In the previous two lectures, we developed the atomic molecular theory and some particular postulates to describe the nature of matter. In this lecture, we're going to begin to build upon those postulates by providing more specificity. The material we're going to begin covering now is from the second Concept Development Study, Atomic Masses and Molecular Formulas. And I would recommend that you familiarize yourself with the material in that Concept Development Study before watching this lecture. Let's begin with a quick review, having to do with the atomic molecular theory. Recall, that we've said that all matter is made up of atoms. Atoms themselves are the fundamental components of the elements, which are the simplest substances from which all the other materials are made. The atoms combine in simple integer ratios to form what we call molecules, and molecules are the fundamental particles of compounds. So these results are actually very important to us, but they don't actually help us very much, because, there is some significant questions which are not yet answered having to do with these molecules. In particular, if the atoms combine in simple integer ratios to form molecules, what are those integer ratios? So we ought to be able to say, in a particular molecule, there are two atoms of this type, and one atom of another type, and maybe three atoms of a third type. But we don't know any of those ratios yet. To figure out those ratios, it would make sense that in some way or another, we would need to be able to count the individual atoms in order to be able to determine what those molecular ratios are. Let's illustrate the problem by actually going back and looking at the data that we ended with in our previous lecture. We were talking about some compounds called nitrogen oxides. Compounds for just between the two elements nitrogen and oxygen. In these compounds, there are three different mass ratios corresponding to the law of definite proportions for each one of those compounds. So, for example, if we highlight these, we might look at the last of those three compounds, and note, that there's a mass ratio of nitrogen 1 to oxygen 0.57. Now, if I knew that the ratio of nitrogen atoms mass, the oxygen atoms mass was 1 to 0.57, then I could actually conclude that what we are dealing with here is a single atom of nitrogen and a single atom of oxygen. In other words, if I knew the mass ratio between the masses of individual atoms, then I could know what the relative numbers of atoms were in those particular compounds. But, of course, I don't know that. What if instead, I knew what the relative numbers of atoms were? So again, if I focus on this last one here, and I say, there's a mass ratio of 1 to 0.57. If I knew that in compound C, that represented a single nitrogen and a single oxygen, then I could conclude that the mass of a nitrogen to the mass of an oxygen was 1 to 0.57. In other words, if I knew the relative numbers of atoms, I could know the relative masses. But notice the circular reasoning here, right? If I knew the relative masses, I could know the numbers of atoms. But, if I knew the relative numbers of atoms, I could know the relative masses. Somehow or another, I'm going to have to break out of the circular reasoning. Somehow or another, I'm going to have to either figure out the relative masses or figure out the relative numbers of atoms. The way we're going to do this is actually to try to figure out a way to count atoms. And we need some mechanism by which it is possible for us to determine how many atoms of each type there are. The way we're going to do this is the same way it was done historically, about 200 years ago, lead by Amedeo Avogadro. By measuring the volumes of gasses involved in reactions. In other words what we're going to do is say take a compound which is gaseous. Break it into its component elements, also gaseous, and measure the relative volumes of those elements, relative to the volume of the gas we started off with. And we're going to make all of those measurements very carefully by keeping the temperature and the pressure constant while we do that. If we do that, we get data that looks that this kind of thing. For example, we can react hydrogen gas and oxygen gas, and then it will in fact in a very powerful, perhaps even explosive combustion, produce water and gas. And if we measure the volumes corresponding to that, we actually discover a rather interesting thing. That if we actually take 2 liters of hydrogen It will react with one liter of oxygen, to produce two liters of water gas. That's actually a very interesting result because it suggests that the volumes are in simple integer ratio. Now you might imagine from that, that that's just because we happen to take integer volumes. But even that's not required. We could have for example taken 2.6 liters of say hydrogen gas. And that's not an integer. And we could have taken the amount of gas of, oxygen gas that would react with that, which turns out to be 1.3 liters of oxygen gas. And we could determine how much water gas, would be produced from that, and it turns out to be 2.6 liters of water gas. 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.
