24-2 Equilibrium between phases: Gibbs energy and phase equilibria

ROFESSOR CIMA: All systems seek their lowest Gibbs energy. He didn't call it that at that time, but we do. So, all systems seek lowest G. And that's sort of the most negative H and largest S. And which is weighted more depends on the temperature according to that equation. Any spontaneous change requires delta G being negative. And something that we don't use here, but you will undoubtedly use when you take biology, is delta G is the maximum work that a system can do. And we, like I said, we won't use that here, but you will soon. OK, so now we're going to talk about phase equilibria. Because, if you look at this, it says that if two phases-- and we'll define a phase in a second --are in equilibrium, that means, equilibrium means, that they're not changing. That means that delta G has to be zero. And so what this requires is that two phases in equilibrium have equal Gibbs energy. OK, so what do we mean by phase? So, that is a region of uniform composition and it means that it's physically distinct. In principle, you could separate them mechanically. In principle. Mechanically separable, in principle, I mean if these are micron-sized phases, you may not be able to do it in practice, but they are different from region to region, and composition. Now, each phase can be composed of a component. And that is a distinct molecular entity or atomic entity. So, in other words, this phase can be a solution. A solution composed of different molecules or different atoms. So, let's see what this means in practice. So, we're going to start by considering only a pure substance. Right? So it has a single component. But we know single components can have different phases. Water can be a liquid, it can be an ice, or solid, it could be a vapor. But each one of those phases will have its own energy and entropy. So if I plot-- I'll take a phase. Let's just take the liquid. I can make a plot of molar Gibbs energy versus temperature, and it'll look something like this. In other words, approximately, if these things are roughly constant with temperature, it's roughly linear, and this slope will be negative because of that sign. It's just an equation of a line. Now we also have the possibility of a solid. And, of course, its entropy, certainly, and its energy are different. And so if I superimpose that on here, it does this. Well, let me do a better line. So that's my solid. And you'll notice I drew a different slope. And it's important that in this case that the slope be less than this one. And why is that? Raise your hand. Yes, sir. STUDENT: The entropy is lower. PROFESSOR CIMA: The entropy. That's right. So, the entropy. Which do we think has greater entropy, the solid, we'll call this a crystal, or the liquid? The liquid, of course. And so that means this has to have a higher slope. Now, if you look at this and go back to this statement here. Any spontaneous change has to have a delta G less than zero. Now, where is the delta G equal to zero? The delta G between these two phases. Only places right here where they equal one another. So that means, if I go down here, that's a very special temperature. And what do you think we call that? STUDENT: The melting point. PROFESSOR CIMA: The melting point. It's the only temperature where the solid and liquid are in equilibrium. Now if I have a liquid at lower than the melting point, you can see that the delta G and going from liquid to solid is going to be which sign? Negative, right? This is increasing negative values. So this is a larger negative number than this one. So when I subtract this, when I subtract this from that, I get a negative number. And likewise, if I go down here, it'll be just the opposite. If I'm the solid above the melting point, it wants to spontaneously convert to the liquid. Right? This system composed of these two phases wants to go to the lowest possible Gibbs energy. Right? Just like that first law there. And so this will be, if I plot the Gibbs energy per mole as a function of temperature, it'll start off as a liquid, convert to a solid and I'll move along that line.