And so the volumes themselves are not integers, but the ratio remains an

integer, right? If we look at these numbers here, this is

a 2 to 1 to:2 ratio which is the same as the ratios that we observed back here to 1

to 2. In other words, the ratio of the volumes

which react is always a constant integer ratio.

Look at this other data here as well. If I react hydrogen gas with chloride gas

to make hydrogen chloride gas, again the ratios of the volumes that are reacting

are 1 to 1 to 2. A simple integer ratio.

We could repeat these experiments for lots and lots of different kinds of gaseous

reactions, and we would discover in each case as long as we hold the temperature

and pressure constant at which we measure the volume of the gas.

Then we always see that the volumes are reacting in simple integer ratios.

Because this always happens, it appears to be a law of nature and we call that law of

nature the law of combining volumes. You can see it here, it just says, when

gases react, the volumes are in simple integer ratio, provided we measure those

volumes at constant or the same temperature and pressure.

Now, that is not at all an obvious result. It doesn't necessarily make sense that the

volumes ought to be in constant volume. Volume is a continuous quantity.

And notice, it's also the case, that volume isn't even a conserved quantity.

So if we go back and look at the first reaction here, what we notice is that 2

liters plus 1 liter produces 2 liters. So volumes are not additive.

Volume, the total volume started off as 3 liters and wound up as 2 liters.

Likewise, in the data that we've highlighted back over here, 2.6 liters was

1.3 liters. That should be 3.9 liters, but instead, it

produces 2.6 liters, so volumes not even conserved, so it's very surprising that in

fact the volumes are reacting in an integer ratio.

So we would like to know, why does this happen?

And the analysis is actually due to Avogadro.

Let's review a little bit of the information that we have available to us.

We know from the atomic molecular theory that atoms react or combine in an integer

ratio. That's one of our postulates of the atomic

molecular theory. Likewise, now, we know from the law of

combining volumes, that volumes of gases properly measured combine in integer

ratios. Now, in the case of the atomic molecular

theory, our problem is we don't know what that ratio is.

It's an unknown ratio. That's what we're trying to find out.

But in the law of combining volumes, we do know what the ratios are.

We actually see them up above. It's two to one to two, in the case of

hydrogen to oxygen to water gas. What Avogadro said was, since there's an

integer ratio of atoms and an integer ratio of volumes, maybe, maybe, it is the

same ratio. Perhaps, we are actually observing the

same ratio when we measure the volumes of the gases and when we measure the

particles. That would seem to be a nice, simple

explanation. But for that to be true, it must also

therefore be true, that, if the volume measures the number of particles.

If the volume is a way of count, of counting the numbers of particles, then

each volume of gas must correspond to a fixed number of particles.

In other words, for example, 1 liter of hydrogen and 1 liter of oxygen have to

have exactly the same number of molecules regardless of the fact that hydrogen and

oxygen are different compounds. The same number of particles must be

present in 1 liter of any gas regardless of what the substance is.

That must be true if, in fact, the ratio between the reacting volumes is the same

as the ratio between the reacting particles.

Let's illustrate this for the examples we were looking at a little while ago.

Here's the hydrogen oxygen example that we looked at.

Remember that 2 liters of hydrogen react with 1 liter of oxygen to produce 2 liters

of water gas. So what that means is, if each liter

contains the same number of particles, then for me to compare say, 2 liters of

hydrogen to 1 liter of oxygen. If each liter contains the same number of

particles, then there are twice as many particles of hydrogen as there are of

oxygen. And furthermore, we produce the same

number of particles of water as we started off with, with the hydrogen.

That would only be true if Avogadro's hypothesis is true.

We actually look at that as well for the other example.

Let's go back and look at the hydrogen chloride example.

Remember, a liter of hydrogen plus a liter of chlorine gives 2 liters of hydrogen

chloride, right? But if each liter contains the same number

of particles, then a single particle of hydrogen and a single particle of chlorine

will create 2 particles of hydrogen chloride, and that sounds like we've

actually answered the question we were pursuing.

Because we've now been able to figure out that we've taken 1 hydrogen and 1 chlorine

and made 2 hydrogen chlorides and it seems like we have the ratio that we're

pursuing. But it's a little trickier than that,

because there's something strange about this data.

In fact, there's a tricky question here that perplexed chemists for maybe 40

years. Look at these data again.

This says, remember, one particle of hydrogen makes two particle of hydrogen

chloride. How is that possible?

How can I take a single atom of hydrogen and make two molecules of hydrogen

chloride out of it each one of which has to contain hydrogen?

That should be impossible, in fact, it would be impossible unless, unless each

particle of hydrogen is not a hydrogen atom, but actually is 2 hydrogen atoms.

