Chemistry: Energy and the Solution Process

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What we want to do now is return to the question of why it is that some things are highly soluble and other things are not soluble in different solutions. Now, we know that when I take a solute, in this case just salt, and put it in water, that up to a reasonable degree, we can dissolve this material, and at some point we reach a limit, a saturation point. So, what again, are the factors that determine where that point of saturation is? Remember, that there are two important natural laws of nature here - nature wants to increase entropy, wants to increase the disorder, and it wants to reach the lowest point of chemical energy possible. So, in other words, exothermic reactions in general are much more spontaneous than endothermic reactions.
So, let's examine those two ideas. The energy involved with solvation versus the disorder involved with solvation. We'll start out looking at the chemical energy here. And what I've done in this diagram is just broken things down into pieces. The basic idea, and if we're going to dissolve something, is we first of all have to pay a price to breaking the bonds between solute particles - in the case of salt, we have to break the ionic bonds; in the case of molecular materials, we have to break the bonds between those molecules, and split those into individual particles. We also have to pay a price in terms of the solvent interactions with themselves. So, we're going to break solvent interactions. We know that's going to cost energy. In the case of water, that would be hydrogen bonds that we have to partially disrupt. So, it's going to cost us energy to break the solute apart. And by the way, we often refer to this as lattice energy - energy required to break these molecules out of their lattice. Especially, if it's an ionic lattice, we describe that as a lattice energy. So it costs us energy to break the solute apart and to break the solvent apart; but what we gain is bringing the solute and solvent together and in that process we form new bonds between the solute and solvent. We solvate the solute, and that releases energy. So, the question of whether or not the overall process is exothermic (gives off heat), or endothermic (requires heat) depends on the relative costs of energy versus the energy gained. And, in fact, nature will do both of these things, depending on the situation. We talked earlier about examples where nature will give a high solubility of materials, even if it's endothermic, in certain cases. Even if there is more cost in breaking the solute and the solvent, than there is energy gained. And the reason for that has to be entropy, remember? So, we'll return to that point in a moment. But, again, my point is that the energy cost and energy gain can be positive overall, or negative overall, and both processes are known.
So, specifically, let's define a term for that, that we can actually measure, that talks about the overall energy loss or gain when we do this process. So, once again, going from solute and solvent to solution. If we measure the heat required for that process to occur, we'll define a DeltaH of solvation, an enthalpy of solvation, in other words, and if this value is positive - remember how we defined this now - if it's positive, energy is required for the process to occur. In other words, energy is a reactant, if you will. It's need as part of the process. So, if it's an endothermic reaction, DeltaH is going to be positive for solvation. On the other hand, if heat is released for the process, it's an exothermic reaction, and DeltaH of solvation is going to be negative. And, again, this is something that we could measure in a calorimeter, for instance. So, we can get an idea, not of the individual costs, but at least of the overall costs or gain for energy.
Now, in particular, if we're talking about water, and so much of the chemistry that we look at is an aqueous solution. We can break this down further. We talked about lattice energy, the idea of it costing a certain amount of energy to break ions apart into individual particles, pull them out of their lattice structure. Well, the flip side of that is the hydration energy, the energy gained by solvating these ions. So, again, down here, just in general, taking an ion and surrounding it or actually just in general it doesn't have to be an ion even, it could be a neutral molecule and hydrating it, surrounding it with water molecules. That process is going to give off energy. That's an exothermic piece of this overall energy process. So, DeltaH we could define enthalpy of hydration - that's always going to be a negative number. We're always going to get a release of energy for this piece, at least, of the overall process in energy.
