WEBVTT 00:01.067 --> 00:02.167 J. MICHAEL MCBRIDE: So as you remember the first 00:02.167 --> 00:07.227 semester we studied bonding and molecular structure. 00:07.233 --> 00:10.033 Then toward the end we did some sort of thermodynamics, 00:10.033 --> 00:13.973 which is what connects structure to energy, which is 00:13.967 --> 00:17.197 what determines what chemistry will happen. 00:17.200 --> 00:20.530 So this semester we're going to talk about that chemistry, 00:20.533 --> 00:25.273 about reaction mechanisms, and about using these reactions to 00:25.267 --> 00:26.567 do synthesis. 00:26.567 --> 00:29.067 And we'll also do some spectroscopy around the middle 00:29.067 --> 00:30.367 of the semester. 00:30.367 --> 00:33.827 So just a brief excursion through what 00:33.833 --> 00:35.273 we're going to be doing. 00:35.267 --> 00:38.027 The first two quarters of the semester are going to be on 00:38.033 --> 00:41.803 how mechanisms are discovered and understood in terms of 00:41.800 --> 00:45.400 structure and energy-- what we talked about last time. 00:45.400 --> 00:47.470 So first we'll look naturally enough at 00:47.467 --> 00:49.297 the simplest reactions. 00:49.300 --> 00:51.270 There can't be anything much simpler than 00:51.267 --> 00:53.427 just cleaving a bond. 00:53.433 --> 00:56.633 But remember there's also the possibility of making a bond 00:56.633 --> 00:59.233 at the same time you break a bond. 00:59.233 --> 01:02.973 And we introduced these ideas last semester, of course. 01:02.967 --> 01:05.567 So we're going to start with free-radical substitution, one 01:05.567 --> 01:08.427 of the earlier reactions to be studied, as you remember, in 01:08.433 --> 01:11.833 the 1830s in France. 01:11.833 --> 01:15.373 But we're going to use it to talk about the concepts of 01:15.367 --> 01:17.427 reactivity and selectivity-- 01:17.433 --> 01:20.273 when you can get different products, how do you control 01:20.267 --> 01:23.497 or predict which ones you'll get? 01:23.500 --> 01:26.630 Then the nice thing about free radicals is they're not 01:26.633 --> 01:30.633 charged, so they're relatively insensitive to solvent. 01:30.633 --> 01:33.003 So you can just think about the molecules themselves 01:33.000 --> 01:36.500 reacting, whether it's in the gas phase or solution, more or 01:36.500 --> 01:38.200 less the same thing. 01:38.200 --> 01:40.870 But it's quite different when ions are involved either as 01:40.867 --> 01:43.697 starting materials or products or both. 01:43.700 --> 01:46.030 Because then solvent effects are very important. 01:46.033 --> 01:48.903 So as we go from free radicals, we're then going to 01:48.900 --> 01:51.370 do solvent effects. 01:51.367 --> 01:54.597 Then go on to nucleophilic substitution reactions, which 01:54.600 --> 01:58.300 almost always involve ions either as starting materials 01:58.300 --> 02:00.200 or products or both. 02:00.200 --> 02:02.830 And going to use that as an example of showing how people 02:02.833 --> 02:07.073 go about proving a mechanism. 02:07.067 --> 02:10.197 Then we'll have the first exam on February 2. 02:10.200 --> 02:13.430 Then we'll go on to electrophilic addition 02:13.433 --> 02:16.033 reactions to alkenes and alkynes. 02:16.033 --> 02:19.573 You'll recognize that these are concepts we introduced 02:19.567 --> 02:22.497 last semester, but this time we're going to focus on how 02:22.500 --> 02:24.930 you know about how they work. 02:24.933 --> 02:27.373 And we're going to talk there, especially about the role of 02:27.367 --> 02:28.297 nucleophiles. 02:28.300 --> 02:31.230 You usually call these additions electrophilic, but 02:31.233 --> 02:35.473 there's quite often a very important nucleophilic 02:35.467 --> 02:37.427 component as well. 02:37.433 --> 02:40.903 Then we'll get onto polymers and their properties for just 02:40.900 --> 02:42.470 a lecture or two. 02:42.467 --> 02:46.597 And then conjugation, aromaticity and pericyclic 02:46.600 --> 02:48.400 reactions, which you'll know what they are 02:48.400 --> 02:50.030 when we get to them. 02:50.033 --> 02:52.533 Then we'll have the second exam. 02:52.533 --> 02:55.603 And then we'll have an interlude about spectroscopy 02:55.600 --> 02:58.830 and go on to more focus on synthesis. 02:58.833 --> 03:01.633 So first, spectroscopy for structure and also for 03:01.633 --> 03:05.173 studying dynamics of molecules and reactions. 03:05.167 --> 03:09.797 So ultraviolet-visible spectroscopy; electronic; IR 03:09.800 --> 03:10.730 spectroscopy-- 03:10.733 --> 03:14.133 vibration, which we've talked about a good deal already; 03:14.133 --> 03:18.203 magnetic resonance imaging and nuclear magnetic resonance. 03:18.200 --> 03:20.870 Then on to aromatic substitution. 03:20.867 --> 03:25.127 And finally carbonyl chemistry and the concepts of oxidation 03:25.133 --> 03:25.773 and reduction. 03:25.767 --> 03:27.827 Then we'll have the third hour exam. 03:27.833 --> 03:30.533 And the last quarter of the course then will be more 03:30.533 --> 03:33.773 having to do with carbonyl chemistry; acid derivatives; 03:33.767 --> 03:38.467 substitution taking place at carbonyl group; reactivity 03:38.467 --> 03:41.097 adjacent to the carbonyl group; the classical 03:41.100 --> 03:45.030 condensation reactions; then something about carbohydrates 03:45.033 --> 03:47.773 and Fischer's classical proof of which 03:47.767 --> 03:50.027 isomer is which of glucose. 03:50.033 --> 03:53.073 And finally we'll talk about some complex synthesis. 03:53.067 --> 03:55.267 We'll be talking about synthetic ideas all through 03:55.267 --> 03:59.967 this, of both unnatural and natural products. 03:59.967 --> 04:01.267 Then we'll have the final. 04:01.267 --> 04:03.527 So that's how long you have to endure. 04:06.567 --> 04:09.267 So at the end of last semester we were talking about energy 04:09.267 --> 04:11.127 and how it related to things-- 04:11.133 --> 04:13.733 that free energy determines what can happen at 04:13.733 --> 04:14.473 equilibrium-- 04:14.467 --> 04:16.327 and remember it was all statistics. 04:16.333 --> 04:19.503 And the statistics filtered down to give us this handy 04:19.500 --> 04:21.830 relationship at room temperature that an 04:21.833 --> 04:24.833 equilibrium constant is 10 to the minus 3/4 of the 04:24.833 --> 04:26.233 difference in free energy. 04:26.233 --> 04:29.833 Or if you're not worried about entropy, the difference in 04:29.833 --> 04:33.033 enthalpy in the heat of the molecules. 04:33.033 --> 04:34.703 So that's both energy and entropy 04:34.700 --> 04:37.370 the Gibbs free energy. 04:37.367 --> 04:40.397 But there's a completely independent question, which is 04:40.400 --> 04:41.900 Will it happen? 04:41.900 --> 04:45.030 You know, graphite is more stable than diamond 04:45.033 --> 04:46.933 as a form of carbon. 04:46.933 --> 04:50.833 But the advertisers tell us that a diamond is forever-- 04:50.833 --> 04:53.073 just because it's not as stable doesn't mean it'll 04:53.067 --> 04:55.627 convert in any reasonable time. 04:55.633 --> 04:59.903 So the questions of kinetics are just as important as the 04:59.900 --> 05:02.630 questions of equilibrium, or at least almost as important. 05:05.400 --> 05:07.830 And we saw last time that we could approach this by 05:07.833 --> 05:12.173 studying lots of trajectories, trying to calculate how all 05:12.167 --> 05:13.727 the atoms move in going from one 05:13.733 --> 05:15.673 arrangement to another one. 05:15.667 --> 05:18.297 But that really provides too much detail. 05:18.300 --> 05:21.370 In fact, over the last couple of weeks we've had interviews 05:21.367 --> 05:24.667 from people who are applying for a faculty position here 05:24.667 --> 05:27.197 and a number of them are talking about fancy new ways 05:27.200 --> 05:29.170 of actually looking at one molecule at 05:29.167 --> 05:32.467 a time as it reacts. 