 So, at some level, the point of everything we're learning in physical chemistry or chemistry whole is to be able to predict what's going to be happening in some chemical process. Perhaps some chemical reaction, perhaps some physical process, but we'd like to be able to predict what's going to happen before we actually observe whether it does or doesn't happen. And the term we use for that in chemistry is spontaneity. We say that a process is spontaneous if the reaction will proceed, if the process will happen, or we say that it's non-spontaneous if it won't happen. So we can certainly identify all sorts of processes, some that will happen, some that won't happen, and sometimes the answer to whether that's a spontaneous process is perfectly obvious. So, for example, if I let go of this marker, it's every single time what's going to happen is the marker will fall. Gravitational energy will pull that marker down. If we write that as a more chemical example, something that will spontaneously move to a lower energy. If I draw an energy ladder for some system, there's some ground state and some excited state. If the particle is in the excited state, it will spontaneously fall down to the lower state. So the particle in the upper wave function will move down to a lower wave function. That is a spontaneous process. The reason that happens is because for that process the energy decreases. Energy one is lower than energy two. Things spontaneously lower their own energy at least under certain conditions. So that's a spontaneous process. That one's not terribly hard to predict. But energy is not the only criterion that we use to explain or to understand when something happens spontaneously. If we think back to when we were talking about the early stages of defining Boltzmann distribution and gas expansion. If I have a box containing molecules of a gas and right now all the molecules are at the lower portion of the gas, perhaps I've just raised the lid on this box of gas molecules. We know that what will spontaneously happen, because we know how gases behave and because we've treated that system mathematically, is that the gas will expand. The molecules confined to the lower portion of the box will spontaneously expand and occupy the larger volume. If this volume was V1 and this volume is V2, I can say that the expansion from V1 to V2 will spontaneously happen. The reason for that is because even if the energy of the two gases is the same in both cases, an ideal gas has no difference in energy in this system versus this system, but the entropy is greater. The reason that expansion takes place is because the second system has a greater entropy. Sometimes we say, of course that's spontaneous because the energy is lower, or of course this is spontaneous because the entropy is larger. How do we know when to use energy as an explanation? Sometimes, in fact, they're in conflict with one another. Let's take a chemical reaction as an example. Maybe not a chemical reaction, just a phase change, melting water from solid phase to liquid phase. That's not changing the chemical identity, just changing the phase of the matter. If I brought an ice cube into the room and I ask you, is it or is it not spontaneous that the ice will melt and turn to liquid? Will that happen? Then yes, because the temperature in here is 25 Celsius or something like that, it's above the melting point of water, then that is a spontaneous process. It will be spontaneous. The water will spontaneously melt from the solid form to the liquid form at room temperature. Let's say the temperature in here is 298 Kelvin, but what if we did that outside on a very cold winter's day where the temperature is below freezing, 260 Kelvin, then of course it wouldn't be spontaneous. Ice would remain in the solid phase and would not spontaneously melt to be in the liquid phase or at a temperature below 273 Kelvin, below the melting point of water. Sometimes the process is spontaneous or not depending on the conditions. As we'll see soon enough, the reason this is true is because the arguments about energy and the arguments about entropy conflict with one another. Melting ice actually increases its energy, but also increases its entropy. Entropy once the water dictates that the water should melt, energy dictates that the water should freeze. Under some conditions, the entropy wins. Under other conditions, the energy wins. Another more complicated example, a more bona fide chemical reaction. Let's take a chemical reaction like, let's say I have methyl benzene and I bring that into contact with some chlorine. What's going to happen in that reaction? So I could give you a product and ask, will that spontaneously form? Or more commonly as a chemist we might say, here's reactant A, reactant B, or bring them together, what will they form? What will they spontaneously form? Will they do nothing? Will they form product C or product D or product E? In fact in this case, depending on the conditions, we might get perhaps nothing will happen. Perhaps the chlorination will happen in the ortho position. Perhaps the chlorination will happen on the methyl group. So there's a variety of different things that could happen in this reaction and again, they'll depend on the conditions. They'll depend on what temperature the reaction happened at. They'll depend on whether there was a particular type of catalyst in the reaction, whether it was in the gas phase or the liquid phase, whether it's in the presence of light, which is commonly used to direct this reaction. So the conditions will affect what goes on. And that's the main goal of many chemists is being able to understand and predict and use these reactions under different conditions to get control over what we get. So it's very important to be able to understand what processes are spontaneous and which ones are not. From a physical chemistry point of view, if we take a step back and ask for any process, whether it's a phase change, a chemical reaction, volume change, whatever it is, we want to ask is some state, is this process alpha turning into beta? Is that a spontaneous process or not? We have an easy way to answer that question. Boltzmann tells us that the probability of this state, the alpha state, is e to the minus energy of that state over kT. And let's not forget that there might be some degeneracy. So the alpha state might have a degeneracy that's not just one. So we'll include that possibility. The beta state has its own degeneracy and its own energy. So here's the key to understanding why some processes, in particular the most interesting chemical processes, are spontaneous or not depending on the conditions because of this conflict between the energy and the entropy. In fact, so pretty clearly this energy term explains how the energy comes into play if the energy of alpha is bigger than or smaller than beta, that can determine which of these two probabilities is greater. In general, it's certainly going to be true that if the probability of alpha is bigger than the probability of beta or the other way around, let's in fact consider this second possibility first, if the probability of beta is bigger than the probability of alpha, then that will be a spontaneous reaction. The probability of seeing this one is larger than the probability of seeing this one. On the other hand, if the probability is larger for alpha than beta, then that will be a non-spontaneous reaction. So if we're able to calculate the probabilities, we'll know whether spontaneous or not. Sometimes energy is what matters. If the energy of beta is lower than the energy of alpha, then the energy can affect the probabilities. On the other hand, sometimes it's the degeneracy or phrased differently, the entropy of these systems that determines which is more probable. So for some systems, the energy is the same and the entropy is all that matters. For other systems, if the degeneracy is the same and the energies are different, that's all that matters. For most interesting chemical systems, both the degeneracy and the entropy matter, and so we need to be able to make more complicated predictions about when one of these is larger than the other. We can do this. In fact, we have done this for several cases using this Boltzmann distribution, but that begins to get a little difficult for large complicated chemical systems. It's going to be much more convenient to be able to do this, not with complicated statistical mechanics equations, but with thermodynamic equations as well. So using just the energy and just the entropy and using some other thermodynamic variables that we'll define very soon to be able to predict whether a reaction is spontaneous or not. So that's where we're going next.