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Gibbs free energy and spontaneity

Intuition behind why spontaneity is driven by enthalpy, entropy and temperature. Introduction to Gibbs free energy. Created by Sal Khan.
Video transcript
We've learned over the last several videos that if we have a system undergoing constant pressure, or it's in an environment with constant pressure, that its change in enthalpy is equal to the heat added to the system. And I'll write this little p here, because that's at constant pressure. So if you have a reaction, let's say A plus B yields C and our change in enthalpy-- so our enthalpy in this state minus the change in the enthalpy in that state-- so let's say our change in enthalpy is less than 0, we know that this is exothermic. Why is that? And once again, I'm assuming constant pressure. How do we know this is exothermic, that we're releasing energy? Because change in enthalpy, when we're dealing with a constant pressure system, is heat added to the system. If the heat added to the system is negative, we must be releasing heat. So we're releasing heat or energy. So plus energy. And we learned in the last video, I think it was either the last video or a couple of videos ago, we call this an exothermic reaction. And then if you have a reaction that needs energy-- so let's say you have A plus B plus some energy yields C, then what does that mean? Well, that means that the system absorbed energy. The amount of energy you absorb is your change in enthalpy. So your delta H is going to be positive. Your change in enthalpy is positive. You've absorbed energy into the system. And we call these endothermic reactions. You're absorbing heat. Now, if we wanted to figure out whether reaction just happens by itself-- whether it's spontaneous-- it seems like this change in enthalpy is a good candidate. Obviously, if I'm releasing energy, I didn't need any energy for this reaction to happen, so maybe this reaction is spontaneous. And likewise, since I'd have to somehow add energy into the system, my gut tells me that this maybe isn't spontaneous. But there's a little part of me that says, well, you know, what if the particles are running around really fast, and they have a lot of kinetic energy that can be used to kind of ram these particles together, maybe all of a sudden this would be spontaneous. So maybe enthalpy by itself wouldn't completely describe what's going to happen. So in order to get a little intuition, and to maybe build up our sense of whether a reaction happens spontaneously, let's think about the ingredients that probably matter. We already know that delta H probably matters. If we release energy-- you know, delta H less than 0, that tends to make me think it might be spontaneous. But what if our delta S, what if our entropy goes down? What if things become more ordered? We've already learned from the second law of thermodynamics, that that doesn't tend to be the case. And just from personal experience, we know that things on their own just don't kind of go to the macro state that has fewer micro states, you know. An egg doesn't just put itself together, and bounce, and kind of jump off the floor on its own, although there's some probability it would happen. So it seems like entropy matters somewhat. And then there's the idea of temperature. Because I already talked about, when I talked about energy here. I was like, well, you know, even if this requires energy, maybe if the temperature is high enough, maybe I could actually ram these particles together in some way, and kind of create energy to go here. So let's think about-- so let's see. let's think about the ingredients, and let's think about what the reactions would look like depending on different combinations of the ingredients. So the ingredients I'm going to deal with-- delta H seems to definitely matter, whether or not we absorb energy or not. We have delta S, our change in entropy. Does the system take on more states or fewer states? Does it become more or less ordered? And then there's temperature, which is average kinetic energy. So let's just think about a whole bunch of situations. So let's think of the first case. Let's think of the situation where our delta H is less than 0, and our entropy is greater than 0. I mean, my gut already tells me that this is going to happen. This is a situation where we're going to be more entropic after the reaction. So one way of looking at entropy, you could more states. Maybe we have more particles. We've seen that entropy is related to the number of particles we have. So this could be a reaction where let's say we have this-- see, we want to have more particles. So let's say I have that guy. And say he's got one guy like that there, and then I have another guy like this, and let's say he's got a molecule like this. Let's say that a more-- well, I won't say stable or not. But let's say that when these guys bump into each other, you end up with this. And I'm making things up on the fly. Maybe one of these molecules bonds with this molecule, so you have one of the dark blues. I'll draw all the dark blues. Bonds with this light blue molecule, one of the dark blues bonds with the magenta molecule. And maybe that brown molecule just gets knocked off all by himself. So we went from having two molecules to having three molecules. We have more disorder, more entropy. This can obviously take on more states. And I'm telling you that delta H is less than 0. So by doing this, these guys, their electrons are in a lower potential, or they're in a more stable configuration. So when the electrons go from their higher potential configurations over here, and they become more