1 00:00:00,000 --> 00:00:00,016 The following content is provided under a Creative 2 00:00:00,016 --> 00:00:00,022 Commons license. 3 00:00:00,022 --> 00:00:00,038 Your support will help MIT OpenCourseWare continue to 4 00:00:00,038 --> 00:00:00,054 offer high quality educational resources for free. 5 00:00:00,054 --> 00:00:00,072 To make a donation or view additional materials from 6 00:00:00,072 --> 00:00:00,088 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:00,088 --> 00:00:00,110 ocw.mit.edu. 8 00:00:00,110 --> 00:00:25,470 PROFESSOR: So, let's finish up new material today, new 9 00:00:25,470 --> 00:00:28,060 material Monday, and then we're done with 10 00:00:28,060 --> 00:00:30,040 the kinetics unit. 11 00:00:30,040 --> 00:00:33,710 So, we're going to talk about temperature, collision theory, 12 00:00:33,710 --> 00:00:38,900 and activated complex theory today. 13 00:00:38,900 --> 00:00:42,980 So on the first day, we talked about kinetics, we talked 14 00:00:42,980 --> 00:00:45,860 about factors affecting the rates, and this was in your 15 00:00:45,860 --> 00:00:49,740 handout on that first lecture, but just to kind of review for 16 00:00:49,740 --> 00:00:52,450 a minute what we have talked about so far 17 00:00:52,450 --> 00:00:53,690 and where we're going. 18 00:00:53,690 --> 00:00:55,930 So these are some of the things we came up with are 19 00:00:55,930 --> 00:00:58,710 factors affecting the rates of reaction. 20 00:00:58,710 --> 00:01:01,360 People said mechanism affects the rate of reaction, so we 21 00:01:01,360 --> 00:01:03,140 talked about mechanism. 22 00:01:03,140 --> 00:01:06,190 Concentration of material, nature of material -- that 23 00:01:06,190 --> 00:01:08,330 pretty much fits in in every lecture. 24 00:01:08,330 --> 00:01:11,145 We've been talking some about that, say, if it's first order 25 00:01:11,145 --> 00:01:13,970 or second order, if you have a concentration term in there, 26 00:01:13,970 --> 00:01:15,690 or if you don't have a concentration term. 27 00:01:15,690 --> 00:01:17,810 The nature of the material, we're going to talk more about 28 00:01:17,810 --> 00:01:18,730 that today. 29 00:01:18,730 --> 00:01:21,450 Temperature is going to be the number one topic for today, 30 00:01:21,450 --> 00:01:26,150 and on Monday the number one topic is the use of catalysts 31 00:01:26,150 --> 00:01:28,030 to speed up reactions. 32 00:01:28,030 --> 00:01:32,980 So, by Monday we'll be done with this list. 33 00:01:32,980 --> 00:01:35,810 So, what about temperature. 34 00:01:35,810 --> 00:01:38,110 So temperature, when I said what affects the rate of 35 00:01:38,110 --> 00:01:40,690 reaction, temperature was one of the things that you yelled 36 00:01:40,690 --> 00:01:43,410 out at me, and that's very much true, it has one of the 37 00:01:43,410 --> 00:01:46,320 biggest effects on the rate of reactions. 38 00:01:46,320 --> 00:01:49,300 So when we were talking about the gas phase, there was an 39 00:01:49,300 --> 00:01:54,090 observation made that the reaction rates tend to 40 00:01:54,090 --> 00:01:56,900 increase as the temperature increases. 41 00:01:56,900 --> 00:02:00,530 And most of you can think about this and are aware of 42 00:02:00,530 --> 00:02:02,820 it, and today we're going to talk more about the 43 00:02:02,820 --> 00:02:06,120 quantitative affect of this, how much does the rate of a 44 00:02:06,120 --> 00:02:09,400 reaction increase when the temperature increases, how do 45 00:02:09,400 --> 00:02:12,530 you know what equation do you use. 46 00:02:12,530 --> 00:02:15,810 So, this idea has been around for awhile. 47 00:02:15,810 --> 00:02:20,620 So in 1889, Arrhenius plotted rate constants versus 48 00:02:20,620 --> 00:02:25,780 temperature, and he found that if he plotted the natural log 49 00:02:25,780 --> 00:02:30,200 of those rate constants versus inverse temperature, then he 50 00:02:30,200 --> 00:02:32,320 would get a straight line. 51 00:02:32,320 --> 00:02:37,390 So let's look at the plot that he had. 52 00:02:37,390 --> 00:02:40,570 So, he found that if he plotted natural log of the 53 00:02:40,570 --> 00:02:44,080 rate constants versus 1 over temperature, so units or 54 00:02:44,080 --> 00:02:47,440 kelvin to the minus 1, that he got a straight line. 55 00:02:47,440 --> 00:02:50,070 Which means that the rate constants are varying 56 00:02:50,070 --> 00:02:52,610 exponentially with inverse temperature. 57 00:02:52,610 --> 00:02:55,470 So you have to use a natural log to get a straight line, if 58 00:02:55,470 --> 00:02:57,080 you don't use natural log, you wouldn't get a 59 00:02:57,080 --> 00:02:59,220 straight line here. 60 00:02:59,220 --> 00:03:02,170 So, let's look at some of these terms that we have here, 61 00:03:02,170 --> 00:03:05,440 and here's our equation for the straight line, the natural 62 00:03:05,440 --> 00:03:11,830 log of k equals minus e a -- e a is activation energy, which 63 00:03:11,830 --> 00:03:15,410 we're going to talk a lot about today -- over r t, r is 64 00:03:15,410 --> 00:03:19,280 our friend the gas constant, and t is temperature, plus 65 00:03:19,280 --> 00:03:21,430 natural log of a. 66 00:03:21,430 --> 00:03:22,530 So what is a? 67 00:03:22,530 --> 00:03:25,760 A is called factor a or sometimes it's called 68 00:03:25,760 --> 00:03:31,190 pre-exponential factor, and had has the same units as k, k 69 00:03:31,190 --> 00:03:34,320 being the rate constant. 