WEBVTT 00:00:01.000 --> 00:00:04.000 The following content is provided by MIT OpenCourseWare 00:00:04.000 --> 00:00:06.000 under a Creative Commons license. 00:00:06.000 --> 00:00:10.000 Additional information about our license and MIT 00:00:10.000 --> 00:00:15.000 OpenCourseWare in general is available at ocw.mit.edu. 00:00:15.000 --> 00:00:20.000 -- sometimes called the van der Waal's interactions. 00:00:20.000 --> 00:00:26.000 And we saw that we could make a molecule between two inert gas 00:00:26.000 --> 00:00:30.000 atoms, like argon two or xenon two, 00:00:30.000 --> 00:00:35.000 by virtue of these dispersion interactions, 00:00:35.000 --> 00:00:41.000 where the instantaneous charge in one atom or molecule produces 00:00:41.000 --> 00:00:45.000 a dipole. That dipole then induces a 00:00:45.000 --> 00:00:52.000 dipole in the neighboring molecule, and the result is a 00:00:52.000 --> 00:00:55.000 stabilization, an attraction. 00:00:55.000 --> 00:01:01.000 And we saw, last time, we had a generic form for the 00:01:01.000 --> 00:01:08.000 interaction potential for the dispersion interactions. 00:01:08.000 --> 00:01:11.000 This Lennard-Jones interaction potential. 00:01:11.000 --> 00:01:17.000 We talked about that in detail. And one of the parameters in 00:01:17.000 --> 00:01:21.000 that Lennard-Jones potential was this quantity epsilon, 00:01:21.000 --> 00:01:25.000 which actually was the well depth. 00:01:25.000 --> 00:01:29.000 And I just wanted to talk a few moments, here, 00:01:29.000 --> 00:01:33.000 about what determines what the well depth is, 00:01:33.000 --> 00:01:38.000 what the strength of that interaction is. 00:01:38.000 --> 00:01:43.000 And the bottom line is, what determines that is the 00:01:43.000 --> 00:01:48.000 polarizability of the atoms or the molecules that are 00:01:48.000 --> 00:01:53.000 interacting. And we give the symbol alpha to 00:01:53.000 --> 00:01:57.000 the polarizability. And what that is, 00:01:57.000 --> 00:02:03.000 is a measure of the ease with which a charge distribution can 00:02:03.000 --> 00:02:09.000 be distorted. That is the polarizability of 00:02:09.000 --> 00:02:13.000 the molecule. That is a term you will hear in 00:02:13.000 --> 00:02:18.000 future courses quite a lot. And, in general, 00:02:18.000 --> 00:02:25.000 the polarizability goes up with the number of electrons present. 00:02:25.000 --> 00:02:31.000 As you go from -- And you can see on the side 00:02:31.000 --> 00:02:37.000 slides, here. As you go from helium to argon 00:02:37.000 --> 00:02:43.000 to xenon, and let me fix my pointer. 00:02:50.000 --> 00:02:54.000 As we go from helium to argon to xenon, this polarizability 00:02:54.000 --> 00:02:57.000 goes up because the number of electrons are going up. 00:02:57.000 --> 00:03:01.000 If the number of electrons are going up, that means we have 00:03:01.000 --> 00:03:05.000 electrons in outer shells, they are farther away from the 00:03:05.000 --> 00:03:09.000 nucleus. They are more easily distorted. 00:03:09.000 --> 00:03:14.000 As this polarizability goes up, helium, argon and xenon, 00:03:14.000 --> 00:03:19.000 that well depth for the Lennard-Jones potential is going 00:03:19.000 --> 00:03:23.000 up, 0.085, 0.996 and 1.8. And here, on this diagram, 00:03:23.000 --> 00:03:28.000 I actually show you what the shape of the Lennard-Jones 00:03:28.000 --> 00:03:32.000 potential is. Sometimes when I draw it on the 00:03:32.000 --> 00:03:37.000 board, it is not so accurate. But you can see this 00:03:37.000 --> 00:03:42.000 Lennard-Jones potentially actually has this repulsive wall 00:03:42.000 --> 00:03:44.000 that goes up really very steeply. 00:03:44.000 --> 00:03:47.000 And, likewise, on the next slide, 00:03:47.000 --> 00:03:52.000 you see some interactions for at least one molecule here, 00:03:52.000 --> 00:03:55.000 helium, nitrogen, and argon. 00:03:55.000 --> 00:03:59.000 You can also have these dispersion interactions, 00:03:59.000 --> 00:04:04.000 and you do have them, between molecules. 00:04:04.000 --> 00:04:06.000 So, the polarizability is going up. 00:04:06.000 --> 00:04:10.000 Helium, nitrogen, argon, the well depth is going 00:04:10.000 --> 00:04:12.000 up. Again, these are the 00:04:12.000 --> 00:04:17.000 Lennard-Jones potentials for those inert gases and for the 00:04:17.000 --> 00:04:20.000 interactions between two nitrogen atoms, 00:04:20.000 --> 00:04:24.000 dispersion interaction. All atoms and molecules have 00:04:24.000 --> 00:04:30.000 these dispersion interactions. It is just that often times the 00:04:30.000 --> 00:04:36.000 dispersion interactions can be so weak compared to some other 00:04:36.000 --> 00:04:40.000 interactions, which we are going to look at 00:04:40.000 --> 00:04:44.000 today, that we don't even think about them. 00:04:44.000 --> 00:04:50.000 But they are actually there. But what I want to do now is to 00:04:50.000 --> 00:04:55.000 talk about what happens as we lower the temperature even 00:04:55.000 --> 00:04:58.000 further. In other words, 00:04:58.000 --> 00:05:03.000 last time we were talking about the deviation from the inert gas 00:05:03.000 --> 00:05:06.000 law as we lowered the temperature. 00:05:06.000 --> 00:05:11.000 And what we said is that it is these dispersion interactions 00:05:11.000 --> 00:05:16.000 that are the microscopic origin for the deviation from the inert 00:05:16.000 --> 00:05:21.000 gas law, which is a macroscopic law, as you lower the 00:05:21.000 --> 00:05:24.000 temperature. But we also know that if you 00:05:24.000 --> 00:05:29.000 lower the temperature enough, that the gas condenses, 00:05:29.000 --> 00:05:34.000 the gas liquefies. And it is these dispersion 00:05:34.000 --> 00:05:40.000 interactions that are also responsible for the condensation 00:05:40.000 --> 00:05:44.000 of these gases. But now, let's talk about, 00:05:44.000 --> 00:05:49.000 a little bit more deeply, what exactly is going on as we 00:05:49.000 --> 00:05:54.000 lower the temperature close to the liquification point. 00:05:54.000 --> 00:06:00.000 Let me draw a Lennard-Jones potential again. 00:06:00.000 --> 00:06:04.000 And now I am going to do it for two nitrogen molecules. 