 So we've talked a fair amount about the spectroscopy of molecules so far, but we've mainly been focusing on the spectroscopy of molecules in the gas phase, and there's some important differences between what the spectrum, the infrared spectrum in particular, looks like for molecules in the gas phase and molecules in condensed phases like say the liquid phase. So first to illustrate that, I'll show you the infrared spectrum of water. So this is the spectrum for H2O specifically in the gaseous phase. So this is the spectrum of the sort we're used to seeing. We know there's some symmetric and anti-symmetric stretch modes that overlap in this portion of the spectrum, a little above 3,500 wave numbers. Down here there's some angle bending modes. We can identify individual real vibrational peaks in this spectrum. If I compare that to the spectrum for liquid water, which I'll show just below here, this is the same spectrum over the same range of frequencies, but for liquid water rather than gaseous water. And you can see right away there's some differences between these two spectra. Most obvious change that jumps out is the line spectrum with individual lines has been broadened and turns into a band spectrum. So we just see a broad absorption peak rather than individual absorption lines. And in fact, in some cases, like this case, the width of that peak is a little wider in the liquid phase than it is in the gaseous phase. Also I've lined up the frequencies here. So let's say this is 3,500 wave numbers on both of these spectra. You can see that the absorption for the OH stretches, which is a little above 3,500, 36, 3,700 in the gas phase, that has been redshifted down to a value that's a little bit less than 3,500 in the liquid phase. So this redshift is one of the important changes that happens in water as we move from the gas phase to the liquid phase. And we also get this broadening of the line spectra into these wider band spectra. And I guess while we're talking about this peak, I should point out that this flat top on the top of the spectrum, that's not actually a flat top. That just indicates that the absorbance was only measured up to this value. And in fact, this is a very, very large peak that goes off the scale of the graph. So what's responsible for these two effects, this redshift effect in the broadening? We can explain both of those. Let's tackle the redshift first. So if we think about the difference between a water molecule in the gas phase. So in the gas phase, there's a water molecule and it's surrounded by vacuum. The nearest other molecule in the gas phase is many, many molecular diameters away. This molecule is surrounded by nothing other than empty space for a long distance, at least at the molecular scale. In the liquid, on the other hand, each water molecule is hydrogen bonded typically to four other water molecules. So every one of these water molecules is surrounded by other molecules, and the liquid is full of molecules. What that means is that the energetics of this OH stretch that describes the real vibrational absorption that's experienced here, these OH stretches are different in the liquid phase than in the gas phase. Because if I think about what that potential energy looks like, remember this is the potential energy curve that we initially approximated with a harmonic oscillator with a parabola to come up with the harmonic oscillator model. So there's energy levels within this potential energy well. The curvature of that well tells us something about the frequency of that vibrational motion. But if this is what the potential looks like in the gas phase, it looks a little bit different in the liquid phase because this distance, r sub e, the distance where the molecule has the lowest potential energy, that corresponds to the distance. If there's an oxygen at the origin, that distance is the length of this OH bond. In liquid, if I imagine what's going to happen as I stretch this bond, it's different than what happens in the gas phase. In the gas phase, if I just have a water molecule in the gas phase, as I lengthen the OH bond, I need to put energy into it. The energy that bond increases. And eventually, if I lengthen the bond long enough, if I pull it far enough away from the oxygen, that bond will break. And I have to insert exactly this much energy to break that bond. But now think about what happens in the liquid. If I start lengthening this OH bond, the hydrogen is still getting further away from the oxygen that it's attached to, but it ends up getting closer to the hydrogen on another molecule. So if I insist on moving this hydrogen further from its own hydrogen and towards another hydrogen, eventually it's going to bond to this oxygen, making either an H3O plus molecule or perhaps kicking a hydrogen off of this water molecule. So what that means is it's not quite as unfavorable in the liquid phase to dissociate that hydrogen because as that bond length increases, eventually it will fall down into a well