70 00:03:34,320 --> 00:03:40,570 So, let's think about this equation and this plot, and 71 00:03:40,570 --> 00:03:45,070 about factor A and this other term, activation energy. 72 00:03:45,070 --> 00:03:49,690 So, factor A and activation energy depend on the reaction 73 00:03:49,690 --> 00:03:50,620 being studied. 74 00:03:50,620 --> 00:03:53,380 So, it depends on the nature of the materials involved. 75 00:03:53,380 --> 00:03:56,860 So I said we'd talk again about nature of the material. 76 00:03:56,860 --> 00:03:59,970 So one kind of reaction's going to have one activation 77 00:03:59,970 --> 00:04:04,070 energy, another one will have a different one. 78 00:04:04,070 --> 00:04:05,860 So, let's think about this term, factor 79 00:04:05,860 --> 00:04:08,880 A. What is it exactly? 80 00:04:08,880 --> 00:04:12,080 Do you think it would be temperature dependent? 81 00:04:12,080 --> 00:04:12,490 What do you think? 82 00:04:12,490 --> 00:04:14,190 How many people think yes, it would 83 00:04:14,190 --> 00:04:16,900 be temperature dependent? 84 00:04:16,900 --> 00:04:20,310 How many people think no? 85 00:04:20,310 --> 00:04:25,100 Some people are not going to commit. 86 00:04:25,100 --> 00:04:26,800 The answer is no. 87 00:04:26,800 --> 00:04:30,370 So, let's think about what factor A is. 88 00:04:30,370 --> 00:04:35,450 So, factor A is the rate constant at some really, 89 00:04:35,450 --> 00:04:38,830 really large temperature. 90 00:04:38,830 --> 00:04:42,960 So, if we look at this plot, the natural log of k equals 91 00:04:42,960 --> 00:04:47,330 the natural log of A, or k equals A if you're 92 00:04:47,330 --> 00:04:49,030 along this axis here. 93 00:04:49,030 --> 00:04:52,130 If you're along that axis here, that's at zero, so 94 00:04:52,130 --> 00:04:57,420 that's when 1 over temperature equals zero, then the rate 95 00:04:57,420 --> 00:05:02,610 constant equals factor A. What would be true about the 96 00:05:02,610 --> 00:05:08,390 temperature for 1 over temperature to equal zero? 97 00:05:08,390 --> 00:05:09,930 Very big. 98 00:05:09,930 --> 00:05:14,920 So, at the biggest, hugest temperature you can imagine, 99 00:05:14,920 --> 00:05:18,420 the rate constant's going to equal A. And so, factor A 100 00:05:18,420 --> 00:05:21,780 depends on the nature of the material being studied and you 101 00:05:21,780 --> 00:05:24,540 would have to determine what that value is. 102 00:05:24,540 --> 00:05:26,370 But it's definitely not temperature dependent. 103 00:05:26,370 --> 00:05:29,880 It's the value of the rate constant at an enormous 104 00:05:29,880 --> 00:05:33,480 temperature. 105 00:05:33,480 --> 00:05:36,060 So, what about activation energy? 106 00:05:36,060 --> 00:05:38,190 Do you think that's temperature dependent? 107 00:05:38,190 --> 00:05:39,490 Why don't you tell me what you think. 108 00:05:39,490 --> 00:06:26,020 All right, let's take 10 more seconds. 109 00:06:26,020 --> 00:06:28,440 All right, so I'd like you to discuss this amongst 110 00:06:28,440 --> 00:07:16,260 yourselves and see whether you're happy with this answer. 111 00:07:16,260 --> 00:07:32,440 All right, go ahead and vote again. 112 00:07:32,440 --> 00:07:39,170 All right, 10 more seconds. 113 00:07:39,170 --> 00:07:39,530 And the correct answer is? 114 00:07:39,530 --> 00:07:43,110 So, I think most of you will remember this answer. 115 00:07:43,110 --> 00:07:46,580 So the activation energy is not temperature dependent. 116 00:07:46,580 --> 00:07:49,980 You can calculate what the activation energy is by 117 00:07:49,980 --> 00:07:53,430 plotting the rate constants versus 1 over temperature, and 118 00:07:53,430 --> 00:07:56,790 then you get it from the slope of the line. 119 00:07:56,790 --> 00:08:00,170 So, activation energy depends on the nature of the material, 120 00:08:00,170 --> 00:08:02,320 but it isn't temperature dependent. 121 00:08:02,320 --> 00:08:04,810 So, we're going to talk a lot more about that today. 122 00:08:04,810 --> 00:08:07,280 Before we leave this, I just want to say one thing about a 123 00:08:07,280 --> 00:08:09,480 clicker question. 124 00:08:09,480 --> 00:08:15,140 So, at the end of last time, we had our first repeat winner 125 00:08:15,140 --> 00:08:17,850 for a clicker competition. 126 00:08:17,850 --> 00:08:21,790 So, we thought that we might have an opportunity for 127 00:08:21,790 --> 00:08:26,950 recitations to see if they can -- if some other recitation 128 00:08:26,950 --> 00:08:28,410 can get a second win. 129 00:08:28,410 --> 00:08:30,630 So on Monday we're going to have our final clicker 130 00:08:30,630 --> 00:08:35,490 competition, and if somebody else does tie, one section, 131 00:08:35,490 --> 00:08:40,370 that we'll have a final one-time clicker question 132 00:08:40,370 --> 00:08:41,700 that'll be a run-off. 133 00:08:41,700 --> 00:08:45,560 And whatever recitation wins, we have special prizes for the 134 00:08:45,560 --> 00:08:47,040 members of that recitation. 