00:06:04.000 --> 00:06:07.000 Here is nitrogen, here is nitrogen, 00:06:07.000 --> 00:06:11.000 two separated nitrogens as a function of r, 00:06:11.000 --> 00:06:14.000 the distance between the two nuclei. 00:06:14.000 --> 00:06:17.000 This is our zero of interaction. 00:06:17.000 --> 00:06:23.000 And, as I said from that slide, this bond association energy 00:06:23.000 --> 00:06:28.000 measured from the bottom of the well is 0.79 kilojoules per 00:06:28.000 --> 00:06:33.000 mole, the bottom of the well, where the molecules actually 00:06:33.000 --> 00:06:38.000 can never be. But that is the well depth. 00:06:38.000 --> 00:06:43.000 Now, let's think about this. At 300 degrees Kelvin, 00:06:43.000 --> 00:06:47.000 what is the average energy of the molecules? 00:06:47.000 --> 00:06:52.000 Well, the average energy is three-halves RT, 00:06:52.000 --> 00:06:56.000 as we saw. And, if I substitute in this 00:06:56.000 --> 00:07:02.000 temperature, I am going to get something on the order of 3.7 00:07:02.000 --> 00:07:06.000 kilojoules per mole, if this has two significant 00:07:06.000 --> 00:07:11.000 figures. 3.7 kilojoules per mole. 00:07:11.000 --> 00:07:16.000 Well, let me do the following. Let me draw 3.7 kilojoules per 00:07:16.000 --> 00:07:20.000 mole, here, on this Lennard-Jones potential. 00:07:20.000 --> 00:07:25.000 When I do that, and I am going to start here at 00:07:25.000 --> 00:07:29.000 the bottom of the well, and I draw 3.7 kilojoules per 00:07:29.000 --> 00:07:35.000 mole, well, that is somewhere way up here, compared to the 00:07:35.000 --> 00:07:40.000 interaction energy. At 300 degrees Kelvin, 00:07:40.000 --> 00:07:46.000 the bottom line is that those two nitrogen molecules have 00:07:46.000 --> 00:07:53.000 enough kinetic energy to totally ignore this interaction energy. 00:07:53.000 --> 00:07:59.000 They are way up here. If they have 3.7 kilojoules per 00:07:59.000 --> 00:08:04.000 mole of energy, they are not going to stick 00:08:04.000 --> 00:08:08.000 together. They are not going to condense. 00:08:08.000 --> 00:08:14.000 They are actually really going to ignore this small interaction 00:08:14.000 --> 00:08:17.000 energy. They are just going to fly 00:08:17.000 --> 00:08:19.000 apart. And they do. 00:08:19.000 --> 00:08:22.000 You have a gas. However, let's lower the 00:08:22.000 --> 00:08:27.000 temperature now. Say we lower the temperature to 00:08:27.000 --> 00:08:33.000 100 degrees Kelvin. When we do that and calculate 00:08:33.000 --> 00:08:38.000 the average energy at degrees Kelvin, 00:08:38.000 --> 00:08:45.000 that is on the order of 1.2 or so kilojoules per mole average 00:08:45.000 --> 00:08:49.000 energy. 1.2 kilojoules per mole, 00:08:49.000 --> 00:08:55.000 we are somewhere here. And now, the relative energies 00:08:55.000 --> 00:09:02.000 between these nitrogen molecules are much lower. 00:09:02.000 --> 00:09:07.000 And it is beginning to be comparable to this well depth. 00:09:07.000 --> 00:09:12.000 And those nitrogen molecules now are deviating from the inert 00:09:12.000 --> 00:09:16.000 gas law. They are kind of hanging around 00:09:16.000 --> 00:09:20.000 each other. They don't hit the walls as 00:09:20.000 --> 00:09:24.000 often, the walls of the vessel that they are in, 00:09:24.000 --> 00:09:29.000 because they are having an attractive interaction with 00:09:29.000 --> 00:09:34.000 their neighboring nitrogen molecule. 00:09:34.000 --> 00:09:39.000 And so, we are deviating, here, from the inert gas law. 00:09:39.000 --> 00:09:45.000 The pressure is not as large if you are doing it under constant 00:09:45.000 --> 00:09:49.000 volume conditions. And then, say we lower the 00:09:49.000 --> 00:09:54.000 temperature to 77 degrees Kelvin, which is actually the 00:09:54.000 --> 00:10:00.000 boiling point of nitrogen to make liquid nitrogen. 00:10:00.000 --> 00:10:06.000 Well, at 77 degrees Kelvin, the kinetic energy is 0.96 00:10:06.000 --> 00:10:11.000 kilojoules per mole. And now, in this case, 00:10:11.000 --> 00:10:17.000 we are fairly comparable to the well depth here at 0.96 00:10:17.000 --> 00:10:22.000 kilojoules per mole. What happens is the gas 00:10:22.000 --> 00:10:27.000 condenses. The interaction energy between 00:10:27.000 --> 00:10:33.000 those two nitrogen molecules is on the order of the kinetic 00:10:33.000 --> 00:10:39.000 energy. And then these molecules stick 00:10:39.000 --> 00:10:44.000 together, the gas condenses, and you have a liquid. 00:10:44.000 --> 00:10:48.000 That is the origin, here, of this temperature 00:10:48.000 --> 00:10:54.000 dependence and the relevance to the microscopic interactions 00:10:54.000 --> 00:11:00.000 between the molecules. You can understand that. 00:11:00.000 --> 00:11:04.000 And then vice versa, if you start to raise the 00:11:04.000 --> 00:11:09.000 temperature, the molecules start to fly apart. 00:11:09.000 --> 00:11:14.000 They ignore this interaction. Their energy is greater than 00:11:14.000 --> 00:11:20.000 that attractive interaction. And so what you can see in the 00:11:20.000 --> 00:11:27.000 macroscopic boiling points is the vestiges of this microscopic 00:11:27.000 --> 00:11:32.000 interaction energy. I think I am going to put the 00:11:32.000 --> 00:11:34.000 center screen down. 00:11:42.000 --> 00:11:52.000 If you look at -- 00:12:00.000 --> 00:12:03.000 -- helium, neon, argon, krypton, 00:12:03.000 --> 00:12:06.000 and xenon. What we said is that this 00:12:06.000 --> 00:12:11.000 polarizability increases as we increase the number of 00:12:11.000 --> 00:12:15.000 electrons. We see that the well depth 00:12:15.000 --> 00:12:19.000 increases. Therefore, the boiling point 00:12:19.000 --> 00:12:25.000 increases as we go down the inert gas column. 00:12:25.000 --> 00:12:29.000 You can see how that macroscopic boiling point is a 00:12:29.000 --> 00:12:35.000 reflection of what is happening on the microscopic scale between 00:12:35.000 --> 00:12:40.000 two individual molecules. You can also see that in this 00:12:40.000 --> 00:12:44.000 plot or in this chart. Here we have molecules, 00:12:44.000 --> 00:12:47.000 hydrogen, nitrogen, and oxygen. 00:12:47.000 --> 00:12:52.000 The polarizability alpha is also increasing as we go down. 00:12:52.000 --> 00:12:58.000 Correspondingly, the well depth is increasing. 