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About this Lesson
 Type: Video Tutorial
 Length: 14:13
 Media: Video/mp4
 Use: Watch Online & Download
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 Posted: 07/14/2009
This lesson is part of the following series:
Chemistry: Full Course (303 lessons, $198.00)
Chemistry: Thermodynamics (8 lessons, $14.85)
Chemistry: Entropy (2 lessons, $4.95)
This lesson was selected from a broader, comprehensive course, Chemistry, taught by Professor Harman, Professor Yee, and Professor Sammakia. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/chemistry. The full course covers atoms, molecules and ions, stoichiometry, reactions in aqueous solutions, gases, thermochemistry, Modern Atomic Theory, electron configurations, periodicity, chemical bonding, molecular geometry, bonding theory, oxidationreduction reactions, condensed phases, solution properties, kinetics, acids and bases, organic reactions, thermodynamics, nuclear chemistry, metals, nonmetals, biochemistry, organic chemistry, and more.
Dean Harman is a professor of chemistry at the University of Virginia, where he has been honored with several teaching awards. He heads Harman Research Group, which specializes in the novel organic transformations made possible by electronrich metal centers such as Os(II), RE(I), AND W(0). He holds a Ph.D. from Stanford University.
Gordon Yee is an associate professor of chemistry at Virginia Tech in Blacksburg, VA. He received his Ph.D. from Stanford University and completed postdoctoral work at DuPont. A widely published author, Professor Yee studies moleculebased magnetism.
Tarek Sammakia is a Professor of Chemistry at the University of Colorado at Boulder where he teaches organic chemistry to undergraduate and graduate students. He received his Ph.D. from Yale University and carried out postdoctoral research at Harvard University. He has received several national awards for his work in synthetic and mechanistic organic chemistry.
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The second law of thermodynamics tells us that the entropy of the universe must increase for any spontaneous process. That tells us that either the entropy's increasing in terms of the chemical reaction or it's increasing in terms of heat being released into the surroundings. And as heat is released into the surroundings, the entropy of the surroundings increases. But overall, we know that entropy must increase for any spontaneous process, thus entropy is a really big deal. It means a whole lot to us in determining whether a reaction is going to happen or not. So let's talk a bit more about entropy and let's define it now mathematically.
There are a lot of different definitions we could give for entropy, but the one that's going to be most useful for us is that the entropy change for a process is the heat divided by the temperature, if the process is reversible  in other words, if it's in equilibrium, then the change in entropy if we put in heat. So imagine, for instance, a phase change where we're holding the temperature constant but we're adding just enough heat to convert from one phase to another  let's suppose we're boiling  that the entropy increase for that process is the heat required to cause the phase change divided by whatever the temperature change is.
Now, for a spontaneous process  one that's not reversible  we don't know exactly what the entropy is, but we know that the entropy change must be greater than this value  the heat that we put in divided by temperature.
Okay, now before I go on here, let me give you a sense of what we're saying in English. If you put in heat, that causes disorder because it's random thermal energy that we're putting into a compound  into a material. But the amount of disorder depends on what the temperature is. If we're at very high temperature, there's already a huge amount of disorder. So adding a certain amount of heat at very high temperature doesn't change things a whole lot. But if we're at a very low temperature  say somewhere down near 0° Kelvin  adding the same amount of heat a low temperature causes a tremendous change in the amount of disorder. So that's why we have this kind of heat, or at least to give you a sense of why this would be.
Now, we know that if we're talking about a chemical reaction that the heat given off or absorbed at a constant pressure is the enthalpy. Remember, that was our definition. Enthalpy was defined as the heat released at constant pressure. And so if we substitute in H  as long as we're talking about a constant pressure system  then S for any spontaneous process has got to be bigger than . And rearranging this, what it tells us is H, for a chemical process, minus TS has got to be less than zero. Now let's hold onto that idea. We're going to come back to that. But that says if we know about S for a chemical reaction and we know about H for a chemical reaction, we have the tools to predict whether the reaction will occur or not. Because, again, this has to do with whether or not it's going to be spontaneous. So hold on to this idea. Again, a spontaneous reaction will only occur if H  TS < 0.