135 00:08:47,040 --> 00:08:48,870 So that's on Monday. 136 00:08:48,870 --> 00:08:54,450 So you may want to review catalysis on Monday, if you 137 00:08:54,450 --> 00:08:58,450 feel that you're in the running for the grand champion 138 00:08:58,450 --> 00:09:01,850 clicker recitation. 139 00:09:01,850 --> 00:09:05,630 All right, so let's go back to this. 140 00:09:05,630 --> 00:09:10,610 So we found out that no, activation energy is not 141 00:09:10,610 --> 00:09:14,500 temperature dependent. 142 00:09:14,500 --> 00:09:18,160 All right, so what are you going to see on your equation 143 00:09:18,160 --> 00:09:21,330 sheet on the final, you may see a couple of different 144 00:09:21,330 --> 00:09:25,210 forms that are all equivalent to each other. 145 00:09:25,210 --> 00:09:28,210 So here is the plot of a straight line. 146 00:09:28,210 --> 00:09:33,220 It will often be written with just natural log of a and e a 147 00:09:33,220 --> 00:09:35,280 over r t terms reversed. 148 00:09:35,280 --> 00:09:38,400 So that's as a straight line, and this is often what you see 149 00:09:38,400 --> 00:09:40,680 for the Araneus equation. 150 00:09:40,680 --> 00:09:45,080 You can also get rid of the natural logs and have the term 151 00:09:45,080 --> 00:09:49,620 here exponential, so you have k equals factor A times e to 152 00:09:49,620 --> 00:09:53,950 the minus, activation energy divided by r t. 153 00:09:53,950 --> 00:09:56,560 So, those are the equations, they're all equivalent to each 154 00:09:56,560 --> 00:10:01,550 other that you might see on your equation sheet. 155 00:10:01,550 --> 00:10:05,950 So, it's also true that non-gases can exhibit this 156 00:10:05,950 --> 00:10:10,080 kind of behavior, and let me just give you one example of a 157 00:10:10,080 --> 00:10:14,340 non-gas that exhibits this kind of behavior and you tell 158 00:10:14,340 --> 00:10:19,440 me what this is. 159 00:10:19,440 --> 00:10:21,250 What is that? 160 00:10:21,250 --> 00:10:22,660 Crickets. 161 00:10:22,660 --> 00:10:25,660 So crickets exhibit Arrhenius behavior. 162 00:10:25,660 --> 00:10:31,070 They will chirp faster as the temperature gets hotter. 163 00:10:31,070 --> 00:10:34,290 So if you're out camping, sometimes it can be in the 164 00:10:34,290 --> 00:10:37,270 summer, it can be actually be quite deafening, and you were 165 00:10:37,270 --> 00:10:39,560 very happy to go back to the city where you only have 166 00:10:39,560 --> 00:10:43,210 ambulances and cars going, and you don't have this incredible 167 00:10:43,210 --> 00:10:45,050 racket at night. 168 00:10:45,050 --> 00:10:48,920 You can actually calculate what the temperature is by 169 00:10:48,920 --> 00:10:53,200 counting the number of chirps of the crickets and using a 170 00:10:53,200 --> 00:10:54,100 little equation. 171 00:10:54,100 --> 00:10:57,940 I think it's you count for 14 seconds and add 40 and that's 172 00:10:57,940 --> 00:11:00,540 the temperature in fahrenheit or something like that. 173 00:11:00,540 --> 00:11:06,920 So, not only gases do this kind of behavior. 174 00:11:06,920 --> 00:11:09,360 All right, so activation energy, we're going to be 175 00:11:09,360 --> 00:11:11,470 talking a lot about this today. 176 00:11:11,470 --> 00:11:14,630 So, what is it exactly. 177 00:11:14,630 --> 00:11:19,600 So let's think about two molecules coming together. 178 00:11:19,600 --> 00:11:22,470 So when two molecules come together, you have this 179 00:11:22,470 --> 00:11:27,630 bimolecular process going on, but every time two molecules 180 00:11:27,630 --> 00:11:29,210 come together, they're not going to go 181 00:11:29,210 --> 00:11:31,650 on and form a product. 182 00:11:31,650 --> 00:11:36,970 You're only going to form a product when those molecules 183 00:11:36,970 --> 00:11:39,620 have a critical amount of energy. 184 00:11:39,620 --> 00:11:44,440 When they have the energy which allows them to react, 185 00:11:44,440 --> 00:11:46,270 that activation energy. 186 00:11:46,270 --> 00:11:49,180 If they have enough energy when they come together, they 187 00:11:49,180 --> 00:11:51,960 will go on and form products. 188 00:11:51,960 --> 00:11:54,580 So, that's what activation energy is, it's this critical 189 00:11:54,580 --> 00:11:59,440 amount of energy that they need to react with each other. 190 00:11:59,440 --> 00:12:03,120 All right, so let's just think about what affects that 191 00:12:03,120 --> 00:12:06,240 critical amount of energy, and of course, temperature is 192 00:12:06,240 --> 00:12:07,910 going to be involved. 