00:12:58.000 --> 00:13:02.000 Correspondingly, that boiling point is also 00:13:02.000 --> 00:13:07.000 getting larger and larger. That macroscopic quantity, 00:13:07.000 --> 00:13:12.000 then, reflects the change in the individual interaction 00:13:12.000 --> 00:13:18.000 energies between the molecules, the microscopic quantity. 00:13:18.000 --> 00:13:23.000 But it also turns out that the shape of the molecules are 00:13:23.000 --> 00:13:25.000 important. For example, 00:13:25.000 --> 00:13:32.000 let's take this molecule, C five H twelve. 00:13:32.000 --> 00:13:36.000 There are several ways I can draw a skeletal structure for C 00:13:36.000 --> 00:13:40.000 five H twelve. One way is to make it pentane, 00:13:40.000 --> 00:13:45.000 making a linear molecule. And another way is to make this 00:13:45.000 --> 00:13:48.000 two, two dimethylpropane, 00:13:48.000 --> 00:13:52.000 carbon in the center, some methyl groups around that 00:13:52.000 --> 00:13:56.000 center carbon. It turns out that the boiling 00:13:56.000 --> 00:14:00.000 point of pentane is 309 degrees Kelvin. 00:14:00.000 --> 00:14:03.000 The boiling point of 2,2-dimethylpropane is 00:14:03.000 --> 00:14:07.000 degrees Kelvin. These are two molecules that 00:14:07.000 --> 00:14:12.000 have the same number of atoms, i.e., the same number of 00:14:12.000 --> 00:14:15.000 electrons, should have the same polarizability. 00:14:15.000 --> 00:14:20.000 However, one has a higher boiling point than the other. 00:14:20.000 --> 00:14:25.000 And the reason for this is because of the different shapes 00:14:25.000 --> 00:14:29.000 of these molecules. In the case of propane, 00:14:29.000 --> 00:14:34.000 if we have an instantaneous fluctuation in our charge 00:14:34.000 --> 00:14:37.000 distribution, it is going to be essentially 00:14:37.000 --> 00:14:40.000 along a line. That instantaneous fluctuation 00:14:40.000 --> 00:14:45.000 is essentially kind of rod-like because of the skeletal nature 00:14:45.000 --> 00:14:48.000 of the pentane. So, one end is a little 00:14:48.000 --> 00:14:53.000 positive, one end is a little negative, the other way around. 00:14:53.000 --> 00:14:58.000 That is going to induce a dipole in a neighboring pentane 00:14:58.000 --> 00:15:02.000 molecule. And then they are going to 00:15:02.000 --> 00:15:06.000 align, positive-negative here, positive-negative there. 00:15:06.000 --> 00:15:10.000 But then, in the case of dimethylpropane, 00:15:10.000 --> 00:15:14.000 you are also going to have this charge fluctuation. 00:15:14.000 --> 00:15:18.000 But in the case of propane, here, this is a more 00:15:18.000 --> 00:15:23.000 spherical-looking molecule. And so, the charge fluctuation 00:15:23.000 --> 00:15:28.000 is not going to be so rod-like. But, nevertheless, 00:15:28.000 --> 00:15:31.000 this charge fluctuation, induced dipole here, 00:15:31.000 --> 00:15:35.000 is going to induce another dipole in a neighboring 00:15:35.000 --> 00:15:40.000 molecule, and you are going to have an attractive interaction. 00:15:40.000 --> 00:15:43.000 But, in the case of the 2,2-dimethylpropane, 00:15:43.000 --> 00:15:47.000 this is a much more spherical distribution than this. 00:15:47.000 --> 00:15:50.000 In this case, these two dipoles are not as 00:15:50.000 --> 00:15:54.000 close together as they are in the case of pentane, 00:15:54.000 --> 00:15:57.000 meaning that the interaction energy, here, 00:15:57.000 --> 00:16:02.000 between the dimethylpropane, is going to be less than it is 00:16:02.000 --> 00:16:08.000 in the case of the pentane. And, again, that is reflected 00:16:08.000 --> 00:16:11.000 in the macroscopic boiling points. 00:16:11.000 --> 00:16:15.000 The boiling point of pentane is larger than that of 00:16:15.000 --> 00:16:20.000 dimethylpropane because that microscopic interaction energy 00:16:20.000 --> 00:16:25.000 is larger for propane because the induced dipoles can get 00:16:25.000 --> 00:16:29.000 closer together. So, the shape is also important 00:16:29.000 --> 00:16:33.000 in determining these boiling points, these energies of 00:16:33.000 --> 00:16:38.000 interactions. That is going to take care of 00:16:38.000 --> 00:16:44.000 our discussion of molecules or discussion of the induced dipole 00:16:44.000 --> 00:16:49.000 - induced dipole interaction energy where we are talking 00:16:49.000 --> 00:16:55.000 about molecules that do not have permanent dipole moments. 00:16:55.000 --> 00:17:01.000 But now we are going to turn to molecules with permanent dipole 00:17:01.000 --> 00:17:05.000 moments, such as HCl. And, of course, 00:17:05.000 --> 00:17:09.000 in these molecules, the dispersion interaction is 00:17:09.000 --> 00:17:14.000 also taking place. It is just that that is going 00:17:14.000 --> 00:17:19.000 to be weak compared to the interaction between two 00:17:19.000 --> 00:17:23.000 permanent dipoles. Here we have one HCl molecule, 00:17:23.000 --> 00:17:27.000 permanent dipole. It is going to then, 00:17:27.000 --> 00:17:31.000 in a collection of HCl molecules, attract another HCl 00:17:31.000 --> 00:17:36.000 molecule. And that HCl molecule is going 00:17:36.000 --> 00:17:39.000 to align in the opposite direction. 00:17:39.000 --> 00:17:43.000 The alignment of those two dipoles is going to lower the 00:17:43.000 --> 00:17:45.000 energy. That is the attractive 00:17:45.000 --> 00:17:48.000 interaction. And then you might say, 00:17:48.000 --> 00:17:52.000 you get this attractive interaction, but you also have 00:17:52.000 --> 00:17:57.000 now this repulsive interaction between the two chlorines and 00:17:57.000 --> 00:18:02.000 the two hydrogens. Doesn't this all cancel out? 00:18:02.000 --> 00:18:06.000 And the answer is no. And that is because of this. 00:18:06.000 --> 00:18:11.000 The positive end of one molecule and the negative end of 00:18:11.000 --> 00:18:17.000 the other, this distance and this distance on the opposite 00:18:17.000 --> 00:18:22.000 end are actually closer than the positive charges. 00:18:22.000 --> 00:18:26.000 The yellow distance, here, is smaller than the 00:18:26.000 --> 00:18:31.000 distance between the two hydrogens, is smaller than the 00:18:31.000 --> 00:18:36.000 distance between the two chlorines. 