1 00:00:00,030 --> 00:00:02,400 The following content is provided under a Creative 2 00:00:02,400 --> 00:00:03,780 Commons license. 3 00:00:03,780 --> 00:00:06,020 Your support will help MIT OpenCourseWare 4 00:00:06,020 --> 00:00:10,100 continue to offer high-quality educational resources for free. 5 00:00:10,100 --> 00:00:12,660 To make a donation or to view additional materials 6 00:00:12,660 --> 00:00:16,580 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,580 --> 00:00:17,250 at ocw.mit.edu. 8 00:00:25,842 --> 00:00:27,050 CATHERINE DRENNAN: All right. 9 00:00:27,050 --> 00:00:30,390 So enzymes, of course, are catalysts, 10 00:00:30,390 --> 00:00:34,240 and that leads us to our next unit, which is kinetics. 11 00:00:34,240 --> 00:00:36,560 And it's our next unit and, in fact, 12 00:00:36,560 --> 00:00:38,160 our last unit of the semester. 13 00:00:38,160 --> 00:00:40,792 So we're going to be talking about kinetics for the rest 14 00:00:40,792 --> 00:00:42,750 of the semester, which sounds like a long time, 15 00:00:42,750 --> 00:00:44,091 but it really isn't. 16 00:00:44,091 --> 00:00:44,590 All right. 17 00:00:44,590 --> 00:00:48,260 So we'll switch to today's handout. 18 00:00:48,260 --> 00:00:51,310 So kinetics and thermodynamics is a sort of yin-yang. 19 00:00:51,310 --> 00:00:55,240 You really have to think about both of them at the same time. 20 00:00:55,240 --> 00:00:58,090 So when you're thinking about whether a reaction will 21 00:00:58,090 --> 00:01:03,190 go forward spontaneously, you're thinking about thermodynamics. 22 00:01:03,190 --> 00:01:06,180 And you're thinking about how fast that reaction is 23 00:01:06,180 --> 00:01:10,080 going to go, you're thinking about kinetics. 24 00:01:10,080 --> 00:01:12,380 So let's just do a little review. 25 00:01:12,380 --> 00:01:15,530 We've talked about this before, but it's a clicker challenge. 26 00:01:15,530 --> 00:01:20,750 So today, let's think back to thermodynamics and tell me 27 00:01:20,750 --> 00:01:25,780 what stable/unstable refers to, thinking about thermodynamics 28 00:01:25,780 --> 00:01:27,100 and kinetics now. 29 00:01:47,620 --> 00:01:48,767 OK, 10 more seconds. 30 00:02:06,030 --> 00:02:08,190 OK. 31 00:02:08,190 --> 00:02:11,840 So most people got stability. 32 00:02:11,840 --> 00:02:13,620 When you're talking about stable/unstable, 33 00:02:13,620 --> 00:02:15,340 you're not talking about rate. 34 00:02:15,340 --> 00:02:17,920 You are talking about delta G. You're 35 00:02:17,920 --> 00:02:21,000 talking about the spontaneous tendency. 36 00:02:21,000 --> 00:02:23,200 A chemist, if it's around a long time, 37 00:02:23,200 --> 00:02:27,080 would talk about it not being stable, but being inert. 38 00:02:27,080 --> 00:02:32,120 And in terms of this one here, if you're 39 00:02:32,120 --> 00:02:34,670 thinking about the delta G for the decomposition 40 00:02:34,670 --> 00:02:40,350 into its elements, that versus the delta G for formation, 41 00:02:40,350 --> 00:02:43,500 if that's negative then it would be stable. 42 00:02:43,500 --> 00:02:47,241 But we want to be positive for the decomposition. 43 00:02:47,241 --> 00:02:47,740 All right. 44 00:02:47,740 --> 00:02:49,670 So let's just look at this up here. 45 00:02:49,670 --> 00:02:56,600 So again, it refers to delta G. And labile and inert 46 00:02:56,600 --> 00:02:58,310 refers to the rate. 47 00:02:58,310 --> 00:03:01,650 And again, when you have a negative delta G of formation, 48 00:03:01,650 --> 00:03:05,080 then that makes something stable. 49 00:03:05,080 --> 00:03:06,160 OK. 50 00:03:06,160 --> 00:03:09,050 So thermodynamics, kinetics. 51 00:03:09,050 --> 00:03:12,280 We want to think about, is the reaction spontaneous? 52 00:03:12,280 --> 00:03:16,670 But we also need to think about how long it's going to take. 53 00:03:16,670 --> 00:03:18,660 So rate is important. 54 00:03:18,660 --> 00:03:25,210 And so if we think about the average rate of a Ferris 55 00:03:25,210 --> 00:03:27,790 wheel-- I looked it up. 56 00:03:27,790 --> 00:03:31,960 It is 31.4 seconds to spin around 57 00:03:31,960 --> 00:03:33,790 if you're at an amusement park. 58 00:03:33,790 --> 00:03:38,140 And you can think about your experience-- or sorry, that 59 00:03:38,140 --> 00:03:41,900 should say imagine-- one revolution for every 5 seconds 60 00:03:41,900 --> 00:03:45,200 or every 5 hours would be a very different experience. 61 00:03:45,200 --> 00:03:46,912 Five seconds would be way too fast. 62 00:03:46,912 --> 00:03:48,620 You'd probably be throwing up everywhere. 63 00:03:48,620 --> 00:03:51,000 In 5 hours, you'd be like, oh, my goodness, 64 00:03:51,000 --> 00:03:52,600 get me off of this thing. 65 00:03:52,600 --> 00:03:55,320 So rate matters. 66 00:03:55,320 --> 00:03:58,600 And chemical kinetics doesn't measure 67 00:03:58,600 --> 00:04:01,180 the rate of Ferris wheels, except maybe it does 68 00:04:01,180 --> 00:04:03,190 if the ferrous is ferrous iron. 69 00:04:03,190 --> 00:04:05,530 Then we might be talking about its rate 70 00:04:05,530 --> 00:04:09,140 if it's spinning around doing things in a chemical reaction. 71 00:04:09,140 --> 00:04:12,020 So we might think about the concentration of ferrous iron 72 00:04:12,020 --> 00:04:14,260 changing with time. 73 00:04:14,260 --> 00:04:16,130 So chemical kinetics experiments, 74 00:04:16,130 --> 00:04:19,790 you measure concentrations and think about how fast they're 75 00:04:19,790 --> 00:04:21,880 changing with time. 76 00:04:21,880 --> 00:04:24,020 So let's think about some of the factors that 77 00:04:24,020 --> 00:04:27,710 are going to affect the rates of chemical reactions, 78 00:04:27,710 --> 00:04:30,630 and we'll write some of these on the board. 79 00:04:30,630 --> 00:04:33,720 So what's one thing that you may have observed 80 00:04:33,720 --> 00:04:37,280 that will affect, either speed up or slow down, say, 81 00:04:37,280 --> 00:04:38,880 a chemical reaction? 82 00:04:38,880 --> 00:04:40,494 What's one thing you can think of? 83 00:04:40,494 --> 00:04:41,410 AUDIENCE: Temperature. 84 00:04:41,410 --> 00:04:42,701 CATHERINE DRENNAN: Temperature. 85 00:04:47,160 --> 00:04:48,743 What's another thing you can think of? 86 00:04:48,743 --> 00:04:50,675 AUDIENCE: [INAUDIBLE]. 87 00:04:50,675 --> 00:04:51,887 AUDIENCE: Catalysts. 88 00:04:51,887 --> 00:04:53,095 CATHERINE DRENNAN: Catalysts. 89 00:04:57,320 --> 00:05:00,450 So right, so changing the sort of environment. 90 00:05:00,450 --> 00:05:02,510 So it depends a little. 91 00:05:02,510 --> 00:05:03,570 It could be pressure. 92 00:05:03,570 --> 00:05:08,000 It depends on what you're talking about, 93 00:05:08,000 --> 00:05:11,490 what kind of nature of material you're talking about. 94 00:05:11,490 --> 00:05:15,090 So possibly pressure could have an effect. 95 00:05:15,090 --> 00:05:23,680 And that brings us to the nature of the material, 96 00:05:23,680 --> 00:05:27,540 whether it's gas or solid or other things. 97 00:05:27,540 --> 00:05:30,140 And that also comes to the other issue, which 98 00:05:30,140 --> 00:05:32,714 is, what is its mechanism? 99 00:05:32,714 --> 00:05:35,860 Oops, sorry, mechanism. 100 00:05:35,860 --> 00:05:37,350 So does it have one step? 101 00:05:37,350 --> 00:05:38,550 Does it have many steps? 102 00:05:38,550 --> 00:05:40,830 Do the steps involve changes in phase? 103 00:05:40,830 --> 00:05:43,380 What's going on in the mechanism? 104 00:05:43,380 --> 00:05:45,850 And so those are all some good things. 105 00:05:45,850 --> 00:05:47,410 One other thing that I'll put on, 106 00:05:47,410 --> 00:05:50,930 which also only applies in some cases, 107 00:05:50,930 --> 00:05:54,090 depending on the type of mechanism and type of reaction, 108 00:05:54,090 --> 00:05:58,940 would be the concentration of the material, which kind of 109 00:05:58,940 --> 00:06:02,810 also gets to this pressure idea, depending on what it is. 110 00:06:02,810 --> 00:06:05,860 How much do you have in there? 111 00:06:05,860 --> 00:06:06,360 All right. 