193 00:12:07,910 --> 00:12:13,300 So let's think about that. 194 00:12:13,300 --> 00:12:23,220 So if we have fraction of molecules on one side, and we 195 00:12:23,220 --> 00:12:30,430 have kinetic energy down here, let's think about how 196 00:12:30,430 --> 00:12:32,130 temperature is involved in this. 197 00:12:32,130 --> 00:12:38,040 So, at a low temperature, the fraction of molecules that are 198 00:12:38,040 --> 00:12:43,620 going to have enough energy to react is going to be less. 199 00:12:43,620 --> 00:12:47,890 And let's think about at a higher temperature, go like 200 00:12:47,890 --> 00:12:54,510 this, so this is high temperature, and we have low 201 00:12:54,510 --> 00:12:56,510 temperature up here. 202 00:12:56,510 --> 00:13:01,210 And then over here we would have our activation energy, 203 00:13:01,210 --> 00:13:04,150 the energy needed for a reaction. 204 00:13:04,150 --> 00:13:07,530 And you see, if you're at low temperature, only a small 205 00:13:07,530 --> 00:13:11,050 number of molecules are going to have enough energy to 206 00:13:11,050 --> 00:13:16,480 react, but if you're at higher temperature, a large number of 207 00:13:16,480 --> 00:13:20,900 molecules are going to have that critical energy to react. 208 00:13:20,900 --> 00:13:24,060 So, at low temperature, not many can react, at higher 209 00:13:24,060 --> 00:13:27,250 temperature, many more will have that energy -- will be 210 00:13:27,250 --> 00:13:31,570 able to overcome that activation energy, will have 211 00:13:31,570 --> 00:13:34,320 it and they can react. 212 00:13:34,320 --> 00:13:38,510 So, temperature plays a big role here. 213 00:13:38,510 --> 00:13:42,850 So we can use this idea of activation energy to predict a 214 00:13:42,850 --> 00:13:46,070 rate constant. 215 00:13:46,070 --> 00:13:49,100 Let's look at an example. 216 00:13:49,100 --> 00:13:56,000 So, often people have sucrose in their diet, and the 217 00:13:56,000 --> 00:14:00,370 hydrolysis of sucrose will form glucose and fructose as 218 00:14:00,370 --> 00:14:02,790 part of this digestive process. 219 00:14:02,790 --> 00:14:06,320 And we can think about the rates at which that would 220 00:14:06,320 --> 00:14:07,880 happen in the body. 221 00:14:07,880 --> 00:14:11,940 So normally, we're at 37 degrees, that's normal body 222 00:14:11,940 --> 00:14:15,600 temperature, and we have the observed rate constant for 223 00:14:15,600 --> 00:14:16,540 that is 1 . 224 00:14:16,540 --> 00:14:20,590 0 times 10 to the minus 3 per molar per second. 225 00:14:20,590 --> 00:14:24,030 But what happens if your body temperature is lowered, what 226 00:14:24,030 --> 00:14:29,150 happens if it was at 35 degrees, and to be able to 227 00:14:29,150 --> 00:14:32,410 answer that question, you need to know what the activation 228 00:14:32,410 --> 00:14:35,830 energy is for this process, and here it's 108 229 00:14:35,830 --> 00:14:41,050 kilojoules per mole. 230 00:14:41,050 --> 00:14:44,180 So, we want to ask the question, what is the new rate 231 00:14:44,180 --> 00:14:47,060 constant at 35 degrees? 232 00:14:47,060 --> 00:14:52,050 So, we can take our Arrhenius equations, and we can put a 1 233 00:14:52,050 --> 00:14:55,280 by the rate constant for temperature 1, and a 2 for the 234 00:14:55,280 --> 00:14:57,760 rate constant at temperature 2. 235 00:14:57,760 --> 00:15:02,040 Now we can combine these equations. 236 00:15:02,040 --> 00:15:05,860 Natural log of a cancels out, it's not temperature dependent 237 00:15:05,860 --> 00:15:07,700 so it doesn't stay in here. 238 00:15:07,700 --> 00:15:11,860 And so we can solve, we can subtract these two, or that's 239 00:15:11,860 --> 00:15:16,400 equivalent to dividing them, and so natural log of rate 240 00:15:16,400 --> 00:15:20,530 constant 2 over rate constant 1 equals minus the activation 241 00:15:20,530 --> 00:15:25,460 energy over the gas constant times this temperature term. 242 00:15:25,460 --> 00:15:27,330 Does this look at all familiar? 243 00:15:27,330 --> 00:15:28,890 Does this look like some other equation you 244 00:15:28,890 --> 00:15:31,740 saw once upon a time? 245 00:15:31,740 --> 00:15:35,450 Do you remember what that equation was called? 246 00:15:35,450 --> 00:15:37,250 Van't Hoff equation, right. 247 00:15:37,250 --> 00:15:38,970 And there we were comparing what 248 00:15:38,970 --> 00:15:41,930 instead of rate constants? 249 00:15:41,930 --> 00:15:45,210 Equilibrium constants, and instead of e a, what term did 250 00:15:45,210 --> 00:15:47,140 we have here? 251 00:15:47,140 --> 00:15:49,100 Delta h, right. 252 00:15:49,100 --> 00:15:51,430 And it's good you remember that because we're going to 253 00:15:51,430 --> 00:15:54,960 come back to that at the end of today's class. 254 00:15:54,960 --> 00:15:57,890 So, we can use this equation and plug in the values. 255 00:15:57,890 --> 00:16:01,230 We put in our activation energy, and remember to pay 256 00:16:01,230 --> 00:16:03,950 attention to units, because if you're going to cancel your 257 00:16:03,950 --> 00:16:06,740 joules with a gas constant, you want to make sure you've 258 00:16:06,740 --> 00:16:10,980 converted your kilojoules to joules, and then we can plug 259 00:16:10,980 --> 00:16:14,450 everything in and solve for k 2. 