00:18:36.000 --> 00:18:40.000 And so, it is this attractive interaction that wins out, 00:18:40.000 --> 00:18:44.000 actually. When you put those two dipoles 00:18:44.000 --> 00:18:49.000 together, the repulsion actually is there, but it is the 00:18:49.000 --> 00:18:54.000 attractive interaction that wins out, and the whole system is 00:18:54.000 --> 00:18:59.000 stabilized because the distance between the unlike charges is 00:18:59.000 --> 00:19:05.000 smaller than the distance between the like charges. 00:19:05.000 --> 00:19:11.000 Now, it also turns out that we have a functional form for the 00:19:11.000 --> 00:19:16.000 dipole-dipole attractive interaction. 00:19:16.000 --> 00:19:23.000 And that attractive interaction turns out to be a minus one over 00:19:23.000 --> 00:19:30.000 r cubed dependence. And this is exact. 00:19:30.000 --> 00:19:34.000 You can actually derive this. You can show that this is the 00:19:34.000 --> 00:19:39.000 interaction between two permanent dipoles is one over r 00:19:39.000 --> 00:19:42.000 cubed. The quantity on the top, 00:19:42.000 --> 00:19:46.000 mu, that is not a reduced mass, this time. 00:19:46.000 --> 00:19:50.000 If we go back to when we started talking about dipole 00:19:50.000 --> 00:19:54.000 moments, this is the dipole moment of the molecule. 00:19:54.000 --> 00:20:00.000 We have to use our symbols for multiple quantities. 00:20:00.000 --> 00:20:04.000 So, that is the dipole moment. We are talking about 00:20:04.000 --> 00:20:07.000 dipole-dipole attractive interactions. 00:20:07.000 --> 00:20:11.000 And that attractive interaction looks like this, 00:20:11.000 --> 00:20:14.000 minus one over r cubed. 00:20:14.000 --> 00:20:18.000 Now, you might say, where is the repulsive part of 00:20:18.000 --> 00:20:21.000 this interaction? In the case of the 00:20:21.000 --> 00:20:25.000 Lennard-Jones potential, remember we had two parts, 00:20:25.000 --> 00:20:30.000 the attractive part and the repulsive part. 00:20:30.000 --> 00:20:34.000 The repulsive part was one over r to the 12. 00:20:34.000 --> 00:20:38.000 The attractive part was one over r to the 6. 00:20:38.000 --> 00:20:42.000 But it turns out that for dipole-dipole interaction, 00:20:42.000 --> 00:20:46.000 we do not have a general form for the repulsive part, 00:20:46.000 --> 00:20:49.000 unlike induced dipole - induced dipole. 00:20:49.000 --> 00:20:53.000 So, the best we can do, in general, is to tell you that 00:20:53.000 --> 00:20:59.000 the dipole-dipole attractive interaction is one over r cubed. 00:20:59.000 --> 00:21:04.000 But I want to compare this one over r cubed to the attractive 00:21:04.000 --> 00:21:09.000 interaction due to the induced dipole - induced dipole 00:21:09.000 --> 00:21:12.000 interaction. You see that the dipole-dipole 00:21:12.000 --> 00:21:17.000 interaction is what we call longer range than the induced 00:21:17.000 --> 00:21:22.000 dipole - induced dipole. What I mean by that is that the 00:21:22.000 --> 00:21:26.000 value of r here, the distance between the two 00:21:26.000 --> 00:21:32.000 dipoles, can be larger. In the case of a longer range 00:21:32.000 --> 00:21:36.000 interaction, it can be larger and still have some non-zero 00:21:36.000 --> 00:21:39.000 quantity for the interaction potential. 00:21:39.000 --> 00:21:41.000 For example, if you are out here, 00:21:41.000 --> 00:21:44.000 if this value of r, you can just see with the 00:21:44.000 --> 00:21:48.000 shorter range interaction, one over r to the 6, 00:21:48.000 --> 00:21:52.000 that the attractive interaction is only the 00:21:52.000 --> 00:21:56.000 difference between the pink curve and the black curve, 00:21:56.000 --> 00:21:59.000 which is zero. Whereas, with a longer range 00:21:59.000 --> 00:22:04.000 interaction, we have more attractive interaction. 00:22:04.000 --> 00:22:08.000 This is more negative. That energy difference is 00:22:08.000 --> 00:22:11.000 larger. That is what we mean by a 00:22:11.000 --> 00:22:15.000 longer range interaction. And I want to just compare, 00:22:15.000 --> 00:22:20.000 in this diagram here, the strength of the dispersion 00:22:20.000 --> 00:22:25.000 interaction to that of the permanent dipole-dipole 00:22:25.000 --> 00:22:30.000 interaction by comparing the interaction between two argon 00:22:30.000 --> 00:22:35.000 atoms to those between two HCl molecules. 00:22:35.000 --> 00:22:39.000 Argon only has the dispersive interaction between it because 00:22:39.000 --> 00:22:42.000 it does not have a dipole moment. 00:22:42.000 --> 00:22:47.000 And you can see that this well depth, here, is one kilojoule 00:22:47.000 --> 00:22:51.000 per mole, roughly speaking. But in the case of HCl, 00:22:51.000 --> 00:22:54.000 that well depth, here, is three kilojoules per 00:22:54.000 --> 00:22:59.000 mole because that has a permanent dipole. 00:22:59.000 --> 00:23:03.000 And, in both cases, HCl and argon-argon, 00:23:03.000 --> 00:23:08.000 we are talking about roughly the same number of electrons, 00:23:08.000 --> 00:23:10.000 not exactly, but roughly, 00:23:10.000 --> 00:23:14.000 meaning the polarizability is roughly the same. 00:23:14.000 --> 00:23:19.000 The dispersion interaction energy is roughly the same for 00:23:19.000 --> 00:23:24.000 HCl as it is for argon, but the difference is that HCl 00:23:24.000 --> 00:23:27.000 has that permanent dipole moment. 00:23:27.000 --> 00:23:30.000 Therefore, the deeper well depth, therefore, 00:23:30.000 --> 00:23:35.000 in HCl, the higher boiling point, 239 degrees Kelvin as 00:23:35.000 --> 00:23:43.000 opposed to 87 Kelvin for argon. What is on this slide is just 00:23:43.000 --> 00:23:49.000 an example of how that dipole-dipole interaction energy 00:23:49.000 --> 00:23:56.000 varies with the dipole moment. The larger the dipole, 00:23:56.000 --> 00:24:02.000 of course, the larger the interaction energy. 00:24:02.000 --> 00:24:05.000 Here, I show you several molecules that all have, 00:24:05.000 --> 00:24:08.000 again, roughly the same number of atoms. 00:24:08.000 --> 00:24:12.000 They have the same mass, they roughly have the same 00:24:12.000 --> 00:24:15.000 number of electrons, so they roughly have the same 00:24:15.000 --> 00:24:19.000 polarizability. The induced dipole - induced 00:24:19.000 --> 00:24:22.000 dipole is the same, but what is changing here, 00:24:22.000 --> 00:24:25.000 as I go down, is the dipole moment. 