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0:03
As we start this next section on thermodynamics, let's begin with the very basic question. What is thermodynamics? Thermodynamics is a branch of physics that describes the relationships between different forms of energy. And it's important for chemistry because it helps us understand all the different energy changes that happen during a chemical reaction. And in understanding that, we can then explain and predict the spontaneous direction of a chemical reaction.
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The field of thermodynamics began in the 19th century, primarily to make steam engines more efficient. So, steam engines like the train shown in the picture below, were driven by heating water until it formed steam. And the steam would be used to push pistons back and forth, that were connected to rods and fly wheels that would move the train wheels. And so ultimately in a steam engine, heat, a form of energy, is being converted into mechanical work. So in the early days,
1:20
the different forms of energies that thermodynamicists were interested in, were how to interconvert heat, work, and temperature with the idea that you want to maximize the work you get out. In the physics point of view, you can think of this steam mention more simply, as a hot reservoir that has heat represented by q coming out. And this arrow turning around the corner just means that you want to convert that heat into work. And the ideal was to extract
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all the heat you could to do all the work that you could. Now, there are three fundamental laws of thermodynamics. And this idea of extracting all the heat to do only work is actually impossible by the second law and forbidden. To understand how thermodynamics impacts a chemical reaction, let's return to the reaction energy diagram. If you recall, in this diagram, we're following that energy changes during a chemical reaction. Energy is along the y-axis and the reaction progress is along
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the x axis where we have reactants at early points, and product at the later point. If you'll remember that the change in energy between reactants and products is represented by this blue arrow, where delta E(reaction) signifies the change in energy of this reaction, which would be equal to the energy of the products minus the energy of the reactants. Also, there is this activation energy barrier shown in red. And if you'll recall, this yellow line represents the trajectory as
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reactants reach the transition state and ultimately can turn to products. And this trajectory is also linked to the mechanism of how this reaction proceeds. So in understanding chemical reaction, we're very much interested in two primary topics: kinetics, which we covered earlier, and thermodynamics. And kinetics is just about how fast. And oftentimes we measure a rate constant. Thermodynamics, on the other hand, covers many more of the fundamental questions, such as what product is favored?
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So as written, we have reactants going to products. but sometimes it's actually the reactants that are favored. That also tells us about what reaction direction is favored. Now, even if the products are favored, it's not necessarily that they will form 100%. That depends on the extent of the reaction or its conversion, which is ultimately tied to the equilibrium constant. So these important thermodynamic questions all can be predicted and explain by thinking about the different energy changes
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happen during this chemical reaction. We spend a lot more time thinking about enthalpy in general chemistry. And now we're into section, we're going to introduce two new kinds of energy. One, entropy will be the focus of this video. And a second one, the Gibbs free energy will be something that we introduce later on. Physicists love to use simple models to explain complex phenomena. So in this case, I'm gonna take a physicist's point of view and start to define things in simple ways.
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So I'm going to define the universe as everything in existence in this blue box. And within my universe, in this yellow circle, I'm going to focus on that and call it, my system. It's probably something that I'm interested in, like the chemical reaction. Now, everything that is in the universe, but not my system, would be called the surroundings. And so my universe is only composed of my system and its surroundings. And if I wanted to tally the total energy of the universe, then
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I could write it neatly as a sum of the energy of my system plus the energy of my surroundings. In this universe, the system and the surroundings are not isolated from one another. And so it's possible for energy to exchange in-between these two components. The ways that energy can be exchanged are through two forms. Heat as represented here by q and work represented by w. Now heat and work can exchange in either direction, either from surroundings to the system,
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or from the system to the surroundings. So to make this case a bit simple, I'm just going to focus on one directional change. So for instance, here, the system is absorbing heat from the surroundings, but the system is performing work on the surroundings. And so if you look at the energy of both of these components before and after this exchange of heat and work. Now notice that while one loses heat, the other gains heat. And if one loses work, the other gains work.
