01 Reaction Rates 2009

THE COLLISION THEORY OF REACTION RATES Introduction These pages describe the collision theory of reaction rates. They cover collision theory, and describe and explain the individual factors which affect the rate of a reaction that is surface area, concentration, pressure, temperature and catalysts on reaction rates. The first part concentrates on the key things which decide whether a particular collision will result in a reaction - in particular, the energy of the collision, and whether or not the molecules hit each other the right way around (the orientation of the collision).We are going to look in detail at reactions which involve a collision between two species. Reactions involving collisions between two species It is pretty obvious that if you have a situation involving two species they can only react together if they come into contact with each other. They first have to collide, and then they may react. Why "may react"? It isn't enough for the two species to collide - they have to collide the right way around, and they have to collide with enough energy for bonds to break. The orientation of collision Consider a simple reaction involving a collision between two molecules - ethene, CH2=CH2, and hydrogen chloride, HCl, for example. These react to give chloroethane.

As a result of the collision between the two molecules, the double bond between the two carbons is converted into a single bond. A hydrogen atom gets attached to one of the carbons and a chlorine atom to the other. The reaction can only happen if the hydrogen end of the H-Cl bond approaches the carboncarbon double bond. Any other collision between the two molecules doesn't work. The two simply bounce off each other. Of the collisions shown in the diagram, only collision 1 may possibly lead on to a reaction. You may wonder why collision 2 won't work as well. The double bond has a high concentration of negative charge around it due to the electrons in the bonds. The approaching chlorine atom is also slightly negative because it is more electronegative than hydrogen. The repulsion simply causes the molecules to bounce off each other. In any collision involving unsymmetrical species, you would expect that the way they hit each other will be important in deciding whether or not a reaction happens.

The energy of the collision Activation Energy Even if the species are orientated properly, you still won't get a reaction unless the particles collide with a certain minimum energy called the activation energy of the reaction. Activation energy is the minimum energy required before a reaction can occur. You can show this on an energy profile for the reaction. It looks like this:

The state of maximum energy of the system is called the activated complex or its transition state. For a simple over-all exothermic reaction (the products are less energetic than the reactants), energy is released as heat or eventually light. The only difference if the reaction was endothermic would be the relative positions of the reactants and products lines. For an endothermic change, the products would have a higher energy than the reactants, and so the green arrow would be pointing upwards. It makes no difference to the discussion about the activation energy. If the particles collide with less energy than the activation energy, nothing important happens. They bounce apart. You can think of the activation energy as a barrier to the reaction. Only those collisions which have energies equal to or greater than the activation energy result in a reaction. The Maxwell-Boltzmann Distribution Because of the key role of activation energy in deciding whether a collision will result in a reaction, it would obviously be useful to know what sort of proportion of the particles present have high enough energies to react when they collide. In any system, the particles present will have a very wide range of energies. For gases, this can be shown on a graph called the Maxwell-Boltzmann Distribution which is a plot of the number of particles having each particular energy.

The area under the curve is a measure of the total number of particles present. The reason for this lies in some maths that you will learn at the end of this year. It is important that you remember that the area under the curve gives a count of the number of particles even if you don't understand why! The Maxwell-Boltzmann Distribution and activation energy Remember that for a reaction to happen, particles must collide with energies equal to or greater than the activation energy for the reaction. We can mark the activation energy on the Maxwell-Boltzmann distribution:

Notice that the large majority of the particles don't have enough energy to react when they collide. To enable them to react we either have to change the shape of the curve, or move the activation energy further to the left.

THE EFFECT OF SURFACE AREA ON REACTION RATES

The facts: What happens? The more finely divided the solid is, the faster the reaction happens. A powdered solid will normally produce a faster reaction than if the same mass is present as a single lump. The powdered solid has a greater surface area than the single lump. Some examples Calcium carbonate and hydrochloric acid In the lab, powdered calcium carbonate reacts much faster with dilute hydrochloric acid than if the same mass was present as lumps of marble or limestone.

Catalytic converters Catalytic converters use metals like platinum, palladium and rhodium to convert poisonous compounds in vehicle exhausts into less harmful things. For example, a reaction which removes both carbon monoxide and an oxide of nitrogen is:

Because the exhaust gases are only in contact with the catalyst for a very short time, the reactions have to be very fast. The extremely expensive metals used as the catalyst are coated as a very thin layer onto a ceramic honeycomb structure to maximise the surface area. The explanation You are only going to get a reaction if the particles in the gas or liquid collide with the particles in the solid. Increasing the surface area of the solid increases the chances of collision taking place. Imagine a reaction between magnesium metal and a dilute acid like hydrochloric acid. The reaction involves collision between magnesium atoms and hydrogen ions.

Increasing the number of collisions per second increases the rate of reaction.