00:24:25.000 --> 00:24:28.000 For propane, dipole moment really small, 00:24:28.000 --> 00:24:32.000 0.1 debye. Dimethyl ethe,r 1.3. 00:24:32.371 --> 00:00:02.700 Acetaldehyde, 00:24:34.387 --> 00:00:03.900 Acetonitrile, 00:24:36.000 --> 00:24:42.000 Dipole moment increases. The boiling point increases 00:24:42.000 --> 00:24:48.000 because that attractive interaction is increasing. 00:24:48.000 --> 00:24:53.000 It scales roughly as the dipole moment squared. 00:24:53.000 --> 00:25:00.000 The dipole-dipole interaction is stronger. 00:25:00.000 --> 00:25:04.000 Now, I just want to briefly then remind you about one other 00:25:04.000 --> 00:25:09.000 attractive interaction that we have talked about before. 00:25:09.000 --> 00:25:14.000 And that is between two ions. There we are talking about the 00:25:14.000 --> 00:25:18.000 Coulomb interaction energy, where the dependence is minus 00:25:18.000 --> 00:25:22.000 one over r. That is the longest range 00:25:22.000 --> 00:25:25.000 interaction. Again, you can see this way out 00:25:25.000 --> 00:25:28.000 here. If I choose this value of r, 00:25:28.000 --> 00:25:33.000 the one over six interaction term would give me a 00:25:33.000 --> 00:25:37.000 very small value for the attractive interaction, 00:25:37.000 --> 00:25:41.000 -- -- because it is one over r to 00:25:41.000 --> 00:25:43.000 the six. You take a large number for r 00:25:43.000 --> 00:25:47.000 and raise it to the 6 power and put in the denominator. 00:25:47.000 --> 00:25:50.000 You are going to have a small value for U of r. 00:25:50.000 --> 00:25:54.000 The one over r to the three gives you some 00:25:54.000 --> 00:25:57.000 interaction energy, but one over r gives you a lot 00:25:57.000 --> 00:26:02.000 of attractive interaction. It is the longest range. 00:26:02.000 --> 00:26:05.000 And you can also see here, in a moment, 00:26:05.000 --> 00:26:09.000 that it is going to be the strongest interaction. 00:26:09.000 --> 00:26:13.000 What I am just doing is comparing several molecules or 00:26:13.000 --> 00:26:17.000 atoms. Here is argon 2 which has only 00:26:17.000 --> 00:26:20.000 the dispersive interaction. Here is the plot, 00:26:20.000 --> 00:26:25.000 well depth minus one kilojoule. Then, there is the HCl 00:26:25.000 --> 00:26:30.000 interaction energy that has the dispersion interaction in it, 00:26:30.000 --> 00:26:36.000 but also the dipole-dipole permanent interaction. 00:26:36.000 --> 00:26:40.000 It is minus three kilojoules. And then we are talking about 00:26:40.000 --> 00:26:44.000 chlorine two. This is a covalent bond. 00:26:44.000 --> 00:26:49.000 This is no longer a Lennard-Jones potential energy, 00:26:49.000 --> 00:26:53.000 but this well depth, here, is minus 200 kilojoules 00:26:53.000 --> 00:26:55.000 per mole. And then, finally, 00:26:55.000 --> 00:27:00.000 this ionic interaction between potassium and chlorine, 00:27:00.000 --> 00:27:06.000 look at how strong that is, minus 450 kilojoules per mole. 00:27:06.000 --> 00:27:11.000 So, these are the relative strengths here of these 00:27:11.000 --> 00:27:18.000 interaction energies. That is all I that want to say 00:27:18.000 --> 00:27:23.000 about these kinds of intermolecular interactions, 00:27:23.000 --> 00:27:30.000 where we are dealing with some kind of dipole. 00:27:30.000 --> 00:27:34.000 But before we move on, I want to talk about one other 00:27:34.000 --> 00:27:39.000 kind of intermolecular interaction potential. 00:28:00.000 --> 00:28:05.000 And that is something called hydrogen bonding. 00:28:15.000 --> 00:28:20.000 All right. A final intermolecular 00:28:20.000 --> 00:28:26.000 interaction, hydrogen bonding. Hydrogen bonding, 00:28:26.000 --> 00:28:33.000 here, occurs between a hydrogen atom that is attached to an 00:28:33.000 --> 00:28:39.000 electronegative atom and another molecule in the gas or in the 00:28:39.000 --> 00:28:43.000 solution. The first requirement is that 00:28:43.000 --> 00:28:50.000 you have hydrogen attached to a very electronegative atom. 00:28:50.000 --> 00:28:56.000 Hydrogen bonding occurs for hydrogens attached to oxygen, 00:28:56.000 --> 00:29:02.000 nitrogen, and chlorine. Those are all electronegative 00:29:02.000 --> 00:29:05.000 atoms. Water is a good example. 00:29:05.000 --> 00:29:12.000 In the case of water-- You have hydrogen bonded to this oxygen. 00:29:12.000 --> 00:29:16.000 This oxygen is really very electronegative. 00:29:16.000 --> 00:29:22.000 What that oxygen does is it pulls those electrons away from 00:29:22.000 --> 00:29:25.000 the hydrogen. This hydrogen is kind of 00:29:25.000 --> 00:29:32.000 partially unshielded. It is partially deshielded. 00:29:32.000 --> 00:29:38.000 And then, there is a lot of electron density here on this 00:29:38.000 --> 00:29:42.000 oxygen. Well, because that hydrogen is 00:29:42.000 --> 00:29:48.000 partially deshielded and because it is really small, 00:29:48.000 --> 00:29:54.000 this hydrogen actually will kind of see the oxygen atoms on 00:29:54.000 --> 00:30:01.000 a neighboring water molecule. And since this is kind of 00:30:01.000 --> 00:30:05.000 partially negative, this hydrogen will interact 00:30:05.000 --> 00:30:10.000 with one of the lone pairs on this oxygen and will form a 00:30:10.000 --> 00:30:14.000 bond. This is a little bit partially 00:30:14.000 --> 00:30:18.000 positive, this is a little bit partially negative, 00:30:18.000 --> 00:30:22.000 and the result, here, is a bond between the 00:30:22.000 --> 00:30:27.000 hydrogen and the oxygen. And that bond is on the order 00:30:27.000 --> 00:30:34.000 of 20 to 60 kilojoules per mole. This bond is not a covalent 00:30:34.000 --> 00:30:36.000 bond. A covalent bond is 00:30:36.000 --> 00:30:39.000 kilojoules per mole. This is 10% of it, 00:30:39.000 --> 00:30:43.000 but it is still a very important quantity or a very 00:30:43.000 --> 00:30:47.000 important phenomenon, this hydrogen bonding. 00:30:47.000 --> 00:30:51.000 The hydrogen bonding is certainly responsible for the 00:30:51.000 --> 00:30:56.000 peculiar properties of water, as you will learn more about in 00:30:56.000 --> 00:31:00.000 5.60, but it is also responsible for the unique shape, 00:31:00.000 --> 00:31:05.000 oftentimes, of biological molecules. 