In this lecture, we're going to begin our study of the material from Concept Development Study 17, Phase Transitions and Intermolecular Forces. We're going to use the material from the previous lectures, having to do with phase equilibrium and dynamic equilibrium. And build upon those concepts to begin to understand the structure of a liquid and in particular the forces that interact that are for interaction of molecules inside of a liquid. Our starting point is going to be this now familiar data set, which is the vapor pressure of a liquid, as a function of a temperature of that liquid. In this particular case, we're looking at water, and we remember that the vapor pressure is the pressure of the vapor when it is in equilibrium with the liquid at each particular temperature. That equilibrium vapor pressure rises with the temperature, according to this graph. Now there's an interesting aspect to this particular data set, again given that it is water. Let's look at the vapor pressure, at what we know to be the boiling point of water, which is 100 degrees C. If we look up and read off of this graph what the vapor pressure is at a 100 degrees C and read across, what we notice is that it's actually equal to 760 torr or 1 atmosphere. In other words, at the boiling point of water, 100 degrees C, the vapor pressure is equal to atmospheric pressure. That might seem to be a coincidence but turns out to be generally true. The boiling point at each pressure turns out to be the temperature at which the vapor pressure is equal to the applied pressure. Let's give it a try. For example, imagine that the atmospheric pressure in some particular case was 600 torr. Then we could ask, at 600 torr, what temperature is required to achieve 600 torr vapor pressure? Turns out to be a little over 90 degrees centigrade. Therefore, at 90 degrees centigrade, the vapor pressure of water is about 600 torr. Well, why would it be the case that the vapor, the boiling point, is the temperature at which the vapor pressure is equal to the applied pressure? Let's actually look at our previous apparatus and see if you can understand why that's true. Remember, our apparatus looks something like this. Here's the actual physical version and the description in the cartoon form is on the screen here. Remember that the vapor pressure is, if I pull back on the syringe here, the pressure of the gas that I trapped in here, in equilibrium with the liquid. Notice however, that I'm having to struggle to hold the syringe back because there's pressure applied to the top of the gauge here by the atmosphere equal to one atmospheric pressure. If I release the syringe, in fact, it pops right back into place and collapses down on to the surface of the liquid because the pressure of the vapor inside was way too low to withstand the pressure being applied by atmosphere. Let's imagine then that we wanted to reach the boiling point. We know what we've done before is to heat this container until, in fact, we see the vapor phase appear. At what point will the vapor phase be stable? On the basis of what we just did, it must be true that I have to heat this until the vapor inside has sufficient pressure to offset the atmospheric pressure being applied above. In other words, in order to boil the liquids vapor pressure, the pressure of the vapor trapped inside, must equal the applied pressure from the outside. Turning that around, we can say, at the boiling point, that is the temperature at which the liquids vapor pressure, equals the applied pressure. So, if we go back and look at this graph again, when we look at this graph, originally we thought that this was, essentially, the vapor pressure as a function of the temperature. But now we can look at it slightly differently. We can say, at each pressure, what would the boiling point of the liquid be? And in order to answer that question, we could pick any particular vapor any particular applied pressure and ask, what is the temperature at which the liquid will have that particular vapume-, vapor pressure? What that tells us then, is that the graph that we have drawn here is not just the vapor pressure as a function of the temperature, it is also the boiling point as a function of the applied pressure. That's very helpful because it tells us at each one of those pressure and temperatures along that curve, we have liquid and vapor in equilibrium with each other. These particular points along this curve are the only points at which liquid and vapor will be in equilibrium with each other. We can also though ask the question, what about points which are not on that line? What if I were looking at a point say, around here? What would we expect to exist at that point? Well, we know we are not sitting on top of the liquid vapor equal equilibrium curve, but what can we say about it? Well, one thing we could say, is we are sitting in a pressure where if I ask what the vapor pressure of the liquid is at this particular temperature, say 20 degrees C, the vapor pressure is actually, oh it looks to be around 20 torr. But the applied pressure at this particular point is about 600 torr. Correspondingly, just like we observed over here. When the applied pressure exceeds the vapor pressure inside the liquid, the syringe collapses on to the liquid and there is no vapor. As a consequence, on this side of the graph here back in this region. For every pressure temperature combination above the curve, only liquid would exist. What about in this region down here? In this particular region, below the curve, at each temperature, the applied pressure is below the vapor pressure. So, for example, image I was looking at a point which was here. At that particular temperature here, the vapor pressure should actually be about here. The vapor pressure, therefore, actually exceeds the applied pressure and as a consequence, the vapor pressure will actually push the syringe back out and all of the