112 00:06:06,360 --> 00:06:08,109 So those are some of the things, and we're 113 00:06:08,109 --> 00:06:11,790 going to talk about most of these in the next unit. 114 00:06:11,790 --> 00:06:12,390 All right. 115 00:06:12,390 --> 00:06:20,900 So let's now think about one example of a chemical reaction, 116 00:06:20,900 --> 00:06:23,700 and this chemical reaction is called the oscillating clock. 117 00:06:23,700 --> 00:06:25,510 And before we see the demo, we're 118 00:06:25,510 --> 00:06:27,490 going to think about what's happening. 119 00:06:27,490 --> 00:06:31,790 So this demo, as with most chemical reactions, 120 00:06:31,790 --> 00:06:35,880 involves thermodynamics, chemical equilibrium, kinetics. 121 00:06:35,880 --> 00:06:37,550 It also has some acid-base. 122 00:06:37,550 --> 00:06:40,250 You have to have some acid in there to get it to go. 123 00:06:40,250 --> 00:06:42,820 It's also an oxidation-reduction reaction. 124 00:06:42,820 --> 00:06:46,450 And it has colors, and we'll see that the colors change 125 00:06:46,450 --> 00:06:48,900 depending on what the oxidation state of the material 126 00:06:48,900 --> 00:06:51,810 is and also what its liganded state is. 127 00:06:51,810 --> 00:06:54,760 So basically, in one demo, you get every unit 128 00:06:54,760 --> 00:06:56,890 that we've had in the second half of the course. 129 00:06:56,890 --> 00:06:59,130 And that's kind of true about any chemical reaction. 130 00:06:59,130 --> 00:07:01,540 Every chemical reaction, if you're interested in it, 131 00:07:01,540 --> 00:07:03,680 involves thinking about all of these things 132 00:07:03,680 --> 00:07:06,071 that we've been talking about. 133 00:07:06,071 --> 00:07:06,570 All right. 134 00:07:06,570 --> 00:07:10,150 So oscillating clock reaction. 135 00:07:10,150 --> 00:07:11,920 It's a fairly complicated reaction. 136 00:07:11,920 --> 00:07:13,880 It has many steps, and we're just 137 00:07:13,880 --> 00:07:16,040 going to break the overall reaction shown 138 00:07:16,040 --> 00:07:18,460 here down into two steps today. 139 00:07:18,460 --> 00:07:21,370 As with many reaction mechanisms, 140 00:07:21,370 --> 00:07:23,550 there are multiple steps. 141 00:07:23,550 --> 00:07:27,320 But here is step 1 that we'll talk about, 142 00:07:27,320 --> 00:07:30,050 and here is step 2 that we'll talk about. 143 00:07:30,050 --> 00:07:35,610 And step 1 occurs when your I2 concentration is low. 144 00:07:35,610 --> 00:07:38,900 I2 here is a product of the reaction, 145 00:07:38,900 --> 00:07:43,310 and when it builds up too much, then that reaction will stop. 146 00:07:43,310 --> 00:07:48,150 And so in this reaction, we have acidic conditions. 147 00:07:48,150 --> 00:07:49,720 You'll see our H+. 148 00:07:49,720 --> 00:07:51,840 And under those acidic conditions, 149 00:07:51,840 --> 00:07:54,640 we're going to change a clear solution-- 150 00:07:54,640 --> 00:08:00,160 so I, iodide, in its certain oxidation states is clear. 151 00:08:00,160 --> 00:08:05,170 But when it goes to I2, it turns an amber color. 152 00:08:05,170 --> 00:08:08,730 In the second reaction, which will only 153 00:08:08,730 --> 00:08:11,710 occur when I2 is high-- so this will build up, 154 00:08:11,710 --> 00:08:15,730 shutting off reaction a and starting reaction b. 155 00:08:15,730 --> 00:08:19,340 In this reaction, you have a complex being formed, 156 00:08:19,340 --> 00:08:21,920 and that's going to change the color. 157 00:08:21,920 --> 00:08:26,190 So we're going to go from amber to a blue complex. 158 00:08:26,190 --> 00:08:26,710 All right. 159 00:08:26,710 --> 00:08:30,030 So before we see this happen-- and I 160 00:08:30,030 --> 00:08:31,790 should say that once you get over here, 161 00:08:31,790 --> 00:08:33,539 you find the blue complex. 162 00:08:33,539 --> 00:08:36,120 This will consume the I2, which will cause 163 00:08:36,120 --> 00:08:38,120 that to drop to be low again. 164 00:08:38,120 --> 00:08:40,570 And then you're going to start reaction a again, 165 00:08:40,570 --> 00:08:45,950 which, when your concentration's built up too much, 166 00:08:45,950 --> 00:08:47,790 you'll start reaction b again. 167 00:08:47,790 --> 00:08:51,800 And so reaction a, then reaction b, then reaction a, reaction b. 168 00:08:51,800 --> 00:08:55,380 And you'll notice that the product of one of the reactions 169 00:08:55,380 --> 00:08:58,630 is a substrate here, product here, substrate here. 170 00:08:58,630 --> 00:09:00,450 So this goes back and forth, hence the name 171 00:09:00,450 --> 00:09:01,420 oscillating clock. 172 00:09:01,420 --> 00:09:01,920 All right. 173 00:09:01,920 --> 00:09:03,580 So before I show you something pretty, 174 00:09:03,580 --> 00:09:05,260 I'm going to make you do work and think 175 00:09:05,260 --> 00:09:08,430 about the oxidation-reduction reactions that are occurring 176 00:09:08,430 --> 00:09:09,910 that you're going to see that lead 177 00:09:09,910 --> 00:09:12,560 to these specular color changes. 178 00:09:12,560 --> 00:09:13,090 All right. 179 00:09:13,090 --> 00:09:16,760 So here we go, clicker question. 180 00:09:37,249 --> 00:09:38,957 All right, let's just do 10 more seconds. 181 00:09:55,420 --> 00:09:56,420 All right. 182 00:09:56,420 --> 00:09:58,340 So somebody asked once, like, how 183 00:09:58,340 --> 00:10:00,430 will I know that it's a peroxide? 184 00:10:00,430 --> 00:10:02,310 So I tried to help you out and said reaction 185 00:10:02,310 --> 00:10:04,110 with hydrogen peroxide. 186 00:10:04,110 --> 00:10:06,780 Let's see how many people-- some people definitely noticed that. 187 00:10:06,780 --> 00:10:07,280 All right. 188 00:10:07,280 --> 00:10:09,570 So let's just take a look over here at what's going on 189 00:10:09,570 --> 00:10:11,480 and fill in our chart. 190 00:10:11,480 --> 00:10:15,820 So here the oxidation state is plus 5. 191 00:10:15,820 --> 00:10:19,920 So we have now this oxygen is its normal minus 2. 192 00:10:19,920 --> 00:10:24,630 So minus 2 times 3 minus 6 equals the whole thing. 193 00:10:24,630 --> 00:10:26,680 Charge needs to equal minus 1. 194 00:10:26,680 --> 00:10:29,330 So we need plus 5 there. 195 00:10:29,330 --> 00:10:32,040 And I2 is 0. 196 00:10:32,040 --> 00:10:37,260 The next one, I-, is being oxidized to I2, minus 1 to 0. 197 00:10:37,260 --> 00:10:41,310 The oxygen in hydrogen peroxide is being oxidized. 198 00:10:41,310 --> 00:10:45,300 So it's minus 1 here because we have 199 00:10:45,300 --> 00:10:47,580 plus 2 for H and two oxygens. 200 00:10:47,580 --> 00:10:50,820 So that's minus 1 each to 0. 201 00:10:50,820 --> 00:10:55,490 And then, again, minus 1, and oxygen and water is minus 2. 202 00:10:55,490 --> 00:10:58,600 So there's lots of oxidation-reduction reactions 203 00:10:58,600 --> 00:10:59,450 going on. 204 00:10:59,450 --> 00:11:02,130 And in fact, this occurs in multiple different steps. 205 00:11:02,130 --> 00:11:05,340 So there's even more different reactions going on 206 00:11:05,340 --> 00:11:06,881 that I didn't even show you. 207 00:11:06,881 --> 00:11:07,380 All right. 208 00:11:07,380 --> 00:11:09,160 So we have one more clicker question 209 00:11:09,160 --> 00:11:14,155 to answer before we do the demo, which is that if I told you-- 210 00:11:14,155 --> 00:11:16,194 you want to think about iodide you're using 211 00:11:16,194 --> 00:11:17,360 because it's changing color. 212 00:11:17,360 --> 00:11:20,340 Why are you using the hydrogen peroxide? 213 00:11:20,340 --> 00:11:24,150 So tell me what is true about hydrogen peroxide 214 00:11:24,150 --> 00:11:25,665 using the information given. 215 00:11:46,090 --> 00:11:47,510 All right, 10 more seconds. 216 00:12:03,130 --> 00:12:04,990 All right. 217 00:12:04,990 --> 00:12:09,190 So if we look over here, the large positive value. 218 00:12:09,190 --> 00:12:12,530 And again, it's a large positive value of the standard reduction 219 00:12:12,530 --> 00:12:18,090 potential is a big value, which makes it a good oxidizing 220 00:12:18,090 --> 00:12:18,750 agent. 221 00:12:18,750 --> 00:12:20,370 The reduction is spontaneous. 