Before we talk about chemical reactions, let's return to the idea of just a substance. Now, we'll define S for a substance the same way we would as H, except that remember, when we talked about H, there wasn't a convenient way to determine the absolute enthalpy for a material. We found it convenient, though, to talk in terms of the state function, H, and that was relatively easy to do. We could measure that directly. Remember, that's the heat released at constant pressure.
But for entropy, it's different story. We actually can determine the absolute entropy for a substance. And so we'll define the S for a process or for a chemical reaction as the entropy  the absolute entropy, the absolute disorder  in the final state minus the entropy in the initial state. So that's just saying if we go from one level to another  one set of reactants to a set of products, for instance  that S for that reaction is just the final entropy minus the initial entropy, just like we've defined things before. But the difference is we can actually calculate values for these things now. So let's see how we would actually do that.
Actually, before we do that, we have to describe the third law of thermodynamics, which essentially says: What is your reference point? Well, our reference point is going to be  we want to pick a place to call zero entropy. Let's pick that place where we have absolute perfect order, and that's going to be where we sucked out all the energy  the random thermal energy  we possibly can from the system.
So we're going to define a substance with zero entropy as a perfect crystalline material at 0° Kelvin. Now what do I mean a perfect crystalline material? I mean as much order as we possibly can have. So for instance, I'm showing a cartoon of a diatomic molecule where the two atoms are different, and I mean, they all not only have to be packed perfectly together  no disorder in how they're packed  but they also have to be aligned properly so that there's no ambiguity about is the molecule pointing this direction or the opposite direction. As soon as we allow for that possibility, then there's disorder in the crystal. So understand, we need to have the perfect crystalline material without any type of disorder at all. That's what we'll define as zero entropy for every substance. Okay?
So now that we have identified a reference point  so here we are. That's what we just said. Zero Kelvins we have zero entropy. Now, as we raise the temperature of the substance, then we're adding heat to it  we're changing temperature as we're adding. Remember, our definition of entropy was heat divided by temperature. And the problem is how much heat we're putting in as we change the temperature depends on what the heat capacity is. Now, the hard part is the heat capacity is changing as we change our temperature.
So this is a difficult calculation. Fortunately, you don't have to do it. It's just the integral of the heat capacity as temperature's changing divided by temperature. But you won't have to do that. This is a value you'll be able to look up for any substance  at least that we're going to be asking you about or that you would be asked on an exam or something. And you can find that in the appendix. Now, again, that's changing with time. We'll talk in a little bit about why heat capacity's changing as we go through this period. But for right now, let's just say that you can find out a value for a substance  you can look it up in a table  and this is corresponding to a solid material, still in its crystalline state. Now, we're going to go through a phase change, from solid to liquid. This is the entropy of fusion we need now. This is fairly easy for us to figure out, because we know the heat that we're putting in to cause that phase change  at constant pressure, remember, that's just the heat of fusion  H of fusion  divided by whatever the temperature is that that occurs at. So that's a value that's easy for us to calculate. Then, we have to go through this period again. This is more difficult to calculate, but once again, we can look up values. Then we go through the entropy change for vaporization, and you'll notice, that's a lot bigger than the entropy change down here.
Why would that be? Well think about what common sense tells you about how much disorder changes going from solid to liquid and going from liquid to gas  a huge amount of disorder when we go from liquid to gas. And in fact, more or less, the amount of disorder  the amount of entropy increase  that we have when we go from liquid to gas is almost a constant for all substances, because it depends so much on just the fact that you're increasing the number of particles in the gas phase.