05:32.467 --> 05:36.467 So that you actually could do something getting closer to 05:36.467 --> 05:37.627 trajectories. 05:37.633 --> 05:41.973 But really that's more detailed than we want. 05:41.967 --> 05:44.597 We want to summarize things statistically to know what's 05:44.600 --> 05:46.500 going to happen in a flask. 05:46.500 --> 05:49.600 So we have collective concepts, enthalpy and 05:49.600 --> 05:52.630 entropy, and then we can have a 05:52.633 --> 05:54.473 reaction coordinate diagram-- 05:54.467 --> 05:57.527 remember we rolled a marble on that thing last time, on that 05:57.533 --> 05:59.473 potential energy surface. 05:59.467 --> 06:02.297 Or we could slice along the potential energy surface and 06:02.300 --> 06:05.330 look at the starting material, the transition 06:05.333 --> 06:07.173 state and the products. 06:07.167 --> 06:12.567 Or we could simplify things to notice that this is just a 06:12.567 --> 06:16.297 sequence of three species: the starting material which is 06:16.300 --> 06:21.130 molecules that we know about, the transition state which we 06:21.133 --> 06:25.303 don't know about, and the products which we know about. 06:25.300 --> 06:28.300 So our challenge is going to be to try to figure out 06:28.300 --> 06:32.030 something about the transition state given what we know about 06:32.033 --> 06:34.673 the starting material and the products, because its energy 06:34.667 --> 06:37.127 relative to those others is going to determine rates. 06:40.067 --> 06:44.697 So we have then free energies with just these three species, 06:44.700 --> 06:47.300 rather than trying to look at a detailed trajectory. 06:50.833 --> 06:54.433 So free energy determines what can happen at equilibrium, but 06:54.433 --> 06:57.033 also how fast it happens in kinetics. 06:57.033 --> 07:01.673 For that purpose we need to know what the energy is, 07:01.667 --> 07:04.267 either the free energy or the heat at least of the 07:04.267 --> 07:06.297 transition state. 07:06.300 --> 07:09.100 And remember we talked about this last time that in 07:09.100 --> 07:13.700 Eyring's transition state theory, the rate constant for 07:13.700 --> 07:18.530 the reaction per second is 10 to the 13th times that sort 07:18.533 --> 07:21.903 of equilibrium constant between the starting material and the 07:21.900 --> 07:23.230 transition state. 07:23.233 --> 07:27.273 So again, we can use at room temperature that 3/4 delta G 07:27.267 --> 07:31.497 when we express it in kilocalories per mole. 07:31.500 --> 07:35.500 So we want to use energies to predict equilibria and also to 07:35.500 --> 07:37.470 predict rates first for the very 07:37.467 --> 07:40.127 simplest one step reactions. 07:40.133 --> 07:43.333 And no reaction is conceptually simpler than just 07:43.333 --> 07:45.533 breaking a bond in the gas phase to give 07:45.533 --> 07:47.303 atoms or free radicals. 07:47.300 --> 07:49.770 So we need to know the energy for that. 07:49.767 --> 07:53.027 Now, in the textbooks that I've handed out to you there 07:53.033 --> 07:54.833 are tables like this one that give 07:54.833 --> 07:56.933 bond dissociation energies. 07:56.933 --> 08:00.703 How much energy does is actually take to break a bond? 08:00.700 --> 08:03.130 This particular one is from a text we used to use in the 08:03.133 --> 08:06.403 course called Streitwieser and Heathcock. 08:06.400 --> 08:11.870 That was in 1993, but as of 2003 there's a new set. 08:11.867 --> 08:13.767 And you can see that these don't change 08:13.767 --> 08:15.627 very much in time-- 08:15.633 --> 08:19.603 98 became 99, 111 became 113. 08:19.600 --> 08:20.730 Some of them are a little bigger-- 08:20.733 --> 08:23.373 81 became 85, and so on. 08:23.367 --> 08:26.167 And these values I refer to as Ellison's. 08:26.167 --> 08:28.397 I mentioned him last semester-- 08:28.400 --> 08:30.470 there's Barney Ellison. 08:30.467 --> 08:34.667 He and his friends compiled these new values, and he's 08:34.667 --> 08:37.067 going to come and talk to you about how he did this 08:37.067 --> 08:38.767 in April some time. 08:38.767 --> 08:42.727 He can't get out of Boulder now-- he's all snowed in out 08:42.733 --> 08:45.473 there, Colorado. 08:45.467 --> 08:50.127 So this is his table of molecular bond dissociation 08:50.133 --> 08:53.533 energies for losing H from something. 08:53.533 --> 08:56.273 RH becomes R plus H atom-- 08:56.267 --> 08:58.427 R radical plus H atom. 08:58.433 --> 09:01.033 So these are experimental bond enthalpies. 09:01.033 --> 09:04.003 And as you can see, some of them are known to very high 09:04.000 --> 09:10.270 precision, like H2 is known to six significant figures. 09:10.267 --> 09:12.567 Most of them, of course, aren't known that well, but 09:12.567 --> 09:15.067 most of the ones in this table are known pretty darn well, 09:15.067 --> 09:18.297 plenty accurately enough for our purposes. 09:18.300 --> 09:21.270 Let's see if we can understand some of these so that we don't 09:21.267 --> 09:23.497 have to memorize the table. 09:23.500 --> 09:26.500 Let's look at the bonds from H to halogen. 09:26.500 --> 09:31.300 You'll notice as we go down to larger halogens from fluorine, 09:31.300 --> 09:34.700 chlorine, bromine, iodine, we go from 136 to 09:34.700 --> 09:37.100 103 to 87 to 71-- 09:37.100 --> 09:40.300 quite a difference in the energy involved. 09:40.300 --> 09:44.270 So the idea is that larger halogens don't overlap as well 09:44.267 --> 09:46.997 with the hydrogens, so they don't make as strong a bond at 09:47.000 --> 09:48.870 their normal bond distances. 09:48.867 --> 09:53.427 And there's less electron transfer to the halogen. 09:53.433 --> 09:57.203 So whereas HF looks like that and the two electrons are 09:57.200 --> 10:02.000 lowered quite a bit, in HI the net amount of lowering of the 10:02.000 --> 10:04.830 electrons in forming the bond isn't nearly as much. 10:04.833 --> 10:07.703 So that makes sense to us. 10:07.700 --> 10:12.600 So less electron stabilization means a weaker bond. 10:12.600 --> 10:18.870 Now here's the Table 2, which is bond enthalpies for 10:18.867 --> 10:23.397 various atoms or groups attached to various 10:23.400 --> 10:24.670 hydrocarbon radicals. 10:30.767 --> 10:35.097 Previously we looked at H attached to halogen, now we're 10:35.100 --> 10:38.130 looking at methyl attached to halogen and you see there's a 10:38.133 --> 10:40.403 very similar trend. 10:40.400 --> 10:43.400 It's strongest for fluorine, weaker for chlorine, weaker 10:43.400 --> 10:47.670 still for bromine, and weakest for iodine. 10:47.667 --> 10:49.627 So many of the same features. 10:49.633 --> 10:52.633 But let's try to understand different radicals. 10:52.633 --> 10:56.233 So we're going to look at the bonding of H to methyl, ethyl, 10:56.233 --> 10:58.603 isopropyl and t-butyl. 10:58.600 --> 11:01.830 And the first thing you notice about this is that they're all 11:01.833 --> 11:04.403 almost the same. 11:04.400 --> 11:08.270 As we went down the halogens it varied by 60 11:08.267 --> 11:10.197 kilocalories per mole. 11:10.200 --> 11:12.430 But as we go across these different methyl, ethyl, 11:12.433 --> 11:16.303 isopropyl, t-butyls, they're all 100 kilocalories per mole, 11:16.300 --> 11:18.730 plus or minus 5. 11:18.733 --> 11:21.373 We're going to look next lecture at this in some more 11:21.367 --> 11:23.527 detail and see if we can understand why 11:23.533 --> 11:24.773 they vary at all. 11:24.767 --> 11:26.697 But they don't vary very much. 11:26.700 --> 11:31.270 On the other hand, some hydrocarbon radicals have 11:31.267 --> 11:35.267 substantially different ones, like vinyl and allyl, phenyl 11:35.267 --> 11:36.197 and benzyl. 11:36.200 --> 11:38.730 The vinyl and phenyl are much stronger, 10 11:38.733 --> 11:40.573 kilocalories stronger. 11:40.567 --> 11:46.467 The benzyl and allyl are about 10 kilocalories weaker. 