THE EFFECT OF CONCENTRATION ON REACTION RATES

The facts: What happens? For many reactions involving liquids or gases, increasing the concentration of the reactants increases the rate of reaction. In a few cases, increasing the concentration of one of the reactants may have little noticeable effect of the rate. These cases are discussed and explained further. Don't assume that if you double the concentration of one of the reactants that you will double the rate of the reaction. It may happen like that, but the relationship may well be more complicated. Some examples The examples on this page all involve solutions. Changing the concentration of a gas is achieved by changing its pressure. Zinc and hydrochloric acid: In the lab, zinc granules react fairly slowly with dilute hydrochloric acid, but much faster if the acid is concentrated.

The catalytic decomposition of hydrogen peroxide: Solid manganese (IV) oxide is often used as a catalyst in this reaction. Oxygen is given off much faster if the hydrogen peroxide is concentrated than if it is dilute.

The explanation Collisions involving two particles In order for any reaction to happen, particles must first collide. This is true whether both particles are in solution, or whether one is in solution and the other a solid. If the concentration is higher, the chances of collision are greater. Reactions involving only one particle If a reaction only involves a single particle splitting up in some way, then the number of collisions is irrelevant. What matters now is how many of the particles have enough energy to react at any one time. Suppose that at any one time 1 in a million particles have enough energy to equal or exceed the activation energy. If you had 100 million particles, 100 of them would react. If you had 200 million particles in the same volume, 200 of them would now react. The rate of reaction has doubled by doubling the concentration.

Cases where changing the concentration doesn't affect the rate of the reaction At first glance this seems very surprising but in certain multi-step reactions in fact it is so. Suppose you have a reaction which happens in a series of small steps. These steps are likely to have widely different rates - some fast, some slow. For example, suppose two reactants A and B react together in these two stages:

The overall rate of the reaction is going to be governed by how fast A splits up to make X and Y. This is described as the rate determining step of the reaction. If you increase the concentration of A, you will increase the chances of this step happening for reasons we've looked at above. If you increase the concentration of B, that will undoubtedly speed up the second step, but that makes hardly any difference to the overall rate. You can picture the second step as happening so fast already that as soon as any X is formed, it is immediately pounced on by B. That second reaction is already "waiting around" for the first one to happen. THE EFFECT OF PRESSURE ON REACTION RATES

The facts: What happens? Increasing the pressure on a reaction involving reacting gases increases the rate of reaction. Changing the pressure on a reaction which involves only solids or liquids has no effect on the rate. An example In the manufacture of ammonia by the Haber Process, the rate of reaction between the hydrogen and the nitrogen is increased by the use of very high pressures.

In fact, the main reason for using high pressures is to improve the percentage of ammonia in the equilibrium mixture, but there is a useful effect on rate of reaction as well. The explanation The relationship between pressure and concentration Increasing the pressure of a gas is exactly the same as increasing its concentration. If you have a given mass of gas, the way you increase its pressure is to squeeze it into a

smaller volume. If you have the same mass in a smaller volume, then its concentration is higher. You can also show this relationship mathematically if you have come across the ideal gas equation: Because "RT" is constant as long as the temperature is constant, this shows that the pressure is directly proportional to the concentration. If you double one, you will also double the other. The effect of increasing the pressure on the rate of reaction The same argument applies whether the reaction involves collision between two different particles or two of the same particle. In order for any reaction to happen, those particles must first collide. This is true whether both particles are in the gas state, or whether one is a gas and the other a solid. If the pressure is higher, the chances of collision are greater.

Reactions involving only one particle Suppose that at any one time 1 in a million particles have enough energy to equal or exceed the activation energy. If you had 100 million particles, 100 of them would react. If you had 200 million particles in the same volume, 200 of them would now react. The rate of reaction has doubled by doubling the pressure. THE EFFECT OF TEMPERATURE ON REACTION RATES

The facts: What happens? As you increase the temperature the rate of reaction increases. As a rough approximation, for many reactions happening at around room temperature, the rate of reaction doubles for every 10°C rise in temperature. You have to be careful not to take this too literally. It doesn't apply to all reactions. Even where it is approximately true, it

may be that the rate doubles every 9°C or 11°C or whatever. The number of degrees needed to double the rate will also change gradually as the temperature increases. Examples Some reactions are virtually instantaneous - for example, a precipitation reaction involving the coming together of ions in solution to make an insoluble solid, or the reaction between hydrogen ions from an acid and hydroxide ions from an alkali in solution. So heating one of these won't make any noticeable difference to the rate of the reaction. Almost any other reaction you care to name will happen faster if you heat it either in the lab, or in industry. The explanation Increasing the collision frequency Particles can only react when they collide. If you heat a substance, the particles move faster and so collide more frequently. That will speed up the rate of reaction. That seems a fairly straightforward explanation until you look at the numbers! It turns out that the frequency of two-particle collisions in gases is proportional to the square root of the Kelvin temperature. If you increase the temperature from 293 K to 303 K you will increase the collision frequency by a factor of just 1.7% for a 10° rise. The rate of reaction will probably have doubled for that increase in temperature - in other words, an increase of about 100%. The effect of increasing collision frequency on the rate of the reaction is very minor. The important effect is quite different. The key importance of activation energy Collisions only result in a reaction if the particles collide with enough energy to get the reaction started. This minimum energy required is called the activation energy for the reaction. You can mark the position of activation energy on a Maxwell-Boltzmann distribution to get a diagram like this:

Only those particles represented by the area to the right of the activation energy will react when they collide. The great majority doesn't have enough energy, and will simply bounce apart. To speed up the reaction, you need to increase the number of the very

energetic particles - those with energies equal to or greater than the activation energy. Increasing the temperature has exactly that effect - it changes the shape of the graph. In the next diagram, the graph labelled T is at the original temperature. The graph labelled T+t is at a higher temperature.

