide in the reaction.
The rate of the reaction doubled. This makes sense if you think about the reaction. For the reaction to proceed, a hydroxide ion must bump into a bromomethane molecule. When the amount of hydroxide in the reaction flask is doubled, there is twice the chance for this encounter to happen.
If instead of doubling the amount of hydroxide, we doubled the amount of bromomethane, we get the following.
The reaction rate again is doubled. Again, there is twice the chance for a hydroxide ion and a bromomethane molecule to encounter each other if the amount of bromomethane is doubled.
The reaction coordinate diagram for a one-step reaction has only one transition state.
Two-step reactions
Reaction Coordinate Diagram for a one-step reaction
Many reactions are not first order with respect to each of its reactants. This may be a little more difficult to understand, but let’s try with an everyday example first. Imagine a group of people making peanut butter and jelly sandwiches. Some people are putting peanut butter on bread. Others take this peanut butter-bread and put jelly on it. Finally, somebody cuts the sandwich in half. We could express this process as a reaction.
The kinetics of making peanut butter and jelly sandwiches
As the reaction proceeds, you can see that if the first step is fast, the second step is slow, and the third step is fast again, that the rate of the reaction (how fast we make peanut butter and jelly sandwiches) is determined by the slow step. The people putting jelly on the sandwiches slow us down. After a bit, you can bet that there will be a pile of peanut butter-bread stacking up at that step. What happens if we double the concentration of the folks putting peanut butter on bread? We do not make sandwiches any faster because more peanut butter-bread would stack up at the jelly station. The reaction is zeroth-order with respect to peanut butter. What happens if we double the amount of people that are cutting the sandwiches? Again, we do not make sandwiches any faster because they would be sitting around waiting for jelly to be put on the sandwiches. The reaction is zeroth-order with respect to sandwich cutting. The only way to step up the rate in which we make sandwiches is by increasing the number of jelly spreaders. If we double the number of people putting jelly on sandwiches, we double the rate at which we make sandwiches. In the end, the rate of this reaction is first-order with respect to jelly. We could write this rate equation as
Rate = kr[Jelly]
The only way to predict the rate equation for this reaction was to do the experiment. If we tried to make sandwiches and the people spreading the peanut butter and adding jelly were working very quickly (fast steps) and the people cutting the sandwiches in half were talking and goofing off and had VERY dull knives (the slow step), then the reaction rate would be zero order with respect to peanut butter and jelly and first order with respect to cutting. The rate equation would be
Rate = kr[Cutting]
The experiment needs to be performed to determine the rates. That is good news as the pressure is off on us to guess!
We’ve learned that the rate is determined by the slowest step in a process. This slowest step is then called the rate-determining step (r.d.s). The highest peak, the highest energy transition state, in a reaction-energy diagram is the transition state for the rate-determining step of a reaction.
Reaction Coordinate Diagram for a two-step reaction