WEBVTT 00:00:00.000 --> 00:00:00.016 The following content is provided under a Creative 00:00:00.016 --> 00:00:00.022 Commons license. 00:00:00.022 --> 00:00:00.038 Your support will help MIT OpenCourseWare continue to 00:00:00.038 --> 00:00:00.054 offer high quality educational resources for free. 00:00:00.054 --> 00:00:00.072 To make a donation or view additional materials from 00:00:00.072 --> 00:00:00.088 hundreds of MIT courses, visit MIT OpenCourseWare at 00:00:00.088 --> 00:00:00.110 ocw.mit.edu. 00:00:00.110 --> 00:00:26.160 PROFESSOR: OK, so kinetics we're continuing with today. 00:00:26.160 --> 00:00:29.200 We talked on Wednesday about first order kinetics and we'll 00:00:29.200 --> 00:00:31.080 do a brief review of some of that. 00:00:31.080 --> 00:00:33.650 And we're going to talk about second order kinetics. 00:00:33.650 --> 00:00:38.210 Today we're going to come back up and talk about chemical 00:00:38.210 --> 00:00:40.540 equilibrium, which is something I love to do to 00:00:40.540 --> 00:00:43.080 review things that we've talked about before. 00:00:43.080 --> 00:00:46.260 And we're going to start in on reaction mechanisms. So, I 00:00:46.260 --> 00:00:48.780 thought I would mention, some of you have may have seen the 00:00:48.780 --> 00:00:52.520 activity in the Infinite Corridor, but today is world 00:00:52.520 --> 00:00:59.210 AIDS day, and today a lot of the compounds that are being 00:00:59.210 --> 00:01:04.360 used to treat HIV were actually designed based on 00:01:04.360 --> 00:01:06.850 making inhibitors to enzymes. 00:01:06.850 --> 00:01:11.410 And so, to design those pharmaceuticals, people had to 00:01:11.410 --> 00:01:14.570 understand the reaction mechanism of the enzyme, and 00:01:14.570 --> 00:01:17.240 enzymes, of course, are catalysts in the body. 00:01:17.240 --> 00:01:22.510 So, knowledge of what medical individuals needed to know to 00:01:22.510 --> 00:01:26.230 design these inhibitors to treat HIV are actually a lot 00:01:26.230 --> 00:01:28.570 from this unit that we're going to be talking about. 00:01:28.570 --> 00:01:30.740 So, we'll be talking about reaction mechanisms, and we're 00:01:30.740 --> 00:01:33.600 also going to be talking about enzyme catalysis, which were 00:01:33.600 --> 00:01:35.910 key points in being able to come up with some of the 00:01:35.910 --> 00:01:40.390 current treatments against HIV. 00:01:40.390 --> 00:01:46.330 All right, so just a little review from last Wednesday. 00:01:46.330 --> 00:01:49.280 We talked about first order half life. 00:01:49.280 --> 00:01:52.810 We talked about first order kinetics, we came up with an 00:01:52.810 --> 00:01:56.510 integrated first order rate law, and we also 00:01:56.510 --> 00:01:58.380 talked about half life. 00:01:58.380 --> 00:02:03.200 And you told me last time that an example of first order half 00:02:03.200 --> 00:02:06.450 life is radioactivity, which we're going to be talking 00:02:06.450 --> 00:02:07.520 about today. 00:02:07.520 --> 00:02:11.700 So, just a little review from last time, you have your first 00:02:11.700 --> 00:02:17.160 order integrated rate law, and the half life is defined as 00:02:17.160 --> 00:02:20.400 the time it takes for half of the original material to go 00:02:20.400 --> 00:02:24.540 away, and half life is abbreviated t 1/2, that's the 00:02:24.540 --> 00:02:28.030 symbol for half life, so the time for half of the original 00:02:28.030 --> 00:02:30.360 material to go away. 00:02:30.360 --> 00:02:34.080 If you plug original material divided by 2 in there, then 00:02:34.080 --> 00:02:40.500 the original material a to the o for original, drops out and 00:02:40.500 --> 00:02:44.100 you come up with this equation of the natural log of 1/2 00:02:44.100 --> 00:02:47.770 equals minus k t 1/2, and k is, of 00:02:47.770 --> 00:02:49.370 course, our rate constant. 00:02:49.370 --> 00:02:52.610 And so, then we can take the natural log of a 1/2 and we 00:02:52.610 --> 00:02:53.580 get a value. 00:02:53.580 --> 00:02:56.700 Rearranging that, you get half life equals 0 . 00:02:56.700 --> 00:02:59.710 6 9 3 1 over k. 00:02:59.710 --> 00:03:04.010 And so you told me last time for this plot for first order 00:03:04.010 --> 00:03:07.060 half life, each half life, half of the original 00:03:07.060 --> 00:03:10.260 material goes away. 00:03:10.260 --> 00:03:14.520 So, one example of a first order half life process is 00:03:14.520 --> 00:03:16.630 radioactive decay. 00:03:16.630 --> 00:03:20.100 And the reason why this is a first order process is because 00:03:20.100 --> 00:03:25.530 the decay of the nucleus is independent of the number of 00:03:25.530 --> 00:03:28.640 surrounding nuclei that has been decayed. 00:03:28.640 --> 00:03:31.650 So it's independent of the original starting 00:03:31.650 --> 00:03:34.850 concentration, and since it's independent, notice that's a 00:03:34.850 --> 00:03:38.630 blank in your notes, since it's independent, then that 00:03:38.630 --> 00:03:42.740 makes it a first order process. 00:03:42.740 --> 00:03:47.380 So, we can apply first order integrated rate laws to 00:03:47.380 --> 00:03:53.120 radioactive decay. 00:03:53.120 --> 00:03:56.500 So here were some of the equations we had last time. 00:03:56.500 --> 00:04:00.090 We had, this is a different expression of the first order 00:04:00.090 --> 00:04:04.930 rate law where the material, concentration material of 00:04:04.930 --> 00:04:07.540 material a, at some particular time equals the original 00:04:07.540 --> 00:04:11.890 concentration, e to the minus k t, where you have your rate 00:04:11.890 --> 00:04:15.670 constant and the time that has elapsed, and we also just 00:04:15.670 --> 00:04:21.690 talked about first order half lifes with this equation here. 00:04:21.690 --> 00:04:25.200 So, we can use those same equations, but often you don't 00:04:25.200 --> 00:04:29.280 see it in terms of concentration of a, you 00:04:29.280 --> 00:04:32.660 usually see these expressions in terms of either the number 00:04:32.660 --> 00:04:36.610 of nuclei or a different a, which is a for activity. 00:04:36.610 --> 00:04:40.710 So instead of concentration, we're talking about the number 00:04:40.710 --> 00:04:47.010 of nuclei that have decay or capital N. 00:04:47.010 --> 00:04:50.460 So, we can write this same expression, but now using N 00:04:50.460 --> 00:04:54.820 instead of concentration of a, same thing, number of nuclei 00:04:54.820 --> 00:04:58.870 equal the original number of nuclei, e, to the minus k t, 00:04:58.870 --> 00:05:02.220 where k is our rate constant, or in this case decay 00:05:02.220 --> 00:05:09.430 constant, and t is time. 00:05:09.430 --> 00:05:12.620 So, with chemical kinetics, we're usually talking about 00:05:12.620 --> 00:05:16.190 the change in concentration of things over time, but with 00:05:16.190 --> 00:05:18.660 nuclear kinetics, we're talking about the number of 00:05:18.660 --> 00:05:20.790 decay events, the number of nuclei that have decayed. 