Chemical Kinetics

How do you go about increasing the speed of a chemical reaction? One simple way might be by adding more of your reactants into the system. That is exactly what the chemists Peter Waage and Cato Guldberg proposed in 1864, under the name of the law of mass action. This law was the birth of the field of kinetics, the study of the rate (or speed) of reaction.

The law of mass action states that the rate of a reaction is proportional to the concentration of the reactants. While this is often true, we now know that there are many other factors that also affect how quickly substances react.

Take the reaction between magnesium and water, for example. Put magnesium in water at room temperature and it will fizz very gently. But combine it with steam and the reaction will be a lot more vigorous. In this article, we’ll look at why that is the case, as well as other questions within the field of kinetics.

• This article is about chemical kinetics.
• Firstly, we’ll define rate of reaction.
• After that we’ll look at the laws of chemical kinetics, including collision theory and factors affecting rate of reaction.
• We’ll then move on to kinetic graphs such as Maxwell-Boltzmann distributions and enthalpy diagrams.
• We’ll also look at how you plot rate of reaction graphs. You’ll be able to practice calculating the reaction rate at a particular point in time.
• After that, we’ll briefly introduce you to rate equations and the Arrhenius equation.
• Finally, we’ll look at applications of chemical kinetics.

Rate of reaction in chemical kinetics

As we defined above, chemical kinetics is a branch of chemistry that deals with the rate of reactions.

Some reactions happen extremely quickly. The reactants are used up rapidly and lots of the products are formed in the blink of an eye. They have a fast rate of reaction. But other reactions are slow. For example, the rusting of an iron nail can take years and years. The iron, one of the reactants, is gradually turned into iron oxide, the product. Because the change in the concentrations of reactants and products is gradual, we say that this process has a slow rate of reaction. Rate of reaction is simply a way of measuring how quickly one species turns into another.

Measuring rate of reaction

You can measure rate of reaction in a number of different ways. Any method is valid, so long as you measure the change in amounts of reactants or products. For example, you could:

• Measure the change in mass of a reaction with gaseous products.
• Measure the volume of gas given off for a reaction with gaseous products.
• Measure light passing through the solution for a reaction that produces a cloudy suspension.
• Measure the change in pH of a solution.

To measure rate of reaction, start your reaction. At regular time intervals, take a measurement as described above and record both the time and the measurement value in a table. Once the reaction is complete, plot a graph with time on the x-axis and your measurement, be it volume of gas or mass of reactants, on the y-axis. Join the points up with a smooth curve. To calculate rate of reaction, you then need to find the gradient of this curve. Don’t worry - we’ll show you how to do this later on.

Units of rate of reaction

The units of rate of reaction vary, depending on what you are measuring. Examples include g s^-1, cm³ s^-1 or mol dm³ s^-1.

Laws of chemical kinetics

Chemical kinetics, and the rate of all reactions, is based on one underlying law: the principle of collision theory. It’s a simple concept, but from it we can derive many of the factors affecting rate of reaction.

First, let’s define collision theory.

Collision theory

Reactions can only happen if two particles collide. However, this on its own isn’t enough. Collision theory dictates that in order to react, the particles must also have the correct orientation and sufficient energy. What does this mean?

Let’s use the reaction between chloroethane, and a hydroxide ion, as an example. They can react together to form an alcohol, in an example of what we call Nucleophilic Substitution Reactions. In order for a reaction to occur, the lone pair of electrons on the oxygen atom must collide with the carbon atom in the C-Cl bond. Nothing will happen if, say, the hydrogen atom in the hydroxide ion collides with the other end of the ethane chain! The molecules need to be orientated in just the right way in order for a reaction to occur.

Particles must collide with the correct orientation in order for a reaction to occur. Anna Brewer, StudySmarter Originals

But orientation isn’t the only requirement. Even if the hydroxide ion and the chloroethane molecule collide with the correct orientation, they still might not react. They also need to have enough energy. This energy is known as the activation energy.

To summarise, in order for a reaction to take place, two particles must first collide. They must also have the correct orientation. Finally, they need enough energy. If, and only if, they meet all these criteria, will a reaction occur. We call a collision that results in a reaction a successful collision.

Factors affecting rate of reaction

Collision theory tells us that particles need to collide with the correct orientation and enough energy in order for a reaction to take place. To increase the rate of reaction, we must therefore change any of the following three things:

• The particles’ orientations.
• The particles’ energy.
• The frequency of the particles’ collisions.