260 00:16:14,450 --> 00:16:16,360 So, here k 2 is 7 . 261 00:16:16,360 --> 00:16:18,750 6 times 10 to the minus 4 per molar per 262 00:16:18,750 --> 00:16:20,930 second, so it's slower. 263 00:16:20,930 --> 00:16:23,710 And this is one reason why it's really nice to have your 264 00:16:23,710 --> 00:16:26,730 body temperature stay the normal temperature. 265 00:16:26,730 --> 00:16:30,830 If you get too cold, your body processes, your enzymes are 266 00:16:30,830 --> 00:16:33,100 not functioning, everything is slowed down. 267 00:16:33,100 --> 00:16:35,270 And if you get too hot, that's not good either. 268 00:16:35,270 --> 00:16:38,670 So you really want to maintain it, and so for some of you who 269 00:16:38,670 --> 00:16:42,720 come to MIT from warmer climates, let me introduce you 270 00:16:42,720 --> 00:16:46,120 to the L.L. Bean catalog, they sell coats, they sell boots, 271 00:16:46,120 --> 00:16:47,220 and all sorts of things. 272 00:16:47,220 --> 00:16:52,000 So, this winter, when you come back for IAP, or for the term, 273 00:16:52,000 --> 00:16:56,030 you're well-prepared, and you don't have to prove that it's 274 00:16:56,030 --> 00:16:58,370 not good if your body temperature 275 00:16:58,370 --> 00:17:03,400 goes below 37 degrees. 276 00:17:03,400 --> 00:17:06,300 All right, let's think about what else this equation tells 277 00:17:06,300 --> 00:17:10,910 us, and the other thing it tells us is that if you have a 278 00:17:10,910 --> 00:17:16,450 very large activation energy, if this e a is a very, very 279 00:17:16,450 --> 00:17:20,370 big number, that means that your rate constants will be 280 00:17:20,370 --> 00:17:22,490 very sensitive to temperature. 281 00:17:22,490 --> 00:17:25,620 So if this is really, really big, there's going to be a big 282 00:17:25,620 --> 00:17:28,790 change in your rate constants as temperature changes. 283 00:17:28,790 --> 00:17:30,280 And keep that in mind, we're going to come 284 00:17:30,280 --> 00:17:34,120 back to that later. 285 00:17:34,120 --> 00:17:38,060 So, what do you think happens to the rate of an enzymatic 286 00:17:38,060 --> 00:17:40,780 reaction at liquid nitrogen temperatures? 287 00:17:40,780 --> 00:17:45,010 We looked at going from 37 degrees to 35, liquid nitrogen 288 00:17:45,010 --> 00:17:47,530 is pretty cold. 289 00:17:47,530 --> 00:17:51,490 So, not a whole lot happens at liquid nitrogen temperatures 290 00:17:51,490 --> 00:17:56,100 as far as enzymes go, and I'll just mention, so it slows way 291 00:17:56,100 --> 00:18:00,570 down, that this is a trick that I use in my research. 292 00:18:00,570 --> 00:18:05,340 So we have crystals of enzymes, and we can try to get 293 00:18:05,340 --> 00:18:10,210 structures in particular states by taking the crystals 294 00:18:10,210 --> 00:18:13,470 that have enzyme in it, and starting a reaction, and then 295 00:18:13,470 --> 00:18:16,870 dunking the crystals in liquid nitrogen to kind of stop it at 296 00:18:16,870 --> 00:18:19,360 a particular stage, and then you look at what the structure 297 00:18:19,360 --> 00:18:20,190 looks like. 298 00:18:20,190 --> 00:18:21,540 So that's one use. 299 00:18:21,540 --> 00:18:24,570 So, we're going to also take a look at other reactions, we 300 00:18:24,570 --> 00:18:27,620 don't have any enzymes here, but some other things, and 301 00:18:27,620 --> 00:18:32,630 look at what happens when we get things to be very cold. 302 00:18:32,630 --> 00:18:50,660 [EXPERIMENTING] 303 00:18:50,660 --> 00:18:53,890 So, Dr. Taylor is pouring out some liquid nitrogen. 304 00:18:53,890 --> 00:19:04,640 PROFESSOR: All right, so what we're going to look at is a 305 00:19:04,640 --> 00:19:07,620 reaction that we can see pretty easily here. 306 00:19:07,620 --> 00:19:11,140 Have any of you used glow sticks before, maybe trick or 307 00:19:11,140 --> 00:19:13,650 treating or some other point. 308 00:19:13,650 --> 00:19:17,030 So basically, you may or may not know how they work. 309 00:19:17,030 --> 00:19:19,540 There's two compartments in glow sticks that have two 310 00:19:19,540 --> 00:19:21,960 different chemicals in them, and they're trade secrets so 311 00:19:21,960 --> 00:19:23,530 we can't put them on the board. 312 00:19:23,530 --> 00:19:26,250 But basically, what we have here is a reaction. 313 00:19:26,250 --> 00:19:29,160 A lot of reactions we know give off heat, or they give 314 00:19:29,160 --> 00:19:30,680 infrared light. 315 00:19:30,680 --> 00:19:32,690 Here we have a reaction that gives off 316 00:19:32,690 --> 00:19:35,180 energy as visible light. 317 00:19:35,180 --> 00:19:37,970 So would you call this an endothermic or an exothermic 318 00:19:37,970 --> 00:19:39,950 reaction here? 319 00:19:39,950 --> 00:19:42,170 Yeah, so this is an exothermic reaction. 320 00:19:42,170 --> 00:19:45,820 So just as Professor Drennan was talking about with slowing 321 00:19:45,820 --> 00:19:48,620 down enzymatic reactions we can think about if we can slow 322 00:19:48,620 --> 00:19:50,340 down this reaction. 