222 00:12:20,370 --> 00:12:24,780 So if you have a large positive E for the reaction written 223 00:12:24,780 --> 00:12:28,500 as a reduction, that means that delta G for that reduction 224 00:12:28,500 --> 00:12:31,300 is going to be negative, which means it's spontaneous. 225 00:12:31,300 --> 00:12:33,010 So things that like to be reduced 226 00:12:33,010 --> 00:12:34,760 are good oxidizing agents. 227 00:12:34,760 --> 00:12:37,890 Actually, hydrogen peroxide is a really good oxidizing agent, 228 00:12:37,890 --> 00:12:41,030 and that's why it's used in a lot of things. 229 00:12:41,030 --> 00:12:41,530 All right. 230 00:12:41,530 --> 00:12:43,600 So let's look at this demo now. 231 00:12:43,600 --> 00:12:47,430 So again, clear to amber, amber to blue. 232 00:12:47,430 --> 00:12:50,750 And the reaction rate is also sensitive to temperature, 233 00:12:50,750 --> 00:12:53,550 and you told me temperature does affect reaction rates, 234 00:12:53,550 --> 00:12:55,040 and it does in this case. 235 00:12:55,040 --> 00:12:55,540 All right. 236 00:12:55,540 --> 00:12:56,299 Let's see it. 237 00:12:56,299 --> 00:12:56,840 AUDIENCE: OK. 238 00:12:56,840 --> 00:12:58,640 So we've got the hydrogen peroxide. 239 00:12:58,640 --> 00:12:59,806 Eric's got that in his hand. 240 00:12:59,806 --> 00:13:02,821 He's going to take that off before he actually unscrews it. 241 00:13:02,821 --> 00:13:03,320 Yay. 242 00:13:03,320 --> 00:13:04,140 OK. 243 00:13:04,140 --> 00:13:08,579 Hydrogen peroxide, as we said, it gets reduced really easily, 244 00:13:08,579 --> 00:13:11,120 which is actually the reason why we kept it in a plastic bag, 245 00:13:11,120 --> 00:13:15,890 because even the presence of oxygen can cause it to react. 246 00:13:15,890 --> 00:13:17,950 So he's going to add solution b. 247 00:13:17,950 --> 00:13:18,930 That was solution a. 248 00:13:18,930 --> 00:13:21,560 Solution b contains the iodate, which 249 00:13:21,560 --> 00:13:25,002 is going to provide the-- huh? 250 00:13:25,002 --> 00:13:26,210 CATHERINE DRENNAN: Oh, sorry. 251 00:13:26,210 --> 00:13:27,035 AUDIENCE: Yeah, I got it stirring. 252 00:13:27,035 --> 00:13:27,470 CATHERINE DRENNAN: All right. 253 00:13:27,470 --> 00:13:28,080 AUDIENCE: It's going to provide-- 254 00:13:28,080 --> 00:13:29,540 CATHERINE DRENNAN: I forgot to turn this on. 255 00:13:29,540 --> 00:13:31,350 AUDIENCE: --the iodine for the solution. 256 00:13:31,350 --> 00:13:33,750 And as you can see, it's turning kind of yellowish, which 257 00:13:33,750 --> 00:13:34,833 is what we were expecting. 258 00:13:34,833 --> 00:13:38,260 So now the iodate is starting to produce the iodine. 259 00:13:38,260 --> 00:13:43,860 And when he adds solution d, we can see it changing. 260 00:13:43,860 --> 00:13:46,615 Yay, it works. 261 00:13:46,615 --> 00:13:48,990 It's always a struggle whether these things will actually 262 00:13:48,990 --> 00:13:51,517 work, but this one usually works very nicely. 263 00:13:51,517 --> 00:13:53,350 I'm going to turn this up a little bit more. 264 00:13:53,350 --> 00:13:57,095 And it will actually continue to do this 265 00:13:57,095 --> 00:13:58,650 for quite a while, I think, right? 266 00:13:58,650 --> 00:13:59,230 So-- 267 00:13:59,230 --> 00:14:00,230 CATHERINE DRENNAN: Yeah. 268 00:14:00,230 --> 00:14:00,583 AUDIENCE: Yay. 269 00:14:00,583 --> 00:14:01,560 CATHERINE DRENNAN: Awesome. 270 00:14:01,560 --> 00:14:01,970 AUDIENCE: Awesome. 271 00:14:01,970 --> 00:14:03,136 CATHERINE DRENNAN: [LAUGHS]. 272 00:14:03,136 --> 00:14:05,465 [APPLAUSE] 273 00:14:11,189 --> 00:14:13,110 CATHERINE DRENNAN: Yeah. 274 00:14:13,110 --> 00:14:15,397 So we can move this off to the side, 275 00:14:15,397 --> 00:14:17,605 and now we're going to see the effect of temperature. 276 00:14:23,120 --> 00:14:26,230 AUDIENCE: Actually, we'll move that in a second. 277 00:14:26,230 --> 00:14:29,094 So as Cathy mentioned, affecting temperature 278 00:14:29,094 --> 00:14:30,510 will affect the rates of reaction. 279 00:14:30,510 --> 00:14:32,074 So this guy will continue to go. 280 00:14:32,074 --> 00:14:34,240 And what we have here is we have all three solutions 281 00:14:34,240 --> 00:14:37,382 again, except they've been put in ice. 282 00:14:37,382 --> 00:14:38,840 So we're going to see if we've kept 283 00:14:38,840 --> 00:14:39,760 this a little bit cold again. 284 00:14:39,760 --> 00:14:41,259 You should have taken the thing off. 285 00:14:43,350 --> 00:14:43,850 All right. 286 00:14:43,850 --> 00:14:46,076 So that's the peroxide. 287 00:14:46,076 --> 00:14:49,730 We've got solution b. 288 00:14:49,730 --> 00:14:51,630 You got it? 289 00:14:51,630 --> 00:14:54,010 OK. 290 00:14:54,010 --> 00:14:56,893 And yeah, we're going to stir in a second, after b. 291 00:15:00,350 --> 00:15:03,760 So as before, you saw the temperature change kind 292 00:15:03,760 --> 00:15:04,876 of quickly. 293 00:15:04,876 --> 00:15:06,750 This time it's not really changing that much. 294 00:15:21,220 --> 00:15:23,470 So before, you saw temperatures change pretty quickly. 295 00:15:23,470 --> 00:15:25,870 This is probably going to take a while to actually change, 296 00:15:25,870 --> 00:15:27,161 and it might not change at all. 297 00:15:27,161 --> 00:15:29,310 It's because the reaction was so cold that you 298 00:15:29,310 --> 00:15:30,660 won't have that second step. 299 00:15:30,660 --> 00:15:32,620 And also I can't-- there we go. 300 00:15:32,620 --> 00:15:35,010 So it happens really, really slowly, as you can tell, 301 00:15:35,010 --> 00:15:38,060 whereas this one happened very, very quickly. 302 00:15:38,060 --> 00:15:39,236 So yay. 303 00:15:39,236 --> 00:15:40,235 CATHERINE DRENNAN: Yeah. 304 00:15:40,235 --> 00:15:42,080 So example of many things. 305 00:15:42,080 --> 00:15:44,780 So we had chemical equilibrium. 306 00:15:44,780 --> 00:15:46,950 We had thermodynamics, talking about which 307 00:15:46,950 --> 00:15:48,640 reactions were spontaneous. 308 00:15:48,640 --> 00:15:51,870 So spontaneous until making the amber. 309 00:15:51,870 --> 00:15:56,790 And then when it's made too much of the iodide, the I2, 310 00:15:56,790 --> 00:15:58,480 then we see the next reaction going 311 00:15:58,480 --> 00:16:00,180 until we now have too little. 312 00:16:00,180 --> 00:16:01,769 And then we switch back and forth. 313 00:16:01,769 --> 00:16:03,310 And yeah, this, I think, very clearly 314 00:16:03,310 --> 00:16:06,914 demonstrates that the temperature is very different, 315 00:16:06,914 --> 00:16:08,080 has a very different effect. 316 00:16:08,080 --> 00:16:11,330 It's a much, much slower reaction. 317 00:16:11,330 --> 00:16:12,210 All right. 318 00:16:12,210 --> 00:16:12,880 Thank you. 319 00:16:12,880 --> 00:16:15,100 We can leave them-- do you want to just leave them up here? 320 00:16:15,100 --> 00:16:15,920 AUDIENCE: I"m going to leave this one up here. 321 00:16:15,920 --> 00:16:16,080 CATHERINE DRENNAN: Yeah, OK. 322 00:16:16,080 --> 00:16:17,496 We'll leave the fast one up there. 323 00:16:17,496 --> 00:16:19,450 It will eventually stop. 324 00:16:19,450 --> 00:16:23,660 So it's good probably, I don't know, maybe five minutes 325 00:16:23,660 --> 00:16:25,410 or more or a little longer. 326 00:16:25,410 --> 00:16:30,924 And then eventually it just kind of stays this more dark brown. 327 00:16:30,924 --> 00:16:32,090 Maybe it's already happened. 328 00:16:32,090 --> 00:16:33,381 We'll see if it switches again. 329 00:16:36,060 --> 00:16:36,940 All right. 330 00:16:36,940 --> 00:16:40,040 So let's talk about measuring reaction rates then, 331 00:16:40,040 --> 00:16:42,010 because we just saw this reaction going 332 00:16:42,010 --> 00:16:43,260 in another reaction rate. 333 00:16:43,260 --> 00:16:45,860 We saw the effect of temperature. 334 00:16:45,860 --> 00:16:48,400 And let's think about how we would actually go 335 00:16:48,400 --> 00:16:50,370 about measuring some of these. 