00:05:20.790 --> 00:05:26.370 And so, here with nuclear kinetics, we measure these 00:05:26.370 --> 00:05:29.410 events using a Geiger counter. 00:05:29.410 --> 00:05:34.390 So this can measure radiation, and I'm going to come around 00:05:34.390 --> 00:05:37.360 and just check the room. 00:05:37.360 --> 00:05:40.510 And so, the gasket's ionized and then you 00:05:40.510 --> 00:05:41.630 hear different clicks. 00:05:41.630 --> 00:05:47.030 See if you can hear the clicks as I come around. 00:05:47.030 --> 00:05:59.580 So let's just see if we have any problems over here. 00:05:59.580 --> 00:06:07.590 Oh, maybe a little bit. 00:06:07.590 --> 00:06:12.800 No, this is fine. 00:06:12.800 --> 00:06:18.190 There's always a little bit of radioactivity, it's all fine. 00:06:18.190 --> 00:06:25.260 So, this is a Geiger counter, which will measure nuclear 00:06:25.260 --> 00:06:29.460 kinetics, it will measure radioactivity. 00:06:29.460 --> 00:06:33.230 And my lab has this particular one, because we use x-rays in 00:06:33.230 --> 00:06:36.640 our experiments. 00:06:36.640 --> 00:06:42.330 OK, we'll leave this on low just to check things 00:06:42.330 --> 00:06:43.620 out as we go along. 00:06:43.620 --> 00:06:49.390 All right, so we do have a term, A, that we talk 00:06:49.390 --> 00:06:50.480 about in this unit. 00:06:50.480 --> 00:06:53.900 Instead of concentration of A, it's activity. 00:06:53.900 --> 00:07:00.330 And so, activity here, sort of the decay rate, is also called 00:07:00.330 --> 00:07:04.290 activity, capital A, and so this is equal to the change in 00:07:04.290 --> 00:07:08.740 the number of nuclei or our decay constant times the 00:07:08.740 --> 00:07:12.510 number of nuclei. 00:07:12.510 --> 00:07:14.520 And people will often talk about the activity of 00:07:14.520 --> 00:07:18.290 particular radioactive compounds. 00:07:18.290 --> 00:07:21.640 So, because activity is proportional to the number of 00:07:21.640 --> 00:07:27.010 nuclei, you can also take this expression and write it as 00:07:27.010 --> 00:07:28.160 this expression. 00:07:28.160 --> 00:07:30.580 So you can have either the number of nuclei equal the 00:07:30.580 --> 00:07:34.500 original number of nuclei, e to the k t, or you can do it 00:07:34.500 --> 00:07:39.150 in terms of activity -- that the activity at some time is 00:07:39.150 --> 00:07:44.330 equal to the original activity, e to the minus k t. 00:07:44.330 --> 00:07:51.580 So, all of these equations can be re-written in this way. 00:07:51.580 --> 00:08:03.170 So, let's talk a minute about units. 00:08:03.170 --> 00:08:08.480 All right, so the activity for units, the new activity is Bq, 00:08:08.480 --> 00:08:11.750 Becquerel. and that, actually is named 00:08:11.750 --> 00:08:14.010 after a French person. 00:08:14.010 --> 00:08:17.260 Henry was his first name, and my French 00:08:17.260 --> 00:08:19.360 pronunciation is not very good. 00:08:19.360 --> 00:08:20.940 This is the current unit. 00:08:20.940 --> 00:08:24.930 It's equal to one radioactive disintegration per second. 00:08:24.930 --> 00:08:28.080 The older unit, which you may be familiar with, is called 00:08:28.080 --> 00:08:30.980 the Curie, and that is 3 . 00:08:30.980 --> 00:08:35.090 7 times 10 to the 10 disintegrations per second. 00:08:35.090 --> 00:08:38.940 Does anyone want to guess, the Curie unit, who 00:08:38.940 --> 00:08:40.110 that was named after? 00:08:40.110 --> 00:08:44.930 STUDENT: Marie Curie? 00:08:44.930 --> 00:08:47.220 PROFESSOR: No, it was named after her husband actually, 00:08:47.220 --> 00:08:49.200 Pierre Curie. 00:08:49.200 --> 00:08:54.530 And I actually always assume, because Marie is actually more 00:08:54.530 --> 00:08:57.800 famous than her husband. 00:08:57.800 --> 00:09:01.860 But she, Marie Curie won two Nobel prizes, so we shouldn't 00:09:01.860 --> 00:09:04.390 feel too sorry for her. 00:09:04.390 --> 00:09:08.540 Her husband shared the first Nobel Prize with her in, I 00:09:08.540 --> 00:09:13.300 think it was 1903, but then in 1906 he was killed in a road 00:09:13.300 --> 00:09:16.020 accident, run over by something that was crossing 00:09:16.020 --> 00:09:17.440 the street. 00:09:17.440 --> 00:09:21.570 So he did not share the second Nobel Prize, because by the 00:09:21.570 --> 00:09:26.630 time that came around about 1911, he had passed away. 00:09:26.630 --> 00:09:30.240 So, at first, we had the Curie, but then that turned 00:09:30.240 --> 00:09:32.400 out to be a really big number. 00:09:32.400 --> 00:09:36.610 And so, when you were talking about sort of safe units for 00:09:36.610 --> 00:09:40.240 workers to be exposed to, if they were being exposed to 00:09:40.240 --> 00:09:44.790 things 10 to the 10, that really isn't very healthy. 00:09:44.790 --> 00:09:49.350 So they wanted to have sort of a much smaller unit. 00:09:49.350 --> 00:09:53.840 And so I guess that Marie Curie at that point talked 00:09:53.840 --> 00:09:58.790 about how her husband would feel about having the Curie 00:09:58.790 --> 00:10:02.050 not being the standard unit, but I guess she was OK with 00:10:02.050 --> 00:10:05.470 it, because if we had kept that same unit, then people 00:10:05.470 --> 00:10:08.500 would have been using it and it would of had to of been a 00:10:08.500 --> 00:10:13.320 really, really small number, because it was sort of picked 00:10:13.320 --> 00:10:15.820 to be set up to something that was too large, and she didn't 00:10:15.820 --> 00:10:18.410 want her husband's name apparently associated with a 00:10:18.410 --> 00:10:22.360 sort of an infinitesimally small quantity of something. 00:10:22.360 --> 00:10:25.550 So, the Curie was sort of done away with. 00:10:25.550 --> 00:10:28.250 And Henry Becquerel, who was one of the people who 00:10:28.250 --> 00:10:31.940 discovered radioactivity and shared that first Nobel Prize, 00:10:31.940 --> 00:10:34.690 had the unit named after him. 00:10:34.690 --> 00:10:38.890 And I always ask the freshman chemistry class that as they 00:10:38.890 --> 00:10:43.710 go through MIT, if they ever discover a unit that is named 00:10:43.710 --> 00:10:46.120 after a female scientist, to please come 00:10:46.120 --> 00:10:47.860 back and let me know. 00:10:47.860 --> 00:10:50.100 This was the one I thought was named after a female 00:10:50.100 --> 00:10:52.560 scientist, but as it turns out, it was 00:10:52.560 --> 00:10:54.670 actually Pierre Curie. 