 All right, so now that we understand this idea of an isotope effect, the fact that when we change the isotope of an atom and a molecule to become heavier, increasing the reduced mass of the covalent bonds in that molecule, that causes the zero point energy of those bonds to go down, and when the zero point energy drops, it requires more energy to dissociate that molecule. So the bond dissociation energy is a larger number for heavier isotopes. That's the basic idea of the isotope effect. That's how it affects bond dissociation energies, but it turns out that affects lots of other properties as well. And to see an example of that, let's take a molecule with a heavy isotope. So instead of talking about HCl and DCL, now let's talk about heavy water, D2O. So you know what water is. Heavy water is just water where the hydrogens have been replaced with the deuteriums, with the heavy isotope of hydrogen. And we can talk about the difference in properties for these species. First of all, D2O is not all that exotic material, as you know from perhaps calculating atomic weights, average atomic weights of different elements. Different isotopes are prevalent in different amounts. The natural abundance of the deuterium isotope, about one-tenth of one percent of all hydrogen atoms are the mass two isotope of hydrogen. So roughly one out of every 1,000 water molecules has a deuterium rather than one of its hydrogen atoms. Roughly one out of a million water molecules will have both of the hydrogens replaced. So you could, in any sample of water, find roughly one in a million molecules of water that has D2O molecule. If you separate those, if you isolate them, if you concentrate them, you can get a sample of pure deuterium, or pure D2O, heavy water. So that's a material that's used due to rated solvents like that are used in a lot of chemistry experiments. They were used in experiments involving neutron scattering. They were heavily used in the Manhattan Project. They're used in NMR all the time. So again, they're not as exotic as they may seem. If we consider some properties, let's say, let's start with a couple of easy ones. First of all, the density of the solvent. You know the density of water is 1 gram per milliliter at around room temperature. Not surprisingly, because the mass of the deuteriums are heavier than the mass of hydrogen. The molar mass of D2O is heavier by 2 grams per mole than the molar mass of water. For that reason, the density of water occupies about the same volume, but it weighs more. So the density of deuterium, D2O, is 1.11 grams per mole. It's heavier by about one part in nine. So that one's not surprising. That's purely a property that depends on the mass. The bond association energy. If I break the OH bonds in water, dissociate that water into oxygen atoms and hydrogen atoms. The average bond association energy of those two. Let's see if we do this one in kilojoules per mole. The bond association energy of the OH covalent bonds in a water molecule, 459 kilojoules per mole on average. You can probably guess based on what we already understand about the isotope effect that in the heavier isotope of water, those bond association energies are larger. And that, in fact, turns out to be true. Bond association energy in D2O is 466 kilojoules per mole. So those, like I said, those two are not particularly surprising. Those directly have to do with the mass of the atoms or what we've learned about the isotope effect. Things get a little more interesting and perhaps more confusing when we start to consider other properties. Let's talk about the pH of a neutral solution, not a solution, neutral solvent. Neutral water, as you know, has a pH of 7.0. This one, like I said, might be a little surprising at first. How could the pH of neutral water be anything other than 7.0, even if the water molecules are heavier? As a weight of understanding that, let's make sure we understand what the pH is telling us. Water can autoionize, dissociate to form hydronium ions and hydroxide ions. And of course, the pH is negative log of the concentration of H3O plus ions. So in neutral water, the reason the pH is 7.0 is because the concentration, the molarity of H3O plus ions is 10 to the minus 7 molar in neutral water. So some tiny fraction of the water is dissociate to form H pluses and OH minuses, 10 to the minus 7 molar hydronium, 10 to the minus 7 molar hydroxide leads to this pH of 7.0. But if we're talking about D2O, then they're going to dissociate into heavy hydroniums and heavy hydroxides with the hydrogen is replaced with deuterium. What we understand about heavy isotopes is that the bonds have a higher dissociation energy. So those bonds, because the dissociation energy is larger, that equilibrium will be less strongly towards the products because those bonds are harder to break. So if we're breaking fewer of those bonds, the concentration of D3O plus is reduced. We've got fewer D3O plus molecules, ions in solution than we had H3O plus molecules. So instead of 10 to the minus 7, it's 10 to the some different