stable, they release energy. So you have plus-- and then I just know that, because I said from the beginning that my change in enthalpy is less than 0. So plus some energy. So it seems pretty obvious to me that this reaction is going to be spontaneous in this rightward direction. Because there's no reason why-- first of all, it's much easier for two particles to bump into each other just right to go in that direction than it is for three particles-- if you just think of it from a probability point of view-- for three particles to get together just right and go in that direction. And even more, these guys are more stable. Their electrons are in a lower potential state. So there's no even kind of enthalpic reason for them to move in this direction, or you know, kind of a energy reason for them to move in this direction. So this, to me, I kind of have the intuition that regardless of what the temperature is, we're going to favor this forward reaction. So I would say that this is probably spontaneous. Now, what happens-- let's do something that's maybe a little less intuitive. What happens if my delta H is less than 0? But let's say I lose entropy. And this seems, you know, with second law of thermodynamics, if the entropy of the universe goes up. I'm just talking about my system. But let's say I lose entropy. So that would be a situation where I go from, let's say, two particles. Let's say I got that particle, and then I have this particle. And then, if they bump into each other just right, their electrons are going to be more stable, and maybe they form this character. And when they do that, the electrons can enter into lower potential states, and when they do, the electrons release energy, so you have some plus energy here. And we know that, because this was the change in enthalpy was less than zero. We have lower energy in this state than that one, and the difference is released right here. Now will this reaction happen? Well, it seems like-- let's introduce our temperature. What's going to happen at low temperatures? At low temperatures, these guys have a very low average kinetic energy. They're just drifting around very slowly. And as they drift around very slowly-- And remember, when I talk about spontaneity-- I wrote sponteous. This is spontaneous. Sponteous should be another thermodynamic. It's a fun word. When I talk about spontaneity, I'm just talking about whether the reaction is just going to happen on its own. I'm not talking about how fast, or the rate of the reaction. That's a key thing to know. You know, is this going to happen. I don't care if it takes, you know, a million years for the thing to happen. I just want to know, is it going to happen on its own? So if the temperature is slow, these guys might be really creeping along, barely bumping into each other. But they will eventually bump into each other. And when they do, they're just drifting past each other. And when they drift past each other, they will configure themselves in a way-- things want to go to a lower potential state. I'm just trying to give you kind of a hand-wavey, rough intuition of things. But because this will release energy, and it will go to a lower potential state, the electrons kind of configure themselves when they get near each other, and enter into this state. And they release energy. And once the energy is gone, and maybe it's in the form of heat or whatever it is, it's hard to kind of get it back and go on in other direction. So it seems like this would be spontaneous if the temperature is low. So let me write that. Spontaneous if the temperate is low. Now what happens if the temperature is high? Remember, these aren't the only particles here. We have more. You know, I'll have another guy like that, and another guy like that. And then this, on this side, I'll have, you know, more particles. There's obviously not just one particle. Then all of these macro variables really make no sense, if we're just talking about particular molecules. We're talking about entire systems. But what happens here if the temperature of our system is high? So let's think of a situation where the temperature is high. Now all of a sudden-- so on the side, people are going to be knocking into each other super fast. You know, if this guy bumps into this guy super fast, you can almost view it as a car collision. Well, even better, this could be car collision. If these were each individual cars, and the atoms were the components of the cars, if they're like smashing into each other, even though they want to be attached to each other, they have screws and whatever else that are holding it together-- if two cars run into each other fast enough, all that screws and the glue and the welding won't matter. They're just going to blow apart. So high kinetic energy-- let me draw that. So if they have high kinetic energy, my gut tells me that on the side of the reaction, these guys are just going to blow each other apart to this side. And these guys, since these guys also have high kinetic energy, they're going to be moving so fast past each other, and they're going to ricochet off of each other so fast, that the counteracting force, or the contracting inclination for their electrons to get more stably configured, won't matter. It's like, imagine trying to attach a tire to something while you're running past the car. You kind of have to do it-- even though that's a more-- well, maybe the analogy is getting weak, here. But I think you get the idea that if the temperature's really high, it seems less likely that these guys are going to kind of drift near each other just right to be able to attach to each other, and their electrons to get more