A-level Chemistry/WJEC/Module 2/Rates

Chemical kinetics is the study of the rates of chemical reactions. You may know if a reaction is capable of happening, and you may know how far the reaction will proceed, but you don't know fast it will happen. Consider two reactions: the rusting of an iron nail and the combustion of propane. Both reactions will occur, and both will occur to completion. The rusting will take years to complete, but propane will combust in an instant. Furthermore, the nail will rust faster when it is moist, and slower in the presence of less oxygen. Obviously, there are factors that affect the rates of chemical reactions. The study of these factors and rates is chemical kinetics.

This iron wire has taken years to become rusty.
This fire took only a moment to start.

Reaction Rate

The reaction rate v measures the speed at which a reaction proceeds. The reaction rate is defined as the rate of change of the concentration of the substances.

The reaction rate can be measured by monitoring the decreasing concentration of a reactant, or the increasing concentration of a product.

In practical terms, v = change of chemical concentration ÷ time taken for the change

On a graph of concentration vs time, the rate of the reaction is represented by the gradient of the graph.

This is because the gradient of a graph = change of y / change of x. When we plot concentration on the y-axis and time on the x-axis, we make a graph where gradient = change of concentration / change of time = reaction rate

In the graph above, the rate (gradient) is not constant - that would be a straight line - so how do we measure the rate? We need to draw a tangent to the curve at the point we want to measure its gradient.

At the beginning of a reaction, we can get away with the "initial rate assumption" - if we measure the rate quickly, we can assume that (1) the concentrations have not changed significantly (even if we do measure the concentration changes to measure the rate!) and (2) the rate is constant i.e. on a graph we are looking at such a small part of the curve that we can treat it as a straight line.

In the example, the concentration falls from 2.50 to 2.05 mol dm^-3 in 10 minutes. This means we can estimate the rate is 0.045 mol dm^-3 min^-1 with the initial rate assumption.

Using a tangent to the graph, we would find the actual initial rate is 0.050 mol dm^-3 min^-1, so the initial rate assumption caused a 10 % error. This error might be acceptable, especially if we only need to compare reaction rates and the error is consistent.

In many cases, we set up experiments where the reaction reaches a specific point after a time:

The reaction mixture becomes so cloudy that a cross at the bottom of the container is no longer visible
Enough iodine is produced to turn the solution dark blue/black

Iodine clock reactions generate iodine after a while, and abruptly change colour.

We usually reckon, not only that;

v = change of chemical ÷ time taken for the change

But, because we designed the chemical change to be the same for each experiment;

v ∝ 1 ÷ time taken for the change (v is proportional to the time taken for the change)

Iodine clock reaction demonstrating the effect of different concentrations of the reactant hydrogen peroxide.

The clock reaction in the above video gives these results

Volume of peroxide (cm³)	Time taken (s)	v ∝ 1/time (s^-1)
10	52	0.019
15	35	0.029
20	26	0.038
25	22	0.045
30	18	0.056

Notice how the volume of peroxide is proportional to the 1/time value. Not only are we using 1/time as a value that is proportional to the reaction rate, but we are also using "volume of peroxide" to mean roughly "concentration of peroxide" - if the same concentration of stock peroxide is used in the mixture, and the total mixture volume is the same, then the volume will be proportional to the concentration. If it works, why make it more complicated?

Collision Theory

All reactions have activation energy regardless of being endothermic or exothermic.

Collision theory predicts that reactions occur when molecules collide. In order for reactants to form products, the reactant molecules must physically collide so that they can rearrange themselves into product molecules. Only some collisions are effective because the collision must involve enough energy to allow the reaction to occur. This is called activation energy, the energy needed to begin a reaction.

Activation energy explains why petrol will not spontaneously ignite. First, a small spark or flame must be present. The heat generated by the spark gives the petrol molecules (a mixture of small hydrocarbon molecules) enough energy to activate the reaction. Being highly exothermic, the combustion of petrol releases a large amount of heat — more than enough to activate further reactions and create a fire.

Factors Affecting Rate

The rate of a reaction is affected by many factors. These effects can be measured empirically or explained by collision theory.