336 00:16:50,370 --> 00:16:53,110 So we can think about measuring two different kinds 337 00:16:53,110 --> 00:16:56,580 of rates-- an average rate and an instantaneous rate. 338 00:16:56,580 --> 00:16:59,980 And so first let's talk about measuring average rate. 339 00:16:59,980 --> 00:17:02,507 And to do that, I should switch back over here. 340 00:17:02,507 --> 00:17:03,700 OK. 341 00:17:03,700 --> 00:17:05,791 So let's consider a different reaction now, 342 00:17:05,791 --> 00:17:07,290 one that's a little less complicated 343 00:17:07,290 --> 00:17:10,670 and kind of made up, but it's a good example. 344 00:17:10,670 --> 00:17:15,160 NO2 plus CO goes to NO plus CO2. 345 00:17:15,160 --> 00:17:17,079 And so if you're measuring a rate, 346 00:17:17,079 --> 00:17:19,440 you could think about measuring the decrease 347 00:17:19,440 --> 00:17:22,859 in either of the reactants or the increase in concentration 348 00:17:22,859 --> 00:17:24,589 of either of the products. 349 00:17:24,589 --> 00:17:27,240 So in this case, let's consider that we're 350 00:17:27,240 --> 00:17:29,120 measuring the change in NO. 351 00:17:29,120 --> 00:17:31,130 And usually people pick the thing 352 00:17:31,130 --> 00:17:33,420 to measure based on what's easiest to measure, 353 00:17:33,420 --> 00:17:34,680 what kind of handle you are. 354 00:17:34,680 --> 00:17:37,140 Does it have a spectroscopic signal or something else 355 00:17:37,140 --> 00:17:39,230 that you can easily measure? 356 00:17:39,230 --> 00:17:42,860 So here we have concentration versus time. 357 00:17:42,860 --> 00:17:45,510 And so we should see none in the beginning, 358 00:17:45,510 --> 00:17:49,220 and then we should see it increase and then level off. 359 00:17:49,220 --> 00:17:52,090 And we can calculate an average rate, 360 00:17:52,090 --> 00:17:54,480 which is just going to be the change in concentration 361 00:17:54,480 --> 00:17:56,340 over the change in time. 362 00:17:56,340 --> 00:17:59,900 We can also express the average rate 363 00:17:59,900 --> 00:18:03,860 as delta the concentration of NO over 364 00:18:03,860 --> 00:18:08,100 delta t, the change in time. 365 00:18:08,100 --> 00:18:11,390 And we can calculate what that would be. 366 00:18:11,390 --> 00:18:15,840 We can pick an interval, say, from 50 to 150. 367 00:18:15,840 --> 00:18:19,490 We can measure some concentrations there and then 368 00:18:19,490 --> 00:18:22,020 calculate the average rate-- the change 369 00:18:22,020 --> 00:18:25,260 in concentration from the time 150 370 00:18:25,260 --> 00:18:29,850 to the time 50 concentration over that time interval. 371 00:18:29,850 --> 00:18:32,090 And it will give us an answer, in this case, 372 00:18:32,090 --> 00:18:36,040 1.3 times 10 to the minus 4 molar per second. 373 00:18:36,040 --> 00:18:36,540 All right. 374 00:18:36,540 --> 00:18:38,340 Well, that could be useful to know. 375 00:18:38,340 --> 00:18:42,940 But the average rate depends on the time interval I picked. 376 00:18:42,940 --> 00:18:44,540 If I picked a different time interval, 377 00:18:44,540 --> 00:18:46,500 I might have gotten a different rate. 378 00:18:46,500 --> 00:18:49,430 So instead of calculating average rate, a lot of people 379 00:18:49,430 --> 00:18:53,580 want to calculate instantaneous rate, where you're asking, 380 00:18:53,580 --> 00:18:57,140 what is the rate at a particular time point? 381 00:18:57,140 --> 00:19:00,690 So now let's talk about instantaneous rate. 382 00:19:00,690 --> 00:19:03,960 We'll have the same equation up there. 383 00:19:03,960 --> 00:19:07,650 Now, instantaneous rate is defined 384 00:19:07,650 --> 00:19:11,850 as the rate where you have a limit of delta t, the change 385 00:19:11,850 --> 00:19:13,640 in time, going to 0. 386 00:19:13,640 --> 00:19:17,580 You're comparing concentrations at time t and time 387 00:19:17,580 --> 00:19:22,650 t plus the interval dt over this time change, 388 00:19:22,650 --> 00:19:26,310 again, as you approach 0. 389 00:19:26,310 --> 00:19:30,690 You can also express this as d change 390 00:19:30,690 --> 00:19:34,430 in concentration of NO dt. 391 00:19:34,430 --> 00:19:39,600 And so as that change in time approaches 0, 392 00:19:39,600 --> 00:19:45,080 then the rate becomes the slope of the line tangent 393 00:19:45,080 --> 00:19:49,220 to the curve at time t. 394 00:19:49,220 --> 00:19:52,720 So if we wanted, say, find the instantaneous rate 395 00:19:52,720 --> 00:19:57,390 at 150-- here's 150-- we can draw a line tangent 396 00:19:57,390 --> 00:20:00,550 to the curve at that time. 397 00:20:00,550 --> 00:20:04,890 So this would be the point at 150, 398 00:20:04,890 --> 00:20:07,070 and then we can calculate the slope 399 00:20:07,070 --> 00:20:10,460 to tell us the instantaneous rate. 400 00:20:10,460 --> 00:20:12,010 So let's do that. 401 00:20:12,010 --> 00:20:14,050 We will calculate the slope. 402 00:20:14,050 --> 00:20:17,620 We have to look what the concentrations are, 403 00:20:17,620 --> 00:20:19,430 what the times are. 404 00:20:19,430 --> 00:20:23,170 And then the instantaneous rate at 150 405 00:20:23,170 --> 00:20:26,680 would be the slope of the line, this change in concentration, 406 00:20:26,680 --> 00:20:28,620 over that time interval. 407 00:20:28,620 --> 00:20:31,170 And to the correct significant figures-- 408 00:20:31,170 --> 00:20:33,220 there should be an extra 0 in there-- 409 00:20:33,220 --> 00:20:38,520 7.70 times 10 to the minus 5 molar per second. 410 00:20:38,520 --> 00:20:41,040 So that would be the instantaneous rate, 411 00:20:41,040 --> 00:20:44,460 again, the slope of the line tangent to the curve 412 00:20:44,460 --> 00:20:46,080 at time 150. 413 00:20:46,080 --> 00:20:48,790 So you could ask, what is the instantaneous rate 414 00:20:48,790 --> 00:20:52,700 at 100 seconds or 200 seconds, and get 415 00:20:52,700 --> 00:20:54,600 that instantaneous rate. 416 00:20:54,600 --> 00:20:57,850 People are often talking about initial rate. 417 00:20:57,850 --> 00:21:02,880 And by initial rate, they mean the instantaneous rate at time 418 00:21:02,880 --> 00:21:04,390 equals 0. 419 00:21:04,390 --> 00:21:06,030 So again, we have two different rates. 420 00:21:06,030 --> 00:21:10,220 We have average rate and instantaneous rate. 421 00:21:10,220 --> 00:21:15,595 So now let's think about rate expressions and then rate laws. 422 00:21:15,595 --> 00:21:16,095 All right. 423 00:21:16,095 --> 00:21:21,420 So keeping with that same reaction, 424 00:21:21,420 --> 00:21:26,860 again, we could monitor NO forming or CO2 forming, 425 00:21:26,860 --> 00:21:31,680 or we could monitor either of our reactants disappearing. 426 00:21:31,680 --> 00:21:35,620 And if we assume that there's no intermediates or very slow 427 00:21:35,620 --> 00:21:39,220 steps, then we could say that the rate of the reaction 428 00:21:39,220 --> 00:21:41,470 should be equal to the disappearance 429 00:21:41,470 --> 00:21:44,660 of the concentration of NO2, or decrease in NO2, one 430 00:21:44,660 --> 00:21:47,030 of our reactants, over time. 431 00:21:47,030 --> 00:21:50,380 It should also be equal to the disappearance of CO, 432 00:21:50,380 --> 00:21:53,730 our other reactant over time, and also 433 00:21:53,730 --> 00:21:59,000 equal to the appearance of NO with time, and also 434 00:21:59,000 --> 00:22:03,020 equal to the appearance of CO2 with time. 435 00:22:03,020 --> 00:22:06,780 And again, for these all to be equal to each other, 436 00:22:06,780 --> 00:22:11,660 we are assuming here there are no intermediates being formed, 437 00:22:11,660 --> 00:22:13,810 or that if we are forming them, then 438 00:22:13,810 --> 00:22:15,300 they're independent of time. 439 00:22:15,300 --> 00:22:19,140 In other words, if, say, there was a large, slow step 440 00:22:19,140 --> 00:22:23,380 somewhere in here, we might see all the reactants disappear. 441 00:22:23,380 --> 00:22:25,760 But there'd be a lag before the products would appear, 442 00:22:25,760 --> 00:22:28,890 because more steps and things are going on. 443 00:22:28,890 --> 00:22:31,380 So these are all equal to each other 444 00:22:31,380 --> 00:22:34,610 if you have no intermediates or the intermediates are not 445 00:22:34,610 --> 00:22:38,110 affecting the overall rate. 446 00:22:38,110 --> 00:22:42,460 So we could think about this for a generic equation. 