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Introduction
Hello! In this article, we will be looking through several important questions on reaction kinetics. In a previous article, we have already discussed reaction kinetics in terms of catalysis, so we will be looking at the rest of reaction kinetics in this article.
The 5 important questions related to reaction kinetics are answered in this article and also summarized below (they can also be found in the table of contents):
- What is activation energy and how does it affect reaction rate?
- What factors speed up rates of chemical reactions?
- What is the rate law or rate equation?
- How to determine and apply the rate law?
- What is the rate law for an uncatalyzed and catalyzed reaction?
My hope is that by the end of this article, we will have solid answers for all of these questions, and at the same time, a concrete understanding of reaction kinetics. Before we get into answering these questions, let us first look at the definition of reaction kinetics.
Reaction kinetics are concerned with the rates of chemical reactions (Fig. 1). These chemical reactions, of course, can be catalyzed or uncatalyzed, as we have highlighted in the previous article (as we have already noted at the beginning of this article).
Fig. 1: Graphing the rates of chemical reactions.
How do we obtain the rates of the chemical reactions? This is what we will learn about in this article, in either a quantitative (obtaining the actual rate) or qualitative (learning about the factors) way. We may chart a diagram based on values obtained, allowing us to perceive the data in a useful way.
And now that we have a basic understanding of what reaction kinetics is, let us begin answering the five questions posed at the beginning of the article.
1. What is activation energy and how does it affect reaction rate?
Before we begin, take note that we have already addressed activation energy when we discussed five aspects of catalysis. However, we will explain activation energy once again, for those who have not read that article and also for people who need a refresher.
The activation energy (Ea) refers to the minimum amount of energy needed for a collision between particles to result in a successful reaction. By the kinetic particle theory, particles react by collision between each particle, but the reaction can only occur if the collision energy is above the activation energy.
Previously, we explained that catalysts can lower the activation energy of the reaction, thus increasing the number of successful collisions. We may not see a direct correlation between the increase in reaction rate and the lowering of the activation energy, which is what we will explain next.
How do we measure reaction rate by the kinetic particle theory? To answer this question, we must first relate particle collisions to reaction rate. The rate of reaction is governed by how often successful collisions between particles occur.
By increasing the likeliness of a collision being successful, we increase the chance of a reaction, and this means that the rate of a reaction is increased! This is how we can link the reaction rate to the activation energy (and since the reaction rate is related to reaction kinetics, to the overarching topic).
The energy of particles in a setup can be visualized with the Maxwell-Boltzmann curve (Fig. 2), which depicts the amount of energy and the number of particles with that energy. We can also chart the activation energy Ea on the graph as shown below.
Fig. 2: The Maxwell-Boltzmann curve.
There are some particles with energies higher than the activation energy, and this means that when such particles collide, the result will definitely be a successful reaction. Note that the proportion of such particles is quite low. Of course, the Maxwell-Boltzmann curve will change when the temperature increases, with more particles above the activation energy.
So, what is the significance of reaction kinetics? One significant point with relations to organic chemistry is that it allows us to predict the mechanism of a reaction. Using organic chemistry, we can determine whether a step would be a slow or fast one.
Then, if we use reaction kinetics, we can determine the rate of the reaction, which can then help us verify if a predicted step is accurate. For example, if we predict using organic chemistry that the first step of a reaction is slow, we look at the reaction kinetics of that reaction. If it is indeed slow, then this provides evidence supporting the mechanism.
2. What factors speed up rates of chemical reactions?
Next, let us look at some of the factors which affect the rates of reactions. We will name just four of these factors; usually, the first two factors are taught at lower levels, while the last two are taught at a higher level:
- Temperature
- Concentration of reactants
- Surface area of reactants
- Presence of catalysts
The first and second factors are the more obvious and intuitive ones, but for complete clarity we will still explain them in detail. The relationship between temperature and rate of reaction is such that when the temperature increases, the rate of reaction will also increase. To explain this, we have to again look at kinetic particle theory.
When the temperature increases, the average kinetic energy of the particles in the mixture will increase, and this means, of course, that the rate of collisions are more common (Fig. 3), because particles will be more excited and thus will bump into one another more often. This causes the rate of the reaction to increase.
Fig. 3: The temperature affects collisions.
At the same time, increasing the temperature also gives particles more energy to move faster. What are the implications of this? They will be bumping into each other at a higher speed, meaning that it is more likely for the collision to achieve the minimum activation energy and for it to be successful. Because of this, increasing the temperature increases the rate of the reaction.
The concentration of reactants is also very significant. Thinking, again, in terms of particles, the higher the concentration of reactants, the more the number of particles. This increases the chance of a collision (Fig. 4), and as such the rate of the reaction will naturally increase.
Fig. 4: The concentration of reactants affects collisions.
The surface area of the reactants themselves can also affect the rate of reaction; however, this is commonly overlooked, in my opinion. It may be because this cannot be explained by kinetic particle theory, unlike the above two factors and the below one.
When the surface area of reactants increase, we can think of it as more reactant particles being ‘exposed’ to attack. This is rather similar to increasing the concentration in the sense that more collisions are able to occur at the same time, and thus it is also similarly able to increase the rate of the reaction.
