Collision theory & rates of reaction
6.1 Collision theory & rates of reaction (7 hours)
Pause for thought
Although students know the factors that affect the rate of a chemical reaction, it is very noticeable when marking the answers to Paper 2 questions that when they are asked to define the term rate of reaction many of the answers show a woeful ignorance. The whole of Topic 6 depends upon understanding exactly what is meant by the term and how it can be applied and measured. The basic definition is that the rate of a chemical reaction is the increase in concentration of one of the products per unit time or the decrease in one of the reactants per unit time. The normal units are therefore mol dm-3 s-1. The problem is that the rate of a reaction changes as the reaction proceeds. This is because it depends upon the concentration of the reactants and this concentration is continually changing as the reactants are used up. To explain this it is useful to refer to graphs of change of concentration of products or reactants against time. The rate at time t can then be seen to be the gradient of the graph at that specified time. Probably the most useful rate is the initial rate as the initial concentration at time t = 0 will be known.
The diagram above shows the graphs obtained by following the rate of reaction between a metal carbonate and a mineral acid. In the first graph the volume of carbon dioxide evolved is plotted against time, in the second graph the loss in mass as the carbon dioxide is evolved from the reaction mixture is plotted against time. Practical details for these two methods are described in the practical Reaction rates.
Many books and teachers claim that increasing the temperature by 10 oC (10 K) will double the rate of the reaction. This is a useful 'rule of thumb' but that is all it is. In fact it works reasonably well when the temperature increases from 298 K to 308 K for typical reactions in which the activation energy is about 50 kJ mol-1 (50000 J mol-1) This can be shown by substituting into the Arrhenius equation and finding the values of the rate constant, k. Since the concentrations of the reactants remain constant and only the temperature is altered then the rate is directly proportional to the rate constant.
At 298 K: k298 = Ae-Ea/RT = Ae-50000/(8.314 x 298) = 1.72 x 10-9 A
At 308 K: k308 = Ae-Ea/RT = Ae-50000/(8.314 x 308) = 3.31 x 10-9 A
By increasing the temperature by 10 oC the rate constant has increased by 3.31 x 10-9 A / 1.72 x 10-9 A which amounts to 1.92 so effectively the rate has nearly doubled.
However if the activation energy is higher or lower than 50 kJ mol-1 then the ratio of the two rate constants changes considerably. For example, if the activation energy is 100 kJ mol-1 (100000 J mol-1) then by doing a similar calculation it can be shown that increasing the temperature from 298 K to 308 K increases the rate by 3.71 (i.e. nearly four times).
Because changes in temperature can have such an effect on the rate of a reaction it is important for students to understand how to use a water bath (left) to maintain a constant temperature when designing an experiment where temperature is a controlled variable.
Another misconception sometimes taught is why increasing the temperature increases the rate of a reaction. It is sometimes claimed that one of the major factors is due to an increase in the number of collisions and hence an increase in rate. It is true that there will be more collisions at higher temperatures but what is much more important is not the number of collisions but the number of successful collisions. Most collisions do not lead to a reaction and it has been estimated that the increased number of collisions due to increasing the temperature only accounts for about 10% of the increase in rate. The dominant factor affecting the rate is that the number of reactants particles that possess at least the minimum activation energy increases. As this number increases exponentially with temperature rise (see the Maxwell-Boltzmann curve) it is by far the most important factor.
Nature of science
Collision theory is a good example of the principle of Occam’s razor. This is used as a guide to developing collision theory based on current atomic models even though we cannot directly see reactions taking place at the molecular level.
Learning outcomes
After studying this topic students should be able to:
Understand
- Reactions occur as a result of collisions between species that have sufficient energy and the correct orientation.
- Rate of reaction is expressed as the change in concentration of a particular reactant or product per unit time.
- The changes in concentration that occur during a reaction can be followed indirectly by monitoring changes in mass, volume or colour.
- The activation energy, Ea, is the minimum energy required by colliding molecules in order to react.
- A catalyst increases the rate of a chemical reaction by providing an alternative pathway with a lower activation energy, Ea, without itself being permanently changed chemically.
Apply their knowledge to:
- Describe kinetic theory in terms of the movement of particles whose average kinetic energy is proportional to temperature measured in Kelvin.
- Analyse graphical and numerical data from rate experiments.
- Explain the effects of temperature, pressure or concentration and particle size on the rate of reaction.
- Construct Maxwell–Boltzmann energy distribution curves to account for the probability of successful collisions leading to a reaction and factors affecting these, including the effect of a catalyst.
- Investigate rates of reaction experimentally and evaluate the results.
- Sketch and explain energy profiles with and without catalysts.