stable, and to do this whole exothermic thing. So my sense is that if the temperature is high enough-- I mean, you know, maybe say, oh, that's not high enough. But what if it's super high temperatures? If it's super high temperatures, then maybe even this guy will bump into that. Instead of forming that, he'll knock this other blue guy off, and then he'll be over here. I should do the blue guy in blue. And maybe he'll knock this guy into his constituent particles, if there's enough kinetic energy. So here I get the idea that it's not spontaneous. And even more, the reverse reaction, if the temperature is high enough, is probably going to be spontaneous. If the temperature is high enough, these guys are going to react, are going to bump into each other, and the reaction is going to go that way. So temperature is high, you go that way, temperature is low, you go that way. So let's see if we can put everything together that we've seen so far and kind of come up with a gut feeling of what a formula for spontaneity would look like. So we could start with enthalpy. So we already know that look, if this is less than 0, we're probably dealing with something that's spontaneous. Now let's say I want a whole expression, where if the whole expression is less than 0, it tells me that it's going to be spontaneous. So we know that positive entropy is something good for spontaneity. We saw that in every situation here. That if we have more states, it's always a good thing. It's more likely to make something spontaneous. Now, we want our whole expression to be negative if it's spontaneous, right? So positive entropy should make my whole expression more negative, so maybe we should subtract entropy. Right? If this is positive, then my whole expression will be more negative. Which tells me, hey, this is spontaneous. So if this is negative, we're releasing energy. And then if this is positive, we're getting more disordered, so this whole thing will be negative. So that seems good. Now what if entropy is negative? If entropy is negative, this also kind of speaks to the idea that if entropy is negative, it kind of makes the reaction a little less spontaneous. Right? In this situation, entropy was negative. We went from more disorder to less disorder, or fewer particles. And what did we say? When temperature is high, entropy matters a lot. When temperature is high, this less entropic state, they ram into each other, and they'll become more entropic. When temperature is low, maybe they'll drift close to each other, and then the enthalpy part of the equation will matter more. So let's see if we can weight that. So when temperature is high, entropy matters. When temperature is low, entropy doesn't matter. So what if we just scaled entropy by temperature? What if I just took a temperature variable here? Now, my claim, or my intuition, based on everything we've experimented so far, is that if this expression is less than 0, we should be dealing with a spontaneous reaction. And let's see if it gels with everything we say here. If the temperature is high-- so this reaction right here was exothermic, in the rightwards direction. When we go to the right, from more of these molecules to these fewer ones, I told you it's exothermic. Now, at low temperatures, my gut told me, hey, this should be spontaneous. These guys are going to drift close to each other, and get into this more stable configuration. And that makes sense. At low temperatures, this term isn't going to matter much. You can imagine the extreme. At absolute 0, this term is going to disappear. You can't quite reach there, but it would become less and less. And this term dominates. Now, at high temperatures, all of a sudden, this term is going to dominate. And if our delta S is less than 0, then this whole term is going to dominate and become positive. Right? And even if this is negative, we're subtracting. So our delta S is negative. We put a negative here. So this is going to be a positive. So this positive, if the temperature is high enough-- and remember, we're dealing with Kelvin, so temperature can only be positive. If this is positive enough, it will overwhelm any negative enthalpy. And so it won't be spontaneous anymore. And so if the temperature is high enough, this direction won't be spontaneous. And this equation tells us this. And then if we go to the negative enthalpy, positive entropy, so we're releasing energy, so this is negative, and our entropy is increasing-- our entropy, we're getting more disordered-- then this becomes a negative as well. So our thing is definitely going to be negative. And we already had the sense that look, if this is negative and this is positive, we're getting more entropic and we're releasing energy, that should definitely be spontaneous. And this equation also speaks to that. So so far, I feel pretty good about this equation. And as you can imagine, I didn't think of this out of the blue. This actually is the equation that predicts spontaneity. And I'm going to show it to you in a slightly more rigorous way in the future, maybe going back to some of our fundamental formulas for entropy and things like that. But this is the formula for whether something is spontaneous. And what I wanted to do in this video is just give you an intuition why this formula kind of makes sense. And this quantity right here is called the delta G, or change in Gibbs free energy. And this is what does predict whether a reaction is spontaneous. So in the next video, I'll actually apply this formula a couple of times. And then a few videos after that, we'll do a little bit more of how you can actually get this from some of our basic thermodynamic principles.