323 00:19:50,340 --> 00:20:01,780 So, we're just going to put it in the liquid nitrogen -- so, 324 00:20:01,780 --> 00:20:04,840 keep an eye on this, we'll do several controls of different 325 00:20:04,840 --> 00:20:05,680 colors here. 326 00:20:05,680 --> 00:20:09,390 So, see if an orange glow stick works the same. 327 00:20:09,390 --> 00:20:10,960 What we're looking to see is if we can 328 00:20:10,960 --> 00:20:12,690 slow down this reaction. 329 00:20:12,690 --> 00:20:14,760 What would we see if we slowed it down or even 330 00:20:14,760 --> 00:20:17,290 if we stopped it? 331 00:20:17,290 --> 00:20:19,370 Yeah, we're not going to see anymore color. 332 00:20:19,370 --> 00:20:21,840 So are you starting to see color loss in this first 333 00:20:21,840 --> 00:20:28,380 reaction here? 334 00:20:28,380 --> 00:20:39,820 So, we'll try green, and yellow. 335 00:20:39,820 --> 00:20:42,360 So, it looks like this first one might have stopped 336 00:20:42,360 --> 00:20:45,400 already, you see there's no color anymore here. 337 00:20:45,400 --> 00:20:47,890 What would you expect if this heated back up to room 338 00:20:47,890 --> 00:20:49,990 temperature? 339 00:20:49,990 --> 00:20:52,860 Yeah, so hopefully, if you just keep your eye on this, 340 00:20:52,860 --> 00:20:55,310 we'll continue on with the lecturing, because I don't 341 00:20:55,310 --> 00:20:57,810 know how long it will take for it to warm back up the room 342 00:20:57,810 --> 00:20:58,900 temperature. 343 00:20:58,900 --> 00:21:02,360 But keep an eye and we'll see if we get the temperature back 344 00:21:02,360 --> 00:21:05,540 high enough to see the glow again. 345 00:21:05,540 --> 00:21:08,670 And since we do have a liquid nitrogen here, it's too hard 346 00:21:08,670 --> 00:21:10,580 to resist freezing a flower. 347 00:21:10,580 --> 00:21:15,310 This has nothing to do with kinetics -- we can't even try 348 00:21:15,310 --> 00:21:17,170 that connection. 349 00:21:17,170 --> 00:21:20,770 But we will be freeze a flower. 350 00:21:20,770 --> 00:21:28,320 OK, she will try making -- good catharsis pre-exam. 351 00:21:28,320 --> 00:21:36,700 PROFESSOR: So, has anyone had liquid 352 00:21:36,700 --> 00:21:41,410 nitrogen applied to them? 353 00:21:41,410 --> 00:21:45,320 It's used in doctor's offices, if you want a little something 354 00:21:45,320 --> 00:21:47,350 removed perhaps, put a little liquid nitrogen 355 00:21:47,350 --> 00:21:48,640 on and burn it off. 356 00:21:48,640 --> 00:21:52,400 Good premed training for you. 357 00:21:52,400 --> 00:21:54,270 I think we're pretty frozen here. 358 00:21:54,270 --> 00:22:04,600 So it looks the same, but as you can see -- 359 00:22:04,600 --> 00:22:07,830 [INAUDIBLE] -- 360 00:22:07,830 --> 00:22:14,924 So I think that's all we can do [LAUGHTER] 361 00:22:14,924 --> 00:22:25,710 [APPLAUSE] 362 00:22:25,710 --> 00:22:30,086 PROFESSOR: So I actually heard something interesting on NPR 363 00:22:30,086 --> 00:22:33,190 about liquid nitrogen removing warts and things like that, 364 00:22:33,190 --> 00:22:35,250 and they were talking about how there was something that 365 00:22:35,250 --> 00:22:36,700 was actually better than liquid 366 00:22:36,700 --> 00:22:38,480 nitrogen for doing that. 367 00:22:38,480 --> 00:22:40,930 Did anyone hear the story about what the thing was that 368 00:22:40,930 --> 00:22:44,230 was better than liquid nitrogen? 369 00:22:44,230 --> 00:22:47,670 It was duct tape. 370 00:22:47,670 --> 00:22:50,610 And so some scientists had looked at what all the uses of 371 00:22:50,610 --> 00:22:51,850 duct tape are. 372 00:22:51,850 --> 00:22:54,390 And since most of you are planning on being scientists 373 00:22:54,390 --> 00:22:57,120 or engineers, duct tape will probably be an important part 374 00:22:57,120 --> 00:22:59,380 of your life in the future. 375 00:22:59,380 --> 00:23:03,130 And so, duct tape worked better than liquid nitrogen 376 00:23:03,130 --> 00:23:04,520 for removing warts. 377 00:23:04,520 --> 00:23:07,180 And they found that duct tape worked really well 378 00:23:07,180 --> 00:23:08,380 for a lot of things. 379 00:23:08,380 --> 00:23:11,000 There was only one thing they tried that it did 380 00:23:11,000 --> 00:23:12,860 not work well for. 381 00:23:12,860 --> 00:23:15,630 Anyone want to guess what that was? 382 00:23:15,630 --> 00:23:19,020 Repairing ducts, yes. 383 00:23:19,020 --> 00:23:21,980 Not really good -- there were many, many, many better ways 384 00:23:21,980 --> 00:23:26,170 to repair ducts than with duct tape, but I guess they decided 385 00:23:26,170 --> 00:23:30,150 that calling it wart removal tape was just not quite as 386 00:23:30,150 --> 00:23:32,670 catchy as duct tape, so it's still 387 00:23:32,670 --> 00:23:38,330 referred to as duct tape. 388 00:23:38,330 --> 00:23:44,970 OK, so when you lower the temperature, things 389 00:23:44,970 --> 00:23:46,240 tend to slow down. 390 00:23:46,240 --> 00:23:51,390 But if molecules are going to react, they need to have 391 00:23:51,390 --> 00:23:54,750 enough energy, they need to have a high enough temperature 392 00:23:54,750 --> 00:23:58,400 to overcome this activation energy. 