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# Rates of ReactionWritten by Tim Sheppard MBBS BSc. Last updated 18/7/12

## What is the rate of a reaction?

When a reaction happens, some reactants go into the reaction, and the products of the reaction come out. The reaction happens very quicky. It would be easy to think of it as lots of reactants to go in, for the reaction to happen, and for the products to come out.

It doesn't actually happen like this, however. Because a lot of reactions in life are in equilibrium, they don't just happen in a batch. They tend to be continuous.

If there were a limit to the amount of the reactants, then eventually the reaction would finish. If we were to time how long it took for a particular amount of reactant to turn into product, we could work out how quickly the reaction happened.

The rate of the reaction is how quickly the reaction happens. If you imagine the reaction is like a machine, the rate of the reaction is the speed at which the reactants go through the machine. If we know the rate of a particular reaction, then if we want to do it in the laboratory, we can work out how long it's going to take.

Rates of reactions are measured in the amount of product produced in a particular period of time. For instance, it could be measured in moles per second. It can also be measured in change of concentration per period of time. If you were given the equation.

A + B → C + D

the rate of the reaction could be given as molarity of C per second, or in grammes of D per minute.

## How does temperature affect the rate of a reaction?

Particles move. It's what they do. Some move quicker than others. Particles in a solid move rather slowly; particles in a liquid will tend to move more quickly; particles in a gas will tend to move even quicker. To speak generally, the speed of the particles depends on the energy of the particles. Like children, those with more energy are more active and will move quicker. So, if particles are hotter, then they will move more quickly.

Why does this have anything to do with reaction rates? Well, basically, for a reaction to take place the particles involved in the reaction have to collide. This is known as the collision theory. And they don't just have to collide in any old way - they have to collide with what is known as a favourable orientation. Basically they two particles have to be facing each other. Well, with particles bouncing around randomly, it's a bit 'hit-and-miss' as to whether or not a reaction is going to take place. However, if the particles are moving more quickly, there's going to be a lot more collisions, which means there's a much higher chance of favourable collisions.

Increasing temperature increases the rate of a reaction, because the increased energy in the particles leads to an increased probability of favourable collisions.

## How do concentration and pressure affect the rate of a reaction?

Imagine you're looking for a football in a haystack. It's not too difficult. However, if the haystack was the size of a barn, it would take a while to wade through. On the other hand, if the haystack had the same amount of hay, but it was all condensed down into the size of a refrigerator, you'd probably find it much easier to locate the football.

It's a similar principle that's applied to explain how concentration and pressure affect reaction rates. All that we need to achieve, as previously discussed, are favourable collisions. So, basically, you need to make sure that one particle of substance A finds one particle of substance B and collides appropriately. Using the image, imagine the pink or purple liquid is substance A, and the green particle is a particle of substance B.

In the pink example, there are six particles floating about but because there isn't a very high concentration, there isn't a high chance of them colliding. They could float about and easily miss each other.

In the purple example, there are six particles floating about again, but because they are more concentrated, they're far more likely to collide with the green particle. Because they're closer together, there's a greater chance of favourable collisions.

Increasing concentration or pressure increases the rate of a reaction, because the particles are closer together and have an increased probability of favourable collisions.

## What is a catalyst?

A catalyst is something which by its very nature increases the rate of a reaction. It's a bit of a complicated topic, and we don't always know exactly how a catalyst works; but we do know that for a catalyst to be a catalyst, it has to remain unchanged at the end of the reaction. Sometimes they're discovered by accident, but there are several theories about.

Often a catalyst is there to provide a favourable surface for a reaction to take place. The animation here is helpful. If there are two molecules which need to collide in a particular way, the catalyst may cause them to come together appropriately. There are several ways that it can do this, so there may be various different substances which act as a catalyst. However, some will be better than others. If a catalyst grabs hold of the reactants too strongly, then the product(s) won't leave very easily; on the other hand, if the catalyst doesn't hold on to the reactants strongly enough, the product(s) won't have enough time to be formed before they fly off again. This is called catalyst affinity for its substrate.

The presence of a catalyst will increase the rate of a reaction.

## What is the rate equation?

If a reaction happens that produces a solution, then the rate may be given as the change in concentration of one of the products, in a given time. It may also be given as the chance in concentration of one of the reactants. These will both give a similar idea of rate. For instance, if A + B → C + D, then if C is increasing in concentration by 2M per second, then A would have to decrease in concentration by 2M per second.

Since the concentration changes during the reaction, so does the rate. If the equation we use to work out the rate depends upon the concentration of the reactants (and it does!) then we need to decide which point of the reaction we're talking about, and realise that the measurement will only be true at that point. Usually we talk about the initial rate - the rate at the start of the reaction.

The rate equation provides us with a way of finding out how particular chemicals affect the rate of a reaction. Let's take our classic reaction:

A + B → C + D

The reactants here are A and B. Well, as discussed earlier, the concentration affects how quickly a reaction goes - but how much? It varies from reaction to reaction. The letters k, m and n can all be changed, and how they change will affect the result.

m and n are known as the orders of the reaction, and m + n is the total order of the reaction. The best way of explaining them is to give examples. If you wanted to say that changing the concentration of A has no effect on the rate of the reaction, you'd say m=0 (because anything to the power of 0 = 1, so A's inclusion in the rate equation has no effect on the answer for the rate).

If you then decided doubling the concentration of B caused the reaction to double, then n=1. If doubling the concentration of B caused the reaction to increase 4 times, then n=2. If n=1, then 2?B doubles the answer (21B = 2B), whereas if n=2, then 2?B increases the answer by 4 (22B = 4B).

It all relates to complicated mathematics. Hopefully, if you spend a while thinking about it, it'll make sense.

The only remaining issue is the units. Rate in this instance is measured in change in concentration per second - so it's units are mol.dm-3.s-1. Unfortunately, that's the simplest it gets. The units for the concentrations of A and B are mol.dm-3, but if their orders are more or less, they change. If the order is 0, then you can just ignore them. If the order is 1, it's mol.dm-3. If the order is 2, then the units are [mol.dm-3]2 = mol2.dm-6.

To work out the units of k, you have to work out the units of everything else, and then rearrange the equation to leave you with k on one side. Then you cancel down the units to their simplest form, and those units will be the same for k. It's very complicated, but hopefully the list and animation explain.

As you can hopefully see in the table and the animation, you take the units of the concentrations of the reactants (taking into account the order of the reaction). Then you divide mol.dm-3 by the units obtained from the reactants.