00:10:54.670 --> 00:10:57.200 So, if you hear of any, please let me 00:10:57.200 --> 00:11:01.420 know for future reference. 00:11:01.420 --> 00:11:05.780 So, the current unit you'll be using is Bq here for 00:11:05.780 --> 00:11:09.000 radioactivity. 00:11:09.000 --> 00:11:11.170 So, you're not responsible for knowing all the different 00:11:11.170 --> 00:11:13.340 types of radioactivity. 00:11:13.340 --> 00:11:16.020 When you're working problems, you can always get this 00:11:16.020 --> 00:11:17.110 information. 00:11:17.110 --> 00:11:19.840 I'll just mention that a number of different kinds of 00:11:19.840 --> 00:11:23.890 radioactivity, some involve a mass change, some do not 00:11:23.890 --> 00:11:25.400 involve a mass change. 00:11:25.400 --> 00:11:28.290 So, alpha decay, this isn't actually in your notes, 00:11:28.290 --> 00:11:30.100 there's a reference to where the table is. 00:11:30.100 --> 00:11:32.530 You're not responsible for memorizing it, so I didn't put 00:11:32.530 --> 00:11:33.800 it in the notes. 00:11:33.800 --> 00:11:37.990 An alpha decay is equivalent to a helium 4 nucleus, so you 00:11:37.990 --> 00:11:41.080 lose two protons, two neutrons, so 00:11:41.080 --> 00:11:42.650 that's a big mass change. 00:11:42.650 --> 00:11:46.490 Whereas say a beta decay involves a loss of electrons, 00:11:46.490 --> 00:11:49.440 so there's no mass change associated with that. 00:11:49.440 --> 00:11:52.590 So just to be aware that there are these differences in 00:11:52.590 --> 00:11:57.040 different types of radiation. 00:11:57.040 --> 00:11:59.760 There's also really big differences in terms of half 00:11:59.760 --> 00:12:03.460 lives of radioactive isotopes, and again, this information 00:12:03.460 --> 00:12:06.620 would be given to you on a test or a problem-set, so you 00:12:06.620 --> 00:12:09.930 don't have to memorize it. 00:12:09.930 --> 00:12:13.620 So, this table is similar to one in your book, and the 00:12:13.620 --> 00:12:17.180 point here is just how different half lifes can be. 00:12:17.180 --> 00:12:23.670 So the abbreviation a here is year, d is day. 00:12:23.670 --> 00:12:28.760 So you see some of these half lifes are in multiple years, 00:12:28.760 --> 00:12:31.810 some of them are days, so there are big differences in 00:12:31.810 --> 00:12:36.000 terms of the half life of some of these radioactive isotopes. 00:12:36.000 --> 00:12:38.660 Some of them stay around for a really, really, 00:12:38.660 --> 00:12:42.700 really, really long time. 00:12:42.700 --> 00:12:47.310 So, I thought I would share with you a poem about half 00:12:47.310 --> 00:12:49.290 lifes today. 00:12:49.290 --> 00:12:52.400 And this was written by a former graduate student at 00:12:52.400 --> 00:12:55.790 MIT, Mala Radhakrishnan, and she is now a professor at 00:12:55.790 --> 00:13:01.690 Wellesley college right here in Wellesley, Massachusetts. 00:13:01.690 --> 00:13:05.640 So, her poem entitled "Days of our half lives," is from her 00:13:05.640 --> 00:13:08.900 collection of chemistry poetry, "Chemistry for the 00:13:08.900 --> 00:13:16.360 Couch Potato." And this particular poem involves the 00:13:16.360 --> 00:13:21.690 uranium 238 decay series. 00:13:21.690 --> 00:13:23.760 So, here we go. 00:13:23.760 --> 00:13:29.520 "Days of our half lives. 00:13:29.520 --> 00:13:33.050 My dearest love, I writing you to tell you all 00:13:33.050 --> 00:13:34.450 that I've been through. 00:13:34.450 --> 00:13:38.720 I've changed my whole identity, but loved, I can not 00:13:38.720 --> 00:13:40.380 pretend to be. 00:13:40.380 --> 00:13:45.950 When I was uranium 238, you were on my case to start 00:13:45.950 --> 00:13:46.690 losing weight. 00:13:46.690 --> 00:13:52.580 For 5 billion years I'd hoped and I prayed, and finally I 00:13:52.580 --> 00:13:55.890 had an alpha decay. 00:13:55.890 --> 00:14:00.200 Two protons, two neutrons went right out the door, and now I 00:14:00.200 --> 00:14:03.230 was thorium 234. 00:14:03.230 --> 00:14:07.630 But my nucleus was still unfit for your eyes, not positive 00:14:07.630 --> 00:14:10.970 enough for it's large size. 00:14:10.970 --> 00:14:14.360 But this time my half life was really not very long, because 00:14:14.360 --> 00:14:17.290 my will to change was quite strong. 00:14:17.290 --> 00:14:21.150 It took just a month, not even a millennium, to beta decay 00:14:21.150 --> 00:14:24.550 into protactinium. 00:14:24.550 --> 00:14:27.490 But you still rejected me right off the bat, 00:14:27.490 --> 00:14:30.050 protactinium, who's heard of that? 00:14:30.050 --> 00:14:35.810 So, beta decay, I did much more to become uranium 234. 00:14:35.810 --> 00:14:39.560 Myself again, but a new isotope, you still weren't 00:14:39.560 --> 00:14:42.240 satisfied, but I still had hope. 00:14:42.240 --> 00:14:45.850 Three alpha decays, it was hard, but I stayed on through 00:14:45.850 --> 00:14:51.120 thorium, through radium, and then radon. 00:14:51.120 --> 00:14:54.170 I thought I would finally please you, my mass was a 00:14:54.170 --> 00:14:59.420 healthy 222, but you said, although I like your mass, I 00:14:59.420 --> 00:15:04.500 do not want to be with a noble gas. 00:15:04.500 --> 00:15:07.810 You had a point, I wasn't reactive, so in order to 00:15:07.810 --> 00:15:10.140 please you, I stayed proactive. 00:15:10.140 --> 00:15:13.420 A few days later I found you and said, two more alpha 00:15:13.420 --> 00:15:18.870 decays and now I am lead. 00:15:18.870 --> 00:15:22.270 You shook your head, you were not too keen on my 00:15:22.270 --> 00:15:24.310 mass number of 214. 00:15:24.310 --> 00:15:28.730 I had a bad experience with that mass before, an unstable 00:15:28.730 --> 00:15:32.660 acitone walked right out the door. 00:15:32.660 --> 00:15:36.350 So in order to change, I went away, but all I could do was 00:15:36.350 --> 00:15:38.330 just beta decay. 00:15:38.330 --> 00:15:41.710 My hopes and my dreams started to go under, because beta 00:15:41.710 --> 00:15:45.120 decays don't change a mass number. 00:15:45.120 --> 00:15:50.310 To bismuth, then polonium, I hoped and I beckoned, my half 00:15:50.310 --> 00:15:53.110 life was 164 micro seconds. 00:15:53.110 --> 00:15:57.510 And then finally I alpha decayed and then I was lead 00:15:57.510 --> 00:16:02.130 with the prize worthy mass of 210. 00:16:02.130 --> 00:16:05.030 I've got to admit I was getting quite tired, my 00:16:05.030 --> 00:16:08.110 patience with you had nearly expired. 00:16:08.110 --> 00:16:12.910 You were more demanding than any I dated, and much of my 00:16:12.910 --> 00:16:17.800 energy had already been liberated. 