393 00:23:58,400 --> 00:24:02,200 So that critical amount. 394 00:24:02,200 --> 00:24:06,490 So again, when the molecules come together, and let's just 395 00:24:06,490 --> 00:24:08,720 look at these for a minute, when they're coming together 396 00:24:08,720 --> 00:24:12,810 to react, and if they're going to react, there needs to be 397 00:24:12,810 --> 00:24:15,130 some energy associated with this, because you're probably 398 00:24:15,130 --> 00:24:17,760 going to have to break a bond, and that's going to take 399 00:24:17,760 --> 00:24:21,190 something, and then you may have to form a 400 00:24:21,190 --> 00:24:22,980 new bond, for example. 401 00:24:22,980 --> 00:24:26,250 So there needs to be a critical amount of energy, you 402 00:24:26,250 --> 00:24:29,730 need to be able to overcome that activation energy barrier 403 00:24:29,730 --> 00:24:32,020 for the molecules to react. 404 00:24:32,020 --> 00:24:35,630 So it always takes some energy for things to react and so you 405 00:24:35,630 --> 00:24:37,500 need to have enough energy. 406 00:24:37,500 --> 00:24:42,080 And so, if those molecules have that energy, they'll come 407 00:24:42,080 --> 00:24:44,330 together, react, and you'll form products. 408 00:24:44,330 --> 00:24:46,580 If they don't have that energy, they're just going to 409 00:24:46,580 --> 00:24:52,060 go back to what they were, unchanged reactants. 410 00:24:52,060 --> 00:24:56,040 So you need to have sufficient energy to overcome that 411 00:24:56,040 --> 00:24:59,060 activation energy barrier. 412 00:24:59,060 --> 00:25:02,560 So, this is just a little movie that shows two molecules 413 00:25:02,560 --> 00:25:06,840 coming together, and if they have enough energy to react, 414 00:25:06,840 --> 00:25:11,940 you will see a spark, and then the molecules will react. 415 00:25:11,940 --> 00:25:13,350 So, here we go. 416 00:25:13,350 --> 00:25:15,630 Molecule in red, in green, they're 417 00:25:15,630 --> 00:25:16,710 checking each other out. 418 00:25:16,710 --> 00:25:19,560 Do they have enough -- they had enough energy, and they 419 00:25:19,560 --> 00:25:25,100 reacted, and went on to product. 420 00:25:25,100 --> 00:25:30,100 All right, so let's talk about this activation energy barrier 421 00:25:30,100 --> 00:25:38,410 and these activated complexes. 422 00:25:38,410 --> 00:25:53,750 OK, so in this example, you have n o 2 plus c o, and they 423 00:25:53,750 --> 00:25:58,320 can come together and form n o plus c o 2. 424 00:25:58,320 --> 00:26:02,590 And that's going to take some amount of energy to react. 425 00:26:02,590 --> 00:26:05,740 And so, I'm drawing something that's called an activated 426 00:26:05,740 --> 00:26:16,260 energy diagram, and we have potential energy on one axis, 427 00:26:16,260 --> 00:26:19,620 and on the other we have what's called a reaction 428 00:26:19,620 --> 00:26:28,560 coordinate. 429 00:26:28,560 --> 00:26:31,420 And so, the reactants are going to have a certain amount 430 00:26:31,420 --> 00:26:36,870 of energy, so our reactants are going to have some amount 431 00:26:36,870 --> 00:26:39,800 of energy, and our products will have 432 00:26:39,800 --> 00:26:45,880 some amount of energy. 433 00:26:45,880 --> 00:26:51,690 But even though in this case the change, the products are 434 00:26:51,690 --> 00:26:56,720 lower in energy, and you have a delta e for the difference 435 00:26:56,720 --> 00:26:59,620 between the reactants and the products, they can't go 436 00:26:59,620 --> 00:27:01,190 directly to products. 437 00:27:01,190 --> 00:27:05,080 They have to overcome an activation energy barrier. 438 00:27:05,080 --> 00:27:08,870 So they have to overcome some kind of barrier 439 00:27:08,870 --> 00:27:12,480 before they can react. 440 00:27:12,480 --> 00:27:16,510 So, only ones that can overcome that barrier, that 441 00:27:16,510 --> 00:27:20,400 have enough energy to overcome this activation energy 442 00:27:20,400 --> 00:27:23,920 barrier, so the activation energy for the forward 443 00:27:23,920 --> 00:27:27,440 reaction, only those will be able to react. 444 00:27:27,440 --> 00:27:31,340 There's also an activation energy barrier for the reverse 445 00:27:31,340 --> 00:27:33,850 reaction on this side. 446 00:27:33,850 --> 00:27:36,340 So, if you go from products to reactants, you have to 447 00:27:36,340 --> 00:27:40,020 overcome that activation energy barrier. 448 00:27:40,020 --> 00:27:47,780 And up here, this is called the activated complex, so you 449 00:27:47,780 --> 00:27:55,120 have some kind of activated complex or transition state, 450 00:27:55,120 --> 00:27:58,260 so the molecules will come together, they'll form some 451 00:27:58,260 --> 00:28:00,820 kind of transition state up here, and then 452 00:28:00,820 --> 00:28:04,660 go down into products. 