Thermodynamics, ideal solutions, entropy

There is an old adage, I don't know who came up with this, that the first time you learn thermodynamics, you don't understand it and the second time you learn thermodynamics, you think you understand it and the third time you learn thermodynamics, you're comfortable with not understanding it And I think that's the category where most professional scientists find themselves, because it is quite a complex topic, but we can understand what we we can understand the basics using a few simple ideas. What is what is the the quantity that must be minimized at equilibrium in any chemical process? Gibbs, free, energy G, so G is the. What is what is G? What is the Gibbs free energy Gibbs? Free energy is the thermodynamic potential that must be minimized at constant temperature and pressure in a chemical system. Okay, that tells us precisely nothing about what it actually is. You may have in first semester, physics or chemistry derived the expression for G and what you ultimately end up with is G which, just as a reminder, is at constant temperature and pressure equals something called H. Minus something called PS H is the enthalpy T. Is the temperature and s is the entropy? Where does or does H come from? Where do the HS come from? Where does it or does H? Come H is heat, so it's the heat of reaction or the heat that results from a particular chemical process. But where does it really come from bonds between atoms bonds between atoms? How about how about intermolecular forces as well? So if you have two molecules that are far away from each other in space and they're not charged and you bring them closer to each other, the and they're not they're not charged, or they have opposite charges. The potential energy over here compared to over here is the potential energy higher in one or two potential energy is higher in one. So we minimize the potential energy by bringing two uncharged molecules together by Vander Waals forces and by conservation of energy. Something has to have to be ejected, and that is Heat, incidentally, do uncharged molecules, attract or all uncharged molecules attract in a vacuum. Is that a true statement, so oil and oil they do they attract in a vacuum there. The only molecules in the universe do they attract; they do how about water and water. Do they attract? Yes, they do. How about oil and water do they attract if it's only one molecule of water and one molecule of oil they do attract, they do attract in a vacuum because they both have protons and electrons, and one has a permanent dipole moment which can induce a dipole moment In the other, they also have electron clouds that transiently deflect each other and create Vander, Waals bonds, which is called the dispersion or London interaction. So the answer is that all uncharged molecules attract pairwise in a vacuum, but a chemical system is not always pairwise or basically never pairwise, because you have lots of different molecules interacting in some environment, so, incidentally, like charged molecules or molecules that are constrained so that the Negative end, so that the same side of a dipole has to come closer if they're not allowed to rotate. That'S that's! That'S that's unfavorable and Delta Klee. So that gives you a positive H, but for uncharged or freely rotating dipoles Delta, H is always is always negative. You get it give off heat because the potential energy is being lowered in that interaction. So we know so so. If G at constant temperature and pressure equals H, minus TS for a h, minus tough for any given process, then Delta G for a process. The change in Gibbs free energy is Delta, H, minus T Delta s. Now. What we're going to be predicting in the next couple of classes is whether or not certain pairs of molecules so solvents when they come together as mixing favorable or unfavorable or polymers, when they come together as mixing favorable or unfavorable, and what we? What we get has a bearing on the Faye's behavior of a solid polymer material, which controls all of its thermal and mechanical properties that we're trying to engineer in a solid material. So everything comes down to to minimizing the the Gibbs free energy through these parameters. Delta. H and Delta s, so H is fundamentally derived from from from bonds, and I mean bonds in a very general sense. You have a chemist's bond, which is a covalent bond which involves formal sharing of electrons between atoms in a molecule, and we also have the physicists bond, which is like a van der Waals bond, which is just an electrostatic interaction that it that comprises components from dipole-dipole Interactions, dipole induced dipole interactions and dispersion interactions, so this is chemical bonds or covalent bonds and also van der Waals bonds and also will say, ionic bonds. These two are really electrostatic in nature. This one is a little bit more quantum mechanical in nature, because you have these atomic orbitals that hybridize to form molecular orbitals, but in terms of their effect on Delta, H, they're, similar Delta s Delta s can mean a lot of different it Delta s comprises a Wide range of entropic terms, but the one we're mostly we mostly care about the only one that we care about in in at least our discussion of this topic in the abstract is configurational entropy, and that is we picture the molecules as spheres as occupying points. On a lattice, the circles or spheres and two-dimensional to three-dimensional spaces, but they have no, they have total rotational symmetry they're, not they're, not rods, because if you have rods, you had a review of rotational degrees of freedom as well. We'Re only talking about configurational entropy. So, where are the the these circles or spheres on a lattice and are there more states available before a chemical process or after a chemical process? Yes, this simplifications. We can express them all in three characters rather than I, if, if you, if you want to in a real system, you have to break Delta s apart into the configurational term and the rotational term and other terms that might that might arise. So this is the change in the number of statistical microstates available and for our discussion this week and for the rest of the class except under specific circumstances. So the mathematical treatment will all be for configurational entropy. Only we're not going to worry about about rotation and a rotational entropy for now or mathematically we're not going to worry about it at all, but I may give you examples of cases where rotational entropy plays a plays. A significant role number is the statistical microstates available and this is configuration only in in our discussion. Okay, so let's modify this equation a little bit with a superscript M which means mixing because ultimately, if we want to learn something about the phase behavior of and the dissolution of polymers, in a solution to do solution, processing or polymers in polymers to do melt casting Or to predict that the phases that we ultimately get, what we care about is mixing, so the unmixed