00:16:17.800 --> 00:16:20.920 But you still weren't happy, but you had a fix, I really 00:16:20.920 --> 00:16:25.930 like the number of 206, So I waited for years until the 00:16:25.930 --> 00:16:30.310 day, which began with another beta decay, and then one more, 00:16:30.310 --> 00:16:34.010 and finally in the end I alpha-ed to 00:16:34.010 --> 00:16:37.020 lead 206, my friend. 00:16:37.020 --> 00:16:40.260 To change any further I wouldn't be able, no longer 00:16:40.260 --> 00:16:42.560 active, but happily stable. 00:16:42.560 --> 00:16:45.940 It took me billions of years to do, and look how I've 00:16:45.940 --> 00:16:49.640 changed and all just for you. 00:16:49.640 --> 00:16:53.180 And wait, what did you say? 00:16:53.180 --> 00:16:57.460 You've gotten so old that I'd rather be with a 00:16:57.460 --> 00:17:02.280 young lass of gold? 00:17:02.280 --> 00:17:04.740 Well, I give up, we're through, my pumpkin. 00:17:04.740 --> 00:17:07.300 Shouldn't all my effort be counting for something? 00:17:07.300 --> 00:17:10.440 Well, you won't be able to rule me any more, because I'm 00:17:10.440 --> 00:17:16.360 leaving you, not for one atom, but four. 00:17:16.360 --> 00:17:20.350 That's right, when you were away defusing, I met some 00:17:20.350 --> 00:17:24.770 chlorines that I found quite amusing. 00:17:24.770 --> 00:17:31.490 So we're going to form lead c l 4, and you won't be hearing 00:17:31.490 --> 00:17:33.360 from me any more. 00:17:33.360 --> 00:17:37.040 See, over the years I've grown quite wise, I've learned that 00:17:37.040 --> 00:17:39.230 love is about compromise. 00:17:39.230 --> 00:17:43.650 You still have half of your half lives to live, so now you 00:17:43.650 --> 00:17:48.500 go out there, it's your turn to give." 00:17:48.500 --> 00:17:58.320 And that is "The days of our half lives." So, Mala takes 00:17:58.320 --> 00:18:01.490 great effort to make sure that all her poetry not only 00:18:01.490 --> 00:18:04.450 rhymes, but it is chemically correct. 00:18:04.450 --> 00:18:08.430 So, it's a good way to review material to read "Chemistry 00:18:08.430 --> 00:18:12.590 from the Couch Potato." 00:18:12.590 --> 00:18:16.750 All right, so let's do an example now and think about 00:18:16.750 --> 00:18:19.950 how things will change over time. 00:18:19.950 --> 00:18:23.520 So we have an example, we want to know the original activity, 00:18:23.520 --> 00:18:26.210 and the activity after 17 years 00:18:26.210 --> 00:18:29.670 of a sample of plutonium. 00:18:29.670 --> 00:18:33.480 So let's take a look at how we'll do this problem. 00:18:33.480 --> 00:18:36.700 So first, given the information up there, the 00:18:36.700 --> 00:18:38.540 first thing we want to do is find the 00:18:38.540 --> 00:18:44.840 original number of nuclei. 00:18:44.840 --> 00:18:53.070 So first, capital N o, the original number of nuclei. 00:18:53.070 --> 00:18:57.750 So, we're given information about grams, so we have 0 . 00:18:57.750 --> 00:19:03.670 5 grams. And now if we want to know the number of nuclei, 00:19:03.670 --> 00:19:08.260 what's the first thing I have to do? 00:19:08.260 --> 00:19:10.270 Convert from grams to what? 00:19:10.270 --> 00:19:11.980 STUDENT: Moles. 00:19:11.980 --> 00:19:13.190 PROFESSOR: Moles, right. 00:19:13.190 --> 00:19:19.250 And here we want to use the molecular mass that's given to 00:19:19.250 --> 00:19:20.970 us in the form of that isotope. 00:19:20.970 --> 00:19:29.190 So here, we are given information about 239, and so 00:19:29.190 --> 00:19:34.710 that's the number we want to use in our conversions. 00:19:34.710 --> 00:19:37.460 So we can convert that over, but that's going to give us 00:19:37.460 --> 00:19:42.410 moles, so how do we go from moles to molecules? 00:19:42.410 --> 00:19:50.780 Avagadro's number, 6.022 times 10 to the 23. 00:19:50.780 --> 00:19:53.260 This time we're going to talk about it in terms of nuclei 00:19:53.260 --> 00:20:00.160 per mole, and so that's going to give us 1.3 times 00:20:00.160 --> 00:20:03.070 10 to the 21 nuclei. 00:20:03.070 --> 00:20:13.210 OK, so now we know the original number of nuclei. 00:20:13.210 --> 00:20:16.470 The next thing we're going to want to do is find k. 00:20:16.470 --> 00:20:23.280 And k is our rate constant for decay or our decay constant. 00:20:23.280 --> 00:20:29.970 So what do we know about k for a first order process? 00:20:29.970 --> 00:20:34.310 We know the equation for what? 00:20:34.310 --> 00:20:36.490 For first order half life, right. 00:20:36.490 --> 00:20:38.210 So that's o . 00:20:38.210 --> 00:20:44.610 6 9 3 1 over t 1/2. 00:20:44.610 --> 00:20:48.510 And in this problem we were given, the half life, and 00:20:48.510 --> 00:20:50.890 often you will be given the half life or you can look it 00:20:50.890 --> 00:20:55.350 up, and so we can put that in, so we have 0 . 00:20:55.350 --> 00:20:59.710 6 9 3 1 over 7 . 00:20:59.710 --> 00:21:04.830 6 times 10 to the 11 seconds. 00:21:04.830 --> 00:21:09.270 And we can calculate our constant, which is 9 . 00:21:09.270 --> 00:21:18.250 1 times 10 to the minus 13 per second. 00:21:18.250 --> 00:21:21.430 So now we were asked to find the original activity and the 00:21:21.430 --> 00:21:27.930 activity after 17 years. 00:21:27.930 --> 00:21:34.770 So, first we'll find the original activity, and the 00:21:34.770 --> 00:21:39.940 original activity is going to be equal to our rate constant 00:21:39.940 --> 00:21:42.900 times our original number of nuclei. 00:21:42.900 --> 00:21:46.000 So we've just solved for both of these, so we can plug these 00:21:46.000 --> 00:21:48.160 in, so we had 9 . 00:21:48.160 --> 00:21:56.070 1 times 10 the minus 13 per second times the number of 00:21:56.070 --> 00:21:57.690 nuclei, 1 . 00:21:57.690 --> 00:22:05.360 3 times 10 to the 21 nuclei, equals 1 . 00:22:05.360 --> 00:22:12.660 2 times 10 to the 9, and what are the units here? 00:22:12.660 --> 00:22:22.910 It's just like a hum, it's hard to understand. 00:22:22.910 --> 00:22:25.390 STUDENT: Nuclei per second. 00:22:25.390 --> 00:22:30.430 PROFESSOR: Nuclei per second, which is the same as what? 00:22:30.430 --> 00:22:34.080 That's equal to something else. 00:22:34.080 --> 00:22:39.410 Yup, so that's the same as the Becquerel or the Bq, so it's 00:22:39.410 --> 00:22:43.280 defined as nuclei per second, or number of disintegrations 00:22:43.280 --> 00:22:47.740 per second. 00:22:47.740 --> 00:22:59.220 All right, so let's do the last one. 00:22:59.220 --> 00:23:10.130 OK, so now after 17 years, so now we can say that the 00:23:10.130 --> 00:23:14.660 activity at some time is equal to the original activity, e to 00:23:14.660 --> 00:23:20.590 the minus k t, and we can put in the activity that we just 00:23:20.590 --> 00:23:21.820 found, which is 1 . 