11:46.467 --> 11:51.397 So let's see if, based on what we did last semester, we can 11:51.400 --> 11:54.270 understand why this might be so. 11:54.267 --> 11:57.767 Are these unusual bond dissociation energies to be 11:57.767 --> 12:01.797 explained as unusual bonds, that is the bonds are 12:01.800 --> 12:03.770 unusually strong or weak? 12:03.767 --> 12:07.727 Or is it the radicals are unusually strong or weak? 12:07.733 --> 12:09.803 This is compared to what? 12:09.800 --> 12:12.500 We have the starting material and go to the products where 12:12.500 --> 12:14.270 the bond is broken, we go uphill in 12:14.267 --> 12:16.867 energy by these amounts. 12:16.867 --> 12:20.267 The question is are things unusual because the starting 12:20.267 --> 12:24.097 bond is weak or unusually strong? 12:24.100 --> 12:27.430 Or is it because the radical is unusually stable or 12:27.433 --> 12:30.003 unusually unstable? 12:30.000 --> 12:31.470 Compared to what? 12:31.467 --> 12:34.197 So let's look at a couple of these cases and see if we 12:34.200 --> 12:36.270 could understand. 12:36.267 --> 12:40.397 First let's look at vinyl, which is the H attached to a 12:40.400 --> 12:42.970 carbon that's double bonded. 12:42.967 --> 12:45.997 Now if we look at the radical we see that we have a SOMO, so 12:46.000 --> 12:48.870 there's the possibility for interacting with something and 12:48.867 --> 12:50.597 changing its energy. 12:50.600 --> 12:53.900 But notice that the HOMOs and LUMOs that it might interact 12:53.900 --> 12:57.200 with are pi and pi-star. 12:57.200 --> 13:00.730 And there's no special stabilization because they're 13:00.733 --> 13:02.373 perpendicular to one another, they're 13:02.367 --> 13:04.897 orthogonal, there's no overlap. 13:04.900 --> 13:07.670 So there's no reason that having this double bond should 13:07.667 --> 13:09.767 make that radical unusually stable. 13:12.700 --> 13:17.900 And notice that, it, in fact, is hard to break as if this 13:17.900 --> 13:18.870 were unstable. 13:18.867 --> 13:20.727 But it's neither stable or unstable, it's 13:20.733 --> 13:22.903 just what it is. 13:22.900 --> 13:26.130 On the other hand, if we look at the starting material where 13:26.133 --> 13:29.073 we have this C-H bond, notice that as compared to these 13:29.067 --> 13:34.397 others, which are 100 plus or minus 5, that this one is made 13:34.400 --> 13:37.600 from an sp squared carbon, right? 13:37.600 --> 13:39.600 So very good overlap. 13:39.600 --> 13:43.000 So in this case, it's that the bond is unusual. 13:43.000 --> 13:44.730 The bond is unusually strong, the 13:44.733 --> 13:46.433 radical is nothing special. 13:46.433 --> 13:47.703 It's very hard to break. 13:51.167 --> 13:54.497 So it's hard, it's 111. 13:54.500 --> 13:58.970 The same thing is true in the phenyl radical where, again, 13:58.967 --> 14:02.167 the C-H bond we're talking about is attached to a double 14:02.167 --> 14:04.067 bonded carbon. 14:04.067 --> 14:06.227 Here it's part of a benzene ring. 14:06.233 --> 14:10.673 But again, the unusual energy orbitals in the ring are 14:10.667 --> 14:14.167 perpendicular, they don't overlap with the singularly 14:14.167 --> 14:17.597 occupied orbital we're talking about. 14:17.600 --> 14:19.530 Therefore, nothing special here. 14:19.533 --> 14:23.073 But again, it's an sp squared carbon to hydrogen bond, and 14:23.067 --> 14:27.367 again, it's unusually strong, 113 kilocalories per mole. 14:27.367 --> 14:30.467 So these are unusual because the starting material has an 14:30.467 --> 14:33.227 unusually strong bond. 14:33.233 --> 14:36.133 Now let's look at these others, allyl and benzyl where 14:36.133 --> 14:40.433 it's an unusually easy bond to break. 14:40.433 --> 14:44.303 Now we look at the allyl radical where we've broken H 14:44.300 --> 14:48.070 off this carbon, and now what's different about that as 14:48.067 --> 14:51.367 compared to the ones above? 14:51.367 --> 14:53.667 We broke the H off, we got a p orbital that 14:53.667 --> 14:58.427 has the single occupancy. 14:58.433 --> 15:01.903 Anybody got an idea about whether it's going to be usual 15:01.900 --> 15:03.130 or unusual? 15:06.400 --> 15:06.870 Sebastian? 15:06.867 --> 15:07.997 STUDENT: [INAUDIBLE]. 15:08.000 --> 15:08.600 PROFESSOR: Pardon me? 15:08.600 --> 15:09.570 STUDENT: It can mix with the pi-star? 15:09.567 --> 15:12.167 PROFESSOR: Now it can mix with the pi-star because it's going 15:12.167 --> 15:15.667 in and out of the plane. 15:15.667 --> 15:18.627 So now it overlaps with the pi and pi-star. 15:18.633 --> 15:20.133 Now what's that going to do? 15:20.133 --> 15:21.803 Well here's the singly occupied 15:21.800 --> 15:23.500 orbital, the red one here. 15:23.500 --> 15:25.230 Here's pi-star, vacant. 15:25.233 --> 15:26.373 They'll mix. 15:26.367 --> 15:28.267 That would suggest that the single electron 15:28.267 --> 15:30.267 would go down in energy. 15:30.267 --> 15:31.967 That would be good. 15:31.967 --> 15:34.667 However, we should also think about the fact that there's an 15:34.667 --> 15:38.367 unusually high HOMO associated with the blue orbitals there, 15:38.367 --> 15:39.967 the pi orbital. 15:39.967 --> 15:43.127 So we could consider instead the pi. 15:43.133 --> 15:46.703 And now we see that that would shift this electron up, but 15:46.700 --> 15:48.430 these two electrons would go down. 15:48.433 --> 15:52.903 Again you would win more down than up. 15:52.900 --> 15:55.130 So this is a little schizophrenic on the part of 15:55.133 --> 15:56.633 the singly occupied orbital. 15:56.633 --> 15:59.273 Does it move up or down? 15:59.267 --> 16:01.597 The answer is "No." 16:01.600 --> 16:04.730 One of them pushes it down, the other pushes it up, stays 16:04.733 --> 16:06.873 the same place it started. 16:06.867 --> 16:12.567 But the others go up and down, the ones that came from the pi 16:12.567 --> 16:13.827 and the pi-star. 16:13.833 --> 16:17.673 So you get net stabilization due to this pair of electrons 16:17.667 --> 16:18.327 going down. 16:18.333 --> 16:21.333 So we have this special "allylic" it's called, 16:21.333 --> 16:26.333 stabilization from mixing the SOMO with the pi and pi-star 16:26.333 --> 16:28.203 orbitals adjacent to one another. 16:28.200 --> 16:31.130 So this radical is unusually stable. 16:31.133 --> 16:33.873 On the other hand, in the starting material, the bond 16:33.867 --> 16:39.427 was just a regular old sp3 C-H bond, nothing special there. 16:39.433 --> 16:42.933 So as compared to here where the starting material was 16:42.933 --> 16:46.503 unusually strong, here the product is unusually stable. 16:49.833 --> 16:53.403 So that was easy to break, 89 kilocalories per mole. 16:53.400 --> 16:56.830 And the same is true for the benzyl radical where the p 16:56.833 --> 17:00.303 orbital on the adjacent carbon, again can overlap with 17:00.300 --> 17:02.430 the pi system of the benzene ring. 17:02.433 --> 17:05.273 So you get special stability and it only takes 90 17:05.267 --> 17:07.467 kilocalories per mole. 17:07.467 --> 17:12.997 So we can understand these special cases of bond 17:13.000 --> 17:18.270 strengths, of bond enthalpies. 17:18.267 --> 17:21.827 Now, we spoke last semester about the 17:21.833 --> 17:24.103 halogenation of alkanes. 17:24.100 --> 17:29.970 So we can use these bond dissociation energies to do 17:29.967 --> 17:32.627 some calculations about the possibility of doing 17:32.633 --> 17:34.503 halogenation of alkanes. 17:34.500 --> 17:38.900 So let's just take as an example methane, some various 17:38.900 --> 17:43.830 dihalogen molecules, and we can trade partners, a double 17:43.833 --> 17:46.673 displacement sort of reaction, as they called it in the early 17:46.667 --> 17:49.997 days, and make CH3 X and HX. 17:50.000 --> 17:54.070 So we break the red bonds and form the green bonds. 