Now, beyond there, we'll need to calculate based on what our heat capacity changes are again. But the point is that somebody else, some other poor guy, has calculated all this for you, so you don't have to go through all this. You can look at up, at room temperature  or wherever room temperature is, depending on what substance you're dealing with  what the value of the absolute entropy is. Great! So you can find that out, and in a moment, we'll see that that allows us to find out S for a chemical reaction. And we need to know S why? Because if we know that and H tells us about G, which tell us  oops  I didn't tell you about G yet. Strike that. It tells us about whether or not the reaction is spontaneous or not though. I just gave you a little glimpse of the future.
Okay, now let's see what a problem would look like. So we've got liquid carbon tetrachloride; it evaporates. It costs heat, of course, to evaporate  34 kilojoules worth at 25 degrees. Now, that's not the boiling point, but it doesn't have to be. This is just describing a phase change at 25 degrees here. We want one mole of liquid. It's got an entropy of so and so. What's the entropy of that liquid when it's converted to the vapor phase  not changing temperature, just putting in enough heat to convert it to the vapor phase? So S then  the change in entropy going through that phase change  is . So we've got 43 X 10^3 joules. Notice I'm describing it in joules so that my units are correct. I'll divide that by temperature and I end up with 144 joules per mole Kelvin. Okay? Now, remember, that was the change in entropy and to find the total entropy of that substance, I need to take what I started with, which was the 214, and add the amount of increased entropy to go through that phase change. So my total entropy, after going through the phase change, is 358 joules. So what am I doing? I'm just simply looking at going from here to here  that change in entropy here. I'm going through that phase change again. So that would be a type of problem you'd get having to do with figuring out absolute entropy of a substance.
Now, talking about this, why is it that heat capacities are different for different materials and why do we have to consult these tables of numbers? Let me give you a little bit of a sense of this, because it's a very important idea. And we understand a lot about the molecular level now. Where does the notion of heat capacity come from? Remember, heat capacity has to do with the ability of a substance to store energy. The more it can store energy, the less its temperature will rise as we add more heat to it. Now the best way I know how to give you a feel for what this means is by analogy. Look at these two different beakers here, and in my analogy, the height of a liquid in these beakers will correspond to temperature. But you'll notice that they have different capacities to store that water, in that this is a bigger diameter than this is. I'm now going to add 100 joules, if you will, of energy to each of these two different substances. And what I'm really going to do is add 100 milliliters of water, but it would correspond to an amount of energy. And so if I put in 100 milliliters of water into this material  or 100 joules of energy into this material  compared to 100 joules into this material, you'll notice that the temperature rose a lot higher  the water level rose a lot higher  in this beaker than this. The analogy is for something with a smaller heat capacity compared to a large heat capacity, the same amount of energy causes very different changes in temperature.
Well, why do things have different heat capacities? It's because they have different ways of storing that energy. Just about all molecules can go through rotations and vibrations and move to some degrees, but that depends on what phase they're in. If they're in the solid phase, they can't easily rotate, for instance. On the other hand, if they're in the liquid phase, not only can they vibrate within their molecule, but they can vibrate against each other. So there are intermolecular vibrations, and those also can help start things. So liquids have a much higher heat capacity than do gases or solids because of these additional vibrations. Plus they have more of these other degrees of freedom in the liquid phase.
So again, the heat capacity for a substance depends on what the atoms are connected together, how they're connected and what kind of bonding you have between the molecules as well as within the molecules. That's why we need to look up heat capacities for every different substance, or look up the absolute entropy for every different substance, because it's going to differ, because these molecules are all different.
Finally, real quickly, how would you calculate S for a chemical reaction? Piece of cake. You go to the tables that tell you the absolute entropy of everything and in this case, our example here is hydrogen and oxygen gives water. We find the absolute entropy of water at the appropriate temperature and subtract from that the absolute entropy of our reactants  in this case hydrogen and oxygen  and that gives us then the entropy change for that chemical reaction. Once again, the reason that's important is once we know S and we can measure H or look up H, then we're all set to go. We can figure out whether the reaction will spontaneously occur or not.
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Entropy
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