00:23:21.820 --> 00:23:31.250 2 times 10 to the 9 Bq, times e to the minus k, which is 9 . 00:23:31.250 --> 00:23:38.100 1 times 10 to the minus 13 per second times 17 years, which 00:23:38.100 --> 00:23:40.130 in seconds is 5 . 00:23:40.130 --> 00:23:44.190 4 times 10 to the 8 second. 00:23:44.190 --> 00:23:47.610 So here, we want to make sure that our units are going to 00:23:47.610 --> 00:23:50.230 cancel, and this is where people often run into 00:23:50.230 --> 00:23:54.130 problems. They'll plug in 17 years, and then a rate 00:23:54.130 --> 00:23:57.470 constant, which was calculated in seconds, and things will 00:23:57.470 --> 00:23:59.210 not cancel appropriately. 00:23:59.210 --> 00:24:02.500 So make sure that you get your units consistent so that your 00:24:02.500 --> 00:24:07.310 seconds are going to cancel. 00:24:07.310 --> 00:24:11.530 And so this term, if we do the math out here with the number 00:24:11.530 --> 00:24:15.560 significant figures, we find that that equals 1.2 00:24:15.560 --> 00:24:18.660 times 10 to 9 Bq. 00:24:18.660 --> 00:24:22.260 That term is insignificant in our problem. 00:24:22.260 --> 00:24:27.110 So, the original radioactivity and the activity after 17 00:24:27.110 --> 00:24:32.420 years are the same in terms of the significant figures. 00:24:32.420 --> 00:24:37.480 And so, I choose this problem to emphasize a problem that we 00:24:37.480 --> 00:24:40.810 have, and that is radioactive waste. 00:24:40.810 --> 00:24:46.190 It takes a very long time for some compounds to decay. 00:24:46.190 --> 00:24:50.690 And so you have to think about storing radioactive waste, and 00:24:50.690 --> 00:24:54.050 think about a container that will outlast 00:24:54.050 --> 00:24:55.760 that radioactive waste. 00:24:55.760 --> 00:24:58.900 And how do you know that the container is going to outlast 00:24:58.900 --> 00:25:00.000 the radioactive waste. 00:25:00.000 --> 00:25:02.860 You can't really do an experiment because the time 00:25:02.860 --> 00:25:05.770 involved in doing the experiment, anyone who designs 00:25:05.770 --> 00:25:08.630 the container won't be alive by the time you're concerned 00:25:08.630 --> 00:25:12.980 about whether the container is going to be stable or not. 00:25:12.980 --> 00:25:16.380 So taking radioactivity is an issue. 00:25:16.380 --> 00:25:19.300 You heard some in the presidential campaign about 00:25:19.300 --> 00:25:23.190 whether both candidates believe in nuclear energy or 00:25:23.190 --> 00:25:27.340 not, and I think that both of them said, it needs to be 00:25:27.340 --> 00:25:31.320 considered, we need to have everything on the table. 00:25:31.320 --> 00:25:34.340 If we're going to have a real uniform energy policy, we need 00:25:34.340 --> 00:25:35.660 to think about everything. 00:25:35.660 --> 00:25:39.320 So, issues of radioactive waste and how to handle 00:25:39.320 --> 00:25:43.290 radioactivity safely are going to come back as being current, 00:25:43.290 --> 00:25:44.490 important topics. 00:25:44.490 --> 00:25:47.180 And so these may be topics that you will, in your 00:25:47.180 --> 00:25:50.340 lifetime, have to deal with, either as a scientist trying 00:25:50.340 --> 00:25:53.420 to come up with new technologies, or as a citizen 00:25:53.420 --> 00:25:57.420 deciding whether having a radioactive plant in your 00:25:57.420 --> 00:25:59.660 hometown is a good idea or not. 00:25:59.660 --> 00:26:02.850 A lot of people are happy about nuclear energy, as long 00:26:02.850 --> 00:26:06.260 as the power plants are nowhere located near them. 00:26:06.260 --> 00:26:09.560 But, these are things that you'll have to face, and you 00:26:09.560 --> 00:26:12.130 probably will be voting on this in the future, if not 00:26:12.130 --> 00:26:13.900 dealing with it directly. 00:26:13.900 --> 00:26:19.770 So that's how you do a problem in this. 00:26:19.770 --> 00:26:23.280 All right, so let's talk about a medical use of 00:26:23.280 --> 00:26:24.690 radioactivity. 00:26:24.690 --> 00:26:28.010 Radioactivity can definitely be our friend, as well as 00:26:28.010 --> 00:26:30.290 something to be concerned about. 00:26:30.290 --> 00:26:33.920 And I think I mentioned this in the first day of class, one 00:26:33.920 --> 00:26:37.990 of the ways that the Chemistry Department has moved to being 00:26:37.990 --> 00:26:40.980 the number one ranked Chemistry Department of U.S. 00:26:40.980 --> 00:26:45.230 News and World Report over the years, is a little extra money 00:26:45.230 --> 00:26:48.770 that came in from the work of -- a patent from Professor 00:26:48.770 --> 00:26:51.720 Alan Davidson that we were able to do some pretty 00:26:51.720 --> 00:26:55.070 exciting things with that money over the years. 00:26:55.070 --> 00:26:59.900 So I always like to mention all the great money-making 00:26:59.900 --> 00:27:03.940 discoveries that occurred using 511-1 material, and this 00:27:03.940 --> 00:27:05.690 is another example. 00:27:05.690 --> 00:27:10.580 So, he used an isotope of technetium, and it's being 00:27:10.580 --> 00:27:17.900 used organ scanning, bone scans, it's one of the leading 00:27:17.900 --> 00:27:19.490 ones for heart imaging. 00:27:19.490 --> 00:27:22.920 It's also been used recently in breast cancer. 00:27:22.920 --> 00:27:28.440 It's estimated 7 million uses annually in the U.S. And so, 00:27:28.440 --> 00:27:33.070 this was patented as cardiolite, and it's really 00:27:33.070 --> 00:27:35.180 just very simple chemistry. 00:27:35.180 --> 00:27:39.240 So you're using a d block metal, an isotope of a d block 00:27:39.240 --> 00:27:42.110 metal, which has your exciting d orbitals. 00:27:42.110 --> 00:27:47.180 And what did he do, he made a coordination complex with that 00:27:47.180 --> 00:27:51.070 metal, an isotope of it, and he found ligands, cyanide 00:27:51.070 --> 00:27:53.770 ligands, those are pretty common ligands. 00:27:53.770 --> 00:27:56.410 You've seen a lot of coordination complexes with 00:27:56.410 --> 00:27:59.530 cyanide ligands, and he tried different ligands to get the 00:27:59.530 --> 00:28:04.090 desired properties of stability and solubility, and 00:28:04.090 --> 00:28:05.410 that's all it was. 00:28:05.410 --> 00:28:08.980 So he used some knowledge of radioactivity, knowledge of 00:28:08.980 --> 00:28:12.190 inorganic chemistry -- he was an inorganic chemist, he's 00:28:12.190 --> 00:28:13.310 retired now. 00:28:13.310 --> 00:28:17.340 And simple coordination chemistry, and made an 00:28:17.340 --> 00:28:21.110 enormous amount of money for MIT, and particularly, the 00:28:21.110 --> 00:28:24.000 Chemistry Department, and also, this has 00:28:24.000 --> 00:28:26.160 saved a lot of lives. 