What is the “rate" of a reaction?

1. What is the “rate" of a reaction? • The rate of a reaction is the speed of the reaction. It is not “how much” of a product is made, but instead “how quickly” a reaction takes place.

2. How can we measure the rate? • If we consider a reaction zinc + hydrochloric acid —> zinc chloride + hydrogen • then there are two possible ways of measuring the rate: 1) measure how quickly one of the products (e.g. the hydrogen) is made2) measure how quickly one of the reactants (e.g. the zinc) disappears • So we could, for example, measure the volume (in ml.) of hydrogen made every 10 seconds or the loss in mass (of the zinc and hydrochloric acid as they change into hydrogen gas escaping from a beaker) every 10 seconds.

3. Measuring a rate of reaction • There are several simple ways of measuring a reaction rate. • For example, if a gas was being given off during a reaction, you could take some measurements and work out the volume being given off per second at any particular time during the reaction. • A rate of 2 cm3 s-1 is obviously twice as fast as one of 1 cm3 s-1. Note:  Read cm3 s-1 as "cubic centimetres per second".

4. Measuring a rate of reaction • However, for this more formal and mathematical look at rates of reaction, the rate is usually measured by looking at how fast the concentration of one of the reactants is falling at any one time. • For example, suppose you had a reaction between two substances A and B. Assume that at least one of them is in a form where it is sensible to measure its concentration - for example, in solution or as a gas. • For this reaction you could measure the rate of the reaction by finding out how fast the concentration of, say, A was falling per second.

5. Measuring a rate of reaction • You might, for example, find that at the beginning of the reaction, its concentration was falling at a rate of 0.0040 mol dm-3 s-1. • This means that every second the concentration of A was falling by 0.0040 moles per cubic decimetre. This rate will decrease during the reaction as A gets used up. Note:  Read mol dm-3 s-1 as "moles per cubic decimetre (or litre) per second".

6. Reactions involving collisions between two species Two species (molecule, ion, or free radical) can only react together if they come into contact with each other. They first have to collide, and then they may react.

7. 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.

8. ineffective collisions Reactions usually require collisions between reactant molecules or atoms. The formation of bonds requires atoms to come close to one another. New bonds can form only if the atoms are close enough together to share electrons. Some collisions are not successful. These are called ineffective collisions. The particles simply hit and then rebound. This animation illustrates what happens in an ineffective collision.

9. effective collisions Collisions that lead to products are called effective collisions. An effective collision must happen with a great enough speed, energy and force to break bonds in the colliding molecules. The animation illustrates an effective collision between two diatomic molecules. The two product molecules formed fly outwards.

10. Reactions involving collisions more than two species All three (or more) particles would have to arrive at exactly the same point in space at the same time, with everything lined up exactly right, and having enough energy to react. That's not likely to happen very often

11. The orientation of collision 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.

12. The orientation of collision Of the collisions shown in the diagram, only collision 1 may possibly lead on to a reaction.

13. The orientation of collision 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 moreelectronegative than hydrogen. The repulsion simply causes the molecules to bounce off each other.

14. Proper Orientation of the colliding molecules

15. The energy of the collision 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.

16. Activation Energy You can show this on an energy profile for a simple over-all exothermic reaction, the energy profile looks like this: It is the minimum energy required before a reaction can occur.

17. Activation Energy

18. Activation Energy You can think if the particles collide with less energy than the activation energy, nothing important happens. They bounce apart. Only those collisions which have energies equal to or greater than the activation energy result in a reaction.

19. Activation Energy Any chemical reaction results in the breaking of some bonds (needing energy) and the making of new ones (releasing energy). Obviously some bonds have to be broken before new ones can be made. Activation energy is involved in breaking some of the original bonds. Where collisions are relatively gentle, there isn't enough energy available to start the bond-breaking process, and so the particles don't react.

20. Activation Energy

21. 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.

22. The Maxwell-Boltzmann Distribution 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.

23. The Maxwell-Boltzmann Distribution The area under the curve is a measure of the total number of particles present.The graph only applies to gases, but the conclusions that we can draw from it can also be applied to reactions involving liquids.

24. 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:

25. 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. You can change the shape of the curve bychanging the temperatureof the reaction. You can change the position of the activation energy byadding a catalystto the reaction.