Finally, we have catalysis. The presence of catalysts lowers the activation energy required for reaction thus more collisions will be successful. More information can be found in the linked post at the start of the article, but for now look at Fig. 5 (reused diagram!) to understand how it works.
3. What is the rate law or rate equation?
It is important to take note that rate law and rate equation mean the exact same thing. However, in chemistry, it is generally more common for us to use equations to represent chemical equations, and because of this we choose to use the term ‘rate law’, instead of the term ‘rate equation’.
Well, what is the rate law? Let us answer this important question. It is simply a mathematical equation (hence the name ‘rate equation’) that demonstrates the relationship between the concentration of reactants and the rate of the reaction. The mathematical equation is shown below:
Rate = k[A]^x[B]^y
Fig. 5: Generalized rate equation.
The x and y values in the above reaction refer to the order of reaction with respect to each reactant, which we will explain later. Meanwhile, A and B are the reactants, and [A] and [B] refer simply to the concentrations of A and B. k represents the rate constant which is constant for a reaction at a fixed temperature.
So, what is the order of reaction? When we look at the rate equation, for example, we see that if x = 2 and we use 2A instead of A, the rate would increase by 4 times. The order of the reaction thus describes the magnitude that change in concentration would cause on the rate of the reaction.
Although all the reactants are included in the rate equation, some of them may not affect the rate of the reaction! This is the case if x = 0. If the order of the reaction were zero, [A]^0 is always 1, and thus changing the concentration of A will never affect the rate of the reaction.
The overall order of the reaction is calculated by linear combination of orders with respect to the different reactants. In the case of Fig. 5, the order of the reaction is (x + y). In an overall zeroth (0) order reaction, changing the concentration of the reactants would not affect the rate of reaction at all.
For a first order reaction, it could be that the order with respect to the reactants is 0 and 1, respectively. The second order reaction could have two cases, with either orders 0 and 2, or orders 1 and 1.
When one of the reactants is in excess, any change in the concentration of this reactant would not affect the rate of the reaction by much. In a second order reaction with two reactants (orders 1 and 1), allowing one of the reactants to be in excess results in a first-order reaction instead, because the reactant in excess can no longer be considered first order.
Since changing the concentration of a reactant in excess would not affect the rate of the reaction, it would be 0th order with respect to this reactant instead of 1st order. Thus, the overall rate of reaction would be 0 + 1 = 1. Thus it is a first-order reaction. We term this as a pseudo-first-order reaction, because it is technically a second-order reaction.
4. How to determine and apply the rate law?
The determination of the rate law is usually obtained via experimental methods. For a reaction with, say, two reactants, we can keep one of the reactants at a constant amount and the other a variable amount. The magnitude of change of the rate can then be recorded.
How, then, you ask, are we able to calculate the rate of reaction? The answer is straightforward; since we are only comparing magnitudes, we do not need to calculate an exact number. Instead, we just observe the time taken for a certain volume of product to be produced. The diagram below demonstrates the technique (Fig. 6, Fig. 7).
Fig. 6: Calculation of rate of reaction with experimental setup.
Fig. 7: Results of the experiment.
Below the beaker, there is a piece of paper with a cross (X) marked out on it. If the reaction mixture is transparent and the product is opaque (i.e. a precipitate of some sort), we should be able to calculate the time taken for the entire cross to be blocked by the product formed. The lower this time, the faster the rate of the reaction.
So, let’s say we doubled the concentration of a reactant while keeping the concentration of the other one constant. Then, the undoubled reactants gave 8s to block the cross while the doubled reactants gave 2s. This shows that the reaction is second order with respect to the reactant that was doubled in the experiment.
Other methods also exist for calculation of rate law, for example, if the reaction produces a gaseous product, a conical flask may be used. The reaction is carried out inside the flask and the gas emitted travels into a gas syringe where the rate of gas produced can then be concluded, which gives us information about the rate.
However, it is generally more convenient to use the method as outlined above in Fig. 6, especially if the product is a solid, insoluble one, because it requires minimal use of apparatus and is more convenient.
5. What is the rate law for an uncatalyzed and catalyzed reaction?
Previously we looked at the rate of a reaction for a catalyzed reaction in the aforementioned article. However, we did not cover the rate law and rate of reaction for the uncatalyzed reactions or the uncatalyzed reaction, which is what we will be doing in this article.
For an uncatalyzed reaction, we note that usually the only species present in the reaction mixture would be the reactants and the products, because catalysts are not present. As such, the rate reaction should be a simple one (Fig. 8).
Rate = k[A]^x[B]^y
Fig. 8: Simplified rate equation for uncatalyzed reactions.
As we have stated before, k refers to the rate constant, [A] and [B] refer to the concentration of the reactants, and x and y indicate the order of the reaction. What about for the catalyzed reaction? Allow yourself to consider this question for a moment.
Since a catalyst is effectively not used up in the reaction, its concentration should not matter in most cases - in fact, the concentration used can be very small, i.e. the catalytic amount. Thus, catalysts are not included in the rate equation.