00:28:26.160 --> 00:28:28.710 So, imaging is something that chemists 00:28:28.710 --> 00:28:30.460 do a lot of, actually. 00:28:30.460 --> 00:28:35.110 Not just imaging for cancer or imaging of organs, but also 00:28:35.110 --> 00:28:38.470 imaging of live cells to try to understand how the cell 00:28:38.470 --> 00:28:40.090 works when it's healthy. 00:28:40.090 --> 00:28:43.840 And so recently, Professor Alice Ting, in the Chemistry 00:28:43.840 --> 00:28:49.630 Department, received an NIH pioneer award, NIH is National 00:28:49.630 --> 00:28:52.400 Institutes of Health, and started giving these pioneer 00:28:52.400 --> 00:28:56.740 awards for people coming up with very innovative ideas, 00:28:56.740 --> 00:29:00.870 the kind of innovative ideas that most people would not 00:29:00.870 --> 00:29:03.150 want to fund, because there's a good chance it might not 00:29:03.150 --> 00:29:05.740 work, but if it did, it would be spectacular. 00:29:05.740 --> 00:29:09.490 So she received one of these awards for trying to develop 00:29:09.490 --> 00:29:13.360 technology to image protein-protein interactions 00:29:13.360 --> 00:29:16.120 in living cells, which is something that people would 00:29:16.120 --> 00:29:17.930 really, really love to be able to do. 00:29:17.930 --> 00:29:20.520 And so she is involved in developing technology. 00:29:20.520 --> 00:29:23.480 So developing of imaging tools is something that a lot of 00:29:23.480 --> 00:29:26.590 chemists do, it's a very popular area in chemistry. 00:29:26.590 --> 00:29:28.380 And if it's something that you're interested in, there's 00:29:28.380 --> 00:29:31.020 definitely a lot of people around that you could think 00:29:31.020 --> 00:29:33.290 about working with for a UROP position. 00:29:33.290 --> 00:29:37.960 OK, so that is first order. 00:29:37.960 --> 00:29:41.400 And now let's go on and talk about second order 00:29:41.400 --> 00:29:43.290 integrated rate laws. 00:29:43.290 --> 00:29:45.670 And we're going to have a little derivation for you, I 00:29:45.670 --> 00:29:48.380 always like to warn people that it's coming, because all 00:29:48.380 --> 00:29:51.830 of a sudden equations are coming in and out, and you 00:29:51.830 --> 00:29:55.280 just want to know where these equations are coming from. 00:29:55.280 --> 00:29:59.640 So, as we talked about last time, this is an expression 00:29:59.640 --> 00:30:00.790 for rate law. 00:30:00.790 --> 00:30:03.480 You have your rate constant, your concentration of 00:30:03.480 --> 00:30:07.380 something, a, and it's raised to a coefficient, and here 00:30:07.380 --> 00:30:09.960 that coefficient is 2, indicating it's a 00:30:09.960 --> 00:30:12.700 second order process. 00:30:12.700 --> 00:30:17.140 So if there's nothing up there, that's 1. 00:30:17.140 --> 00:30:21.840 And then 2, and again, the order of the reaction can be 00:30:21.840 --> 00:30:25.640 positive, negative, it can be integers, it can be fractions. 00:30:25.640 --> 00:30:29.420 But this is second order, so we have 2. 00:30:29.420 --> 00:30:32.710 Now, as we did with the first order expression, we're going 00:30:32.710 --> 00:30:36.560 to separate our concentration terms and our time terms. So 00:30:36.560 --> 00:30:39.240 we're going to bring our concentration term over to one 00:30:39.240 --> 00:30:42.610 side, another concentration term here, and we're going to 00:30:42.610 --> 00:30:47.400 have our rate constant and our time term on the other side. 00:30:47.400 --> 00:30:49.640 And now we're going to integrate, because it is an 00:30:49.640 --> 00:30:51.420 integrated rate law. 00:30:51.420 --> 00:30:55.030 So we can integrate from the original concentration of a to 00:30:55.030 --> 00:30:59.760 the concentration of a at some time, t, and then we'll also 00:30:59.760 --> 00:31:02.740 integrate from zero time to that time, t, 00:31:02.740 --> 00:31:04.460 on the other side. 00:31:04.460 --> 00:31:06.880 Now, I'm going to take this expression and just bring it 00:31:06.880 --> 00:31:09.490 up to the top of the page, so that's the exact same 00:31:09.490 --> 00:31:11.590 expression, nothing has happened. 00:31:11.590 --> 00:31:14.170 And now we're going to solve that integral. 00:31:14.170 --> 00:31:17.550 So we can solve that integral, and if you want to look at 00:31:17.550 --> 00:31:20.730 these -- the back of your textbook has all of these 00:31:20.730 --> 00:31:23.950 conversions, if you want to look at them. 00:31:23.950 --> 00:31:26.400 So, we're going to solve that integral, now we have minus 00:31:26.400 --> 00:31:31.040 parentheses 1 over the concentration of a at some 00:31:31.040 --> 00:31:34.150 time, t, minus 1 over the original concentration 00:31:34.150 --> 00:31:36.940 equals minus k t. 00:31:36.940 --> 00:31:40.560 We can get rid of some of these minus signs. 00:31:40.560 --> 00:31:46.110 So we're going to bring the concentration of time, t, over 00:31:46.110 --> 00:31:49.050 on this side, we have our k t, and now we have this other 00:31:49.050 --> 00:31:51.940 term, the original concentration term is on the 00:31:51.940 --> 00:31:57.950 other side, and this is expressed in a certain way 00:31:57.950 --> 00:32:01.720 that gives you the equation for a straight line. 00:32:01.720 --> 00:32:05.530 And again, kinetics, you need experimental data for 00:32:05.530 --> 00:32:08.630 kinetics, and so when you measure your data, you plot 00:32:08.630 --> 00:32:11.800 your data, and so there's a lot of equations for straight 00:32:11.800 --> 00:32:14.450 lines that you have, because it's all about trying to plot 00:32:14.450 --> 00:32:19.910 data, and figure out what the order is experimentally. 00:32:19.910 --> 00:32:24.090 So, here's an equation for a straight line, and we can plot 00:32:24.090 --> 00:32:59.750 this, and you can tell me what the intercept of this line is. 00:32:59.750 --> 00:33:13.020 OK, let's just take 10 more seconds. 00:33:13.020 --> 00:33:17.680 Yup, so all of you know how to analyze the equation for a 00:33:17.680 --> 00:33:20.990 straight line. 00:33:20.990 --> 00:33:26.650 So, here we have 1 over the original concentration, and 00:33:26.650 --> 00:33:32.980 then our slope is equal to what here? k. 00:33:32.980 --> 00:33:36.500 So, you can plot your data as your concentration of a 00:33:36.500 --> 00:33:37.610 changes with time. 00:33:37.610 --> 00:33:41.640 You can plot the data, and if the data, if it's plotted as 1 00:33:41.640 --> 00:33:44.700 over the concentration of a versus time and it gives you a 00:33:44.700 --> 00:33:47.250 straight line, that's consistent with it being a 00:33:47.250 --> 00:33:50.940 second order process. 