Clarification notes
The calculation of reaction rates from tangents of graphs of concentration, volume or mass plotted against time is required.
Students should be able to interpret graphs of changes in concentration, volume or mass plotted against time.
International-mindedness
The catalytic action of CFCs is largely responsible for the depletion of stratospheric ozone and this is of particular concern in the polar regions. These chemicals are released from a variety of countries and sources, so global cooperation has been needed (e.g. The Montreal Protocol) to lower the amount of ozone depletion.
Teaching tipsIt is worth starting this topic by building on what students already know. Ask them what factors affect the rate of a chemical reaction and you are likely to get the correct answers: concentration, particle size (or surface area), temperature and a suitable catalyst. You might also like to add light for some reactions (see the flash photolysis video in extra resources below). If you then ask what is meant by rate of reaction you may well find that students cannot answer this (see Pause for thought above). I then try to draw it out of them by discussion to arrive at a correct definition involving change of concentration of reactant (or product) divided by time. Emphasise that the rate changes during the reaction and the actual rate depends upon the particular time at which it is measured. Stress the units of rate. This then leads to a discussion as to how the rate can be determined. Essentially concentration (or a property related to it) needs to be measured over time, a graph plotted and the gradient taken at time t. Ask students to suggest how the concentration of a particular reactant or product could be followed. Hopefully they will make suggestions such as: change in volume of a gas, change in pH, change in colour, change in mass (if a gas is released) etc. and you can fill them in on other less obvious ways such as change in conductivity. You can then get them to sketch the type of graph they would expect for change in both a reactant and a product. By taking tangents they can see that the initial rate will be the fastest and the rate decreases as the reactant concentration diminishes until eventually the rate is zero when the reaction reaches completion. All of this can then be backed up by suitable experiments e.g. the iodine clock, acid with a carbonate or thiosulfate with acid. Collision theory seems to depend very much on 'common sense'. You can actually get students to deduce most of the theory for themselves except for the Maxwell-Boltzmann curve. I start by getting them to understand the kinetic theory of matter so they have the idea of particles moving in rapid random motion then get them to suggest what the necessary conditions will be for a reaction to occur. They should understand that just colliding is not enough, the particles need to collide with the right orientation and with sufficient energy to overcome what is called the activation energy. For surface area I get them to calculate the surface area of a cube with sides of 2 metre. By making three equal cuts they will see that they now have eight cubes with sides of one metre each and the surface area has doubled from 24 m2 to 48 m2. An increase in both concentration and pressure means more particles in a given volume hence more collisions and increasing the temperature means the particles are moving faster and hence will collide more frequently. They should understand what happens to the shape of the Maxwell-Boltzmann curve when the temperature is increased. The curve shifts to the higher energy end, the maximum is lower and broader and the area under the curve remains constant as the number of particles has not changed. Stress that at higher temperatures more particles will possess the necessary activation energy and this is the main reason why increasing the temperature increases the rate (see Pause for thought above). This graph can also be used to explain how catalysts work as more particles will contain the lower activation energy associated with the catalysed pathway. | Study guide
Page 47 - 48 QuestionsFor ten 'quiz' multiple choice questions with the answers explained see MC test: Collision theory & rates of reaction. For short-answer questions on collision theory which can be set as an assignment for a test, homework or given for self study together with model answers see Collision theory questions. For short-answer questions on rates of reaction which can be set as an assignment for a test, homework or given for self study together with model answers see Rates of reaction questions. Vocabulary listkinetic theory IM, TOK, Utilization etc.See separate page which covers all of Topic 6 Practical work
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Teaching slides
Teachers may wish to share these slides with students for learning or for reviewing key concepts.
Collision theory & rates of reaction:
Collision theory & rates of reaction:
Collision theory & rates of reaction:
Collision theory & rates of reaction:
Collision theory & rates of reaction:
Collision theory & rates of reaction:
Collision theory & rates of reaction:
Collision theory & rates of reaction:
Collision theory & rates of reaction:
Other resources
1. An animated video to show the importance of collision theory by Richard Thornley.
2. You can find several videos showing the effect of surface area on rate e.g. exploding flour and lycopodium powder in a flame. Here is one which I'm sure your students could do for themselves and not leave a mess on the floor!
3. A good video produced by Carleton University, Ottawa to illustrate that the enthalpy of reaction gives no information about how fast a reaction will proceed. It uses two examples with very similar enthalpy values (the rusting of iron and the Thermite reaction) that proceed at very different rates.
4. The IB includes the effects of concentration, temperature, surface area and a catalyst on the rate of a reaction but some reactions are also affected by light. Also, how do you measure the rate of very fast reactions in a laboratory? This video gives a good explanation of the technique of flash photolysis and provides a sophisticated example of the use of data logging.