00:31:05.000 --> 00:31:10.000 The helix in DNA owes its structure to hydrogen bonding. 00:31:10.000 --> 00:31:16.000 The hydrogen bonding is what makes trees stand upright. 00:31:16.000 --> 00:31:21.000 The long cellulose molecules in trees are actually bonded 00:31:21.000 --> 00:31:27.000 together by hydrogen bonding. Nylon owes its strength to 00:31:27.000 --> 00:31:33.000 hydrogen bonding. And hydrogen bonding is also 00:31:33.000 --> 00:31:40.000 responsible for whether or not you have a bad hair day. 00:31:40.000 --> 00:31:47.000 As an example of that, I want you to look at the slide 00:31:47.000 --> 00:31:53.000 up there on the walls. What you see is a protein 00:31:53.000 --> 00:32:00.000 molecule. This is the structure of hair. 00:32:00.000 --> 00:32:05.000 The molecules that make up the strands of your hair look like 00:32:05.000 --> 00:32:07.000 this. It is a polymer. 00:32:07.000 --> 00:32:12.000 Well, it is a polypeptide. This unit right in here, 00:32:12.000 --> 00:32:17.000 carbon-oxygen bound to carbon-hydrogen bound to 00:32:17.000 --> 00:32:20.000 nitrogen-hydrogen is the peptide. 00:32:20.000 --> 00:32:24.000 It is repeated. You see the next unit over? 00:32:24.000 --> 00:32:26.000 CO-CH-NH. CO-CH-NH. 00:32:26.000 --> 00:32:32.000 That keeps repeating. That is the repeat unit. 00:32:32.000 --> 00:32:36.000 And, of course, this carbon-hydrogen right 00:32:36.000 --> 00:32:41.000 there, you can see it has a line there, indicating that it is 00:32:41.000 --> 00:32:46.000 bonded to something. And it is bonded to something. 00:32:46.000 --> 00:32:51.000 If that carbon-hydrogen is bound to another hydrogen, 00:32:51.000 --> 00:32:56.000 then you have a polypeptide which has been made from an 00:32:56.000 --> 00:33:02.000 amino acid that you might know of as glycine. 00:33:02.000 --> 00:33:07.000 If that carbon is bound to a CH three group, 00:33:07.000 --> 00:33:13.000 then that peptide was made from an amino acid that you might 00:33:13.000 --> 00:33:18.000 know of as alanine. And if it is bound to a CH two 00:33:18.000 --> 00:33:23.000 S H group, well, that was an amino acid 00:33:23.000 --> 00:33:28.000 known as cysteine. But what I want you to notice 00:33:28.000 --> 00:33:35.000 here is that these hydrogens on the nitrogen -- 00:33:35.000 --> 00:33:38.000 That nitrogen is an electron negative atom. 00:33:38.000 --> 00:33:42.000 And that hydrogen, if your hair is wet, 00:33:42.000 --> 00:33:46.000 it is actually hydrogen bonded to a water molecule. 00:33:46.000 --> 00:33:51.000 Here is that hydrogen bond. And then in the next strand 00:33:51.000 --> 00:33:57.000 over, this oxygen is hydrogen bonded to a water molecule when 00:33:57.000 --> 00:34:02.000 your hair is wet. And the bottom line is that 00:34:02.000 --> 00:34:08.000 when your hair is wet, you have the strands of your 00:34:08.000 --> 00:34:12.000 hair that kind of slip by each other. 00:34:12.000 --> 00:34:16.000 There is no registry of one strand to another, 00:34:16.000 --> 00:34:21.000 because each strand has this coating, here, 00:34:21.000 --> 00:34:26.000 of water molecules due to hydrogen bonding. 00:34:26.000 --> 00:34:32.000 Suppose you take your hair and put it in a very contorted 00:34:32.000 --> 00:34:38.000 configuration like this. And then you drive off the 00:34:38.000 --> 00:34:41.000 water molecules, you dry your hair. 00:34:41.000 --> 00:34:47.000 What happens is that these water molecules then leave, 00:34:47.000 --> 00:34:53.000 the hydrogen bonds are broken. This is not such a strong bond, 00:34:53.000 --> 00:34:58.000 20 to 60 kilojoules per mole, those hydrogen bonds are 00:34:58.000 --> 00:35:02.000 broken. And then this hydrogen on this 00:35:02.000 --> 00:35:07.000 nitrogen looks around and sees the oxygen with its lone pairs 00:35:07.000 --> 00:35:11.000 on this strand, and so you form a hydrogen bond 00:35:11.000 --> 00:35:14.000 between this strand and this strand. 00:35:14.000 --> 00:35:19.000 And so now the strands of your hair are in registry with each 00:35:19.000 --> 00:35:22.000 other. They are actually stronger. 00:35:22.000 --> 00:35:27.000 And they do tell you not to brush your hair when it is wet, 00:35:27.000 --> 00:35:33.000 because it isn't so strong. Well, it is not so strong 00:35:33.000 --> 00:35:39.000 because these water molecules are insulating each one of these 00:35:39.000 --> 00:35:42.000 strands. And when it is dry these two 00:35:42.000 --> 00:35:48.000 strands are bond to each other. They are in registry with each 00:35:48.000 --> 00:35:51.000 other. And so, if you do this right, 00:35:51.000 --> 00:35:56.000 and you then let go of the contorted configuration, 00:35:56.000 --> 00:36:01.000 which I am having trouble doing, those strands are in 00:36:01.000 --> 00:36:08.000 registry with each other now. And you have a good hair day. 00:36:08.000 --> 00:36:13.000 So, that is the importance of hydrogen bonding. 00:36:13.000 --> 00:36:19.000 I curled my hair just for this demo, a little asymmetric, 00:36:19.000 --> 00:36:22.000 here. [LAUGHTER] But now, 00:36:22.000 --> 00:36:26.000 if you are as fortunate, or unfortunate, 00:36:26.000 --> 00:36:33.000 depending on your preference, to have naturally curly hair, 00:36:33.000 --> 00:36:40.000 then what you have are a lot of sulfur-sulfur bonds. 00:36:40.000 --> 00:36:49.000 You have a lot of cysteine peptide groups. 00:36:49.000 --> 00:36:58.000 What happens there is this. On the CH groups, 00:36:58.000 --> 00:37:02.000 you have CH two sulfur H. 00:37:02.000 --> 00:37:07.000 And on the next strand over you have S, CH two, 00:37:07.000 --> 00:37:11.000 and CH bonded to nitrogen, bonded to a CO. 00:37:11.000 --> 00:37:17.000 And you actually have a covalent bond between these two 00:37:17.000 --> 00:37:21.000 sulfurs, here. This is a strong bond. 00:37:21.000 --> 00:37:27.000 The strands of your polymers in your hair are in registry all of 00:37:27.000 --> 00:37:32.000 the time. And if you want to make your 00:37:32.000 --> 00:37:36.000 natural curly hair straight you have to do drastic things like 00:37:36.000 --> 00:37:40.000 use drastic chemicals to break this sulfur-sulfur bond. 00:37:40.000 --> 00:37:43.000 You can do it, but it is not easy. 00:37:43.000 --> 00:37:48.000 Likewise, if you have naturally straight hair and you want to 00:37:48.000 --> 00:37:51.000 curl it and make it semi-permanently curly, 00:37:51.000 --> 00:37:55.000 then you have to build in the sulfur-sulfur bonds. 