00:33:50.940 --> 00:33:54.700 So, in terms of second order half life, we talked about 00:33:54.700 --> 00:33:59.590 first order half life, and for any half life, it's just the 00:33:59.590 --> 00:34:04.530 time it takes for half of the original material to go away. 00:34:04.530 --> 00:34:08.940 So we can rewrite this and take a to the t, and 00:34:08.940 --> 00:34:13.100 substitute in the original concentration divided by 2, 00:34:13.100 --> 00:34:18.080 and then we can have t have a special name t 1/2, so that's 00:34:18.080 --> 00:34:19.500 the half life. 00:34:19.500 --> 00:34:23.410 And now we can just simplify this expression. 00:34:23.410 --> 00:34:26.770 We can bring the 2 up here, and now we can combine our 00:34:26.770 --> 00:34:28.970 concentration terms on the side. 00:34:28.970 --> 00:34:32.890 So we take 2, we bring this over, minus 1. 00:34:32.890 --> 00:34:37.440 And that simplifies 1 over the concentration of the original 00:34:37.440 --> 00:34:40.720 material here. 00:34:40.720 --> 00:34:44.940 And now we can solve for it in terms of the half life. 00:34:44.940 --> 00:34:49.760 So the half life for a second order process equals 1 over k 00:34:49.760 --> 00:34:54.780 times the original concentration of the material. 00:34:54.780 --> 00:35:01.140 So, a second order half life depends on the starting 00:35:01.140 --> 00:35:02.640 concentration. 00:35:02.640 --> 00:35:05.460 So that's very different from a first order half life 00:35:05.460 --> 00:35:10.260 process where concentration term cancels out entirely. 00:35:10.260 --> 00:35:14.480 So for a first order process, the concentration of the 00:35:14.480 --> 00:35:19.280 original material does not affect the half life, or for 00:35:19.280 --> 00:35:23.010 radioactive decay, the original number of nuclei -- 00:35:23.010 --> 00:35:25.950 it's independent of how many nuclei were 00:35:25.950 --> 00:35:27.300 around at the time. 00:35:27.300 --> 00:35:30.960 But for second order process, the starting concentration 00:35:30.960 --> 00:35:36.160 does matter. 00:35:36.160 --> 00:35:38.920 So again, chemistry is experimental. 00:35:38.920 --> 00:35:41.870 And so what you would be doing in a lab, you would be trying 00:35:41.870 --> 00:35:45.720 to figure out what the order of the reaction is, and so you 00:35:45.720 --> 00:35:47.080 could try out your data. 00:35:47.080 --> 00:35:50.130 You say I don't know if it's first or second order, so for 00:35:50.130 --> 00:35:53.200 a first order plot, you're going to be plotting the 00:35:53.200 --> 00:35:56.600 natural log of your concentrations versus time, 00:35:56.600 --> 00:35:59.680 and if second order, you plot 1 over the concentration 00:35:59.680 --> 00:36:00.730 versus time. 00:36:00.730 --> 00:36:04.250 And so you could plot your data and see that oh, look at 00:36:04.250 --> 00:36:08.040 this, it fits a straight line really well if I plot it as 1 00:36:08.040 --> 00:36:09.680 over the concentration. 00:36:09.680 --> 00:36:13.170 If I plot it as the natural log versus time, the data 00:36:13.170 --> 00:36:14.850 doesn't fit a straight line at all. 00:36:14.850 --> 00:36:18.700 So this is not a first order process, this is much more 00:36:18.700 --> 00:36:21.230 consistent with a second order process. 00:36:21.230 --> 00:36:24.550 So again, figuring out where something is first order or 00:36:24.550 --> 00:36:31.850 second order is done experimentally. 00:36:31.850 --> 00:36:32.280 All right. 00:36:32.280 --> 00:36:35.110 Now we're going to talk about kinetics 00:36:35.110 --> 00:36:37.330 and equilibrium constants. 00:36:37.330 --> 00:36:40.740 So, I always get very excited, as you know, when we come back 00:36:40.740 --> 00:36:45.660 to equilibrium constants, so am always very happy at this 00:36:45.660 --> 00:36:48.370 time in the course when we can relate kinetics and 00:36:48.370 --> 00:36:50.690 equilibrium constants. 00:36:50.690 --> 00:36:53.580 So, at equilibrium, another way to think about what's 00:36:53.580 --> 00:36:56.960 happening at equilibrium, is that the rate of the forward 00:36:56.960 --> 00:37:01.210 reaction and the rate of the reverse reaction are equal to 00:37:01.210 --> 00:37:04.310 each other. 00:37:04.310 --> 00:37:08.470 So, we can now talk about big letter K, which is our 00:37:08.470 --> 00:37:11.780 equilibrium constant again, and our little letter k's, 00:37:11.780 --> 00:37:13.730 which our rate constant. 00:37:13.730 --> 00:37:17.670 So the equilibrium constant for a chemical reaction a plus 00:37:17.670 --> 00:37:21.600 b equals c plus d is going to be equal to what, what do I 00:37:21.600 --> 00:37:25.560 put on the top? 00:37:25.560 --> 00:37:31.070 Concentration of? c, and concentration of d, right. 00:37:31.070 --> 00:37:34.570 So our products, and at the bottom we put our 00:37:34.570 --> 00:37:41.180 concentration of our reactants, or a and b. 00:37:41.180 --> 00:37:47.210 Now, we can also think about this reaction in terms of 00:37:47.210 --> 00:37:50.090 little rate constants. 00:37:50.090 --> 00:37:56.330 So we have small letter k 1 on top, and small letter k to the 00:37:56.330 --> 00:37:59.070 minus 1 on the bottom. 00:37:59.070 --> 00:38:03.100 So, the forward reaction, the rate of forward reaction is 00:38:03.100 --> 00:38:08.440 going to be equal to k 1 times the concentration of a and the 00:38:08.440 --> 00:38:11.740 concentration of b. 00:38:11.740 --> 00:38:16.600 And on the bottom, our rate is going to be equal to the 00:38:16.600 --> 00:38:20.120 little rate constant, so for the reverse reaction it's the 00:38:20.120 --> 00:38:23.730 reverse rate constant, k minus 1, and in the reverse 00:38:23.730 --> 00:38:27.440 direction, our reactants are the products for the forward 00:38:27.440 --> 00:38:32.780 direction, or c and d. 00:38:32.780 --> 00:38:37.610 So, here we have these rates, and at equilibrium, those 00:38:37.610 --> 00:38:39.220 rates are going to be equal. 00:38:39.220 --> 00:38:43.300 So at equilibrium, little k 1, a times b is going to be equal 00:38:43.300 --> 00:38:47.890 to little k minus 1 times c times d. 00:38:47.890 --> 00:38:59.460 And at equilibrium we had c d over a b is equal to then k 1 00:38:59.460 --> 00:39:04.290 over k minus 1, so if we just rearrange this expression and 00:39:04.290 --> 00:39:08.250 move the rate constants to one side and concentration terms 00:39:08.250 --> 00:39:11.210 to the other side, this expression is the same as this 00:39:11.210 --> 00:39:15.210 expression, and we also know what this expression is equal 00:39:15.210 --> 00:39:20.800 to, which is our big K. So, therefore, our equilibrium 00:39:20.800 --> 00:39:23.840 constant equals the rate constant for the forward 00:39:23.840 --> 00:39:26.700 reaction over the rate constant 00:39:26.700 --> 00:39:29.660 for the reverse direction. 