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And what that then means mathematically, as if I were to write the change in the energy of the surroundings plus the change in the energy of the system and sum that up, these components would all sum to 0. And remember that the universe is composed entirely of system and surroundings. So that means then the change in the energy of the universe is 0. The idea that the change in energy of the universe must always be 0 is the first law of thermodynamics. And so again, that means energy cannot
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be created and it cannot be destroyed. And there's always this conservation of energy. Another way of putting it in the words of one of the founding fathers of thermodynamics, Rudolf Clausius is that the energy of the universe is constant. So this plot here kind of shows the first law of thermodynamics, where we have energy on the y-axis and all time, so from the Big Bang through the age of dinosaurs, through today and to eternity, no matter what, this will be a flat constant line
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because there will be no change in energy. Before we discuss the second law of thermodynamics, let's talk about the many definitions of entropy that are all related. Entropy is sometimes defined as a measure of the amount of energy that is unavailable for work. It can also be a measure of the disorder of a system or the multiplicity of a system. And in a very specialized case of a reversible process, the entropy change can be related to the heat of that reversible process
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divided by the temperature. Now disorder is often the most common word associated with entropy. And so there's lots of analogies made to messy rooms. And like in this cartoon, a messy office where there is at Department of Entropy [sign] on the door, that this is a natural order for things. For thermodynamicists, this is what entropy meant. That if you have a hot reservoir, you can't extract all the heat into work. That some of that heat will naturally be lost.
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Because this hot reservoir exist in a surrounding that is colder than its temperature. And so Qc represents that amount of energy that is unavailable for work because it is simply lost as radiation of heat into the environment. In addition to disorder, higher multiplicity or more freedom of motion are also associated with a larger, more positive entropy. To help think about these concepts, I have some images shown below. And in each of these boxes, one of these images has the highest entropy.
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In the first box, we have two dice that were thrown. And it's showing that there is only one combination that can sum to two. However, if you were looking for a sum of seven, then you have many more combinations that can sum towards seven. This is a concept called multiplicity. In both of these states, there's only two dice, but there's a different energy level associated with the total sum of what's rolled. And for seven, it has more chances of getting a seven than a two. So in other words,
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you can also think of multiplicity as probability. And typically, a higher multiplicity has a higher entropy and therefore is more probable. On the other side, we have three flasks where we have a solid, a liquid, and a gas. And to compare these three states or phases, basically the higher entropy relates to the more disorder or freedom of motion. A solid is typically highly ordered [and little freedom of motion]. A liquid has some freedom of motion, but not as much freedom of motion as it gas.
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And so for phases, the entropy of the gas is always much greater than the entropy of a liquid, which is greater than the entropy of the solid. And so in this set of images, it would be the gas. The second law of thermodynamics states that the Universe always moves towards greater entropy. Another way of writing that is that the change in entropy of the universe, delta S universe, must be greater than 0. And one way I like to think about the first and the second law of
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thermodynamics is simply by these equations. So in the first law, the change in energy of the universe must be equal to 0. But in the second law, the change in entropy of the universe must always be greater than 0. So for the first law, it states, "you can't win". You can't get more than what you start with. The second law, on the other hand, says, "you can't break even". So not only can you not get more than what you start with, but some of what you started with will be
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lost irreversibly and you can't get it back. And so you won't even end up even because of the second law and the fact that the universe will always go towards greater entropy. The second law is one of the most profound laws in physics. And this is sort of captured by the quote here from Rudolf Clausius. "The more the universe approaches this limiting condition in which the entropy is maximum, the more do the occasions of further change diminish. And supposing this condition to
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be at last completely attained, no further change could ever more take place. And the universe would be in a state of unchanging death." It sounds very grim, but it's also extremely fascinating to think about the universe from, this image here, the Big Bang and then exploding and cooling to form different galaxies and also our planet Earth. And so today our universe is cooler, more disordered and more spread ou than the universe at initial time. And to think that with time we'll
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continue that disorder until we reach a state of maximum entropy in which no more change could ever happen. Let's return to chemical reactions. The reason we need entropy is because enthalpy by itself cannot predict whether a reaction will be spontaneous. In these two examples below of chemical reactions, these are both spontaneous and do occur. We have in the first example, a molecule of N2O4 splitting, breaking the nitrogen- nitrogen bond to form two molecules of NO2.