00:37:55.000 --> 00:37:58.000 And you have to do, again, some rather drastic 00:37:58.000 --> 00:38:05.000 chemistry to make that happen. Hydrogen bonding is important, 00:38:05.000 --> 00:38:12.000 especially if you go to do anything in biologically- 00:38:12.000 --> 00:38:16.000 related sciences, you will see that. 00:38:16.000 --> 00:38:22.000 Now, I am going to change topics here. 00:38:30.000 --> 00:38:36.000 I am going to change topics, and we are going to talk a 00:38:36.000 --> 00:38:42.000 little bit about thermodynamics in preparation to get up to 00:38:42.000 --> 00:38:48.000 chemical equilibrium so that Professor Cummins can come in 00:38:48.000 --> 00:38:55.000 next Wednesday and start talking about acid-base equilibrium. 00:38:55.000 --> 00:39:00.000 He is great. You will love him. 00:39:00.000 --> 00:39:04.000 We are going to review some thermodynamics today. 00:39:04.000 --> 00:39:08.000 I am going to go kind of quickly because some of this I 00:39:08.000 --> 00:39:12.000 think you know, but I want to make sure 00:39:12.000 --> 00:39:15.000 everybody is on the same page. First of all, 00:39:15.000 --> 00:39:19.000 bond energies. We talked about bond energies 00:39:19.000 --> 00:39:23.000 as delta E sub D. And we measured it from the 00:39:23.000 --> 00:39:27.000 bottom of the well. And I told you a few days ago, 00:39:27.000 --> 00:39:32.000 I lied to you. The measured energies are 00:39:32.000 --> 00:39:35.000 really from v equals zero, and they are. 00:39:35.000 --> 00:39:39.000 But what I am going to do is change my language. 00:39:39.000 --> 00:39:43.000 Instead of talking about energies, I am going to talk 00:39:43.000 --> 00:39:47.000 about enthalpies. I am going to talk about delta 00:39:47.000 --> 00:39:51.000 Hs rather than delta Es. The reason I am going to do 00:39:51.000 --> 00:39:56.000 this is because it is easier for us to measure a bond enthalpy 00:39:56.000 --> 00:40:00.000 than a bond energy. And that has to do with the 00:40:00.000 --> 00:40:04.000 fact that we usually make measurements in bulk under 00:40:04.000 --> 00:40:09.000 constant pressure conditions. And that is the quantity that 00:40:09.000 --> 00:40:12.000 comes out. The relationship between delta 00:40:12.000 --> 00:40:15.000 H and delta E is this. Delta H is equal to delta E 00:40:15.000 --> 00:40:18.000 plus delta PV. 00:40:18.000 --> 00:40:22.000 This is a relationship that you will learn 00:40:22.000 --> 00:40:25.000 about in a lot of detail in 5.60, in Chemical 00:40:25.000 --> 00:40:29.000 Thermodynamics. At this point, 00:40:29.000 --> 00:40:32.000 we are going to take it as a given. 00:40:32.000 --> 00:40:38.000 For gases, delta H differs on the order of 1% to 2% from delta 00:40:38.000 --> 00:40:39.000 E. It is not much, 00:40:39.000 --> 00:40:44.000 but if you are doing some precise calculation, 00:40:44.000 --> 00:40:48.000 you need to be aware of that. For liquids and solids, 00:40:48.000 --> 00:40:54.000 delta H and delta E are really the same for all intrinsic 00:40:54.000 --> 00:40:57.000 purposes. The delta PV term is really 00:40:57.000 --> 00:41:02.000 very small. And, in thermodynamics, 00:41:02.000 --> 00:41:06.000 since we are most always looking at changes in energy, 00:41:06.000 --> 00:41:10.000 we need what we call standard states. 00:41:10.000 --> 00:41:13.000 And we are going to put a nought, here, 00:41:13.000 --> 00:41:18.000 on all of our delta Hs to designate the standard state. 00:41:18.000 --> 00:41:22.000 And our standard state that your book uses, 00:41:22.000 --> 00:41:26.000 and will use, refers really to the pressure. 00:41:26.000 --> 00:41:33.000 And the pressure is one bar. And one bar is equal to 10^5 00:41:33.000 --> 00:41:37.000 Pascal. That is equal to 10^5 kilograms 00:41:37.000 --> 00:41:43.000 per meter second squared. The delta Hs we are going to 00:41:43.000 --> 00:41:47.000 talk about are also, just about all of them, 00:41:47.000 --> 00:41:51.000 measured at 298.15 degrees Kelvin. 00:41:51.000 --> 00:41:57.000 Delta H does depend on temperature, but we actually are 00:41:57.000 --> 00:42:04.000 not going to look at that in the next few days. 00:42:04.000 --> 00:00:05.600 You are going to do that in 00:42:07.000 --> 00:42:12.000 Our delta Hs are going to be delta Hs at 298.15 degrees 00:42:12.000 --> 00:42:15.000 Kelvin. On the first slide here, 00:42:15.000 --> 00:42:20.000 I show you a bunch of bond enthalpies for CH bonds. 00:42:20.000 --> 00:42:25.000 And, of course, those bond enthalpies are a 00:42:25.000 --> 00:42:30.000 little bit different, depending on what molecule you 00:42:30.000 --> 00:42:33.000 have. But they are not that 00:42:33.000 --> 00:42:36.000 different. And so, what is often done, 00:42:36.000 --> 00:42:40.000 and your book does this, is that somebody goes and 00:42:40.000 --> 00:42:45.000 calculates the average of the bond energies for lots of CH 00:42:45.000 --> 00:42:50.000 bonds and lots of molecules and they prepare a table that looks 00:42:50.000 --> 00:42:53.000 like this. This is the mean bond enthalpy. 00:42:53.000 --> 00:42:56.000 And they have CH, CC, carbon-carbon. 00:42:56.000 --> 00:43:01.000 But these are average bond enthalpies. 00:43:01.000 --> 00:43:04.000 Now, why are bond enthalpies important to us? 00:43:04.000 --> 00:43:08.000 Well, they are important because they determine the 00:43:08.000 --> 00:43:13.000 enthalpy of a chemical reaction. If the bonds are stronger in 00:43:13.000 --> 00:43:18.000 the products than in the reactants, that is going to give 00:43:18.000 --> 00:43:22.000 us an exothermic reaction. If the bonds are stronger in 00:43:22.000 --> 00:43:27.000 the reactants than the products, that gives us an endothermic 00:43:27.000 --> 00:43:31.000 reaction. And so let's look at this 00:43:31.000 --> 00:43:34.000 reaction. This is an important reaction. 00:43:34.000 --> 00:43:36.000 This is the oxidation of glucose. 