Hi, welcome to this first lecture. In this course Chemistry Concept Development and Application. The second half, of a two part course, which the first part was offered last spring. For those of you who are new to the course, I'd encourage you to watch the introductory video, that describes the philosophy, and the concept development study approach that we're going to be using in this class. For those of you are veterans from the first semester, you're already familiar with the approach and have an idea of what we're going to cover here. Our first lecture is going to cover the material from Concept Development Study number 14, having to do with the physical properties of gases. Before getting into that material I would like to spend a minute talking about how this semester will differ somewhat from the previous semester. You may recall in the first semester that we spent most of our time talking about atoms and molecules. What were the structures of atoms? And what were the structures of the molecules? And what were the properties of atoms, and properties of molecules? We focused then on what we might call particle properties. And those particle properties included molecular formula, the structures of molecules. That is how did [INAUDIBLE] atoms bond together? The polarity of molecules generated for example by their molecular geometry, polarizability of molecules, which is whether or not the molecules could form a dipole when in the presence of other charged particles. Intermolecular forces such as hydrogen bonding, bond energies, meaning the strengths of the bonds that hold the atoms together. In this semester, we're going to spend most of our time talking about bulk properties. That is, properties that we mo, more likely associate with large quantities of material like the kinds of materials that we would deal with on an every day basis. The bulk properties of materials might include, for example, the density of the material, the pressure of the material. Might include its temperature or a concentration, very simple idea such as vapor pressure and boiling point. So these two contrast each other. And in this semester we're going to spend much more time talking about what might be called macroscopic properties as opposed to what we dealt with in the previous semester, which were the microscopic properties. An interesting part of what we're going to be attempting to do then, is to figure out, if we take these bulk properties, how do we relate those to the particle properties that we studied last semester? In fact, that's going to be the bulk of what we will do in this semester, is attempt to tie these two together. In the first semester, we actually did a bit of this. We connected bulk properties to particle properties in a couple of examples. For example, remember we studied the concept of bond energies. Bond energies are how strongly are the bond, are the atoms held together in a molecular bond. We were able to relate those bond energies to reaction energies by summing the bond energies of the products, and summing the bond energies of the reactants. And taking the difference between the two. Another example had to do with the properties of metals. We were able to relate the properties of individual metal atoms, as well as the ways in, which metal atoms bond together. And to relate them to the properties of bulk samples of the metal such as the fact that metals are malleable and the fact that metals are conductive. We're actually going to begin this semester, though, by talking about gas properties. And, the three most important gas properties we're going to deal with, at the bulk level, are going to be the pressure of the gas. Basically, how much force does the gas exert per unit area of the container surrounding the gas. What is the temperature of the gas? What is the density of the gas? We'll talk about density in two different ways, the somewhat more common way, which is the mass per unit volume, but also sometimes what we'll call the particle density, which is the number of particles per volume. And in chemistry, we most commonly we'll measure the number of particles by the number of moles. So our goal here is going to be to relate the properties of gases to each other and then in the subsequent concept development study we're going to do the work of relating these properties to the properties of the individual gas molecules. We'll begin again as always by looking at experimental data and here is our experimental setup. We're going to relate the pressure of a gas to the volume of the gas. I'm going to use this very simple apparatus. We're going to use this apparatus a lot this semester, in studying the properties of materials. So let's get used to this. What do we have here? We have a, a cylinder into, which we have inserted a piston. And by pushing in on the piston I can change the volume of the sample of gas, which is contained in there. I've hooked up a pressure gauge here so that I can measure the pressure of the gas, which is contained in here. And then we'll measure the volume of the gas. And most of you might recognize that what we're actually looking at here is a syringe. That if we had grad, graduations along side of the syringe here were we could just read off the volume, then we've just hooked up that syringe to the pressure. We've captured a certain sample of gas inside the cylinder there by moving the piston back and forth. We're going to vary the volume of the gas. And what we'll discover is that the pressure is going to vary as well. Our goal here is then to measure the pressure as a function of the volume. We can collect a bit of experimental data for this particular sample. And here is an example of what this data looks like. This is pressure on the y-axis, and volume on the x-axis. So this is pressure versus volume. And what you can see here on the graph, is a steadily decreasing function where the pressure declines as the volume increases. They seem to be inversely related to each other. But it's also pretty clear that this is not a straight line. This is not