In this lecture we will continue our study of phase transitions, the transitions that take place from one phase, say liquid, to another phase gas. And in particular we're going to try to unlock the riddles having to do with vapor pressure and use those to develop a model of the kinetic molecular theory of a liquid. Let's go back and review very quickly what we learned in the previous lecture The quantity called vapor pressure which can be observed with this particular apparatus. We have a quantity of liquid, trapped in a syringe. We pull that syringe back to trap a particular volume. Inside that volume is gas, corresponding to the same substance as the liquid. We measure the pressure of that gas as a function of the temperature of the entire apparatus, and what we discover is that the pressure is a constant for a given temperature, and for a given liquid. What does the vapor pressure depend upon? We observed last time that it depends upon what kind of liquid we have trapped inside the syringe. As well as the temperature of the liquid. But what we're really going to focus on in this lecture, is this interesting puzzle: that the vapor pressure does not depend upon the volume of the container. And that's surprising, because if we change the volume, which traps the gas, then the Ideal Gas Law would have suggested to us that for example, an increase in the volume should have resulted in a decrease in the pressure. So let's draw just a little schematic here and figure out what we think is going on, so here is the schematic of a syringe, here's some liquid across the bottom here there's gas, up above we measure a volume here. And we can measure the pressure of that gas. Now, the temperature is being held constant, we're varying the volume, and the pressure does not change. The pressure remains constant. How is that possible? If we look at the ideal gas law, we can say that pv is equal to nrt, we've developed that before and the pv is equal to nrt then what happens when we actually pull back the syringe? Well, temperature is fixed, pressure didn't change, even though the volume has increased. Then then only thing that can compensate for that must be that the number of moles of the gas is increased. So, as v increases, it must be true that n increases, in order to hold the pressure constant. But how is that possible? How could we increase the amount of gas which is trapped here. While the answer is of course something to do with the liquid which is also trapped inside the cylinder. Apparently, when we pulled the syringe back, there must have been a net migration of molecules from the liquid into the gas phase so that we get increased the number of moles which of gas are present, that's the only possibility. There's no other way to increase n except they have more gas molecules and those gas molecules must have come from the liquid phase. But that's an interesting result, how could it be that pulling back the syringe caused more gas molecules to evaporate or more liquid molecules to evaporate into the gas? That seems strange because the syringe is not in contact with the liquid. The liquid in essence doesn't know that the syringe has been moved because the syringe itself is not imparting any kind of a force on the liquid. And yet, pulling the syringe back results in an additional number of molecules of liquid moving into the gas net. There's only one possiblity, and that is that there were gas molecules always moving from the liquid into the gas. Evaporation must always be occurring. Evaporation. Always occurs. But if evaporation is always occurring, why isn't the pressure always increasing? If evaporation's always taking place, there's always an increase in the number of moles of gas it would seem, and the pressure should go up. But it doesn't. What that means, is that at the same time that molecules are leaving the liquid and going into the gas, molecules must be leaving the gas and going into the liquid. Corronspondingly then, condensation always occurs. So evaporation and condensation are constantly taking place. When the volume of the syringe is held constant here, up above, then the pressure does not change; therefore, the number of molecules in the gas phase inside this cylinder is not changing, even though evaporation and condensation are constantly taking place. How can that be? It must be true that these two events are occurring with exactly the same rate. So the rate at which molecules are leaving the liquid and going into the gas, must be exactly offset by the rate at which the gas molecules are leaving the gas and moving into the liquid. We refer to this situation as, equilibrium. What that means is that, at the macroscopic level, the properties are not changing as long as I don't change the volume. Pressure stays the same. Temperature stays the same. The amount of gas, in the gas phase and the amount of liquid, in the liquid phase all remain fixed. But, that doesn't mean that nothing's happening. In fact, we have just figured out that it must be true, that liquid is constantly evaporating and gas is constantly condensing just at the same rate. We refer to this, then, as Dynamic Equalibrium. Meaning, even though the properties are remaining constant, things are constantly in motion. Let's try to get a better understanding then of what's happening during dynamic equilibrium. Dynamic Equilibrium requires us to understand the rate at which condensation occurs. And also requires us to understand the rate at, at which evaporation occurs. So what determines the rate of condensation? Imagine there's a molecule sitting here in the gas phase, and we wanted to know whether that molecule was going to condense. The rate at which molecules condense can be no greater than, the rate at which those molecules encounter the surface of the liquid. Because to condense, they must join the liquid. What is it that determines the rate at which the molecules condense then? What rate determines the rate at which they impact the surface of the liquid? Well, we studied that when we developed the kinetic molecular theory of gasses, and remember this is a gas up here. It is, in fact, the density of the gas molecules that will determine the rate at which the molecules encounter the container. As well as the speed at which they move. At constant temperature those speeds remain the same. So what will vary is the number of molecules in the gas phase. And of course, that's determined by the pressure. So what determines the rate of condensation is, in fact, the pressure. Or correspondingly, the number of molecules of the gas per volume. Either one of those. We'll just home in on the pressure. If that's the case, then what is it that determines the rate of evaporation if we've now concluded that what determines the rate of condensation is the pressure. Well, imagine we have a molecule in the liquid. And we want to know, what is the chance that it'd escape. Well what else could it depend upon? We know that if we vary the temperature of the liquid, we will vary the vapor pressure of the liquid. Apparently the temperature comes into play here. We also know, from our study of the kinetic molecular theory of gasses, that temperature is related to the kinetic energy of particles. If we see at the higher temperature, that the vapor pressure is larger, then it must be true that more molecules escape at the higher temperature. And, that must be because we've increased their kinetic energy, making it easier for them to escape into the gas phase. So, what determines the rate of evaporation is in fact the temperature. Correspondingly then, in order to have the same rate of evaporation and condensation, it must be true that at each temperature there's a certain rate of evaporation, that must be matched by a certain rate of condensation, which must be matched by the particular pressure that generates that rate of condensation, hence, for every temperature of the liquid, there's only one pressure at which the rate of evaporation will be matched by the rate of condensation. And for every pressure, there's only one temperature at which the rate of evaporation will be matched by the rate of condensation, hence, when before we have looked at the vapor pressure as a function of the temperature, there's only one pressure for each temperature at which we will see equilibrium between the vapor and the liquid. That is what we gain by understanding the vapor pressure holding constant when we vary the volume. We've developed this model based upon by Dynamic Equilibrium and it has revealed to us that changing the temperature of the liquid changes the kinetic energy of the liquid molecules on average such that more of them are able to evaporate. What we next like to understand then is, why does the vapor pressure depend upon the type of liquid? After all, we don't believe that the pressure of a gas depends upon the type of gas molecule. So, we might have guessed that the vapor pressure will be independent of the type of liquid because the vapor up here is behaving as an ideal gas. It must be that there's some change in the liquid. The rate of condensation presumably does not depend upon the type of gas, but the rate of evaporation very well might. We're going to pick that up in the next lecture.