Concentration

Increasing the concentration of the reactants will (almost always) increase the rate they react.

Collision theory explains this. Higher concentrations means more molecules packed into a given space. Therefore, there will be more collisions. More collisions mean more effective collisions (and also more ineffective collisions, but who cares about them?) and therefore products will form faster.

Pressure

In a reaction of gaseous reactants, the partial pressure of the gases has the same function as the concentration.

Adding an inert gas like argon will not affect the rate because the partial pressures of the reacting gases remain the same.

However, increasing the overall pressure (or decreasing the volume if you remember the gas laws) will also result in a greater reaction rate. The increased pressure causes the molecules to collide more frequently. More collisions mean that products will form faster.

Surface Area and Stirring

In a heterogeneous reaction there are two or more phases of matter interacting, such as a solid dissolving into a liquid, or two immiscible liquids such as oil and water. The reaction can only occur at the interface between the two phases.

Increasing the surface area of the interface will increase the reaction rate. This might be by breaking up a solid reactant into smaller pieces, or by emulsifying an oily liquid into tiny droplets so it can react with an aqueous solution.

The concentrations at the interface will change rapidly - reactants are depleted and products accumulate. There might still be plenty of reactant in the rest of the mixture, so stirring or shaking the mixture will speed up the reaction rate.

There are a lot of links here with the biological process of digestion. Many aspects of digestion are breaking up food into smaller pieces (e.g. chewing, emulsification of fats by bile salts).

The factors above only affect the number of collisions. The last two factors (below) also affect the energy in each collision:

Catalysts

A catalyst is a substance that helps a reaction proceed without being consumed. A catalyst provides a reaction pathway with lower activation energy.

In biochemistry, an enzyme is a protein that serves as a catalyst.

Temperature

As you should already know, a molecule's kinetic energy is directly proportional to its temperature. By increasing the temperature, molecules collide more vigorously, and therefore more collisions will exceed E_a and be effective.

Increasing the speed of the particles also increases the number of collisions. This effect is not as important as the increase in average energy.

The Maxwell-Boltzmann Distribution

In the 19th century, James Clerk Maxwell and Ludwig Boltzmann developed a theoretical understanding of how temperature affects the speeds and energies of particles in a gas. The Maxwell-Boltzmann distribution is a graph of the number of particles (or the probability of one particle) across a range of possible speeds or energies.

Energy depends on speed and mass, and it is simplest to use Maxwell-Boltzmann energy distributions because they are the same for any gas particles, regardless of the mass. Maxwell-Boltzmann energy distributions are also simpler to relate to the activation energy of the reaction, and the effect of catalysts.

Key features of the curve are:

The proportion of particles with zero energy is zero.
The proportion of particles with higher energies tends towards zero but never actually reaches zero. (This is similar to the quantity of radioisotopes left after each half life - ¹/₂, ¹/₄, ¹/₈, ¹/₁₆, etc, but never actually reaching zero.)

Make sure you clearly show both these features if you are asked to draw the curve.

At higher temperature, the curve stretches to the right. The area under the curve represents the total number of particles, which is constant. If the curve stretches to the right then it must also be compressed from the top - this keeps the total area constant.

The mode changes position at higher temperature; The mode moves to a higher energy but a lower probability as the energies of the particles spread out to higher values. The mode of the energy is proportional to the temperature, and the probability is inversely proportional to temperature. Heating from 300 K to 600 K for example, the mode moves from 2.5 to to 5.0 kJ mol^-1. The proportion of particles at the energy of the mode falls from 14.75 % to 7.374 %.

Again, make sure you show the correct changes if you have to draw a curve at a higher or lower temperature; Increased temperature moves the mode to the right and makes it lower.

The proportion of particles which have a greater energy than E_a is shown on the Maxwell-Boltzmann energy distribution as the area under the curve to the right of the E_a value. As the temperature increases, there is a higher proportion of particles that have a greater energy than E_a.

Catalysts work by lowering the activation energy. If the E_a value moves to a lower value to the left on the graph, this indicates that there will be a greater number of particles which are able to react.