26. THE EFFECT OF SURFACE AREA ON REACTION RATES This effect applies to reactions: involving a solid and a gas, or a solid and a liquid. It includes cases where the solid is acting as a catalyst.

27. THE EFFECT OF SURFACE AREA ON REACTION RATES 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.

28. Why normally? What exceptions can there be? Imagine a case of a very fine powder reacting with a gas. If the powder was in one big heap, the gas may not be able to penetrate it. That means that its effective surface area is much the same as (or even less than) it would be if it were present in a single lump. A small heap of fine magnesium powder tends to burn rather more slowly than a strip of magnesium ribbon, for example.

29. 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.

30. The catalytic decomposition of hydrogen peroxide Solid manganese(IV) oxide is often used as the catalyst. Oxygen is given off much faster if the catalyst is present as a powder than as the same mass of granules.

31. 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.

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

33. 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 maximize the surface area.

34. The effect of particle size • Solids with a smaller particle size (e.g. powders or small chips) react more quickly than solids with a larger particle size (e.g large chips). Here is why: • Look at this diagram The perimeter of the large chip is 12 units. The acid particles can only collide with the edge of the chip. However, if we break up the large chip into 9 smaller chips:

35. The effect of particle size • However, if we break up the large chip into 9 smaller chips: • then the perimeter around each chip is 4 units, but there are 9 of them so the total perimeter is 4 x 9 = 36 units. Notice how the acid in the second diagram can reach what used to be the centre of the large chip.

36. THE EFFECT OF CONCENTRATION ON REACTION RATES 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. 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. The mathematical relationship between concentration and rate of reaction is related with the orders of reaction.

37. Some examples to the concentration effect: 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.

38. The reaction between sodium thiosulphate solution and hydrochloric acid When a dilute acid is added to sodium thiosulphate solution, a pale yellow precipitate of sulphur is formed. As the sodium thiosulphate solution is diluted more and more, the precipitate takes longer and longer to form.

39. The explanation of the concentration effect:Collisions involving two particles In order for any reaction to happen, those 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.

40. The explanation of the concentration effect: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.

41. The explanation of the concentration effect: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 concentration.

42. Cases where changing the concentration doesn't affect the rate of the reaction Suppose you are using a small amount of a solid catalyst in a reaction, and a high enough concentration of reactant in solution so that the catalyst surface was totally cluttered up with reacting particles. Increasing the concentration of the solution even more can't have any effect because the catalyst is already working at its maximum capacity.

43. In certain multi-step reactions 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.

44. In certain multi-step reactions 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.

45. In certain multi-step reactions • The overall rate of reaction isn't entirely independent of the concentration of B. If you lowered its concentration enough, you will eventually reduce the rate of the second reaction to the point where it is similar to the rate of the first. Both concentrations will matter if the concentration of B is low enough. • However, for ordinary concentrations, you can say that (to a good approximation) the overall rate of reaction is unaffected by the concentration of B.

46. Orders of reaction • Orders of reaction are always found by doing experiments. You can't deduce anything about the order of a reaction just by looking at the equation for the reaction. • So let's suppose that you have done some experiments to find out what happens to the rate of a reaction as the concentration of one of the reactants, A, changes. Some of the simple things that you might find are:

47. Orders of reaction • One possibility: The rate of reaction is proportional to the concentration of A • That means that if you double the concentration of A, the rate doubles as well. If you increase the concentration of A by a factor of 4, the rate goes up 4 times as well. • You can express this using symbols as: Writing a formula in square brackets is a standard way of showing a concentration measured in moles per cubic decimetre (litre).

48. Orders of reaction • You can also write this by getting rid of the proportionality sign and introducing a constant, k.

49. Orders of reaction • Another possibility: The rate of reaction is proportional to the square of the concentration of A • This means that if you doubled the concentration of A, the rate would go up 4 times (22). If you tripled the concentration of A, the rate would increase 9 times (32). In symbol terms:

50. Orders of reaction • Generalising this • By doing experiments involving a reaction between A and B, you would find that the rate of the reaction was related to the concentrations of A and B in this way: • This is called the rate equation for the reaction. • The concentrations of A and B have to be raised to some power to show how they affect the rate of the reaction. These powers are called the orders of reaction with respect to A and B.