447 00:22:42,460 --> 00:22:47,070 So if we consider A plus B going to C plus D, 448 00:22:47,070 --> 00:22:49,384 when we're talking about the rates of disappearance 449 00:22:49,384 --> 00:22:51,550 or appearance, we have to remember the stoichiometry 450 00:22:51,550 --> 00:22:52,790 of the reaction. 451 00:22:52,790 --> 00:22:55,920 So if we have a stoichiometry of little a, 452 00:22:55,920 --> 00:23:02,890 then we would say minus 1/a dA dt, stoichiometry of little b 453 00:23:02,890 --> 00:23:09,860 for reactant B, minus 1/b dB dt. 454 00:23:09,860 --> 00:23:16,280 Then formation of products, 1/c dC dt, and our other product, 455 00:23:16,280 --> 00:23:19,595 1/d dD dt. 456 00:23:19,595 --> 00:23:20,450 I got through it. 457 00:23:20,450 --> 00:23:21,640 OK. 458 00:23:21,640 --> 00:23:26,130 So let's look at an example reaction, 459 00:23:26,130 --> 00:23:29,420 and why don't you tell me what the rate is equal to. 460 00:23:34,094 --> 00:23:37,162 I didn't announce whether this would be in the program or not. 461 00:23:37,162 --> 00:23:39,411 Why don't you look at the results and make a decision? 462 00:23:44,230 --> 00:23:45,765 OK, 10 seconds. 463 00:24:00,635 --> 00:24:03,130 All right. 464 00:24:03,130 --> 00:24:06,396 Still haven't gotten much into the 90s, but still I'm happy. 465 00:24:06,396 --> 00:24:07,230 All right. 466 00:24:07,230 --> 00:24:11,660 So here, again, we're talking about the disappearance 467 00:24:11,660 --> 00:24:13,590 of our reactant. 468 00:24:13,590 --> 00:24:18,810 So it will be minus 1/2, and the formation 469 00:24:18,810 --> 00:24:22,090 of one of our products and the formation 470 00:24:22,090 --> 00:24:24,851 of the other product as well. 471 00:24:24,851 --> 00:24:25,350 All right. 472 00:24:25,350 --> 00:24:29,410 So don't forget about the stoichiometry of the reaction. 473 00:24:29,410 --> 00:24:33,770 So these are called rate expressions, 474 00:24:33,770 --> 00:24:37,590 and you don't want to get that confused with rate laws. 475 00:24:37,590 --> 00:24:40,990 So a problem might ask, write the rate expression. 476 00:24:40,990 --> 00:24:42,840 This is what it's looking for. 477 00:24:42,840 --> 00:24:45,560 If it says write the rate law, it's 478 00:24:45,560 --> 00:24:48,850 going to be looking for the following thing. 479 00:24:48,850 --> 00:24:55,790 So a rate law is a relationship between rate and concentration, 480 00:24:55,790 --> 00:24:59,120 and they are related by a proportionality constant, 481 00:24:59,120 --> 00:25:02,580 little k, which is called the rate constant. 482 00:25:02,580 --> 00:25:05,314 So big K is what? 483 00:25:05,314 --> 00:25:06,230 AUDIENCE: Equilibrium. 484 00:25:06,230 --> 00:25:08,000 CATHERINE DRENNAN: Equilibrium constant. 485 00:25:08,000 --> 00:25:10,661 Little k is a rate constant. 486 00:25:10,661 --> 00:25:11,160 All right. 487 00:25:11,160 --> 00:25:13,940 So let's look at a reaction. 488 00:25:13,940 --> 00:25:18,490 And so reaction of A plus B going to C plus D, 489 00:25:18,490 --> 00:25:22,570 the rate law could be expressed, rate equals 490 00:25:22,570 --> 00:25:26,950 rate constant k times the concentration of A 491 00:25:26,950 --> 00:25:31,800 to the m and B to the n, where m and n are 492 00:25:31,800 --> 00:25:35,390 the order of the reaction in A and B respectively, 493 00:25:35,390 --> 00:25:38,760 and k, again, is our rate constant. 494 00:25:38,760 --> 00:25:39,260 All right. 495 00:25:39,260 --> 00:25:43,424 So let's look at what I call the truth about rate laws. 496 00:25:46,150 --> 00:25:50,880 So the first thing, you cannot just look at the stoichiometry 497 00:25:50,880 --> 00:25:56,780 of the equation and say, oh, it's going to have this m for A 498 00:25:56,780 --> 00:26:00,760 based on its stoichiometry, unless it's what's called 499 00:26:00,760 --> 00:26:02,370 an elementary reaction. 500 00:26:02,370 --> 00:26:04,410 And we're going to get to that on Wednesday 501 00:26:04,410 --> 00:26:05,320 after Thanksgiving. 502 00:26:05,320 --> 00:26:07,370 Make sure you come Wednesday after Thanksgiving. 503 00:26:07,370 --> 00:26:08,900 That's the lecture on mechanism. 504 00:26:08,900 --> 00:26:11,150 It's a really important lecture in kinetics. 505 00:26:11,150 --> 00:26:13,780 So we'll learn about elementary reactions. 506 00:26:13,780 --> 00:26:15,760 So you can't just look at the stoichiometry 507 00:26:15,760 --> 00:26:17,130 and write the rate law. 508 00:26:17,130 --> 00:26:19,630 You need experiment. 509 00:26:19,630 --> 00:26:22,450 So the rate law is not just limited 510 00:26:22,450 --> 00:26:26,790 to reactants, although largely it's true 511 00:26:26,790 --> 00:26:29,500 that the rate laws will just have reactants. 512 00:26:29,500 --> 00:26:31,860 It can also have a product term, like C 513 00:26:31,860 --> 00:26:33,960 could appear in the rate law. 514 00:26:33,960 --> 00:26:35,030 How would you know this? 515 00:26:35,030 --> 00:26:36,970 Well, it would be experiment would tell you 516 00:26:36,970 --> 00:26:40,470 whether this was true or not. 517 00:26:40,470 --> 00:26:44,290 So for this rate law, we saw this already, 518 00:26:44,290 --> 00:26:49,980 the order of the reaction in A is m, 519 00:26:49,980 --> 00:26:53,250 and the order of the reaction in B is n. 520 00:26:53,250 --> 00:26:57,270 And m and n can be integers. 521 00:26:57,270 --> 00:26:58,970 They can be fractions. 522 00:26:58,970 --> 00:27:03,280 They can be positive, and they can be negative. 523 00:27:03,280 --> 00:27:05,380 So now we're going to think about all 524 00:27:05,380 --> 00:27:10,890 these different orders of reaction and think about what-- 525 00:27:10,890 --> 00:27:14,680 and we'll do it just for A-- what m is equal to. 526 00:27:14,680 --> 00:27:16,680 So we're going to fill in this table here. 527 00:27:16,680 --> 00:27:19,120 And some of these things are in your notes, some of them 528 00:27:19,120 --> 00:27:20,690 you need to fill in. 529 00:27:20,690 --> 00:27:24,630 So we're going to start with m equals 1, 530 00:27:24,630 --> 00:27:29,380 and this is called a first-order reaction. 531 00:27:29,380 --> 00:27:34,610 The rate law for this, the rate would equal the rate constant 532 00:27:34,610 --> 00:27:38,370 times the concentration of A. And now 533 00:27:38,370 --> 00:27:41,420 let's just think, if this is a first-order reaction that just 534 00:27:41,420 --> 00:27:47,750 depends on A, if you double the concentration of A, what do you 535 00:27:47,750 --> 00:27:49,771 expect will happen to the rate? 536 00:27:49,771 --> 00:27:51,823 AUDIENCE: It'll double. 537 00:27:51,823 --> 00:27:52,823 CATHERINE DRENNAN: What? 538 00:27:52,823 --> 00:27:53,570 AUDIENCE: Double. 539 00:27:53,570 --> 00:27:56,140 CATHERINE DRENNAN: It will double, right. 540 00:27:56,140 --> 00:27:57,740 So in a first-order reaction, you 541 00:27:57,740 --> 00:27:59,810 double the concentration of something, 542 00:27:59,810 --> 00:28:00,950 and the rate will double. 543 00:28:00,950 --> 00:28:03,750 And this is how you figure out what the order of the reaction 544 00:28:03,750 --> 00:28:04,490 is. 545 00:28:04,490 --> 00:28:06,270 You double the concentration of something, 546 00:28:06,270 --> 00:28:07,650 leaving everything else the same, 547 00:28:07,650 --> 00:28:09,350 and see the effect on rate. 548 00:28:09,350 --> 00:28:12,150 So again, these are experimentally determined. 549 00:28:12,150 --> 00:28:15,240 Now let's consider m equals 2. 550 00:28:15,240 --> 00:28:20,030 And notice the blue went away here, but it's still there. 551 00:28:20,030 --> 00:28:20,811 So you can see it. 552 00:28:20,811 --> 00:28:21,310 All right. 553 00:28:21,310 --> 00:28:24,320 Second order-- what does the rate equal? 554 00:28:24,320 --> 00:28:26,780 So it would equal k, our rate constant, 555 00:28:26,780 --> 00:28:30,770 times the concentration of A, and now we have a 2. 