00:39:29.660 --> 00:39:32.780 And so here is an expression that compares equilibrium 00:39:32.780 --> 00:39:37.920 constants with rate constants. 00:39:37.920 --> 00:39:41.760 So now, let's think about what is true about this. 00:39:41.760 --> 00:39:44.800 So our equilibrium constant, then, is the ratio or the 00:39:44.800 --> 00:39:48.000 forward rate over the reverse rate for 00:39:48.000 --> 00:39:51.690 these elementary reactions. 00:39:51.690 --> 00:39:55.880 And if we think about rate constants in kinetics terms, 00:39:55.880 --> 00:39:59.380 if k is greater than 1, if there are more products than 00:39:59.380 --> 00:40:03.920 reactants at equilibrium, what's true about k 00:40:03.920 --> 00:40:06.560 1 and k minus 1? 00:40:06.560 --> 00:40:12.670 Is k 1 greater than or less than k minus 1? 00:40:12.670 --> 00:40:13.820 Right. 00:40:13.820 --> 00:40:17.100 So the forward rate constant is greater than the reverse 00:40:17.100 --> 00:40:19.410 rate constant. 00:40:19.410 --> 00:40:23.810 And if K, big equilibrium constant, K is less than 1, if 00:40:23.810 --> 00:40:28.690 at equilibrium there are more reactants than products, what 00:40:28.690 --> 00:40:33.240 is true about this relationship? 00:40:33.240 --> 00:40:35.590 It would be less than. 00:40:35.590 --> 00:40:39.070 So, you can think about equilibrium constants now in 00:40:39.070 --> 00:40:42.070 terms of rate constants, which we'll be doing a lot on 00:40:42.070 --> 00:40:43.870 Wednesday, too. 00:40:43.870 --> 00:40:44.980 All right. 00:40:44.980 --> 00:40:48.920 So let me introduce you to a couple of more terms in the 00:40:48.920 --> 00:40:50.270 last few minutes. 00:40:50.270 --> 00:40:53.990 So reactions don't usually occur in one step, but occur 00:40:53.990 --> 00:40:55.820 in a series of steps. 00:40:55.820 --> 00:41:02.070 Each step is called an elementary reaction. 00:41:02.070 --> 00:41:07.340 So, the overall reaction, the order and the rate law, can be 00:41:07.340 --> 00:41:13.180 derived from the stoichiometry for an overall reaction, you 00:41:13.180 --> 00:41:16.370 can't use the stoichiometry, but for an elementary 00:41:16.370 --> 00:41:18.000 reaction you can. 00:41:18.000 --> 00:41:21.120 So, for an elementary reaction, say one step in the 00:41:21.120 --> 00:41:25.010 reaction mechanism, that step occurs exactly as written so 00:41:25.010 --> 00:41:27.750 you can use stoichiometry. 00:41:27.750 --> 00:41:31.190 And that's going to be handy in coming up with mechanisms. 00:41:31.190 --> 00:41:35.010 So, let's just look at one example very briefly. 00:41:35.010 --> 00:41:38.780 So here we have the decomposition of ozone, which 00:41:38.780 --> 00:41:42.790 is another environmental issue that you will be faced with in 00:41:42.790 --> 00:41:45.760 your lifetime. 00:41:45.760 --> 00:41:49.940 So this is the overall reaction, and you can't use 00:41:49.940 --> 00:41:53.160 the stoiciomery to figure out the order of the reaction, but 00:41:53.160 --> 00:41:56.760 if you divide it up into elementary reaction steps, 00:41:56.760 --> 00:42:01.000 then you can use the stoiciomery to write the rate 00:42:01.000 --> 00:42:04.920 law for each step of that reaction. 00:42:04.920 --> 00:42:08.740 So, the first step here is a unimolecular step. 00:42:08.740 --> 00:42:15.130 You have one thing going to two things, and molecularity 00:42:15.130 --> 00:42:18.760 is the number of reactant molecules the come together to 00:42:18.760 --> 00:42:20.060 form product. 00:42:20.060 --> 00:42:24.410 So, unimolecular you just have one thing that's forming some 00:42:24.410 --> 00:42:26.020 kind of product. 00:42:26.020 --> 00:42:28.350 What do you think it's called if you have two 00:42:28.350 --> 00:42:32.260 things forming a product? 00:42:32.260 --> 00:42:34.030 Bimolecular. 00:42:34.030 --> 00:42:37.460 These are good little one or two point questions on a test, 00:42:37.460 --> 00:42:40.660 they're not very hard, they should be pretty 00:42:40.660 --> 00:42:42.410 easy to think about. 00:42:42.410 --> 00:42:46.110 So, we have unimolecular, examples would be some kind of 00:42:46.110 --> 00:42:48.800 decomposition or radioactive decay. 00:42:48.800 --> 00:42:50.930 Bimolecular, two reactants coming 00:42:50.930 --> 00:42:52.740 together to form products. 00:42:52.740 --> 00:42:57.040 And termolecular is three reactants coming together to 00:42:57.040 --> 00:43:00.770 form a product, and that's rare. 00:43:00.770 --> 00:43:03.930 And you can remember that it's rare if you think about how 00:43:03.930 --> 00:43:07.120 you would hold three tennis balls in your hand and have 00:43:07.120 --> 00:43:10.620 them all come together at the same time to form product, 00:43:10.620 --> 00:43:12.530 that is a difficult thing to do. 00:43:12.530 --> 00:43:14.750 Two things coming together is easy, 00:43:14.750 --> 00:43:16.800 bimolecular is very common. 00:43:16.800 --> 00:43:21.220 Termolecular not very common, that they'd all come together 00:43:21.220 --> 00:43:25.090 at the same time to form a product. 00:43:25.090 --> 00:43:32.310 All right, so we can write rate laws for each step here. 00:43:32.310 --> 00:43:36.000 For the first step here, the rate would be equal to a k -- 00:43:36.000 --> 00:43:38.490 I don't have the k written up here, but there's always going 00:43:38.490 --> 00:43:40.850 to be a little k over the arrow. 00:43:40.850 --> 00:43:44.770 So, k times the reactant would be here. 00:43:44.770 --> 00:43:48.740 For bimolecular, again, assume a k over there. 00:43:48.740 --> 00:44:13.910 What's that rate going to be equal to? 00:44:13.910 --> 00:44:16.890 OK, let's just take 10 more seconds since 00:44:16.890 --> 00:44:27.900 class is almost over. 00:44:27.900 --> 00:44:34.700 Yup, so it's this one right down here. 00:44:34.700 --> 00:44:37.970 So we have the rate is equal to k 00:44:37.970 --> 00:44:39.370 times these two reactants. 00:44:39.370 --> 00:44:43.760 You can sum up the steps and get the overall reactants. 00:44:43.760 --> 00:44:47.300 Notice that o is an intermediate, it's formed 00:44:47.300 --> 00:44:48.920 here, decayed here. 00:44:48.920 --> 00:44:53.070 It goes away, and so o doesn't appear in the overall 00:44:53.070 --> 00:44:54.250 expression. 00:44:54.250 --> 00:44:56.190 So we're going to talk a lot about reaction 00:44:56.190 --> 00:44:58.700 intermediates next time. 00:44:58.700 --> 00:45:01.730 And also, remember that you can't prove reaction 00:45:01.730 --> 00:45:05.700 mechanisms to be correct, they're just consistent with 00:45:05.700 --> 00:45:07.720 the data that you have.