just a negative slope. There's in fact, some other kind of inverse relation here. We might want to figure out what those kinds of inverse relations look like. What kinds of functions often look like in inverse. Well, one such function is, in fact, the exponential function. Which decreases something like that. That's an e to the minus x function. But another inverse function is the inverse function in, which we have an inverse proportionality. And the distinct difference between these two is that the function asymptotically approaches x and y. For the function 1 over x, but in fact hits the y axis at x equal to 0 for the exponential function. That might lead us to believe as we look at this particular graph that this is an inverse function. And the way we could test that would be to simply take the inverse. Because if we take this function y as a function of x, and invert the value of of, of x along here by taking the inverse of y. Or plotting y versus 1 over x either way. We will wind up with a straight line and in fact that straight line will go through the origin. Let's see what this looks like if we attempt this. On this function here, we have plotted one over the pressure versus the volume for the same set of data we were looking at on the previous slide, and notice what we get. We get a straight line and in fact that straight line seems to extrapolate through zero. And if it does, what that tells us is that this is in fact an inverse function along the lines of what we observed back over on this graph. What we can say, then, is that if P versus V looks like this, then P versus 1 over P versus V is a straight line, as we've observed here. That means that 1 over P versus V is a proportionality, and we've written that function down below here, 1 over P is proportional to the volume. That's what the graph above shows us. That's an observation, which is consistent with something, which is referred to as Boyle's law, after Robert Boyle, who was the first to discover it. What he observed here is what we just observed, 1 over P is proportional to V, or as is very often written, PV is a constant for these particular conditions. Remember, we trapped a sample of gas and we trapped it at a particular temperature. What happens, though, if we were to change that? This function is only valid for one sample of gas at one temperature. A different way of asking the question is, what do you suppose this constant has to do with? The answer it has to do with what sample of gas did we take, and what temperature of the gas did we take? If we move a little bit forward, then, what would happen if we were to change the sample of the gas? Here's what happens. What we're going to do is take two different samples of the gas now, meaning initially back in that cylinder. We'll trap a larger volume of gas than we did originally, at the original pressure that we started off with. So we have two different samples, two different volumes at the same pressure and temperature. According to Avogadro's hypothesis that we studied last semester, if we have two samples of gas at the same temperature and pressure, one with a larger volume than the others. The number of moles or the number of particles of gas trapped is proportional to the volume. So by increasing the volume we've increased the number of moles of gas, which are present. So in these two samples here, we have two different amounts of gas here in n1 and n2, and n2 is larger than n1. What do we observe? Here's our original data. This is exactly what we looked at before for the n1 data. Now that we've trapped a larger volume of gas with a larger number of moles, what does the rest of the data look like? Well, look, it's a straight line again. But is it the same straight line? It's a proportionality, but it's a different proportionality than the one that we looked at before. What that means is, as we observed before, remember, 1 over the pressure is proportional to the volume and the proportionality constant then is the proportionality constant for n1. And 1 over the pressure 2, corresponding to the sample, second sample of the gas, is proportional to the volume as well. And the proportionality constant is a function of n2, the sample that we took secondly. What that tells us is back in Boyle's Law, that constant that we looked at before here, is in fact a function of the number of particles, which are present in the sample. In other words, PV is a constant, provided that we keep the number of moles constant. If we change the number of moles, we get a new constant. PV is again a constant, but with a different value of the proportionality. So overall then we can conclude, Boyle's Law tells us that 1 over P is equal to a constant, which is actually a function of the number of moels of gas, multiplied by the volume. Or alternatively, PV is a constant, which is a function of the number of moles. This function is now true for any sample of gas, provided that we're holding the temperature constant. Because we use Avogadro's hypothesis to know that when we change the volume, we change the number of moles of gas. What happens if we change the type of gas instead of changing the number of moles of gas? What if, for example, we capture neon instead of hydrogen, or oxygen instead of nitrogen, or methane instead of any of the above? The answer is, we get exactly the same functions that we observed before. These two functions drawn down at the bottom of the page here are independent of the type of gas, which we captured. The pressure of the gas is exactly the same, provided that the number of moles of the gas is the same. Therefore, Boyle's Law is general, and applies across all samples of all types of gas. We'll actually see some limitations on that later on in the semester, but for now, our data tell us that the pressure of the gas doesn't depend upon what the type of gas is. What does it depend upon? Well, it depends upon now the number of moles in the volume. What about the temperature? What happens if we change the temperature? That is the subject for the next lecture.
