Rate of Reaction and Temperature

Relationship between rate of reaction and temperature

To understand the relationship between the rate of reaction and temperature, we need to first define what the rate of reaction is. We then need to understand the general principle behind the rate of any reaction: collision theory.

Rate of reaction

Collision theory

Collision theory dictates that a successful reaction requires a collision between two particles. However, not all collisions result in a reaction. The particles must first be pointed in the correct direction. They must secondly meet with enough energy to break the original bonds within them.

Now, let's find out how temperature affects the rate of any reaction according to the principles of collision theory.

Rate of reaction, collision theory, and temperature

The effect of reaction rate with the increase in temperature can be explained by collision theory in two ways:

• An increase in temperature increases the average speed of particles.
• An increase in temperature increases the average kinetic energy of particles.

An Increase in the above two phenomena increases the number of collisions per second.

Fig. 1: The behaviour of particles at the start and the increase in temperature, StudySmarter originals

Have a look at the above figures. Figure 1 illustrates the behaviour of particles at the temperature at which a chemical reaction started (can be termed as initial temperature). The length of the arrows in both figures represents the kinetic energy of the particles. Notice that in Fig-1, only a very few particles have enough kinetic energy to participate in the reaction.

Figure 2, on the other hand, illustrates the behaviour of the particles after an increase in temperature. Notice the increase in the length of arrows representing an increase in speed, or you could say the kinetic energy of particles. More number of particles in figure-2 have sufficient energy to collide and cause a reaction (provided they are in the correct orientation). The encircled particles in both the figures are in the correct orientation and have sufficient energy to collide.

Thus, from collision theory, we can conclude that the rate of reaction is directly proportional to temperature.

The next question that arises is- How do we know the minimum energy required for particles to undergo collisions?

This question can be answered by the Maxwell-Boltzmann distribution curve.

Maxwell-Boltzmann distribution curve

The Maxwell-Boltzmann distribution shows us the distribution of energies of particles in a gas at a constant temperature. It gives us information about how many particles have low energy, moderate energy and energy higher than the activation energy.

Fig. 2: Maxwell-Boltzmann distribution curve showing the distribution of energies of particles, StudySmarter Originals

Based on the above Maxwell-Boltzmann distribution curve, we can deduce the following:

• The area under the curve is the total number of particles
• Activation energy- The minimum amount of energy required for particles to collide for the reactions to occur is called activation energy. Observe the portion in the graph marked in yellow. It represents the number of particles which achieved the milestone of activation energy. Notice that the portion is tiny as compared to the total area under the graph. It means that only a few particles have energy enough for collisions to occur.
• No particles have zero energy
• The peak of the curve- Most probable energy: Most of the particles have this particular energy

Let us now understand what happens when we increase the temperature.

Fig. 3: Maxwell-Boltzmann curve after increase in temperature, StudySmarter originals

Observe the two curves in the above graph. The curve in blue is the energy of particles at a certain temperature when the reaction started. The curve in pink is the energy of particles after we increase the temperature. The curve in pink shifted to the right.

What does it mean?

In simple terms, the number of particles that meet or overcome the milestone of activation energy (Ea) is increased. This means that you can expect more collisions which helps the reaction to occur at a faster pace. Thus, we can deduce that an increase in temperature increases the rate of a reaction.

Also, notice that, from the graph, the area under both curves is the same, that is the total number of particles remains the same. We are not bringing in any new particles, or the number of particles will not increase with the increase in temperature. Only the number of particles that can surpass or meet the activation energy will increase. For example, if the total number of particles is 100, it is always going to be 100. At the start of the reaction, maybe 25 particles would have enough energy to collide (meet or exceed the Ea). However, when you increase the temperature, out of the same 100 particles, now 50 particles will meet or exceed the Ea.

You might want to know about the other energies represented in the Maxwell-Boltzmann distribution curve-such as the average kinetic energy of particles, most probable energy and a deep dive into activation energy, head over to this article- Maxwell-Boltzmann Distribution. In the same article, we will also explain to you the other factors that increase the rate of a reaction-Catalyst and Concentration.

Method and expriment for temperature and rate of reaction

Through an experiment, we can see for ourselves the effects of temperature on the rate of a chemical reaction: increasing the temperature of a chemical system increases its rate of reaction.

You can use a variety of different experiments to justify this statement. Here, we'll consider the reaction between sodium thiosulfate and hydrochloric acid.

The reaction goes something like this:

$$ Na_2S_2O_3 + 2HCl \rightarrow 2NaCl + S + SO_2 + H_2O $$

The reactants are transparent. They produce a cloudy suspension of solid sulfur, which is much more opaque. We can use the opacity of the system as an indicator of the time it takes for the reaction to go to completion, and then repeat the process at different temperatures. This allows us to compare the rate of the reaction as we vary the temperature.

Equipment

For this experiment, you'll need:

• 0.05 mol dm^-3 solution of sodium thiosulfate.
• 1.0 mol dm^-3 Hydrochloric acid.
• 2 graduated cylinders.
• 1 conical flask.
• Bunsen burner or 400cm³ water bath.
• Thermometer.
• Stopwatch.
• Piece of paper.
• Hot plates.

Method

Here's how you carry out the experiment:

1. Measure 100 cm³ of sodium thiosulfate solution in a graduated cylinder, and pour it in the conical flask.
2. On a piece of paper, draw an X mark and place the conical flask on the paper so that you can see the mark through the flask.
3. Measure 10 cm³ of hydrochloric acid in the other graduated cylinder and pour it in the conical flask.
4. Give the flask a swirl and quickly start the stopwatch.
5. Observe the mark through the flask.
6. When you can no longer see the mark through the flask, stop the stop watch and note the time. This is the time taken for the reaction to go to completion.
7. Note the room temperature on the thermometer.
8. Enter the time next to the temperature in a notebook.
9. Throw away the contents of the flask and wash it.
10. Repeat the experiment multiple times at different temperatures [ For example: (Room temp + 20)°C, (T+ 30)°C, (T+40°C) ]
11. Use the hot plate to heat sodium thiosulfate solution and hydrochloric acid separately, then mix it and note the time. Alternatively, you can use a water bath.

Fig. 4: Experiment to observe effects of temperature on rate of reaction | Turton School

Effect of temperature on rate of reaction: graph

After this experiment, you will have a table of the time taken for the reaction to go to completion, and the temperature at which the reaction took place. You can calculate the rate of the reaction by taking the reciprocal of time.

$$ reaction~rate = \frac{1}{time~taken~by~the~reaction~to~complete} $$

If you plot the rate and time of the reaction against the temperature, you'll get graphs something like this -

Fig. 5: Graphs representing the effect of temperature on reaction time and rate, StudySmarter originals

From the graphs, we can see two things.

• As temperature increases, the time taken for the reaction to go to completion decreases.
• This means that as temperature increases, the rate of reaction increases.

We now know from collision theory and the sodium thiosulphate experiment, that the rate of reaction increases with the increase in temperature.