17:54.067 --> 17:57.927 So we have a cost to pay in breaking bonds, we have a 17:57.933 --> 18:01.003 return from making the bonds, and we're going to see whether 18:01.000 --> 18:05.500 we get a net profit from trying to run this operation. 18:05.500 --> 18:07.900 So we're going to do it for fluorine, chlorine, bromine 18:07.900 --> 18:09.070 and iodine. 18:09.067 --> 18:11.697 Now, of course, in all those cases the C-H bond is the 18:11.700 --> 18:15.570 same, it's 105 kilocalories per mole. 18:15.567 --> 18:19.827 Now, but the halogen-halogen bonds are different. 18:19.833 --> 18:28.333 It's fairly weak for fluorine, strong for chlorine, but then 18:28.333 --> 18:30.873 weaker again for bromine, and back to 18:30.867 --> 18:32.297 the start for diiodine. 18:34.900 --> 18:38.300 What does that tell you that as you go down the rows of the 18:38.300 --> 18:43.870 periodic table, you don't get some monotonic up or down in 18:43.867 --> 18:47.097 the bond strength, but it goes up and down? 18:47.100 --> 18:48.630 What do you infer from that kind of thing 18:48.633 --> 18:49.903 when you get curve? 18:53.233 --> 18:54.973 STUDENT: There must be two factors. 18:54.967 --> 18:56.027 PROFESSOR: There must be at least two 18:56.033 --> 18:59.473 factors involved in this. 18:59.467 --> 19:03.667 And those factors are probably the overlap of the sigma bond, 19:03.667 --> 19:06.297 which is best for fluorine-fluorine, but the 19:06.300 --> 19:11.100 interaction of unshared pairs which is worst for fluorine. 19:11.100 --> 19:13.300 So you have two things going on. 19:13.300 --> 19:15.900 Anyhow, we can add those two together to see what it's 19:15.900 --> 19:19.830 going to cost us to break those two bonds. 19:19.833 --> 19:22.633 And there are the values, they're in the range of 150 19:22.633 --> 19:24.503 kilocalories per mole. 19:24.500 --> 19:27.600 But then when we do the reaction we're going to profit 19:27.600 --> 19:31.600 by making the bonds on the right, so that we have various 19:31.600 --> 19:35.230 values for the carbon-X bond that we got out of that table 19:35.233 --> 19:36.633 we just showed. 19:36.633 --> 19:40.873 And for the H-X bond, and there's the return we get. 19:40.867 --> 19:44.197 Now are these going to be favorable reactions? 19:44.200 --> 19:48.530 Well, in the case of fluorine it's wildly favorable. 19:48.533 --> 19:51.533 It's favorable by 109 kilocalories per mole. 19:55.567 --> 20:02.967 But it's only 19 kilocalories per mole for chlorine, only 9 20:02.967 --> 20:07.767 for bromine, and it's 12 kilocalories UPHILL in that 20:07.767 --> 20:09.397 case of iodine. 20:09.400 --> 20:12.200 So you're not going to make a profit if you try to set up a 20:12.200 --> 20:16.000 factory to convert methane and iodine to 20:16.000 --> 20:18.600 methyl iodide and HI. 20:18.600 --> 20:23.530 In fact, you'd want to run at the opposite direction. 20:23.533 --> 20:26.673 But the others, at least overall, are favorable. 20:26.667 --> 20:30.027 So we know from equilibrium now that for three of the 20:30.033 --> 20:33.703 halogens this reaction should be favorable. 20:33.700 --> 20:35.570 And for one of them it should be unfavorable. 20:38.600 --> 20:41.400 But how about the rate? 20:41.400 --> 20:44.530 How fast will it be? 20:44.533 --> 20:47.703 Now if this were the mechanism, first you break two 20:47.700 --> 20:52.200 bonds, then you change partners and re-attach, 20:52.200 --> 20:55.500 the activation energy for getting up to the transition 20:55.500 --> 20:58.700 state for this where both bonds are broken is going to 20:58.700 --> 21:03.800 be this cost. Right? So is break-two-bonds-then-make-two a 21:03.800 --> 21:05.100 plausible mechanism? 21:05.100 --> 21:06.870 Could we get a rate that's reasonable on 21:06.867 --> 21:09.027 the basis of that? 21:09.033 --> 21:12.203 If you know the activation energy you have to get to, how 21:12.200 --> 21:14.630 do you go about calculating the rate? 21:14.633 --> 21:15.473 Debby? 21:15.467 --> 21:17.427 STUDENT: 10 to the 13th. 21:17.433 --> 21:20.103 PROFESSOR: Right, it's 10 to the thirteenth per second, 21:20.100 --> 21:21.070 times 10 to the-- 21:21.067 --> 21:23.867 STUDENT: Negative 3/4th 21:23.867 --> 21:26.867 PROFESSOR: 10 to the minus 3/4 of that energy. 21:26.867 --> 21:28.997 So let's think about it then in this case. 21:29.000 --> 21:33.370 Suppose we take one of these that's about 140. 21:33.367 --> 21:37.067 So at room temperature, 300K, which is where your 21:37.067 --> 21:41.597 approximation works, the 3/4, we find that it's 10 to the 21:41.600 --> 21:45.200 thirteenth per second times 10 the minus 106 21:45.200 --> 21:48.070 3/4 of one of these numbers. 21:48.067 --> 21:51.827 So it'll be 10 to the minus 93 per second. 21:51.833 --> 21:54.433 That's a very unfavorable number. 21:54.433 --> 21:55.833 So forget that. 21:55.833 --> 21:59.333 There's no way a mechanism like that could work at room 21:59.333 --> 22:00.473 temperature. 22:00.467 --> 22:05.667 What might you be able to do to realize such a reaction? 22:05.667 --> 22:06.697 Yeah, Amy? 22:06.700 --> 22:07.530 STUDENT: Heat it. 22:07.533 --> 22:08.703 PROFESSOR: Higher temperature. 22:08.700 --> 22:13.300 So suppose you go to 3,000K instead of 300K? 22:13.300 --> 22:18.200 Now instead of 3/4 it's 3/40. 22:18.200 --> 22:21.700 So if we go to 3,000K, then it's 10 to the thirteenth 22:21.700 --> 22:24.330 times 10 to the minus 10.6, which would 22:24.333 --> 22:27.433 be 250 times a second. Right? 22:27.433 --> 22:30.703 So that would be accessible. 22:30.700 --> 22:34.330 Except that there probably is something else lthat could 22:34.333 --> 22:38.103 happen when you're at that very high temperature. 22:38.100 --> 22:43.970 So fundamentally this is not a reasonable mechanism. 22:43.967 --> 22:47.567 And we already know a better way to go about it from 22:47.567 --> 22:51.467 looking at these potential energy surfaces for 22:51.467 --> 22:55.197 transferring an atom between two other atoms. Remember we 22:55.200 --> 22:59.130 start with H plus H2, and then we can move around on this 22:59.133 --> 23:03.133 surface and have, for collinear three Hs, we can 23:03.133 --> 23:08.273 get the energy differences between two of the Hs and the 23:08.267 --> 23:10.767 other two Hs. 23:10.767 --> 23:13.497 So there's the product we want to go to where a hydrogen has 23:13.500 --> 23:15.800 been transferred from the right to the left. 23:15.800 --> 23:19.230 And one way to do it, the way we've been talking about, is 23:19.233 --> 23:23.803 to go by way of three separate atoms. Which means we go up 23:23.800 --> 23:27.270 there, way up in energy, very slow, and once we get there 23:27.267 --> 23:29.667 then zing, we go down. 23:29.667 --> 23:33.397 But it's very hard to get up to this plateau. 23:33.400 --> 23:37.030 On the other hand, as we knew from the marble, the way it 23:37.033 --> 23:40.273 actually works is to transfer a hydrogen between two rather 23:40.267 --> 23:42.997 than to break a bond first and then make a bond. 23:43.000 --> 23:46.030 So make it as you break it that way and that's going to 23:46.033 --> 23:47.303 be much faster. 23:47.300 --> 23:50.430 So this kind of displacement reaction is the way we want to 23:50.433 --> 23:55.173 do it-- to make a new bond as we break the old one. 23:55.167 --> 23:56.967 That's how we're going to do it, and we already talked 23:56.967 --> 23:58.227 about this last semester. 23:58.233 --> 24:01.033 First you take chlorine and you break its bond. 24:01.033 --> 24:03.633 That's going to require some energy. 24:03.633 --> 24:06.633 But once you have the free radical, then you can transfer 24:06.633 --> 24:10.033 a hydrogen atom making a bond as you break a bond. 24:10.033 --> 24:11.903 So going through that pass rather than 24:11.900 --> 24:13.870 over the big plateau. 