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And in this reaction, enthalpy actually favors the reactant. So the N-N bond requires energy to break. On the other hand, entropy favors the product of this reaction because we have now two moles of gas instead of just one. In the second example, we also have a case that is known to spontaneously occur. If you leave a class of water out at room temperature, it will slowly evaporate. And so this is the vaporization of water from the liquid form to the gas form. Again, if we think about enthalpy,
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it actually favors the liquid form because we have all these hydrogen bonds that require energy to break to have these water molecules be in the gas state. However, entropy favors the gas state because now each of these water molecules has a much greater freedom of [motion]. And so the entropy change in this vaporization is extremely large. And both of these reactions, that delta H of the reaction is endothermic or positive. However, because both these reactions
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gain in entropy, then the delta S of the reaction is positive and large and favored. On the flip side, the entropy change of a reaction also does not predict whether a reaction is spontaneous. So here's a counterexample. We have magnesium burning in oxygen to form magnesium oxide. Now in this reaction, entropy favors the reactants because we have oxygen and it's a gas. On the other hand, enthalpy favors the product because the strong magnesium oxygen bonds that are
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formed release a lot of heat in this reaction. So that delta H of the reaction is highly exothermic and that is very favored. On the other hand, the change in entropy is negative, and that means it's disfavored. The fact that this reaction occurs still actually is back to the second law of thermodynamics, where delta S of the universe must be greater than 0. If this is not satisfied, then those events or that chemical reaction would never take place. So how does this work?
19:24
Well, in this chemical reaction, the delta S is not representative of the universe. Rather, delta S of the reaction might be represented by delta S of the system. And we also have to take into account what the delta S of the surrounding is. Because this reaction is highly exothermic, that means our system, the chemical reaction, is releasing heat into its surroundings. And as we release heat to the surroundings, the temperature of the surroundings will increase and
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therefore the entropy of the surroundings will increase. And so we can think of delta S universe as equal to the sum of the change in entropy of the reaction, which is indeed negative. But now if we account for all that, he got was released into the surroundings, then the delta S surrounding is actually a very large positive number that out weighs what's lost from the system such that the second law of thermodynamics is still satisfied. The third law of thermodynamics
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is really just defining what is 0 entropy. And that would have to be a perfectly ordered crystal at 0 Kelvin. Now, if you raise the temperature above 0 Kelvin, atoms can vibrate and that would add entropy, so it has to be at 0 Kelvin, where these atoms are absolutely still. Because of the zero point, we can actually have [absolute] entropy values for different chemicals. And oftentimes these are reported as standard molar entropies. And the standard refers to the fact that for gases,
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this would be at one atmosphere pressure. For solutions, this would be at one molar and typically the temperature is 298 Kelvin. Now, the units of standard molar entropy is joules per moles times Kelvin. Also, standard molar entropies will increase with temperature. They will also depend on phase, as we saw in the earlier example, where the standard molar entropy for gases will be much greater than that for liquids, which will be greater than that for solids.
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Because the entropy of a gas is so much greater than the entropy of a liquid or solid, then we can say that in a vaporization reaction, where a liquid is changing to gas, the change in entropy will be much larger than a fusion reaction, where a solid is turning into a liquid. And again, that's simply because gas is being formed in the vaporization reaction. We can also talk about dissolution and the entropy change related to that. So when you to solve a solid in a liquid,
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typically delta S increases. There are some rare exceptions, such as highly cationic metal ion salts [e.g. Al+3] that dissolve in water. And that's because they actually order the water quite well rather than disorder. But in general, most dissolutions of salts and solids in solution are positive for an entropy change. Now, if you dissolve a gas in a liquid, the delta S there will be negative. And that's because you have a gas with lots of freedom of motion.
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But when you dissolve it in a liquid, you're severely restricting its ability to move. And so the entropy will decrease for dissolving a gas. The standard molar entropy will also increase for chemicals with increasing atomic size or molecular complexity. So to illustrate molecular complexity, here are three related chemicals: NO, NO2 and N2O4. And by looking at their standard molar entropies, we can see that entropy is increasing as we go down the set.
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The primary reason for this increase in entropy is the fact that with increasing size and complexity, we have more degrees of motion available to these molecules. So in the top case, a simple diatomic molecule, aside from translation and rotation, the only other degree of motion is this bond stretch of the NO bond, where the bond can vibrate like this. But if we move to a triatomic molecule, now we have two bond stretches. And we also have a potential to bend the molecule.
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And that bending motion then is another degree of freedom. If we move to N2O4, you can see now we have multiple bond stretches, multiple bending motions, and also therefore the largest standard molar entropy of the set.
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