In this concept development study, we're going to begin our study of spontaneous processes, events which are actually occurring at the macroscopic level. We've spent a lot of time so far talking about equilibrium systems. Equilibrium systems consist of those in which the macroscopic properties are not changing. we know that that is not because nothing is happening, rather that because there's a dynamic equilibrium amongst the process that might be taking place. We're going to begin to study instead now processes in which the properties are changing, and the process will actually learn a bit more about processes which are at equilibrium. Let's compare equilibrium versus spontaneity then, to make sure we understand what we mean by a spontaneous process. At equilibrium the macroscopic properties of the system the numbers of moles, materials which are present over their concentrations, the temperature they're held at or the pressure that we observe. All of those are constant despite the flurry of activity taking place at the molecular level. In a spontaneous process the macroscopic properties. Are changing, and they're changing in a way which is irreversible. For example, if I put a drop of ink into a glass of water, that drop of ink will dissipate throughout the glass of water, that's clearly a change in a macroscopic property, and in addition, it's a change which is very, very difficult to reverse. It's not an equilibrium. And, in addition to not being equilibrium, it's difficult to undo. Another example might be taking hydrogen gas and oxygen gas and sparking them to create an explosion in which hydrogen and oxygen produce water. Clearly that's a significant change in the macroscopic properties. I no longer have hydrogen and oxygen, and instead, I have H2O. And furthermore, it's very difficult to undo that reaction. Take the water molecules back apart, and turn them back into Hydrogen and Oxygen, and again. There's some interesting examples of spontaneous process that I want to consider here because we're going to use them for illustrations. Clearly as you can see on the camera over here. I've got a deck of cards. And one of the aspects that we see in this spontaneous process is a nice illustration, is in fact, the shuffling in the deck of card. This particular deck of cards has been carefully ordered to be in order, two through ace of diamonds, two through ace of clubs, two through ace of hearts. And two through ace of spades. And you know from your own experience with cards that I've had to do a lot of work to put them in this direction. If, instead, what I do is simply shuffle this deck of cards in the normal fashion, doing a quick rifle shuffle, we know what the outcome of this experiment is going to be. Spontaneously. The deck is going to go from a well-ordered deck into a significantly disordered deck. We now turn the cards back over again. There are some cards which are in order, but there are other cards which are not in order. And, in fact, by shuffling repeatedly, what I'll discover is that I generate greater and greater disorder. And reversing the process by which we've gone from the shuffled deck to the ordered, the ordered deck to the shuffled deck will require some extra intervention. We never see that happen spontaneously during the shuffling process. Another simple example would be the process of simply scattering things. Scattering seeds into a field or tossing things out on the floor. We rarely thin, see the occasion that we might spread some seeds and have them all stacked up on top of each other or aggregate in one location. Rather they scatter rather randomly. I mentioned the example of mixing a little while ago. If we mix two fluids together, one of which has say, color, and one of which does not. We rapidly see that the color fluid dissipates throughout the non colored liquid, and does so in a way which is irreversible. What about chemical processes? Well, the burning of methane in a stove converts the methane into into water and into carbon dioxide. And the process of turning that water and carbon dioxide back in to methane is extremely difficult, but it happens spontaneously all we have to do is spark the combination of methane and oxygen, or on a cold day we see the condensation of a or on a cold glass of water within a high humidity area. We see this spontaneous condensation of water on the outside of a cold glass. That happens without any intervention from us, and clearly is a change in macroscopic properties. Or, we might observe over a very long period of time the formation of rust in an object of iron which is continually exposed to the elements, particularly oxygen or some other oxidizing agent like water. Those processes occur at very different rates, the burning of methane is extremely rapid, the formation of rust is extremely slow, but they're all spontaneous. Indicating that a spontaneous process has nothing to do with how fast the reaction occurs, but rather whether the reaction occurs without any external intervention, and in such a way at to not be spontaneous. Now knowing what a spontaneous process is we might ask the question, why is it that some processes are spontaneous and others are not? Let me click back and look at the previous line, for example in the formation of rust we never see rust spontaneously separate into iron and oxygen. We never see the carbon dioxide in water spontaneously turn back into methane. What is it that causes the forward process, the burning or the rusting, to occur spontaneously, and not the reverse? Also, we know that sort of the contrast to a spontaneous process is an equilibrium process. If things are not occurring spontaneously then we must be at equilibrium. Understanding why things happen spontaneously may also give us some clues as to why things come to equilibrium. Let's further our study now by considering, then, the following simple case for the possibility of, say, a crystal turning into a gas or a gas turning into a crystal. Let's imagine we have a simple universe in which we have only four atoms, and we have a container in which they could be placed in which there are only 16 places that those four atoms might belong. If the four atoms are together, we're going to regard that in a sense as a crystal, because it's a well-ordered structure in which all of the pieces are near to one another. Sorry. If the particles are not near to one another as in the case on the right we're going to regard that as a gas. What we're going to consider then is the possibility of which one of these is a more probable outcome. To do that, let's actually count the numbers of ways in which we might be able to form that crystal. There are a variety of ways. We think about this box in which we have now contained 16 possible locations for