If you now mark the position of the activation energy, you can see that although the curve hasn't moved very much overall, there has been such a large increase in the number of the very energetic particles that many more now collide with enough energy to react.

Remember that the area under a curve gives a count of the number of particles. On the last diagram, the area under the higher temperature curve to the right of the activation energy looks to have at least doubled - therefore at least doubling the rate of the reaction. Summary Increasing the temperature increases reaction rates because of the disproportionately large increase in the number of high energy collisions. It is only these collisions (possessing at least the activation energy for the reaction) which result in a reaction.

THE EFFECT OF CATALYSTS ON REACTION RATES

The facts: What are catalysts? A catalyst is a substance which speeds up a reaction, but is chemically unchanged at the end of the reaction. When the reaction has finished, you would have exactly the same mass of catalyst as you had at the beginning. Some examples Some common examples which you may need for other parts of your syllabus include: reaction

catalyst

Decomposition of hydrogen peroxide

manganese(IV) oxide, MnO2

Conversion of SO2 into SO3 to make sulphuric acid

vanadium(V) oxide, V2O5

Hydrogenation of a C=C double bond

nickel

Manufacture of ammonia by the Haber Process

iron

The explanation The key importance of activation energy Collisions only result in a reaction if the particles collide with enough energy to get the reaction started. This minimum energy required is called the activation energy for the reaction. You can mark the position of activation energy on a Maxwell-Boltzmann distribution to get a diagram like this:

Only those particles represented by the area to the right of the activation energy will react when they collide. The great majority doesn't have enough energy, and will simply bounce apart. Catalysts and activation energy To increase the rate of a reaction you need to increase the number of successful collisions. One possible way of doing this is to provide an alternative way for the reaction to happen which has a lower activation energy. In other words, to move the activation energy on the graph this way:

Adding a catalyst has exactly this effect on activation energy. A catalyst provides an alternative route for the reaction. That alternative route has a lower activation energy. Showing this on an energy profile:

PROBLEMS ON REACTION RATES 1- The graph shows three curves for the thermal self decomposition of hydrogen peroxide. a- Write a word and a balanced equation for this reaction. b- Why are transition metal oxides added? c- Which oxide seems to be most effective? d- When did the reaction finished? e- How should the curve for manganese (IV) oxide look if the temperature were raised? f- Sketch the three curves if instead of measuring the volume of oxygen formed, the mass of the system was continuously recorded by setting the open flask on a top balance. g- This is an exothermic reaction. Sketch an energy-reaction course diagram for the three experiments using the same pair of axes. 2- A similar experiment to the one with manganese (IV) oxide was carried out but at a higher temperature. The data are shown in the table below. Time (min) 1 2 3 4 5 6 7 8 0 Vol. of gas (cm3) 4 6 9 10 11 12 12 120 0 0 5 2 7 5 0 0 abcdefg-

Plot the data. Which point doesn’t fit properly with the rest of the set? Which could be a reasonable value for it? How would you check your answer to c? What will be the reading at time 9 minutes? Why? How long did it take to 50 cm3 of oxygen to be produced? Explain how and why the rate of reaction changed as it proceeded.

3- The figure shows diagrams for two different reactions. a- Are the reactions endo or exothermic? b- Is there any endothermic process in the diagrams? c- Name all labels from 1 through 8 d- Show the activation energies. e- Mark the energy exchanged with the environment.

4- The reaction between hydrochloric acid and marble (calcium carbonate essentially) was studied under different conditions. Experiment Acid Size of marble Temperature concentr. A 5% Chips 20°C B 10% Powder 60°C C 10% Chips 20°C D 5% Powder 60°C abcd-

Write the balanced equation for this reaction Sketch two different apparatus, suitable for carrying out this experiment Sketch the curves you would expect for each of the two apparatuses Decide in which the reaction was the fastest and in which the slowest. Give reasons for your answer e- Which would you expect to be the third one? Are you 100% sure about your choice? 5- The self decomposition of substance X is a relatively slow two step exothermic reaction in which a gas is formed. The first step is the most difficult (rate determining) step. a- Sketch an “energy- reaction course” plot for it b- Sketch a plot to show how the mass of the reactants changes during the reaction if it is carried out in an open flask. c- A small amount of nickel catalyses the reaction. Show the effect of nickel in both graphs. d- Label the axes for the graph shown. e- Explain the three shadowed zones in the sketch at the right of the page if they refer to the reaction with and without the addition of nickel