Now, just how strong this is, depends again on how powerful the attractive forces are between the water molecules and the solute. That's going to depend primarily on charge, secondarily on polarity of the solute. But let's particularly look at charge, because we deal with ions and solution so much. It costs a lot, or rather we gain more stability by solvating a small, highly charged ion, than we do a larger, low-charged ion. Now, in the example I'm showing you here, lithium and potassium, they have the same charge, but the difference is the size -- lithium being a much a smaller cation than potassium. Although there are fewer water molecules that can get around the lithium, they can get much closer to the center of charge, right in the middle of that iron. So the attractive forces are stronger, the energy released for the hydration process is higher, more energy is going to be released so we're going to have very hydration energy for small, highly charged ions - lithium, sodium to a lesser extent, calcium for instance, magnesium those are 2+ ions, very high heats of hydration in that case. Likewise, we can hydrate negative ions. Notice that the dipole moment in water - remember which way that points now - dipole moment now is going to be pointing towards the oxygen, meaning the negative part of the water molecule is around the oxygen, the slightly positive portion is around the hydrogens. So, by orienting the hydrogens around the fluoride, we end up with, again, stabilization of that negative charge. In this particular case, we have hydrogen bonding that is set up with the ion, so we get a good high heat of hydration for solvating anions as well, just like with the cations, the larger that anion is, the less energy is released by the solvation process. Because we don't get quite as much attraction between the dipole moments and the charge if the charge is spread out over a much larger volume, if you will.
So that tells us again about the energy, the chemical energy if you will, involved, the enthalpy of the solubility process, but what about the entropy? Remember that one of the problems about ordering water molecules around ions is that it orders them, and if it orders them, we actually could lose entropy rather than gain entropy.
So now let's turn again to the idea of entropy of solvation. Once again, the basic notion of combining a solvent in a solute to give a mixture; that certainly is going to increase entropy in general. So, for most solubility processes, entropy is going to increase. But, be aware, there are some cases that we're going to have to worry about where we have a lot of ordering of the solvent. We just saw a case where that happened. If you have very, very high heats of hydration, we're also going to have the possibility of a negative entropy, or at least of very low entropy of solvation. So we're going to look out for that, especially in cases of small ions. And here's another place where this shows up, very unexpectedly. When we through in a nonpolar solute, a very nonpolar solute that doesn't have good interactions with the water. The water tends to cluster to form cages around the nonpolar substrate and in doing so, actually increases the order of the solvent. And so entropy can be very negative for this process, too.
Now, this is so important, it's worth spending another minute on. This, in fact, has a special term. It's called the hydrophobic effect. And it is responsible for all kinds of things in nature, especially in biochemistry. Lots of this happening in your body. Very important effect. Let me describe in a little more detail what's going on. When you have a nonpolar substrate, this could be methane or ethane, or a very long oily hydrocarbon chain or a nonpolar portion of a protein, the water molecules tend to form these cages around this nonpolar material and in doing so, the overall order of the water molecules increases. Now it used to be that people thought the hydrophobic effect, scientists thought the hydrophobic effect had to do with the solute particles just simply breaking hydrogen bonds between water molecules. So, in other words, the old explanation used to be solvent molecules are stuck together, you throw something nonpolar, it breaks the bonds between the solvent, and it doesn't make up for that, if you will, by attraction to the solvent particles, to the water molecules, in particular. That turns out not to be the case. In fact, this process very often can be slightly exothermic, just slightly. But usually very close to zero. But it doesn't cost a lot of chemical energy to dissolve this material. What it does cost is entropy. Because, again, the water molecules order around the nonpolar material and that's bad for the overall system again. Nature doesn't like to increase order. So, again, the net result, the important net result, is that nonpolar things tend not to dissolve in water. And, again, hydrophobic originally comes from the notion that it's water fearing, if you will, that nonpolar things don't like to be around water. Well, it's actually the water that has the problem, not the nonpolar things. The water tends to order. That causes a problem with the entropy, and so, the net result, again, is oil and water don't mix. Proteins tend to fold up in such a way that they bury the nonpolar portions of them to keep it away from the surface of water. Oil tends to cluster together. Again, as I say, it doesn't dissolve in water. So there's a lot of very profound consequences. You'll see later on, in fact, how much water influences the structure of proteins, the secondary and the tertiary structure of proteins. And it's all governed by this basic idea of the hydrophobic effect.
So, once again, let's just quickly summarize what we've said here. When we worry about soluble something is, we're worried about how much energy it costs or how much energy is gained, released if you will, by the process, but we're also worried about the entropy. Do we order the system more or do we go to greater disorder? Depending upon which we do, and combining both of those ideas together, that ultimately determines how soluble something is going to be.
Physical Properties of Solutions
Characterizing Solutions
Energy and the Solution Process Page [1 of 2]