556 00:28:30,770 --> 00:28:34,350 So it's raised to the power of m, and that's 2. 557 00:28:34,350 --> 00:28:37,070 So that's how we would write the rate law for something that 558 00:28:37,070 --> 00:28:41,220 was second order in A. So now let's think about 559 00:28:41,220 --> 00:28:43,253 if you double the concentration of A, 560 00:28:43,253 --> 00:28:46,800 what you would you observe for the rate? 561 00:28:46,800 --> 00:28:48,970 What would happen? 562 00:28:48,970 --> 00:28:49,890 AUDIENCE: Quadruple. 563 00:28:49,890 --> 00:28:52,850 CATHERINE DRENNAN: It would quadruple, right. 564 00:28:52,850 --> 00:28:56,326 Now, what about if it triples? 565 00:28:56,326 --> 00:28:58,200 Why don't you tell me what would happen then. 566 00:29:07,360 --> 00:29:10,127 All right, 10 seconds, very fast. 567 00:29:21,920 --> 00:29:23,990 90%, yes! 568 00:29:23,990 --> 00:29:26,510 OK. 569 00:29:26,510 --> 00:29:31,210 So yes, 9 times. 570 00:29:31,210 --> 00:29:31,730 All right. 571 00:29:31,730 --> 00:29:35,370 And in problem set 9, which is already posted, 572 00:29:35,370 --> 00:29:37,820 there's all sorts of problems where you see the effects, 573 00:29:37,820 --> 00:29:40,891 and you can figure out what the order of the reaction is. 574 00:29:40,891 --> 00:29:41,390 All right. 575 00:29:41,390 --> 00:29:44,760 So now let's consider minus 1 over here, 576 00:29:44,760 --> 00:29:47,690 which is often not referred to by any name. 577 00:29:47,690 --> 00:29:52,150 The rate here would be equal to k concentration of A 578 00:29:52,150 --> 00:29:54,910 to the minus 1. 579 00:29:54,910 --> 00:29:58,130 And if we double the concentration of this-- 580 00:29:58,130 --> 00:30:00,580 you can just yell out-- what would happen to the rate? 581 00:30:00,580 --> 00:30:00,905 AUDIENCE: Half. 582 00:30:00,905 --> 00:30:01,530 AUDIENCE: Half. 583 00:30:01,530 --> 00:30:04,130 CATHERINE DRENNAN: Half, yes. 584 00:30:04,130 --> 00:30:04,670 All right. 585 00:30:04,670 --> 00:30:11,080 Now, to m equals minus 1/2. 586 00:30:11,080 --> 00:30:15,040 So the rate here would be k equals concentration 587 00:30:15,040 --> 00:30:18,410 of A raised to the minus 1/2. 588 00:30:18,410 --> 00:30:22,200 And now if we double, that's our last clicker question 589 00:30:22,200 --> 00:30:24,510 on this sheet. 590 00:30:24,510 --> 00:30:26,214 So why don't you tell me what happens, 591 00:30:26,214 --> 00:30:27,380 and this should be fast too. 592 00:30:43,290 --> 00:30:44,530 All right, 10 more seconds. 593 00:30:59,760 --> 00:31:02,010 All right. 594 00:31:02,010 --> 00:31:05,470 So going back over here, right, we 595 00:31:05,470 --> 00:31:11,290 have 0.7 times, which is 2 to the minus 1/2. 596 00:31:11,290 --> 00:31:13,510 And when you're looking at the effects 597 00:31:13,510 --> 00:31:15,270 of the rate on concentration, you'll 598 00:31:15,270 --> 00:31:16,630 see the concentration double. 599 00:31:16,630 --> 00:31:19,460 And you're like, what on earth happened to the rate? 600 00:31:19,460 --> 00:31:24,380 Keep in mind this minus 1/2, because it's very hard to think 601 00:31:24,380 --> 00:31:26,560 about what the relationship is. 602 00:31:26,560 --> 00:31:31,140 So again, they can be fractions, positive, or negative. 603 00:31:31,140 --> 00:31:31,770 All right. 604 00:31:31,770 --> 00:31:37,000 So back up here now, this actually is called half order. 605 00:31:37,000 --> 00:31:40,680 So we would have a rate that is equal to k 606 00:31:40,680 --> 00:31:43,880 times the concentration of A raised to the 1/2. 607 00:31:43,880 --> 00:31:46,140 And if we double that-- you can just 608 00:31:46,140 --> 00:31:48,440 yell out-- what would happen? 609 00:31:48,440 --> 00:31:50,150 AUDIENCE: [INAUDIBLE]. 610 00:31:50,150 --> 00:31:55,260 CATHERINE DRENNAN: So 1.4 times the rate. 611 00:31:55,260 --> 00:31:59,440 And finally, m equals 0. 612 00:31:59,440 --> 00:32:01,910 What do you think that is likely to be called? 613 00:32:01,910 --> 00:32:04,200 AUDIENCE: Zero order. 614 00:32:04,200 --> 00:32:06,510 CATHERINE DRENNAN: That is zero order. 615 00:32:06,510 --> 00:32:11,140 So at least some things are pretty easy to guess. 616 00:32:11,140 --> 00:32:13,480 And if we think about the rate, what 617 00:32:13,480 --> 00:32:15,113 would the rate be equal to? 618 00:32:15,113 --> 00:32:16,040 AUDIENCE: k. 619 00:32:16,040 --> 00:32:17,500 CATHERINE DRENNAN: Just k, right. 620 00:32:17,500 --> 00:32:19,700 It's just going to be equal to k. 621 00:32:19,700 --> 00:32:25,670 So zero order, the A term is not there. 622 00:32:25,670 --> 00:32:28,210 So if we double the concentration of something 623 00:32:28,210 --> 00:32:31,040 that is zero order, what happens to the rate? 624 00:32:31,040 --> 00:32:31,950 AUDIENCE: Nothing. 625 00:32:31,950 --> 00:32:33,366 CATHERINE DRENNAN: Nothing, right. 626 00:32:33,366 --> 00:32:34,670 No effect on rate. 627 00:32:34,670 --> 00:32:38,420 The concentration term isn't part of the equation. 628 00:32:38,420 --> 00:32:42,260 So the problem set 9 will have a lot of experiments, 629 00:32:42,260 --> 00:32:44,350 and you need to figure out by looking 630 00:32:44,350 --> 00:32:48,640 at what is happening what the order of the reaction is. 631 00:32:48,640 --> 00:32:50,580 Is it doubling when you double the rate? 632 00:32:50,580 --> 00:32:51,840 Is it quadrupling? 633 00:32:51,840 --> 00:32:53,310 Is it doing some weird thing that 634 00:32:53,310 --> 00:32:56,290 seems to be a negative-- an inverse fraction? 635 00:32:56,290 --> 00:33:00,040 And that will allow you to figure out what the order is. 636 00:33:00,040 --> 00:33:01,100 OK. 637 00:33:01,100 --> 00:33:05,810 So once you figure out the order of the reaction, 638 00:33:05,810 --> 00:33:09,130 then the next truth about rate laws 639 00:33:09,130 --> 00:33:12,480 is that the overall order of the reaction 640 00:33:12,480 --> 00:33:17,640 is just the sum of the exponents in the rate law. 641 00:33:17,640 --> 00:33:22,100 So for example, if we had this reaction, 642 00:33:22,100 --> 00:33:23,790 what would be the overall order? 643 00:33:23,790 --> 00:33:25,182 You can just yell it out. 644 00:33:25,182 --> 00:33:25,952 AUDIENCE: 3. 645 00:33:25,952 --> 00:33:26,910 CATHERINE DRENNAN: Yep. 646 00:33:26,910 --> 00:33:28,130 It would be a third order. 647 00:33:28,130 --> 00:33:30,070 The order would be 3. 648 00:33:30,070 --> 00:33:34,290 Now, some people get this wrong on the test. 649 00:33:34,290 --> 00:33:36,110 It's like, no, you want to save your points 650 00:33:36,110 --> 00:33:37,730 for something that's hard. 651 00:33:37,730 --> 00:33:39,800 2 plus 1 is 3. 652 00:33:39,800 --> 00:33:41,770 So remember that. 653 00:33:41,770 --> 00:33:42,320 OK. 654 00:33:42,320 --> 00:33:45,540 And this would be then second order in A. 655 00:33:45,540 --> 00:33:51,170 You would say that's first order in B, overall third order. 656 00:33:51,170 --> 00:33:52,870 So if you're going to lose points 657 00:33:52,870 --> 00:33:56,440 on an exam on this material, I recommend 658 00:33:56,440 --> 00:33:58,890 losing them determining the units for the rate 659 00:33:58,890 --> 00:34:00,490 constant, because that's much more 660 00:34:00,490 --> 00:34:02,790 complicated than figuring out the overall order 661 00:34:02,790 --> 00:34:03,930 of the reaction. 662 00:34:03,930 --> 00:34:07,500 The units, it depends on the order. 663 00:34:07,500 --> 00:34:08,860 You can have squared. 664 00:34:08,860 --> 00:34:11,429 You can have molar squared, quadrupled, 665 00:34:11,429 --> 00:34:13,630 molar to the minus fractions. 666 00:34:13,630 --> 00:34:16,210 All sorts of crazy things happen in your units 667 00:34:16,210 --> 00:34:17,449 of rate constants. 668 00:34:17,449 --> 00:34:19,929 So save your points if you're going to lose some. 669 00:34:19,929 --> 00:34:22,384 And I think it would be great if everyone got 100, 670 00:34:22,384 --> 00:34:24,550 but if you're going to lose some, lose some on that. 671 00:34:24,550 --> 00:34:26,440 That's harder. 