We can do this in a number of different ways.

Surface area

Increasing the surface area of a solid increases the rate of reaction. This is because there are more particles exposed on the surface of the solid. Liquid, aqueous or gaseous particles can collide with these exposed solid particles, potentially causing a reaction. So, increasing the surface area increases the frequency of collisions.

Concentration

Increasing the concentration of a solution increases the rate of reaction. This is because there is a greater number of solute particles in a given volume, which increases the frequency of collisions.

Pressure

Increasing the pressure of a gas increases the rate of reaction. Similar to increasing concentration, this increases the number of particles in a given volume and so increases the frequency of collisions.

Temperature

Increasing the temperature of a reaction increases the rate of reaction. This is for two reasons. Heating the particles supplies them with more energy. Some of this is turned into kinetic energy, meaning the particles move faster. This means that they collide more frequently. But more importantly, having more energy means that the particles are more likely to meet the activation energy when they do collide. Heating a reaction not only increases the frequency of collisions, but also the frequency of successful collisions.

Catalysts

Adding a catalyst increases the rate of reaction. This is because catalysts provide an alternate reaction pathway with a lower activation energy. Although they don’t change the frequency of collisions, catalysts increase the proportion of successful collisions.

Chemical kinetic graphs

Now that we know what kinetics is, and have learnt about factors affecting rate of reaction, we can turn our attention to kinetic graphs. There are a few different types of graphs you might come across in kinetics. We’re going to look at three in particular:

• Enthalpy diagrams
• Maxwell-Boltzmann distributions
• Rate of reaction graph

Enthalpy diagrams

Look at the graph below. It is a great example of an enthalpy diagram for the formation of sodium chloride. In this reaction, sodium reacts with chlorine gas to produce the salt sodium chloride.

An enthalpy diagram for sodium chloride. Anna Brewer, StudySmarter Originals

The graph tells us a few things.

• The products have less energy than the reactants. This makes the reaction an exothermic reaction - overall, energy is released.
• There is a peak in the curve between the reactants and the products. This is the activation energy we talked about earlier. To start a reaction, particles must collide with enough energy to get over this energy barrier.

Let’s now look at an enthalpy diagram for an endothermic reaction. One such example is the reaction between sodium carbonate and ethanoic acid.

An enthalpy diagram for the formation of sodium ethanoate. Anna Brewer, StudySmarter Originals

Note the following:

• The products are higher up on the graph than the reactants. This means that they have more energy - overall the reaction is endothermic.
• There is still a peak in the curve representing activation energy.

Let’s now go back to one of the factors affecting the rate of reaction: the presence of a catalyst. Catalysts reduce the activation energy requirements of a reaction. How do you think they change the reaction’s enthalpy diagram?

Well, the peak will be lower. Remember that the peak represents the activation energy. So, if the activation energy is lower, the height of the peak will decrease too. You can see this in the graph below.

Maxwell-Boltzmann distributions

Another type of graph found in kinetics is the Maxwell-Boltzmann distribution.

Different particles within a gas have different energy levels. Some have a lot of energy, while others only have only a little. Most have a medium amount of energy. We can plot these energy levels on a Maxwell-Boltzmann distribution, a graph showing the number of particles on the y-axis and energy on the x-axis. We get something looking a little like the following. You’ll notice that three points have been marked: the most probable energy, the average energy and the activation energy.

The Maxwell-Boltzmann distribution. Anna Brewer, StudySmarter Originals

What does this tell us?

• The area under the graph represents the total number of particles in the system.
• The most probable energy is the mode energy value. It is the one particular energy value that the greatest number of particles have.
• The average energy is the median energy value. Exactly half of the particles have more energy than this and exactly half of the particles have less energy than this.
• The area under the graph to the right of the activation energy represents the number of molecules that meet or exceed the activation energy. The greater this area, the greater the proportion of successful collisions.

Rate of reaction graphs

Earlier in the article, we explored how you measure the rate of reaction. You do this by measuring how the amount of reactants or products changes over time. Now we are going to focus on graphing this information.

Let’s go back to our example of sodium carbonate and ethanoic acid. This produces the gas carbon dioxide, . We can therefore measure the rate of reaction by measuring the volume of carbon dioxide given off. To do this, we use a gas syringe, taking readings at regular time intervals and recording them in a table. We can then plot these points on a graph with time on the x-axis and volume on the y-axis. Ideally, your data points should show a smooth curve.

