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## Arrhenius equation and reaction mechanisms

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# Elementary rate laws

## Video transcript

- [Voiceover] Let's say we have
a simple elementary reaction where we have only one reactant, A, turning into our products. We can classify this reaction
according to its molecularity, which refers to the number
of participating molecules. So if we think about one molecule of A giving us our products, this would be a unimolecular reaction. We have only one molecule, so we call this a unimolecular reaction. Next let's think about
writing the rate law. So we know when we're writing rate laws, we write the rate of our reaction is equal to the rate constant k times the concentration of our reactants. And here we have only one reactant, so we say times the concentration of A. For the exponents, we can actually take the coefficient in our balanced equation and
turn that into the exponent. So we have a one here for our coefficient, so we make that a one right here. So you can only do this for an elementary, one-step reaction. You can't do this for an overall equation with a detailed mechanism like
we'll see in the next video. But for these elementary
reactions, you can do this. So the rate of our reaction is
equal to the rate constant k times the concentration
of A to the first power. So for this unimolecular reaction, it's first order in A. Next, let's look at another reaction. A, one molecule of A
plus one molecule of B gives us our products. Here we have two molecules,
two participating molecules. So this is a bimolecular reaction. So I write bimolecular here. So we can think about these two molecules colliding in space. So molecule A is going to collide with molecule B to give us our products. And so it makes sense that the rate of the formation of our products depends on how frequently A and B collide. And that depends on the
concentration of A and B. If you increase the
concentration of A and B, you increase the frequency of collisions, and therefore you increase the overall rate of your reaction. So when you write your rate law, so the rate of our reaction is equal to the rate constant k times the concentration of A, and since this is an
elementary, one-step reaction, we can take the coefficient and
turn that into our exponent. So times the concentration
of A to the first power, times the concentration of B, and once again, we can
take our coefficient, which is a one, and turn
that into our exponent. And so now we have the rate law for this bimolecular reaction. Let's look at another
bimolecular reaction. This time we have two molecules of A reacting to give us our products. So we could say that this is A plus A gives us our products or we could say that this is
two A gives us our products. So either one. If we stick with the first version, we have a one for our coefficient here, and a one for our coefficient here, and so we write the rate law
for this bimolecular reaction, the rate is equal to the rate constant k times the concentration of A and we look at our coefficient
here which is a one so we make that to the first power, and then times the
concentration of A again, and once again we look at our coefficient and we turn that into our exponent. And so that of course will become, this will just be the rate is equal to the rate constant k times
the concentration of A, this will be to the second power. A to the first times A to the first is equal to A squared. Or we could have looked at our other version of writing it, a two A, and once again our coefficient would become our exponent. So this is another example
of a bimolecular reaction. Finally, let's look at a reaction where we have three
participating molecules. So one A plus one B plus one C gives us our products. So one molecule of A
plus one molecule of B plus one molecule of C. There are three
participating molecules here so we call this a termolecular reaction. And for this to occur in one step, these would all have to
collide at the same time. So if we had A, B, and C, they would all have to collide at this point in space at the same time. And this is rare if you think about it, trying to get three
molecules to collide at once is pretty difficult to do. So these termolecular reactions are rare, but we can write the rate law. So the rate of our reaction is equal to the rate constant k times
the concentration of A and we have a coefficient of one here so this is to the first power, times the concentration of B and once again this would
be to the first power, and times the concentration of C and this would also be to the first power. So for these elementary rate laws, for these elementary reactions, we can take the coefficients and turn them into the
exponents in our rate laws. Once again, in this next video, you'll see that we can't do that, we can't look at an
overall balanced equation with a detailed mechanism
and just take the exponents and figure out the rate law. The rate law needs to be
determined experimentally.