numbers, a smaller concentration of D3O plus. When I take the negative log of that small concentration, instead of getting 7.0, I'm going to get a different value. In fact, the pH of neutral heavy water is 7.4. So again, the change in this property is a direct result of the fact that those bonds are more difficult to break. The bond dissociation energy is higher. It's a little bit interesting, confusing to think about. This is still neutral water. The fact that the pH is above 7 does not mean that this is a basic solution. It's still a neutral solution. I still have just as many D3O pluses as OD minuses. It's just that I have less of each of them. The solution is both less acidic, I've got less D3O plus, and simultaneously less basic. I've got less OD minus. I've just got less ionization taking place altogether. So a neutral solution of D2O has a pH. We should really be calling it a PD, a power of deuterium ions of 7.4. So let's consider a few more properties about boiling point. Boiling point of regular water, as you know, is 100 degrees Celsius. So this is going to be measured in degrees Celsius. What will the boiling point of deuterium, heavy water, be? Let's draw a little picture here to make sure we understand what's going on and how that affects. So here's some water molecules in liquid water. Molecules in liquid water involve hydrogen bonds between the waters and the liquid in order for molecule to escape up into the gas phase. So here's a molecule up in the gas phase. In order to escape from the liquid up into the gas phase, that hydrogen bond between the hydrogen on some of the molecules and the oxygen on others needs to be broken for that molecule to escape. So even though that's not a covalent bond, still it's true that not just for covalent bonds, but also for hydrogen bonds, for any type of bonds, the heavier isotopes will have larger reduced masses, reduced zero point energies. And so it will be a little harder to break the hydrogen bond in heavy water than it is in regular water. Again, same idea, bonds are a little harder to break in the heavier solvent. Because that bond, that hydrogen bond is harder to break, we have to heat the liquid to a higher temperature in order to evaporate enough water to get the vapor pressure to one atmosphere and to boil. So the boiling point of heavy water is not 100 degrees C, but 101.4 degrees Celsius, a little higher than the boiling point of regular water. So very similarly to that, you can now probably predict, if I ask you about the heat of vaporization of water for regular water, light water, that's 40.6 kilojoules per mole. You tell me now, is it going to be larger or smaller for D2O? And the answer is, again, because the isotope is heavier, those bonds are a little bit harder to break. The energy required to evaporate a molecule of water, heavy water out of the liquid phase into the gas phase is going to be larger. And in fact, it's 41.5 instead of 40.6. All right. How about we talk about another property of the liquid in this case? In this case, let's talk about viscosity. So we won't talk much about viscosity as a property in chemistry. So qualitative understanding of viscosity is good enough. Viscosity is just how thick or viscous or resistant to flow a liquid is. So a thin liquid that flows very easily has a low viscosity, a thick molasses or honey-like liquid has a very high viscosity. Water happens to have a viscosity in units. Again, don't stress too much about the units of viscosity. It's milli-pascale seconds. In those units of milli-pascale seconds, water has a viscosity of 1. What do you think the viscosity of heavy water is going to be? I've got, again, liquid. I've got a bunch of molecules in the liquid phase. When we're talking about viscosity, we're talking about diffusion. In order for the liquid to flow as a liquid, molecules have to rearrange their positions, break some of the hydrogen bonds between these molecules, and exchange neighbors in order to flow. So flow, viscosity requires that molecules break their hydrogen bonds. Those hydrogen bonds, again, are more difficult to break for the heavier solvent than for the lighter isotope of the solvent. So that means if the bonds are harder to break, molecules flow less easily. The liquid is going to behave a little more viscous-ly. So it turns out that the viscosity of heavy water is about 25% higher than regular water. High enough that you could actually feel that difference quite noticeably. All right, next property we can consider. We've already sort of talked about this for water in the example of pH, but let's take another acid. So this is now no longer for water. This would be, let's take an acid like acetic acid. If I have acetic acid acting as an acid, when it dissociates, it's going to form acetate and hydronium ion or protons. The acid constant is going to be the concentration of the conjugate base times the concentration of the protons divided by concentration of the acid. Now that I've reminded you what a pKa is, pKa is the negative log of this quantity, knowing what we