state before and the mixed state is after yes, yes, they can be measured, they can be measured, color, calorimetric, ly, Delta H's is the easiest because, because it just Just comes off as as heat, and you can measure the other quantities by various curve, fitting that we're not going to talk about in the class, but they are measurable. Okay, so Delta s of Delta s for a mixing process configuration only. So you have two separate species over here and then in the mixed state. They'Re jumbled up is Delta s positive or negative Delta. S is going to be positive for the configurational change in entropy upon mixing every time. Yes, the there are. So why do unlike solvents? Sometimes not mix so, if Delta, we know that for a spontaneous process, so something that that lowers the Delta G we have. If we have a positive Delta s term, then this term is all negative and contributes toward making this process happen because it gives us a negative Delta G. So why would say say: cyclohexane and a seed, a nitrile, don't mix sorry, so we're taking the mixed state. We'Re just saying that there is a mixed state, even though they don't mix the mixed state has all the molecules. Jumbled together, we can all agree that there are way more distinguishable microstates available when they're all mixed together versus when they're all when they're separate in like oil and water. The reason they don't mix is because delta h of mixing must be unfavorable, but i just told you that uncharged molecules attract in a vacuum and have a negative Delta H. So how is the enthalpy of mixing unfavorable yeah yeah? That'S halfway there. So you've all heard the phrase life dissolves like that. That gets you part of the way there, but it's still kind of wrong. The reason it's still kind of wrong is because a a molecule with a relatively low Vander, Waals coefficient. So because we have all these dipole terms in the Osito nitrile, it has a very high Vander volts coefficient. It likes interacting with other things and because you have two things: if you have two molecules of this, that both have a high vander waals coefficient, then that's a very favorable interaction. This - and this also has a favorable interaction, but it's, but it's less favorable than this end this. So, while it's really because the heceta nitrile is excluding the cyclohexane that they separate, because it's more favorable for these, these molecules to continue interacting with itself rather than mixing cyclohexane, as if cyclohexane had a brain and it had like crushes on things, it would say I Really wish to see de nitrile would like me because it has a really high vander waals coefficient and I would really like to interact with it. But heceta nitrile says no. I, like my own friends so so the result is not that like dissolves like, but that more the one of the greater intermolecular forces excludes the one with the with the less favorable intermolecular forces. That'S quite a simplified picture because there are some examples like the hydrophobic effect, for example, which has a best L on water, what we always think about with immiscible solvents. But in fact the Delta H is slightly favorable upon mixing. But it's actually entropically quite unfavorable to mix because of rotational terms that again we're not going to talk about, because if you we're not going to talk about mathematically I'll, tell you why the hydrophobic effect happens because you get solvent cages of of hydrogen bonds that are Tangential to dissolved hydrophobic species in water and that restricts the rotational freedom of water molecules that have to soluble eyes the the organic species and therefore, even though the Delta H is, is even a hair favorable, the entropy is very unfavorable, so this is. This is really our analysis depends on the fact that we're considering only configurational, entropy, okay, so like solvents, tend to to two like each other, like chemical species tend to dissolve in in each other. So let's take, let's take [ Applause ]. This is called toluene and this is styrene vinyl benzene. So would we predict, based on the argument that similar molecules tend to be soluble in each other, that these would be soluble in each other? They would form a miscible mixture, yeah yeah. They definitely would but polystyrene, where you have a long zigzag with a bunch of benzene rings that hang off of it. If you have really high molecular weight polyester in does it become less soluble or more soluble in the in the toluene less valuable and that that's a little bit intuitive from our everyday experience, because we have you know we have high molecular weight polyethylene that won't dissolve In solvents, because we have solvent bottles that we have in high molecular weight, polyethylene and but the reason is, is a little bit know counterintuitive! It'S not it's not that easy to understand just by just by you know, thinking because the toluene and the styrene, so the monomer is soluble. But if you have a certain number of repeat units, it becomes more and more insoluble, the more repeat units you add and even though the enthalpy of mixing isn't going to change to too much because you still have this interacting with this, which is pretty similar. The entropy term, the change in entropy, could be comes much and much much much much less, because what you're doing is by making a polymer you're confining the monomers you're telling them that they have to be next to each other. They can't be anywhere. They have to be next to each other, so the entropy of mixing is much less favored. So if you have infinite molecular weight, the entropy of mixing goes to goes to zero, and even the slightly the slightly unfavorable enthalpy of mixing takes over and makes them insoluble. In each other yep, you see an increased effect of that and continuously polymers, because there's so the question is: do you see more mixing in isotactic and syndiotactic of like polypropylene or polystyrene, because they're so chemically similar? You would certainly predict more mixing in that case, based on based on these arguments, but the. But if you take into account crystallization and the fact that one wants to crystallize and the other doesn't then you would predict a different kind of phase segregation that resulted from crystallization. But that's a good. That'S a good question: okay, okay, let's think about polymers in solution - and these are just a couple of sort of high-level points that I'm going to write down and by the end of the by the end of next week, we'll kind of understand why why this is In a good solvent - and this is favorable intermolecular forces - can I abbreviate that IMS: favorable intermolecular forces a polymer coil expands in order to increase interactions with the solvent relative to in a poor, solvent it contracts. If you see a homogeneous solution - and this is of a polymer or molecules taken together, what you can say about it, if you see some sprite, you know that that it's it's Delta G of mixing is less than zero and we got Delta G by considering the Delta G M equals G of of 1