672 00:34:26,440 --> 00:34:27,500 OK. 673 00:34:27,500 --> 00:34:29,360 So we'll end there for today. 674 00:34:29,360 --> 00:34:33,780 And Wednesday, we're going to be talking about integrated rate 675 00:34:33,780 --> 00:34:39,639 laws, half-life for first order, nuclear chemistry. 676 00:34:39,639 --> 00:34:44,920 It's going to be very exciting and slightly radioactive. 677 00:34:44,920 --> 00:34:46,406 So where were we? 678 00:34:46,406 --> 00:34:49,920 We were talking about the fact about how 679 00:34:49,920 --> 00:34:55,150 you measure instantaneous rates and average rates. 680 00:34:55,150 --> 00:34:58,640 And one of the issues of doing kinetics experiments, 681 00:34:58,640 --> 00:34:59,690 it's all experimental. 682 00:34:59,690 --> 00:35:01,090 You want to measure things. 683 00:35:01,090 --> 00:35:04,370 But it can be very challenging to measure initial rates, 684 00:35:04,370 --> 00:35:08,010 because you're often talking about a very small change 685 00:35:08,010 --> 00:35:09,610 in concentration. 686 00:35:09,610 --> 00:35:13,480 And so it can be helpful sometimes 687 00:35:13,480 --> 00:35:15,950 to use integrated rate laws, which 688 00:35:15,950 --> 00:35:19,950 allow you to measure a lot of different concentrations 689 00:35:19,950 --> 00:35:25,980 as times elapses and plot that data to get out rate constants 690 00:35:25,980 --> 00:35:27,340 and things like that. 691 00:35:27,340 --> 00:35:31,410 So we're going to talk about integrated rate laws. 692 00:35:31,410 --> 00:35:35,630 And so the alternative, then, is to use this integrated rate 693 00:35:35,630 --> 00:35:36,220 law. 694 00:35:36,220 --> 00:35:40,350 Again, expresses concentrations directly as a function of time 695 00:35:40,350 --> 00:35:43,550 and gets at this small changes problem. 696 00:35:43,550 --> 00:35:44,050 All right. 697 00:35:44,050 --> 00:35:47,010 So we're going to talk about first order now, 698 00:35:47,010 --> 00:35:50,560 and then we'll talk about second order in a little bit. 699 00:35:50,560 --> 00:35:54,970 So for a first-order equation, we have A going to B. 700 00:35:54,970 --> 00:35:58,470 And we learned last time that we can write a rate 701 00:35:58,470 --> 00:36:03,110 expression for a first-order process, or for this process 702 00:36:03,110 --> 00:36:03,730 here. 703 00:36:03,730 --> 00:36:05,640 So we could talk about the rate expression 704 00:36:05,640 --> 00:36:12,070 as the disappearance of A minus d concentration of A dt. 705 00:36:12,070 --> 00:36:18,110 We can also write the rate law for a first-order equation, 706 00:36:18,110 --> 00:36:20,500 and that would be k, our rate constant, 707 00:36:20,500 --> 00:36:22,330 times our concentration. 708 00:36:22,330 --> 00:36:26,180 So the rate expression has the d dt, 709 00:36:26,180 --> 00:36:30,381 and the rate law has k, our rate constant, in it. 710 00:36:30,381 --> 00:36:30,880 All right. 711 00:36:30,880 --> 00:36:34,160 So using these two things that we learned last time, 712 00:36:34,160 --> 00:36:39,160 we can do a derivation to get our integrated first-order rate 713 00:36:39,160 --> 00:36:40,350 law. 714 00:36:40,350 --> 00:36:43,440 So in this derivation, we're going 715 00:36:43,440 --> 00:36:47,050 to separate our concentration terms on one side and our time 716 00:36:47,050 --> 00:36:49,970 terms on the other side. 717 00:36:49,970 --> 00:36:55,120 So we're going to bring over our concentration of A over here. 718 00:36:55,120 --> 00:36:58,070 So we'll divide by the concentration of A. 719 00:36:58,070 --> 00:37:01,820 We have our d concentration of A term from here. 720 00:37:01,820 --> 00:37:04,680 We're going to take our minus sign, put it on the other side. 721 00:37:04,680 --> 00:37:07,260 And we're going to take our dt, our time term, 722 00:37:07,260 --> 00:37:10,420 and put it over there as well with our rate constant. 723 00:37:10,420 --> 00:37:14,030 So we have the terms that have concentration of A on one side, 724 00:37:14,030 --> 00:37:18,090 and we have our terms with rate constant and time on the other. 725 00:37:18,090 --> 00:37:21,100 Now we can integrate both sides, and we 726 00:37:21,100 --> 00:37:25,600 will integrate from our original concentration of A. 727 00:37:25,600 --> 00:37:29,930 So that's A to the O, for our original concentration, 728 00:37:29,930 --> 00:37:34,500 up to concentration at whatever time t we stop the experiment 729 00:37:34,500 --> 00:37:38,150 and through all the times in between, over 1 730 00:37:38,150 --> 00:37:40,930 over the concentration of A dA. 731 00:37:40,930 --> 00:37:44,810 And on the other side, we have our minus rate constant k, 732 00:37:44,810 --> 00:37:47,930 and we're looking at the time from time 0 to time t, 733 00:37:47,930 --> 00:37:50,230 when we stop the experiment. 734 00:37:50,230 --> 00:37:50,730 All right. 735 00:37:50,730 --> 00:37:53,250 So we can take this expression now and move it up, 736 00:37:53,250 --> 00:37:55,140 because I have more derivations to go. 737 00:37:55,140 --> 00:37:57,800 So I'm going to put it on the top of the screen. 738 00:37:57,800 --> 00:38:01,050 And now I am going to solve it. 739 00:38:01,050 --> 00:38:05,070 So this integral solves to the natural log 740 00:38:05,070 --> 00:38:07,470 of the concentration of A at time t 741 00:38:07,470 --> 00:38:11,996 minus the natural log of our original concentration of A, 742 00:38:11,996 --> 00:38:15,700 on the other side minus kt, our time. 743 00:38:15,700 --> 00:38:19,490 So there are two ways we can rewrite this equation. 744 00:38:19,490 --> 00:38:22,730 We can write it as the equation for a straight line. 745 00:38:22,730 --> 00:38:26,760 And all I did was take this natural log of A0, 746 00:38:26,760 --> 00:38:30,540 or A original over here. 747 00:38:30,540 --> 00:38:34,310 And we could also rearrange this term. 748 00:38:34,310 --> 00:38:37,050 Instead of minus, we have natural log 749 00:38:37,050 --> 00:38:39,250 of the concentration of A at time t 750 00:38:39,250 --> 00:38:42,540 over our original concentration. 751 00:38:42,540 --> 00:38:47,390 And now we can take the inverse natural log of both sides. 752 00:38:47,390 --> 00:38:50,860 And so we get rid of natural log here, and on the other side 753 00:38:50,860 --> 00:38:54,770 we have e to the minus kt, again, the rate constant times 754 00:38:54,770 --> 00:38:56,890 the time. 755 00:38:56,890 --> 00:39:00,330 And then I can write it-- break this out here, 756 00:39:00,330 --> 00:39:02,420 moving the original concentration of A 757 00:39:02,420 --> 00:39:03,470 to this side. 758 00:39:03,470 --> 00:39:06,980 And now this is the equation for the integrated first-order rate 759 00:39:06,980 --> 00:39:09,860 law, where you have the concentration of A 760 00:39:09,860 --> 00:39:14,070 at some point t equals its original concentration 761 00:39:14,070 --> 00:39:18,440 times e to the minus k, the rate constant, times the time. 762 00:39:18,440 --> 00:39:21,960 So if you know a rate constant and how much time has elapsed, 763 00:39:21,960 --> 00:39:24,760 and you know how much you have of something originally, 764 00:39:24,760 --> 00:39:27,580 you can figure out how much you should have now. 765 00:39:27,580 --> 00:39:34,091 Or if you figure out how the concentration changes over time 766 00:39:34,091 --> 00:39:35,590 and how much you had originally, you 767 00:39:35,590 --> 00:39:40,250 can calculate the rate constant for that particular material. 768 00:39:40,250 --> 00:39:43,630 And you can do those calculations for rate constants 769 00:39:43,630 --> 00:39:47,830 by plotting, using this equation for a straight line. 770 00:39:47,830 --> 00:39:52,070 So here I'm going to plot natural log of A. 771 00:39:52,070 --> 00:39:53,690 So I measured the concentration of A 772 00:39:53,690 --> 00:39:58,250 at various different times against time. 773 00:39:58,250 --> 00:40:00,214 And we have an equation for a straight line. 774 00:40:00,214 --> 00:40:01,880 So we should get a straight line if this 775 00:40:01,880 --> 00:40:03,084 is a first-order process. 