A graph showing volume of gas given off against time. This is a measure of rate of reaction. Anna Brewer, StudySmarter Originals

Note the following:

• The curve starts off steep. This means that lots of the product is produced very quickly and so the rate of reaction is initially fast.
• The curve gradually levels out. This means that the product is produced less quickly and so the rate of reaction is slower.
• The curve eventually levels out completely. At this point, no more product is produced - the reaction is over. Here, that happens at 80 seconds.

Overall rate of reaction

Remember, rate of reaction is a measure of how quickly reactants are used up or products are formed in a chemical reaction. Here, we measured the volume of a product given off, . To calculate the overall rate of reaction, we divide the change in volume of by the time taken for the reaction to finish. Here, the reaction stops at 80 seconds - after that, no more is produced.

Calculating overall rate of reaction. Anna Brewer, StudySmarter Originals

The overall rate of reaction is therefore

Instantaneous rate of reaction

Sometimes you might not want to find the overall rate of reaction, but instead calculate the rate at a particular point in time. To do this, you draw a tangent to the curve at the required time and calculate its gradient.

Let’s say you want to find the rate of reaction at 10 seconds.

1. First, draw a tangent to the curve at 10 seconds. This is a straight line that just touches the curve at the 10 second mark.
2. Next, mark any two points on the tangent. Here we’ve chosen the points where t (time) = 0 and t = 30.
3. Calculate the change in height of the tangent between these two points. In our case, height represents volume. You do this by subtracting the volume at t = 0 from the volume at t = 30, using values taken from the tangent, not the curve itself. Here, .
4. Calculate the change in width of the graph between these two points. Here, .
5. Find the gradient of the tangent by dividing the change in height by the change in width. Here, .

Here’s a diagram of the calculation to help you understand the process.

Calculating instantaneous rate of reaction. Anna Brewer, StudySmarter Originals

Chemical kinetics equations

We’ll now turn our attention to equations in chemical kinetics. These include:

• Differential equations
• Rate equations
• The Arrhenius equation

Differential equations and rate equations

Take the reactant A. We can represent its concentration using [A]. In mathematical terms, its change in concentration is the derivative of [A]: . But you’ll remember that rate of reaction is just the change in amount of reactants or products. Therefore, is simply a way of representing rate of reaction.

In chemical kinetics, we use differential equations to show how the rate of reaction, , depends on the concentration of A, [A], at a particular instant. One example of a differential equation that you do have to know is the rate equation.

We explored earlier how concentration affects the rate of a reaction. However, this effect isn’t always linear. Sometimes changing the concentration of a particular product has a small effect on the rate of a reaction. Sometimes it has a large effect, and sometimes it has no effect whatsoever. The rate equation links the concentrations of reactants with the rate of reaction using powers, called orders, and a rate constant, k. It typically takes the following form:

Note the following:

• k is the rate constant, a value that varies for each reaction.
• [A] represents the concentration of A.
• x represents the order of the reaction in respect to A.
• x + y equals the total order of the reaction.

The Arrhenius equation

We know that changing the concentration of some of the species involved in a reaction can change the rate of reaction. But how about the other factors that affect rate of reaction, such as temperature? These are all cleverly combined into the rate constant, k. However, k is only constant if you keep the temperature and catalyst the same. This is shown in the Arrhenius equation, which links k to several other factors.

Here’s what the Arrhenius equation looks like:

In this equation:

• k is the rate constant.
• A is the pre-exponential factor.
• e is Euler's number.
• Ea is the activation energy of the reaction you are studying.
• R is the gas constant, which you’ll also come across in the ideal gas law.
• T is the temperature.

Overall, the expression provides a rough approximation of how many particles within a gas meet the reaction’s activation energy at a certain temperature. (See Ideal Gas Law for more on this topic.)

Using this equation, we can clearly see how changing some of the conditions changes the rate of reaction. For example, increasing the temperature increases the value of , the number of particles that meet or exceed the activation energy of the reaction. This in turn makes k larger. Rate of reaction depends on k, so overall, the rate of reaction increases.

Applications of chemical kinetics

You can imagine that controlling the rate of a reaction has many different uses. For example, you might want to slow down the decay of a product or increase the rate of an industrial reaction. Chemical kinetics therefore has lots of applications. These include:

• Storage of drugs and pharmaceuticals to increase their shelf life.
• Adding preservatives to food to prevent it from going bad.
• Choosing the best catalyst for industrial processes.
• Deciding on the optimal temperature for baking biscuits and cakes.
• Radiocarbon dating.