liquid will evaporate into gas. Therefore, in the region of the graph down here, only gas exists and along the line between those two regions we have equilibrium, between vapor and gas. Because of these reasons, we actually refer to this diagram as a phase diagram, because at each pressure and temperature it tells us what phases should exist at equilibrium. Of course this particular phase diagram has only liquid and gas on it. A more complete phase diagram should also include another phase, the solid phase. There must also exist then, a transition boundary for pressures and temperatures where the solid is in equilibrium with the gas. Or where the solid is in equilibrium with the liquid. Here, again, we see the now familiar liquid gas equilibrium curve. We also see this region corresponding to liquid only, and this region corresponding to gas only. The solid, actually, as you can tell from this graph, exists at a lower temperature and at a higher pressure than the gas. And at a lower temperature than the liquid. There also exists a set of points at which the liquid and the vapor are in equilibrium with one another. I'm sorry, the liquid and the solid are in equilibrium with one another. Notice that the temperature at which they are at equilibrium doesn't really vary with the pressure. That's simply because the most gases, I'm sorry, most liquids and solids are so incompressible, that changing the pressure really doesn't change the properties of those materials very much. And as a consequence, the temperature doesn't change very much for the dynamic equilibrium between liquid and solid. Let's actually see if we can begin to examine this a bit by considering now, this is all for water, variations as we move from one liquid to another. Before, we have looked at this graph as the vapor pressures of different liquids as a function of the temperature. But on the basis of what we've just looked at, we now know that these curves actually correspond to phase diagrams. Let's consider for example, dimethyl ether which is here. Here's the curve for dimethyl ether. It's shaped just like the curve for water, which is back over here that we examined a little while ago. And for this particular graph, for any pressure which is above the curve, we would have only liquid dimenthyl ether and for any points below that curve we would have only gaseous dimenthyl ether. Notice that the variation of one phased diagram to another for liquids and gasses looks very similar. But the location of the curve changes quite a lot. To see that, we could say, sit at 760 torr up here, and look straight across. And remembering now, that the boiling point is the temperature at which the vapor pressure is equal to the applied pressure, of 760 torr. We see that the boiling point of dimethyl ether is oh, of the order of minus 40 degrees C. Where the boiling point of phenol to the right here is of the order of a 150, 160 degrees C. A 200 degree change just for these particular liquids. That gives us an idea for how we might begin to systematize our information. What we would like to understand. What we would like to understand is why different liquids have different vapor pressures and different boiling points. And we can, you and, and what the differences of those liquids would be that would produce that. And we can use our model of dynamic equilibrium to help explain this. Remember, according to dynamic equilibrium. When we have a liquid and a vapor and equilibrium with one another, inside of a container here, here is the liquid, and here is the gas above it. And when the pressure of the gas in constant here for a constant temperature of the liquid. We have a dynamic equilibrium in which ga-, liquid molecules leaving the liquid and going into the gas. Are being exactly offset in their rate by the numbers of gas molecules leaving the gas and going into the liquid. The rate of condensation is equal to the rate of evaporation. What would make a high rate of evaporation? Well, if we had a high rate of evaporation, we'd have lots of molecules going into the gas phase. And in order to have a corresponding rate of condensation be high, we'd have to have a high pressure of the gas. So a higher rate of evaporation means that the vapor pressure of the gas is higher. But a higher vapor pressure means, of course, from what we have just seen, a lower boiling point. It takes a lower temperature to achiev-, achieve a, a vapor pressure equal to the applied pressure. So, a higher rate of evaporation means a lower boiling point. But when would we have a higher rate of evaporation? That would be true when it is easier for the molecules to leave the liquid phase and escape one another. And in order to escape they must overcome the attractions between the liquid molecules and adjacent liquid molecules. So we'll refer to these as intermolecular forces. If these forces are weak, it is easier for the molecules to escape, that would give rise to a higher rate of evaporation and correspondingly, a lower boiling point. So what we wind up with then is a correlation between weak intermolecular forces and a lower boiling point. Correspondingly as well, we will see a correlation between higher intermolecular forces and a higher boiling point. So our conclusion, based upon dynamic equilibrium, is that we see a variation in the boiling points of the liquids. And those boiling point variations are telling us about the variations and the strengths of the intermolecular forces in the liquids. In particular, a high boiling point corresponds to strong intermolecular forces and a low boiling point corresponds to weak intermolecular forces. We're going to examine now the variations of boiling points with different kinds of molecules. And use that data to tell us, do these molecules have strong intermolecular forces and if so, why? Or do they have weak intermolecular forces and if so, why? And we'll pick those up in the next lecture.