776 00:40:06,660 --> 00:40:10,170 And so what would this be up here? 777 00:40:10,170 --> 00:40:11,470 What is the y-intercept? 778 00:40:15,880 --> 00:40:17,738 What is it? 779 00:40:17,738 --> 00:40:20,020 AUDIENCE: Natural log of the original concentration. 780 00:40:20,020 --> 00:40:21,020 CATHERINE DRENNAN: Yeah. 781 00:40:21,020 --> 00:40:24,610 So that's the natural log of our original concentration. 782 00:40:24,610 --> 00:40:29,253 And this you can yell more loudly-- what is our slope? 783 00:40:29,253 --> 00:40:30,730 AUDIENCE: Minus k. 784 00:40:30,730 --> 00:40:32,154 CATHERINE DRENNAN: Yes. 785 00:40:32,154 --> 00:40:33,820 It's a little bit easier to yell loudly. 786 00:40:33,820 --> 00:40:35,900 Minus k. 787 00:40:35,900 --> 00:40:39,100 So you can experimentally determine 788 00:40:39,100 --> 00:40:40,730 the rate constant from this. 789 00:40:40,730 --> 00:40:42,760 So if you measure how the concentration 790 00:40:42,760 --> 00:40:45,430 of A changes with time, plot your data, 791 00:40:45,430 --> 00:40:48,180 natural log of those concentrations versus time, 792 00:40:48,180 --> 00:40:50,460 get a lot of data points, from the slope 793 00:40:50,460 --> 00:40:52,070 you can measure the rate constant. 794 00:40:52,070 --> 00:40:54,900 And so rate constants for a lot of different materials 795 00:40:54,900 --> 00:40:58,050 have already been measured in this kind of way. 796 00:40:58,050 --> 00:40:58,550 All right. 797 00:40:58,550 --> 00:41:02,830 So for a first-order process, these are important equations. 798 00:41:02,830 --> 00:41:05,100 But also for first order, we spend 799 00:41:05,100 --> 00:41:09,200 a lot of time talking about half-life. 800 00:41:09,200 --> 00:41:12,040 So half-life is the time it takes 801 00:41:12,040 --> 00:41:16,740 for half of the original material to go away. 802 00:41:16,740 --> 00:41:18,850 So it's a really easy thing. 803 00:41:18,850 --> 00:41:22,100 I like it when things are called what they are. 804 00:41:22,100 --> 00:41:26,740 And here the time involved has a little special abbreviation, 805 00:41:26,740 --> 00:41:27,450 t 1/2. 806 00:41:27,450 --> 00:41:29,410 So whenever you see t 1/2, that's 807 00:41:29,410 --> 00:41:32,470 talking about a half-life. 808 00:41:32,470 --> 00:41:35,740 So we can derive this expression as well 809 00:41:35,740 --> 00:41:39,290 for the first-order half-life using the expressions that we 810 00:41:39,290 --> 00:41:43,090 just looked at, so from the expression 811 00:41:43,090 --> 00:41:45,540 we had above, where we had the natural log 812 00:41:45,540 --> 00:41:46,960 of the concentration of A at time 813 00:41:46,960 --> 00:41:49,100 t over our original concentration 814 00:41:49,100 --> 00:41:52,350 equals minus the rate constant k times time. 815 00:41:52,350 --> 00:41:54,050 And now we can substitute in. 816 00:41:54,050 --> 00:41:56,020 So we're not interested in just any old time. 817 00:41:56,020 --> 00:41:58,010 We're interested in time 1/2, so we're going 818 00:41:58,010 --> 00:41:59,510 to want to put a 1/2 in there. 819 00:41:59,510 --> 00:42:03,900 And that is the time it takes for the original amount 820 00:42:03,900 --> 00:42:07,350 to go to half, so to be divided by 2. 821 00:42:07,350 --> 00:42:08,640 So we can put that in. 822 00:42:08,640 --> 00:42:12,730 So now our At, our concentration of A at time t, 823 00:42:12,730 --> 00:42:15,970 is our original concentration divided by 2, 824 00:42:15,970 --> 00:42:18,930 and our t is t 1/2. 825 00:42:18,930 --> 00:42:23,320 So you'll see that the A0 terms are going to cancel out. 826 00:42:23,320 --> 00:42:26,040 And you're going to end up with natural log of 1/2 827 00:42:26,040 --> 00:42:30,810 equals minus k times our half-life, t 1/2. 828 00:42:30,810 --> 00:42:35,220 And so then we can put in our value for the natural log 829 00:42:35,220 --> 00:42:39,620 of 1/2 and get rid of all those minus signs and rearrange it. 830 00:42:39,620 --> 00:42:42,870 And so then our half-life for this first-order process 831 00:42:42,870 --> 00:42:47,430 is going to be equal to 0.9631 divided 832 00:42:47,430 --> 00:42:50,290 by k, the rate constant. 833 00:42:50,290 --> 00:42:53,510 So you'll note a couple of perhaps important things 834 00:42:53,510 --> 00:42:55,060 about this expression. 835 00:42:55,060 --> 00:42:56,690 And one of the important things is 836 00:42:56,690 --> 00:42:59,350 that half-life doesn't depend on the concentration. 837 00:42:59,350 --> 00:43:02,860 So the concentration term has dropped out. 838 00:43:02,860 --> 00:43:05,120 So what does half-life depend on then 839 00:43:05,120 --> 00:43:07,160 if it doesn't depend on the concentration? 840 00:43:07,160 --> 00:43:09,730 Again, this is for first order. 841 00:43:09,730 --> 00:43:12,670 So it's going to depend on k. 842 00:43:12,670 --> 00:43:14,130 That's all that's in there. 843 00:43:14,130 --> 00:43:15,755 There's only one thing that's in there. 844 00:43:15,755 --> 00:43:18,140 There's a number, a constant, and there's k. 845 00:43:18,140 --> 00:43:20,980 So half-life depends on k, this rate constant, 846 00:43:20,980 --> 00:43:24,430 and the rate constant depends on the material in question. 847 00:43:24,430 --> 00:43:27,467 So different materials will have different values 848 00:43:27,467 --> 00:43:28,175 of rate constant. 849 00:43:28,175 --> 00:43:30,530 And we just saw how you can calculate a rate constant. 850 00:43:30,530 --> 00:43:33,960 You can measure it and get the slope of the line 851 00:43:33,960 --> 00:43:35,670 and tells you about what k is. 852 00:43:35,670 --> 00:43:36,170 All right. 853 00:43:36,170 --> 00:43:38,400 So let's use this expression now. 854 00:43:38,400 --> 00:43:42,580 And why don't you tell me for the same material, 855 00:43:42,580 --> 00:43:44,257 which of these events will take longer. 856 00:43:54,197 --> 00:43:55,503 All right, 10 more seconds. 857 00:44:08,830 --> 00:44:12,360 So it takes, in fact, the same amount of time, 858 00:44:12,360 --> 00:44:15,710 because the concentration doesn't show up in there, 859 00:44:15,710 --> 00:44:18,250 and it was the same material. 860 00:44:18,250 --> 00:44:18,750 All right. 861 00:44:18,750 --> 00:44:21,350 So before we move away from this, 862 00:44:21,350 --> 00:44:23,870 you can write same amount of time in your notes. 863 00:44:23,870 --> 00:44:27,190 Let's take a look at this plot on the bottom of the page 864 00:44:27,190 --> 00:44:29,460 and just think about what's happening. 865 00:44:29,460 --> 00:44:31,360 Because you can talk about a first half-life 866 00:44:31,360 --> 00:44:33,910 and a second half-life and a third half-life. 867 00:44:33,910 --> 00:44:35,970 So we can just fill this right in. 868 00:44:35,970 --> 00:44:40,470 So for a concentration at your first half-life, how much 869 00:44:40,470 --> 00:44:42,750 is left? 870 00:44:42,750 --> 00:44:43,850 So what's this number? 871 00:44:43,850 --> 00:44:46,570 The concentration is what? 872 00:44:46,570 --> 00:44:47,830 Half. 873 00:44:47,830 --> 00:44:49,230 Second half-life, what do we got? 874 00:44:49,230 --> 00:44:51,170 AUDIENCE: 0.25. 875 00:44:51,170 --> 00:44:52,170 CATHERINE DRENNAN: 0.25. 876 00:44:52,170 --> 00:44:52,669 Third? 877 00:44:52,669 --> 00:44:53,730 AUDIENCE: 0.125. 878 00:44:53,730 --> 00:44:55,110 CATHERINE DRENNAN: 0.125, right. 879 00:44:55,110 --> 00:44:56,714 So this is pretty easy to think about. 880 00:44:56,714 --> 00:44:59,130 But sometimes when you have data and you're looking at it, 881 00:44:59,130 --> 00:45:02,130 you have to remember what the sort of possibilities are. 882 00:45:02,130 --> 00:45:02,940 OK. 883 00:45:02,940 --> 00:45:05,025 So that's first-order half-life, and that's 884 00:45:05,025 --> 00:45:06,025 the end of this lecture. 885 00:45:06,025 --> 00:45:09,420 But we're not really moving away from the topic, 886 00:45:09,420 --> 00:45:11,790 because now we're going to talk about an example 887 00:45:11,790 --> 00:45:16,650 of a first-order process, which is radioactive decay.