00:43:36.000 --> 00:43:40.000 This is a reaction very exothermic, minus 00:43:40.000 --> 00:43:44.000 kilojoules per mole. It is a reaction that is being 00:43:44.000 --> 00:43:48.000 carried out in every cell of your body as we speak. 00:43:48.000 --> 00:43:53.000 It is the reaction that is providing the energy to maintain 00:43:53.000 --> 00:43:56.000 your body temperature, the energy to move your 00:43:56.000 --> 00:44:03.000 muscles, the energy to repair tissue, and the energy to think. 00:44:03.000 --> 00:44:06.000 Important reaction. This is the reason why we eat. 00:44:06.000 --> 00:44:10.000 This is the reason why we breathe, this is the reason why 00:44:10.000 --> 00:44:13.000 we exhale, and this is the reason why we pee. 00:44:13.000 --> 00:44:15.000 [LAUGHTER] 00:44:23.000 --> 00:44:27.000 What do we need to do to calculate the enthalpy for this 00:44:27.000 --> 00:44:30.000 reaction? We have to figure out how much 00:44:30.000 --> 00:44:35.000 energy is required to break all of the bonds of the reactants 00:44:35.000 --> 00:44:38.000 because that is how much energy we put in. 00:44:38.000 --> 00:44:43.000 And then we have to figure out then how much energy we get back 00:44:43.000 --> 00:44:47.000 when we form the product bonds. Bottom line is, 00:44:47.000 --> 00:44:51.000 the enthalpy necessary to break all of the bonds, 00:44:51.000 --> 00:44:54.000 you can calculate, is 12,452 kilojoules per mole. 00:44:54.000 --> 00:44:59.000 That number comes from using these average bond energies I 00:44:59.000 --> 00:45:04.000 told you about. We can then get back some 00:45:04.000 --> 00:45:07.000 energy, minus 15,000, approximately, 00:45:07.000 --> 00:45:12.000 when we form some new bonds. That number comes from those 00:45:12.000 --> 00:45:17.000 average bond enthalpies. The difference between these 00:45:17.000 --> 00:45:22.000 two energy levels is the exothermicity of the reaction. 00:45:22.000 --> 00:45:25.000 Now, what did we do to get the enthalpy? 00:45:25.000 --> 00:45:31.000 Well, what I did is took the bond enthalpies of each bond of 00:45:31.000 --> 00:45:36.000 the reactants and summed them. Then, I took the bond 00:45:36.000 --> 00:45:40.000 enthalpies for each one of the products, summed them, 00:45:40.000 --> 00:45:44.000 and subtracted the two to get the enthalpy of the reaction. 00:45:44.000 --> 00:45:47.000 I want you to notice something here, important. 00:45:47.000 --> 00:45:49.000 This is reactants minus products. 00:45:49.000 --> 00:45:52.000 In a moment, I am going to show you another 00:45:52.000 --> 00:45:55.000 way to calculate the enthalpy for a reaction. 00:45:55.000 --> 00:46:00.000 And it is going to be products minus reactants. 00:46:00.000 --> 00:46:03.000 You have to know this. But you also see that the 00:46:03.000 --> 00:46:07.000 calculated enthalpy is not the experimental enthalpy. 00:46:07.000 --> 00:46:10.000 Why? Because we use the average bond 00:46:10.000 --> 00:46:13.000 enthalpies. We did not use the exact bond 00:46:13.000 --> 00:46:18.000 enthalpies because if we had to use the exact bond enthalpies, 00:46:18.000 --> 00:46:23.000 can you imagine the size of the table of data that we would have 00:46:23.000 --> 00:46:26.000 to have? We would have to have a bond 00:46:26.000 --> 00:46:31.000 enthalpy for every bond for every known molecule. 00:46:31.000 --> 00:46:34.000 That is a lot. What are we going to do, 00:46:34.000 --> 00:46:37.000 then? Is there a more accurate way to 00:46:37.000 --> 00:46:41.000 do that? Yes, with knowing the absolute 00:46:41.000 --> 00:46:45.000 bond enthalpies. But that is too much data. 00:46:45.000 --> 00:46:47.000 Is there some other way to do it? 00:46:47.000 --> 00:46:50.000 Yes. We are going to use heats of 00:46:50.000 --> 00:46:53.000 formation. A heat of formation, 00:46:53.000 --> 00:46:57.000 delta H nought with an F as a subscript. 00:46:57.000 --> 00:47:02.000 The heat of formation is the 00:47:02.000 --> 00:47:08.000 enthalpy of a reaction that forms one mole of a compound 00:47:08.000 --> 00:47:14.000 from the pure elements in their most stable form in their 00:47:14.000 --> 00:47:17.000 standard state. For example, 00:47:17.000 --> 00:47:21.000 here is water. We are forming one mole of 00:47:21.000 --> 00:47:25.000 water from its elements, hydrogen and oxygen. 00:47:25.000 --> 00:47:31.000 The enthalpy for this reaction is defined as the heat of 00:47:31.000 --> 00:47:36.000 formation of water. Why is this the heat of 00:47:36.000 --> 00:47:39.000 formation of water? Well, because we are forming 00:47:39.000 --> 00:47:44.000 one mole, and that is important, from the elements that make up 00:47:44.000 --> 00:47:46.000 water. What elements are they? 00:47:46.000 --> 00:47:49.000 They are hydrogen. But notice that this hydrogen 00:47:49.000 --> 00:47:52.000 is H two. It is not hydrogen atoms 00:47:52.000 --> 00:47:56.000 because H two is the most stable form of hydrogen. 00:47:56.000 --> 00:48:00.000 Oxygen is O two, not oxygen atoms because this 00:48:00.000 --> 00:48:05.000 is the most stable form of oxygen at bar pressure. 00:48:05.000 --> 00:48:08.000 Look at this here. What is the heat of formation 00:48:08.000 --> 00:48:12.000 of oxygen? Well, the enthalpy change for 00:48:12.000 --> 00:48:16.000 this reaction is zero. That is the heat of formation 00:48:16.000 --> 00:48:17.000 of oxygen. Why? 00:48:17.000 --> 00:48:22.000 Because we are forming one mole of oxygen from the elements in 00:48:22.000 --> 00:48:27.000 their most stable form. For elements like oxygen, 00:48:27.000 --> 00:48:30.000 hydrogen, nitrogen, chlorine, two 00:48:30.000 --> 00:48:34.000 in the gas phase, those all have heats of 00:48:34.000 --> 00:48:39.000 formation that are equal to zero. 00:48:39.000 --> 00:48:42.000 And then, finally, here is the expression or the 00:48:42.000 --> 00:48:45.000 reaction that gives us one mole of glucose. 00:48:45.000 --> 00:48:49.000 The enthalpy for this reaction is the heat of formation of 00:48:49.000 --> 00:48:51.000 glucose. We get it from its elements, 00:48:51.000 --> 00:48:55.000 hydrogen, oxygen, and look at the elemental form, 00:48:55.000 --> 00:49:00.000 the most stable form of the element carbon is graphite. 00:49:00.000 --> 00:49:02.000 Is there an 18.0-something exam? 00:49:02.000 --> 00:49:03.000 Yes? Okay. 00:49:03.000 --> 00:49:06.000 See you on Monday.