the particles. The numbers of ways in which we might have put four of the particles together would include. For example, that arrangement. Or, they may have included, this arrangement. And in fairly rapid fashion, you'll be able to discover that there are in fact a total of nine ways in which we can form a crystal. With all four of the particles together. By contrast, the number of ways in which we can form a gas is really quite large. In order to count those, it's much easier actually to count, in total, how many ways are there to arrange the four particles over the cross of the 16 different places? Here's the total ways in which we could do that. Well, let's see. There's 16 locations, so there's 16 places in which I could put the first particle, and 15 places I could put the second, and 14 where I could put the third, and 13 where I could put the fourth. But, of course, it's random which of the four particles I chose to make the first one. There are four different particles that could have been the first one, three which could have been the second, two which could have been the third, and one, then, which would have to be the last. This turns out to be the total number of ways of arranging four particles, four identical particles, into those sixteen locations. Just plugging this into a calculator, we discover there are 1,820 ways to arrange those particles across the entire grid here. And nine of those correspond to forming a crystal. So correspondingly it must be that there are 1,811 ways. In which we can form a gas. Very significantly different there are nine ways to do this. There are 1,811 ways to do this. That suggests actually that the more ordered something is the fewer ways there are to be able to produce that order. And that begins to give us a hint as to what we want to look at. We're going to begin to look at probability as a means of making predictions. So, for example, we ask the question, why did the ordered deck become the disordered deck? The answer is, because it's much more probable to have a shuffled deck when we shuffle the cards. It's certainly possible that I could shuffle these cards and wind up with them all completely in order but it's extremely improbable. And since it's so improbable in fact I never observe it. Even though it is in fact a possibility. Similarly. Comparing to the idea of the crystal versus the non crystal it's certainly possible that I could throw the four marbles into these boxes and see a crystal, but the odds are only about one in 200 that that might happen. So in general if I throw the particles down I'm going to observe something we would describe as a gas. What that suggests is in general, systems almost always go from a state of low probability to a state of higher probability. And things that happen, generally happen because they are higher in probability. But what do we mean by the probability of a state? What are we actually describing here because for example, if I go back to this deck of cards. There is in fact a state in which the bottom card is the 10 of diamonds. The next card is the three of clubs. The next card is the eight of hearts. The next card is the two of diamonds. And the probability for arranging the cards that way is exactly the same as the probability for arranging the cards as they were at the start of this lecture. Ace, I'm sorry, two through ace of diamonds, two through ace of clubs, and so forth. So there's something else going on here that we describe in terms of macrostates and microstates. In the case of the deck of cards, the microstate tells you where is every single card in the deck in a particular order. There are a huge number of microstates. Corresponding to 52 choices for the first card, 51 choices for the second card, all the way down to the last card. Where as the mi, macro state is simply a description of the macroscopic particle property. Is the deck shuffled, or is the deck ordered? And it turns out there are a great many ways to arrange the cards that we call shuffled, and very few ways to arrange the cards that we call ordered. A different way of saying that is there are a great many micro states corresponding to the macro state, which is disordered. And very few micro states. Corresponding to the macro-state which is ordered. Let's apply that to the idea of a collection of molecules. The micro-state is where are each of the molecules like this. This is a particular microstate. So is this. They both belong to the macrostate that we call the crystal. So, the macrostate called crystal and a macrostate called the gas, the number of ways of arranging the number of microstates corresponding to the crystal is quite small. The number of macro, microstates corresponding to the gas is actually quite large. That suggests that we begin to measure that probability, and we measure it with a number we call W. W is the number of microstates which correspond to a particular macrostate, as we've seen here. Don't know why that's in the way. We then define something we'll call the entropy. The entropy is a measure of probability in just the same way that W is a measure of the probability. That is back over here the probability of the gas is very much greater than the probability of the crystal. The way in which we define the entropy is in fact in terms of. The logarithm. We take the entropy to be the logarithm of W, where W is a measure of the number of microstates for a particular macrostate. In other words, there's an entropy associated with each macrostate that corresponds to a particular arrangement in the number of particles. Notice in this equation. The entropy is large when W is large where W is the number of microstates. And W is large when the probability is large because the more microstates that there are the the more, the larger the probability will be for spontaneously choosing one of those microstates. As in the case of the shuffled deck of cards. That suggests if the probability always increases, that is, we always move from a less probable state to a more probable state, then W always increases. And if W always increases, then S always increases. This is actually going to be our first stab at the Second Law of Thermodynamics. That if we define S to be k times the logarithm of W, then S will increase in any spontaneous process because W will increase in any spontaneous process, because the probability will increase in any spontaneous process. This turns out not to be a fully qualified statement of the Second Law of Thermodynamics. But it's a great start because it tells us at the outset that there's a relationship between spontaneity and probability, that which happens is that which is most probable in the universe. We now have to define this more carefully and bring it into the context of chemical systems.