A molecule of hydrogen, and likewise, if we look at the chlorine, the same must be

true of the chlorine as well, right? I can't take a single particular, a single

atom of chlorine and make two molecules of hydrogen chloride unless each chlorine is

a molecule consisting of two chlorine atoms.

So the answer to our question is found the way that Avogadro found it, by referring

to diatomic molecules. 1 liter of hydrogen plus 1 liter of

chlorine making 2 liters of hydrogen chloride must therefore mean that a

particle of hydrogen is in fact an H2 molecule, and a particle of chlorine, is a

Cl2 molecule. And if that's the case, then we can now

actually say that a molecule of HCl must be of, of hydrogen chloride, must be HCl.

Because, in order to take two particles of hydrogen chloride out of 1 H2, each

particle must contain 1 hydrogen and likewise 1 chlorine.

And notice, that we now have our first balanced chemical equation, in which we

have determined both the formula of hydrogen chloride is HCl, and, that

particles of hydrogen and chlorine are each diatomic molecules.

Let's reinforce this a little bit by looking at our other example of hydrogen

and oxygen. Here, what we have is two particles of

hydrogen. And now we know that a particle of

hydrogen is H2 reacting with one particle of oxygen to make two particles of water.

Well, in order to take 1 oxygen and turn it into 2 waters, each oxygen must be O2.

So we've now shown that oxygen gas is diatomic O2, just like is widely known.

Furthermore, if I combine 1 H2s and 1 O2 to make two molecules of water, each

molecule of water must contain 2 hydrogens and 1 oxygen.

So, in fact, the molecular formula of water is H2O, just as is commonly known.

So we've actually successfully, now, shown how we can count particles by using

volumes, and by taking the relative numbers of volumes, the relative ratio of

volumes, we get the relative number of particles in a particular compound.

Okay, let's go back and look at the nitrogen oxides that we started off the

lecture with. Remember these data again.

Here, what we have shown is the relative masses of the nitrogens and the oxygens.

And in order to figure out which one of these compounds maybe has a one to one

ratio between nitrogen atoms and oxygen atoms, I need to do some volume

measurements. So we'll go back to the law of combining

volumes, and here is what we wind up with. For each of compound A, B, and C, if we

take 2 liters of those compounds and break them into the nitrogen and oxygen

components, here are the ratios that we get.

Let's look at the simplest one of these. The simplest one is clearly B, because the

ratio of the nitrogen to the oxygen is one to one.

So let's look at that for a moment. This says, 1 liter of nitrogen plus 1

liter of oxygen makes 2 liters of compound B.

But of course, what that means is one particle of nitrogen plus one particle of

oxygen, will make two particles of compound B.

But for that to be true, we've already shown that oxygen has to be O2.

But it must also now be true that nitrogen is N2, because, in order to make two

particles of B out of 1 nitrogen, that nitrogen has to have 2 oxygen, I'm sorry,

2 nitrogen atoms in it. So we can now write that N2 plus O2 goes

to 2B, and therefore, B has to be in O, because there's a one to one ratio between

the numbers of nitrogen and the numbers of oxygens.

Let's test that now, by actually looking a little bit more closely at say, compound

A. Let's look at the data in compound A and

see if this will make sense. So, again, what we have is 1 N2 plus 2 O2

must give us 2A molecules. And therefore, let's say each a molecule

must contain a single nitrogen atom, but must contain 2 oxygen atoms.

So A is NO2. And likewise, we would find that C in N2.

Furthermore, we can figure out from that the mass ratio.

The ratio of the mass of an N to the mass of an O, atom must be 1.00 to 1.14.

Because, in compound B, there's a one to one ratio between the nitrogen atoms and

the oxygen atoms. And the mass ratio, according to what we

see up above, is 1.00 to 1.14. So that's also the ratio of the masses of

the nitrogens and the oxygens. Well, it would seem that we've actually

completed our task. We figured out how to count atoms by what

by taking volumes. And we figured out how to use those

volumes to figure out the relative ratio of atoms in a particular molecule.

And by using data, just like we did on this slide here, we can use those to

figure out the relevant masses of the atoms.

And that works perfectly, as long as we're talking about gases.

Because Avogadro's hypothesis only works when we're talking about the law of

combining volumes and the law of combining volumes only applies to gases which are

reacting. But not very many of the elements actually

are gases and not all compounds are gases. So, if in fact, we're going to use this

approach, how do we deal with non-gaseous elements?

Most of the elements are non-gaseous. Most of them are solid.

Carbon would be a great example. It's one of our most important elements.

And yet, I can't take gaseous carbon element gas carbon exists as a solid in

its elemental form and forming gaseous carbon requires very, very high

temperatures. So I'm going to have to find some other

way, to count carbon atoms, and thus, some other way to figure out what the mass of a

carbon atom actually is. We're going to take that up in the next

lecture.