24:13.867 --> 24:16.497 And now the product of that is HCl, one of the 24:16.500 --> 24:17.730 products you want. 24:17.733 --> 24:20.533 But the other one is another free radical made without 24:20.533 --> 24:22.903 having to spontaneously break a bond. 24:22.900 --> 24:26.530 And now it can react with Cl2 to give the other product we 24:26.533 --> 24:29.673 want and the chlorine atom, and then we go back 24:29.667 --> 24:31.927 to the beginning in this free-radical chain, and this is 24:31.933 --> 24:33.603 what we talked about last semester. 24:33.600 --> 24:38.130 Ok, another way of writing the same thing 24:38.133 --> 24:40.573 is to say we could have the starting materials here 24:40.567 --> 24:44.267 to the top left and bottom right, the halogen and 24:44.267 --> 24:49.227 the alkane, and we could have the X atom that we got somehow. 24:49.233 --> 24:53.203 It could be by heat breaking the relatively weak bond, it could 24:53.200 --> 24:57.530 be by light, it could be by some chemical reaction that generates 24:57.533 --> 24:59.973 a free radical, but somehow we get a radical. 24:59.967 --> 25:01.627 Then it could react in a hydrogen 25:01.633 --> 25:05.903 atom transfer to give one of the products, the green XH here, 25:05.900 --> 25:09.230 and another radical, and it could react with the halogen 25:09.233 --> 25:12.673 to give the other product and go back where we started. 25:12.667 --> 25:16.867 So what we have is a cyclic machine that just cranks round 25:16.867 --> 25:23.327 and round. It preserves the radicalness of the situation. 25:23.333 --> 25:26.633 You don't have to break any new bonds spontaneously-- 25:26.633 --> 25:28.803 only to get the first radical. 25:28.800 --> 25:33.800 We're going to talk about this some more later on. 25:33.800 --> 25:37.900 But to look now at how we're going to rearrange things-- 25:37.900 --> 25:40.470 if you want to have a mechanism for a reasonable 25:40.467 --> 25:44.997 rate, what you're going to do is trade two of these columns. 25:45.000 --> 25:48.530 Instead of breaking two and then making two, we'll trade 25:48.533 --> 25:53.433 those two columns so that on the left we make and break; on 25:53.433 --> 25:57.033 the right in Step 2 we make and break. 25:57.033 --> 25:59.873 So now when we look at how much each of these takes, 25:59.867 --> 26:01.497 Step 1 now in the case of 26:01.500 --> 26:04.430 fluorine is actually favorable. 26:04.433 --> 26:08.133 Step 2 is wildly favorable in the case of fluorine and 26:08.133 --> 26:10.933 overall it's very favorable, as we knew. 26:10.933 --> 26:14.703 But now you can see that these others, although overall 26:14.700 --> 26:18.770 favorable, one of the steps is unfavorable, but not 26:18.767 --> 26:20.297 drastically unfavorable-- 26:20.300 --> 26:25.300 only 2 or 10 or 20 kilocalories per mole. 26:25.300 --> 26:27.700 That kind of barrier you could get over. 26:27.700 --> 26:29.730 You can't get over the barriers of 50 26:29.733 --> 26:31.733 kilocalories or more. 26:31.733 --> 26:35.103 So now you have two steps, each of them a very simple 26:35.100 --> 26:38.070 make as you break atom transfer. 26:38.067 --> 26:41.927 And, of course, here the first one is so high that you're not 26:41.933 --> 26:44.633 going to be able to get over it, and even if you could you 26:44.633 --> 26:47.433 wouldn't give the product, the reaction would run backwards. 26:51.733 --> 26:58.233 So we know the energies of the starting material and products 26:58.233 --> 27:01.533 for each of these steps, but we don't really know the 27:01.533 --> 27:03.933 activation energy-- how much you have to come up 27:03.933 --> 27:06.373 before you come down. 27:06.367 --> 27:08.667 And that's what we're going to be starting to look at next 27:08.667 --> 27:13.097 lecture is how could we predict the activation energy 27:13.100 --> 27:18.570 for a simple one-step reaction if we know how exothermic or 27:18.567 --> 27:20.027 endothermic it is. 27:23.067 --> 27:27.927 But even if we could predict the rate of Step 1 or step 2, 27:27.933 --> 27:31.673 there's still a problem because the overall process is 27:31.667 --> 27:34.097 not just one step, it's two steps. 27:34.100 --> 27:36.870 And how would we know the overall rate if there are two 27:36.867 --> 27:38.497 reaction steps going on? 27:38.500 --> 27:40.070 This is a little more complicated. 27:40.067 --> 27:44.267 So we're going to take a little digression now to learn 27:44.267 --> 27:49.097 to cope with complex reactions that involve several steps. 27:49.100 --> 27:51.170 So this is a digression on reaction 27:51.167 --> 27:53.827 order and complex reaction. 27:53.833 --> 27:58.173 Now the reaction order is the kinetic, the rate analog of 27:58.167 --> 28:01.227 the law of mass action that we talked about at the end last 28:01.233 --> 28:03.933 time-- remember, it was just statistical, how likely is it 28:03.933 --> 28:07.033 that there are going to be two things next to one another? 28:07.033 --> 28:09.833 The same thing, getting next to one another is the same 28:09.833 --> 28:12.773 problem if things are going to react with one another in 28:12.767 --> 28:15.127 getting to the transition state as well. 28:15.133 --> 28:17.733 So there's going to be a dependence of rate on 28:17.733 --> 28:21.803 concentration, the same way that equilibrium depends on 28:21.800 --> 28:25.170 concentrations, as we saw last semester. 28:25.167 --> 28:29.967 Moreover, this dependence of the rate on concentration can 28:29.967 --> 28:33.527 give us information about what kind of mechanism the reaction 28:33.533 --> 28:35.303 might be undergoing. 28:35.300 --> 28:38.030 So that's why we're particularly interested in it. 28:38.033 --> 28:42.533 Now just to look at some simple ideas first. The rate 28:42.533 --> 28:46.073 is how much per second, say, or per minute or hour a day or 28:46.067 --> 28:48.867 whatever, how much per second. 28:48.867 --> 28:51.697 So we could have a faucet, we turn it on and the water comes 28:51.700 --> 28:54.870 out a certain rate per second. 28:54.867 --> 28:56.567 Now what would happen if you had two faucets? 29:00.700 --> 29:03.870 Well, if things were simple the rate would double. 29:03.867 --> 29:06.697 You know, if you think carefully about it, it won't 29:06.700 --> 29:08.830 quite do that because there might be a restriction in how 29:08.833 --> 29:11.433 much water can get to the two faucets. 29:11.433 --> 29:13.573 But in a simple point of view if you double the number of 29:13.567 --> 29:16.127 faucets, you double the rate. 29:16.133 --> 29:18.573 There's another way of doubling the rate, which is to 29:18.567 --> 29:23.567 use a bigger faucet, one that's twice as big, twice the 29:23.567 --> 29:26.497 cross-sectional area. 29:26.500 --> 29:31.530 Now in chemistry we can look at how many moles or molecules 29:31.533 --> 29:33.603 we get per second. 29:33.600 --> 29:38.830 And if we have one beaker and then have another beaker, or a 29:38.833 --> 29:43.573 single beaker with twice the volume, we double the rate. 29:43.567 --> 29:44.897 So that will double the rate. 29:44.900 --> 29:46.700 But chemists are clever. 29:46.700 --> 29:50.500 They can not only change the volume, they can also change 29:50.500 --> 29:53.830 the concentration in the same volume, and that's the 29:53.833 --> 29:56.973 question we have. Obviously you'd expect it to get faster 29:56.967 --> 30:00.397 if you have more stuff, but how much faster? 30:00.400 --> 30:02.530 Will it double? 30:02.533 --> 30:05.573 So this has to do with what are called rate laws. 30:05.567 --> 30:10.797 What that exponent is going to be that says if you double the 30:10.800 --> 30:13.870 concentration of a reagent, how much will the rate change, 30:13.867 --> 30:17.467 the number of molecules you get per second? 30:17.467 --> 30:23.497 So the rate is the increase in product with time. 30:23.500 --> 30:26.870 Then there's a rate law that's some constant times the 30:26.867 --> 30:29.397 concentration of something. 