know about isotope effects, is that going to be larger or smaller for a heavy isotope? So if we're talking about acetic acid, it has a Ka, it's a weak acid, it has a Ka of 1.8 times 10 to the minus 5. If I take the negative log of that, the pKa for acetic acid is 4.75, again showing it's a relatively weak acid. So that's ourselves now how that would be different if we were talking about not acetic acid, but either CH3COOD is really all we need to talk about for a heavy isotope because we're talking about the loss of this particular proton. If I turn that proton into a deuterium, so then we'd be talking about deuterium ions in solution providing our acidity rather than light hydrogen ions. Again, that's involving breaking of a bond, the bond between the oxygen of the acid group and the proton, the heavy proton. In a heavy isotope, that bond is more energetic, it takes more energy to break that bond. So this dissociation is going to happen less. We've got less of the conjugate acid in the proton in solution. We've got more, slightly more of the acid remaining behind in solution. So the Ka is going to go down, the acid becomes even weaker for the heavy isotope of the molecule. So what that means is the pKa is, because it's the negative log, is going to become larger for the heavy isotope of acetic acid. What that means is the pKa goes from 4.75 to 5.27. The acid has become weaker when we deuterated it. And now we'll consider just one more case and that is kinetics. Everything we've talked about so far has been an equilibrium thermodynamic property. If we want to talk about the kinetics of a reaction, how fast, so this is a rate constant. How fast the rate constant is for a reaction involving a hydrogen compared to the rate constant for a reaction involving a deuterium. The way to think about that process in general, so if this is an energy, reactions have reactants and products. They go over some activation barrier. They might become a product with higher energy than the reactant or lower energy than the reactant. The energy of the product doesn't affect the rate of the reaction so much. The rate of the reaction is determined by this activation energy. We'll talk about kinetics quite a bit in a different portion of the course. But the rate of this reaction, the higher the activation barrier is, the slower the reaction is, the less likely we are to get over that barrier. You may have seen the equation before and we'll see it later that the rate constant is proportional to e to the minus activation energy over kT or RT. The way to think about this now for a heavy isotope of a molecule, if this reaction involves breaking some bond, then for the deuterated solvent, again, the bond gets stronger in the heavier isotope of the solvent. In the protonated reactant, maybe this is the energy, in the deuterated reactant, I have to put in more energy to get up to that activation barrier than I do in the protonated solvent, the light hydrogen version of the reactant. What that means is because the activation energy has gotten larger for the heavy isotope, the reaction is going to get slower. Generally, what's true is that I find the right color marker. The reaction is slower for the deuterium than for the hydrogen and the rate is faster for the hydrogenated solvent reactant than for the deuterated reactant. So, without giving any specific examples, I'll just say that those rates, instead of being a 1% change or 25% change, those changes can actually be quite large. They can be a factor of 2 or 5 or 10 and that's because this change in the activation energy is in the exponent. So, making a change up here in the exponent becomes magnified when I exponentiate it and this difference in the rates of the reactions can be quite large. So, we can have rates of chemical reactions being very different for a deuterated reactant than a light version of those. What that means is if you have, rather than the usual, 0.1% deuterated hydrogens in your body, if you were to take a sample of D2O and drink it, for example, replacing many of the hydrogens in your body with deuteriums, that means that the kinetics of all the biochemical reactions going on in your body would be very different. So, D2O is in fact a fairly poisonous solvent to drink. Lab experiments where rats are fed D2O as their water source, in fact, develop quite serious problems and die when a significant fraction of their H2O in their body gets replaced with D2O and that's because the rates of these biochemical reactions are significantly different and it messes with the biochemistry in the body. So, deuterated solvents are very interesting, properties are very different, useful to play around with in lab, but they're definitely not something to play around with in your diet. Okay, so that just summarizes the fact that bond association energy, this one property that changes as a result of this quantum mechanical change, the zero point energy being different for a heavy isotope of molecule, leads to a bunch of other changes and lots of other properties of these molecules.