where it's bonded to the other oxygen. So as we move the hydrogen closer to the oxygen to which it's hydrogen bonding, it will eventually start losing energy rather than gaining energy. So the net effect is we've softened the vibrational well. We've softened this potential. So on this pink curve, I've decreased the curvature. Near the minimum of the well, the curvature is about the same, but at the higher vibrational levels, the well has gotten a little bit softer. K has decreased because of how K affects the vibrational frequency. That means the vibrational frequency has also decreased. And that's the source of the red shift that we've observed. So when this hydrogen, when this water molecule is favorably interacting with another molecule, so those favorable interactions, hydrogen bonding in particular, that leads to a red shift in the condensed phase relative to the gas phase. So that's exactly what we see happening for these water molecules. These absorption bands get red shifted down to lower frequencies in the liquid phase. The exact opposite can happen if we have unfavorable interactions. Let's imagine what would happen if I take a water molecule and surround it by molecules that it's not favorably interacting with. So in that case, let's take a water molecule. So here's a water molecule. So rather than surrounding it in the liquid phase by other water molecules to which it can favorably hydrogen bond, I don't want to surround it with anything polar in which it can have favorable dipole dipole interactions, certainly nothing that it could hydrate a bond with. If I want to have it interact as unfavorably as possible, let's go ahead and surround that molecule with some rare gas atoms like argon. But instead of rare gas in the gaseous phase, let's pack them close to each other and put them in the liquid phase. So now, as I try to dissociate this OH bond, the bonding well, instead of looking like it does in the gas phase with a potential energy curve that looks something like this in this liquid, because there's no favorable interactions between this hydrogen and the argon atoms that surround it. It's in this very cold liquid where I've condensed the liquid argon around some water molecules. If the interactions are unfavorable, this hydrogen is just going to physically occupy the same space as the argons near it. So what that's going to do is it's going to stiffen the bonding well rather than softening it. So the exact opposite thing will happen. The curvature of that well has increased. The vibrational frequency will increase. And the result will be that if I have unfavorable interactions between a solute and the solvent that surrounds it, then in that condensed phase in that liquid, I'll get a blue shift in the absorption band. So as we go from gas to liquid, it's not always true that we get a red shift in all the absorption bands. But in fact, that red shift or sometimes blue shift tells us something about the strength of the interactions with that molecule and the molecules that surround it in the liquid phase. So that explains our red shift to explain what's going on with the broadening of this peak, turning this line spectrum into a band spectrum. The explanation there is the fact that in the liquid phase, the environment of all of these water molecules is heterogeneous. Each individual water molecule, maybe hydrogen bonding to four neighbors, maybe only hydrogen bonding to three neighbors, maybe in the process of having some of those bonds breaking or forming, each one of these hydrogen bonds is at a slightly different angle, slightly different length. So the amount of the red shift is different for every water molecule. So as these spectra get redshifted by a few hundred wave numbers, maybe some of them get redshifted a little more than others. So we get many, many copies of this line spectrum overlapping with each other here and causing this blurred out, broadened and redshifted spectrum. So that heterogeneity, that difference in the environment of each of these molecules in the liquid phase, a liquid macroscopic liquid is going to have many, many molecules, moles worth of molecules. So if I take 10 to the 23rd of these line spectra, shift them by varying amounts and overlap them, I get this incredibly smoothed out or broadened spectrum. So that leads to this effect called heterogeneous broadening or heterogeneous line broadening because of the different environment of all the molecules. In the gas phase, every molecule is an island surrounded by nothing other than vacuum, so they all have the same spectrum as one another in the liquid phase because every molecule is surrounded by a slightly different micro environment that heterogeneity leads to this broadening. So those two features typically occur when we take a molecule from the gas phase into a condensed phase like the liquid or the solid. The spectrum gets broader and experiences usually a redshift, sometimes a blueshift in most of these different types of absorption bands.