30:29.400 --> 30:31.630 And maybe several concentrations, but that 30:31.633 --> 30:33.373 question mark is the exponent-- 30:33.367 --> 30:35.327 what power do we raise it to? 30:35.333 --> 30:39.003 That's what we mean in talking about the kinetic order. 30:39.000 --> 30:42.570 If it's to the zeroth power, it's a zeroth order; first 30:42.567 --> 30:46.967 power, first order; second power, second order and so on. 30:46.967 --> 30:51.097 But those exponents will have to do with what the mechanism 30:51.100 --> 30:52.770 of the reaction is. 30:52.767 --> 30:57.327 So the only way to discover it is by experiment. 30:57.333 --> 31:00.433 So let's first look at some simple one-step reactions, and 31:00.433 --> 31:03.903 then we're going to look at complicated reactions. 31:03.900 --> 31:06.230 So in a simple one-step reaction you 31:06.233 --> 31:09.233 could have zero order-- 31:09.233 --> 31:11.073 this sounds weird, doesn't it? 31:11.067 --> 31:14.827 That the rate doesn't depend on how much material you have. 31:14.833 --> 31:16.703 You double the amount of material, double the 31:16.700 --> 31:19.970 concentration of material and it doesn't change the rate. 31:23.500 --> 31:24.930 How can that be? 31:24.933 --> 31:27.603 Well here's a picture that helps illustrate it for 31:27.600 --> 31:30.100 sheep getting from one field to the other. 31:30.100 --> 31:35.300 Now in this situation, if the shepherd had more sheep, would 31:35.300 --> 31:36.530 the rate increase? 31:38.933 --> 31:41.373 Would you get sheep from one field to the other faster? 31:41.367 --> 31:44.267 No, they're going as fast as they can no matter how many 31:44.267 --> 31:47.697 sheep are lined up. 31:47.700 --> 31:49.630 Because it's saturated. 31:49.633 --> 31:52.233 It can't go any faster because of how wide 31:52.233 --> 31:53.503 he's opening the gate. 31:55.933 --> 31:59.403 So there are real cases like this in chemistry where you 31:59.400 --> 32:03.400 have a catalyst that's involved in converting the 32:03.400 --> 32:05.070 starting material to the product. 32:05.067 --> 32:09.227 When the catalyst is working as fast as it possibly can, 32:09.233 --> 32:11.173 increasing the starting material isn't going to 32:11.167 --> 32:13.897 increase the rate of the reaction anymore. 32:13.900 --> 32:16.930 The gate can't open any wider. 32:16.933 --> 32:18.703 And that's often the case with enzymes. 32:21.333 --> 32:26.633 So you have the substrate, the starting material, which 32:26.633 --> 32:28.873 interacts with the catalyst in order to get a product. 32:28.867 --> 32:32.027 But if the catalyst is rate limiting, if it's saturated, 32:32.033 --> 32:33.673 you can't go any faster. 32:33.667 --> 32:35.897 So the rate then is proportional to how much 32:35.900 --> 32:37.300 catalyst you have, of course. 32:37.300 --> 32:39.200 If you doubled the amount of catalyst under those 32:39.200 --> 32:42.000 situations you'd double the rate. 32:42.000 --> 32:45.000 But the substrate is raised to the zero power, it doesn't 32:45.000 --> 32:47.570 make any difference. 32:47.567 --> 32:52.267 So the rate is actually just proportional to the catalyst, 32:52.267 --> 32:56.367 independent of the substrate. 32:56.367 --> 33:02.397 But if doing the experiment you didn't realize that there 33:02.400 --> 33:05.070 was a catalyst in there doing it, you just thought it was 33:05.067 --> 33:11.067 happening spontaneously, then you would say it's zero order. 33:11.067 --> 33:13.797 So that's a zero order reaction, zero order kinetics. 33:16.600 --> 33:22.430 But that works only when the sheep are really crowded here. 33:22.433 --> 33:24.903 If the sheep were all over the fields and some coming 33:24.900 --> 33:29.130 through, if the concentration were lower, then having more 33:29.133 --> 33:31.033 sheep would allow them to get through faster. 33:31.033 --> 33:35.903 You're not saturating the catalyst. But it becomes first 33:35.900 --> 33:39.600 order in substrate when you have very low concentration of 33:39.600 --> 33:41.900 substrate, but at some higher concentration it 33:41.900 --> 33:43.530 becomes zero order. 33:43.533 --> 33:45.833 So it's always, in principle, possible to lower the 33:45.833 --> 33:49.203 concentration until it becomes first order. 33:49.200 --> 33:51.830 But, in fact, under many conditions it would be 33:51.833 --> 33:54.003 zero order. 33:54.000 --> 33:56.300 So that's an example of zero order. 33:59.333 --> 34:02.333 Now, first-order says the rate is proportional to the first 34:02.333 --> 34:05.473 power of the amount of reagent you're using. 34:05.467 --> 34:07.627 And that's, of course, very reasonable-- it's like the 34:07.633 --> 34:11.703 water coming through the taps or something like that. 34:11.700 --> 34:15.800 Now if you have first order kinetics, the amount of 34:15.800 --> 34:18.730 product you get in time looks like this. 34:18.733 --> 34:23.703 It's an exponential approach to the 100%. 34:23.700 --> 34:26.430 Or this particular one is drawn with a 34:26.433 --> 34:27.903 certain rate constant. 34:27.900 --> 34:29.530 If the rate constant were faster it 34:29.533 --> 34:31.203 would rise more quickly. 34:31.200 --> 34:33.500 If the rate constant were lower it would rise more 34:33.500 --> 34:38.470 slowly, but always it would go, in this case, to 100%. 34:38.467 --> 34:40.927 You could, instead of monitoring the product, you 34:40.933 --> 34:42.503 could look at the disappearance of starting 34:42.500 --> 34:44.970 material, which is then an exponential decay, just the 34:44.967 --> 34:46.197 same thing upside-down. 34:48.733 --> 34:51.303 So exponential decay means you have a 34:51.300 --> 34:54.230 constant, so-called half-life. 34:54.233 --> 34:58.003 Now I chose 0.69 here for a reason. 34:58.000 --> 35:01.670 It's because the half-life, the time it takes for half the 35:01.667 --> 35:07.297 material to go away, is 0.69 divided by whatever k is. 35:07.300 --> 35:13.630 So if I chose k to be 0.69, the half-life is 1. 35:13.633 --> 35:20.503 So after 1 second, half of the material remains. 35:20.500 --> 35:24.770 After another 1 second, a quarter, then an eighth, then 35:24.767 --> 35:27.797 a sixteenth and so on. 35:27.800 --> 35:29.600 And that's the necessary-- 35:29.600 --> 35:33.830 you can prove it easily by mathematics for 35:33.833 --> 35:35.173 a first-order reaction. 35:35.167 --> 35:36.667 There is a repeating half-life. 35:39.567 --> 35:43.297 Now, suppose you have a more complex situation where it's 35:43.300 --> 35:46.630 first-order kinetics but it's reversible. 35:46.633 --> 35:49.473 So the starting material at a certain rate goes to product, 35:49.467 --> 35:52.497 but the product can also come back to starting material, 35:52.500 --> 35:55.970 suppose at a much lower rate. 35:55.967 --> 36:00.267 So once you reach equilibrium the two rates balance so 36:00.267 --> 36:03.327 things cease changing. 36:03.333 --> 36:06.033 In fact, you know, in the nineteenth century, 36:06.033 --> 36:12.373 equilibrium situations were initially discussed not as 36:12.367 --> 36:15.067 equilibria, but as balanced rates. 36:18.033 --> 36:20.603 So at any rate, they're the same thing. 36:20.600 --> 36:24.170 So whatever k1 is times the concentration of starting 36:24.167 --> 36:26.667 material will be equal to whatever k-1 is times the 36:26.667 --> 36:29.997 concentration of product. 36:30.000 --> 36:34.100 Or we could divide through by starting material 36:34.100 --> 36:35.330 here and k1 over here. 36:35.333 --> 36:40.203 So k1 over k-1 is the equilibrium constant. 36:43.600 --> 36:47.400 So now the product doesn't go to 100% nor the starting 36:47.400 --> 36:49.470 material to zero. 36:49.467 --> 36:52.797 But if you start with all starting material, you get 36:52.800 --> 36:57.470 these exponential behaviors, it's still exponential. 36:57.467 --> 37:00.127 That's what's interesting. 37:00.133 --> 37:02.903 But it doesn't approach zero. 37:02.900 --> 37:06.730 So here, after 1 second where with that rate constant you 37:06.733 --> 37:11.333 would have fallen to half, you don't fall quite to half, 37:11.333 --> 37:13.103 because some stuff is coming back. 37:15.600 --> 37:20.100 But if you go to the ultimate goal of equilibrium 37:20.100 --> 37:24.330 here, then you find-- 37:24.333 --> 37:27.073 notice the equilibrium constant is 3, I chose that to 37:27.067 --> 37:28.127 be a third of that. 37:28.133 --> 37:34.503 So there's one quarter of the red material and three 37:34.500 --> 37:37.670 quarters of the blue material at equilibrium. 37:37.667 --> 37:43.097 But if we draw this at 25%, the value that the starting 37:43.100 --> 37:47.630 material actually approaches asymptotically, exponentially, 37:47.633 --> 37:51.873 we find now there is a repeating half-life-- 37:51.867 --> 37:54.527 this is truly an exponential. 37:54.533 --> 37:58.233 But the interesting thing is that it's an exponential decay 37:58.233 --> 38:04.673 to the equilibrium mixture, but the half-life is 0.69 38:04.667 --> 38:07.997 divided by the SUM of the two rate constants. 38:08.000 --> 38:11.370 Again, this is easy to demonstrate using calculus, 38:11.367 --> 38:14.397 but it's just sort of cute that you add forward and 38:14.400 --> 38:17.600 reverse rate constants together to get how rapidly it 38:17.600 --> 38:18.870 approaches equilibrium. 38:21.467 --> 38:25.327 So they're first-order reactions, both just one way 38:25.333 --> 38:27.133 and reversible. 38:27.133 --> 38:29.603 Now, a second-order reaction is proportional to 38:29.600 --> 38:31.000 the square of [A]. 38:31.000 --> 38:34.070 That's obviously true if two A's have to get together in 38:34.067 --> 38:38.697 order to reach the transition state. 38:38.700 --> 38:42.030 But it could also be second-order if you have an A 38:42.033 --> 38:45.073 interacting with a B. In that case you say it's first order 38:45.067 --> 38:48.867 in A and first-order in B and second-order overall. 38:52.800 --> 38:57.100 But what if B is effectively constant? 38:57.100 --> 39:02.170 So as time goes on, A is decreasing but B is not 39:02.167 --> 39:03.827 decreasing. 39:03.833 --> 39:06.433 How could that possibly be the case? 39:06.433 --> 39:09.103 How could you have a reaction where B doesn't decrease? 39:13.400 --> 39:14.830 STUDENT: B is a catalyst. 39:14.833 --> 39:17.203 PROFESSOR: Ah, if B were a catalyst, 39:17.200 --> 39:18.170 it doesn't get consumed. 39:18.167 --> 39:18.627 That's one way. 39:18.633 --> 39:26.203 Another way is that the B is in gross excess compared to A. 39:26.200 --> 39:29.630 So even though A consumes a B, it doesn't change its 39:29.633 --> 39:32.503 concentration appreciably, because the concentration is 39:32.500 --> 39:35.730 so large compared to that of A. So if [B] is much greater 39:35.733 --> 39:37.003 than [A] you get that. 39:37.000 --> 39:42.670 And in that situation you say that you can neglect [B] 39:42.667 --> 39:46.727 by incorporating it into the k. 39:46.733 --> 39:49.673 Whatever [B] is, it's not changing. 39:49.667 --> 39:52.227 For all you know when you're doing the experiment you might 39:52.233 --> 39:54.703 not even though there's a catalyst there, but it's there 39:54.700 --> 39:56.930 in always the same amount, you always get 39:56.933 --> 39:57.933 the same rate constant. 39:57.933 --> 40:00.533 And in a situation like that you say it's 40:00.533 --> 40:02.533 pseudo first order. 40:02.533 --> 40:05.473 It behaves as if it's first order, even though it really 40:05.467 --> 40:08.327 depends on something else as well. 40:08.333 --> 40:12.373 And so a second-order process could be a pseudo first order 40:12.367 --> 40:13.967 rate constant. 40:13.967 --> 40:18.397 For example, suppose B were the solvent. 40:18.400 --> 40:21.230 Then it appears that it's a first-order reaction, even 40:21.233 --> 40:24.003 though it turned out that the solvent had to react with the 40:24.000 --> 40:26.700 thing in order to do it. 40:26.700 --> 40:29.130 So that's pseudo first order. 40:29.133 --> 40:32.403 Now, if you have a second-order reaction compared to a 40:32.400 --> 40:35.070 first-order reaction, that is a regular second-order 40:35.067 --> 40:38.297 reaction where two molecules of A have to get together, 40:38.300 --> 40:41.730 what you find is that a first-order reaction 40:41.733 --> 40:42.233 goes like this. 40:42.233 --> 40:45.903 But the second order starts faster and ends slower. 40:45.900 --> 40:47.800 So it's no longer exponential. 40:47.800 --> 40:50.770 Obviously it's decreasing but not with a half-life, not 40:50.767 --> 40:53.497 exponentially, not a repeating half-life because it gets 40:53.500 --> 40:55.700 slower as it goes along because it depends on the 40:55.700 --> 40:57.870 square of the concentration. 40:57.867 --> 40:59.097 So it slows faster. 40:59.100 --> 41:00.200 It's not exponential. 41:00.200 --> 41:01.800 There is no constant half-life. 41:01.800 --> 41:02.930 So that's how you would know that 41:02.933 --> 41:04.073 something is second order. 41:04.067 --> 41:07.127 You measure how much in the first increment of time, the 41:07.133 --> 41:10.773 second increment, and they're not exponential. 41:10.767 --> 41:14.597 Now we'll get on to complex reactions and the idea of the 41:14.600 --> 41:18.100 rate-limiting step. 41:18.100 --> 41:21.070 So suppose that you go to an intermediate and then it goes 41:21.067 --> 41:21.697 to product. 41:21.700 --> 41:25.930 But suppose the transition state energies are like this. 41:25.933 --> 41:29.033 So it's very slow to get to the intermediate. 41:29.033 --> 41:31.003 But once you're at the intermediate it rapidly goes 41:31.000 --> 41:33.300 to product. 41:33.300 --> 41:37.900 Now this reactive intermediate never builds up, you never 41:37.900 --> 41:40.900 have an appreciable amount of it, because even if it were at 41:40.900 --> 41:44.400 equilibrium with this there's very little of it with a big 41:44.400 --> 41:45.830 energy difference here. 41:45.833 --> 41:47.303 So you might not even know that the 41:47.300 --> 41:49.630 intermediate is there. 41:49.633 --> 41:52.203 You get there and it immediately goes to product. 41:52.200 --> 41:58.630 In that case, who cares really about what rate this is, as 41:58.633 --> 42:02.133 long as it's fast? The rate at which you get product is the 42:02.133 --> 42:03.803 rate at which you get this. 42:03.800 --> 42:05.170 It never builds up. 42:05.167 --> 42:07.297 Every time you get it, it goes immediately to product, or 42:07.300 --> 42:08.430 very quickly. 42:08.433 --> 42:11.473 So this first step then, even though it's a two-step 42:11.467 --> 42:14.897 reaction, the first step is the one whose rate makes a 42:14.900 --> 42:15.900 difference. 42:15.900 --> 42:18.770 If you double the rate of the first step then you'll double 42:18.767 --> 42:22.427 the overall rate of the reaction, because the second 42:22.433 --> 42:23.703 step doesn't make any difference. 42:23.700 --> 42:26.870 So that's called the rate-limiting step. 42:26.867 --> 42:29.697 On the other hand, suppose that that first reaction is 42:29.700 --> 42:32.800 fast and the second one is slow. 42:32.800 --> 42:36.470 So you have a rapid pre-equilibrium formed between 42:36.467 --> 42:39.727 these two-- again, not very much of the intermediate. 42:39.733 --> 42:42.503 But it reaches an equilibrium concentration compared to 42:42.500 --> 42:47.030 this, or almost, and then slowly it goes to product. 42:47.033 --> 42:50.233 Now two things that are in equilibrium with the same 42:50.233 --> 42:54.103 thing are in equilibrium with each other. 42:54.100 --> 42:57.070 So to the extent that that intermediate is in equilibrium 42:57.067 --> 43:00.727 with the starting material, and we treat the rate of going 43:00.733 --> 43:05.673 over here as an equilibrium between the intermediate and 43:05.667 --> 43:10.367 this transition state, we could also pretend that the 43:10.367 --> 43:12.867 transition state is in equilibrium with the starting 43:12.867 --> 43:15.867 material, since they're both in equilibrium with the 43:15.867 --> 43:18.027 intermediate. 43:18.033 --> 43:20.773 So now, who cares that there's an intermediate, that there's 43:20.767 --> 43:21.897 a first step. 43:21.900 --> 43:25.130 We can calculate the rate just on the basis of getting how 43:25.133 --> 43:28.433 much of this transition state there is by assuming it's in 43:28.433 --> 43:29.803 equilibrium with that starting material. 43:34.100 --> 43:38.970 So now the second step or the second transition state is 43:38.967 --> 43:39.697 rate-limiting. 43:39.700 --> 43:41.970 All we have to know is how high it is compared to the 43:41.967 --> 43:42.997 starting material. 43:43.000 --> 43:44.970 We don't care about the intermediate. 43:44.967 --> 43:47.667 So you can have one step or the other step be 43:47.667 --> 43:50.367 rate-limiting. 43:50.367 --> 43:54.267 Or if they're not drastically different, both of them could 43:54.267 --> 43:55.867 affect the rate. 43:55.867 --> 43:59.167 Many cases one or the other is rate-limiting. 43:59.167 --> 44:02.427 But if you want to see how it works out in a complicated 44:02.433 --> 44:04.633 case, where you have a starting material that can go 44:04.633 --> 44:07.533 reversibly to the intermediate, and then the 44:07.533 --> 44:08.973 intermediate goes to product all with 44:08.967 --> 44:11.627 certain rate constants, 44:11.633 --> 44:14.273 on the website you can get an Excel program, which is a 44:14.267 --> 44:15.627 crummy Excel program. 44:15.633 --> 44:18.033 I'm sorry, it executes very slowly. 44:18.033 --> 44:21.103 You can change the parameters to make it go a little faster. 44:21.100 --> 44:24.100 But you can put in what energy you want for the starting 44:24.100 --> 44:27.800 material, the intermediate and the product; and what energy 44:27.800 --> 44:31.170 you want for the transition states, one and two, and see 44:31.167 --> 44:34.697 how the overall rate compares with what you would have 44:34.700 --> 44:38.170 calculated if it had been just the first step that you had to 44:38.167 --> 44:41.227 get over, or just the second step that you had to get over. 44:41.233 --> 44:44.903 In this particular case where each of these is about between 44:44.900 --> 44:47.530 a kilocalorie and a kilocalorie and a half, the 44:47.533 --> 44:49.903 difference between those two and the difference between 44:49.900 --> 44:53.830 these two, you get this. 44:53.833 --> 44:57.033 So this is the actual rate. 44:57.033 --> 44:58.903 Notice the amount of starting material 44:58.900 --> 45:00.870 immediately falls quickly-- 45:00.867 --> 45:02.727 that's when you're establishing equilibrium 45:02.733 --> 45:03.833 between these two. 45:03.833 --> 45:05.903 So starting material is going to intermediate. 45:05.900 --> 45:09.430 And then slowly it goes away as the 45:09.433 --> 45:11.973 intermediate goes to product. 45:11.967 --> 45:13.597 Here is the intermediate. 45:13.600 --> 45:17.130 It immediately builds up to some concentration and then it 45:17.133 --> 45:18.633 changes very slowly. 45:18.633 --> 45:23.103 It stays fairly stable for any short period of time. 45:25.800 --> 45:31.330 Now, if you didn't have the first barrier and had only the 45:31.333 --> 45:33.803 second one, it was a one-step reaction. 45:33.800 --> 45:35.470 This is what you would have calculated 45:35.467 --> 45:36.897 for those same energies. 45:36.900 --> 45:37.970 So not too bad. 45:37.967 --> 45:42.027 So, in fact, the second transition state is pretty 45:42.033 --> 45:45.703 much rate-limiting-- you get pretty much the same result. 45:45.700 --> 45:48.830 On the other end, if transition state two weren't 45:48.833 --> 45:51.733 there and you only had to get over transition state one, 45:51.733 --> 45:54.233 then you'd have that blue one there, if it 45:54.233 --> 45:55.603 were the sole barrier. 45:55.600 --> 45:56.930 So very far from that. 45:56.933 --> 46:01.103 But even in this situation, you don't make a very big 46:01.100 --> 46:04.100 mistake if you just ignored the intermediate and 46:04.100 --> 46:07.230 the first transition state, and said it 46:07.233 --> 46:09.173 was only transition state two. 46:09.167 --> 46:11.467 It's rate limiting. 46:11.467 --> 46:14.927 And if you fiddle with this you'll find that if you start 46:14.933 --> 46:18.503 changing these differences very much, then one of them or 46:18.500 --> 46:20.770 the other one becomes clearly rate-limiting-- 46:20.767 --> 46:24.197 you get much better agreement. 46:24.200 --> 46:27.230 Now, I said that this was between a kilocalorie and a 46:27.233 --> 46:31.573 kilocalorie and a half, 3/4 of that is about one, so the 46:31.567 --> 46:33.967 equilibrium ratio is about 10-- 46:33.967 --> 46:37.297 or actually, I said 9 here, 9 times as much starting 46:37.300 --> 46:39.000 material as intermediate. 46:39.000 --> 46:43.000 So once the intermediate reaches its steady sort of 46:43.000 --> 46:47.770 equilibrium relationship with the starting material, this 46:47.767 --> 46:52.227 very quick rise here, once you get there, then there's 9 46:52.233 --> 46:54.473 times as much starting material as there is in 46:54.467 --> 46:55.227 intermediate. 46:55.233 --> 46:59.573 That's 9 times as much as this. 46:59.567 --> 47:02.697 And that persists then, that ratio. 47:02.700 --> 47:05.330 When you get to here it's 9 times as much of one or the 47:05.333 --> 47:08.633 other and so on. 47:08.633 --> 47:12.273 Now this is also a factor of 10 between this. 47:12.267 --> 47:15.297 But this has to do with rates, remember. 47:15.300 --> 47:18.500 So this is how fast the intermediate goes back to 47:18.500 --> 47:22.030 starting material is 10 times faster than how fast it goes 47:22.033 --> 47:28.133 to product because of those differences in the delta H of 47:28.133 --> 47:29.373 activation. 47:31.167 --> 47:34.767 And what that means is that once the intermediate reaches 47:34.767 --> 47:38.167 its steady state, its equilibrium relationship with 47:38.167 --> 47:43.567 the starting material, it yields product 1/10 as fast as 47:43.567 --> 47:44.797 it is formed. 47:44.800 --> 47:49.170 So it forms very rapidly, you can see that here. 47:49.167 --> 47:52.967 But now individual molecules are still being formed just as 47:52.967 --> 47:56.467 rapidly, or almost as rapidly, but they're going away just as 47:56.467 --> 47:59.097 rapidly as they're formed. 47:59.100 --> 48:03.130 Every one that's formed at a certain rate goes back to 48:03.133 --> 48:06.933 starting material 10 times for every 48:06.933 --> 48:09.573 time it goes to product-- 48:09.567 --> 48:12.267 9 times for every time it goes to product. 48:12.267 --> 48:15.727 So 1/10 of the time it goes on to product. 48:15.733 --> 48:19.633 So now the rate of going from starting material to product 48:19.633 --> 48:25.173 is however fast it goes over the first one times 1/10, 48:25.167 --> 48:27.197 because it's not changing. 48:27.200 --> 48:30.530 It's reached the so-called steady state. 48:30.533 --> 48:32.373 It's changing very slowly. 48:32.367 --> 48:36.697 Individual molecules are going very rapidly. 48:36.700 --> 48:39.270 So the rate of an individual molecule to go from starting 48:39.267 --> 48:42.727 material to product is how fast it goes to intermediate 48:42.733 --> 48:46.233 times 1/10. 48:46.233 --> 48:49.673 So that's a sequential reaction -- the idea of the 48:49.667 --> 48:51.097 rate-limiting step. 48:51.100 --> 48:55.130 Now a really interesting concept is fractional order. 48:55.133 --> 48:57.973 But I see that we've reached the time now, so we'll have to 48:57.967 --> 49:00.897 wait for fractional order until the next lecture.