453 00:28:04,660 --> 00:28:08,290 OK, so most of you are sort of familiar with the concept, I 454 00:28:08,290 --> 00:28:10,350 think, of this activation energy, we've been talking 455 00:28:10,350 --> 00:28:14,200 about it, but the idea of an activation energy barrier, I 456 00:28:14,200 --> 00:28:16,470 think is something that probably all of you can 457 00:28:16,470 --> 00:28:18,180 personally connect with. 458 00:28:18,180 --> 00:28:23,270 So, for me, one of the things that I find really hard to do 459 00:28:23,270 --> 00:28:26,510 is get started writing a long National 460 00:28:26,510 --> 00:28:28,300 Institutes of Health grant. 461 00:28:28,300 --> 00:28:33,710 They're about 25 pages long, they're single spaced, font 462 00:28:33,710 --> 00:28:37,870 11, and they have point 5 margins on every side of the 463 00:28:37,870 --> 00:28:42,390 page, and it's really dense, and it takes a long time to 464 00:28:42,390 --> 00:28:43,990 sort of get going on that. 465 00:28:43,990 --> 00:28:47,660 And so, there is deadlines, and MIT is very particular, 466 00:28:47,660 --> 00:28:50,830 you need to have it to the Office of Sponsored Research 467 00:28:50,830 --> 00:28:54,060 five full business days before it's due at the National 468 00:28:54,060 --> 00:28:56,680 Institutes of Health, and then the Department needs 469 00:28:56,680 --> 00:28:57,800 to sign off on it. 470 00:28:57,800 --> 00:28:59,830 And I'll be looking at my calendar and I have those 471 00:28:59,830 --> 00:29:03,160 dates marked, and checking how many days I have left, and 472 00:29:03,160 --> 00:29:06,290 eventually, just like getting started, it's like oh, there's 473 00:29:06,290 --> 00:29:09,400 so much to do, I have to read the literature, the new stuff 474 00:29:09,400 --> 00:29:11,160 that's come out on my topic. 475 00:29:11,160 --> 00:29:13,460 And I have to think about what projects I'm going to do in 476 00:29:13,460 --> 00:29:16,080 the future, and I have to write about the progress that 477 00:29:16,080 --> 00:29:19,220 I've made so far, which is not really what I want it to be. 478 00:29:19,220 --> 00:29:23,910 And so, I think a lot about how -- it's just overwhelming. 479 00:29:23,910 --> 00:29:25,940 But then eventually something happens. 480 00:29:25,940 --> 00:29:29,490 Either it's tremendous fear that there's so few days left 481 00:29:29,490 --> 00:29:31,360 and you just have to do it. 482 00:29:31,360 --> 00:29:34,300 Sometimes it's going and getting an enormous cup of 483 00:29:34,300 --> 00:29:36,750 coffee and sitting down. 484 00:29:36,750 --> 00:29:38,520 You know, people have been known to sort of chain 485 00:29:38,520 --> 00:29:40,890 themselves to their desk, like they're not going to get to 486 00:29:40,890 --> 00:29:45,120 get up until they've written the introduction to the grant. 487 00:29:45,120 --> 00:29:47,330 So, a lot you can connect with this. 488 00:29:47,330 --> 00:29:51,030 That any new thing you start, there's some barrier that you 489 00:29:51,030 --> 00:29:53,360 have to overcome to get started with it. 490 00:29:53,360 --> 00:29:56,332 And often once you're started it's not that bad, and some of 491 00:29:56,332 --> 00:30:00,250 you may be thinking, exam 1 was a long time ago, I recall 492 00:30:00,250 --> 00:30:02,760 there was a lot of material on exam 1. 493 00:30:02,760 --> 00:30:04,670 And it seems really scary. 494 00:30:04,670 --> 00:30:07,760 But then the fact that I mention the final exam over 495 00:30:07,760 --> 00:30:11,710 and over in class is helping you get that energy that you 496 00:30:11,710 --> 00:30:15,790 need to overcome that activation energy barrier and 497 00:30:15,790 --> 00:30:18,017 start studying, because once you start studying you go, Oh 498 00:30:18,017 --> 00:30:19,970 yeah, I remember this, this wasn't so bad. 499 00:30:19,970 --> 00:30:23,860 So you just need to get over that activation energy barrier 500 00:30:23,860 --> 00:30:25,060 and you're all set. 501 00:30:25,060 --> 00:30:28,330 So, molecules have to do the same thing, and the ones that 502 00:30:28,330 --> 00:30:32,640 have higher temperature have an easier time getting over 503 00:30:32,640 --> 00:30:34,670 that barrier. 504 00:30:34,670 --> 00:30:39,530 So, here we can talk about this general process. 505 00:30:39,530 --> 00:30:42,470 We can look at the individual numbers involved. 506 00:30:42,470 --> 00:30:45,550 So in this particular case, there's an activation energy 507 00:30:45,550 --> 00:30:53,170 for the forward reaction of 132 kilojoules per mole, and 508 00:30:53,170 --> 00:30:57,310 there is an activation energy for the reverse reaction of 509 00:30:57,310 --> 00:31:01,770 358 kilojoules per mole. 510 00:31:01,770 --> 00:31:05,640 And there's also a delta e for the reaction, which is this 511 00:31:05,640 --> 00:31:08,680 line, from reactions to products, which in this case 512 00:31:08,680 --> 00:31:13,410 is minus 226 kilojoules per mole. 513 00:31:13,410 --> 00:31:15,850 So do you think this reaction is endothermic or exothermic? 514 00:31:15,850 --> 00:31:23,170 What do you think, exothermic or endothermic? 515 00:31:23,170 --> 00:31:29,770 It's exothermic, and if you look back in your notes, we 516 00:31:29,770 --> 00:31:32,970 talked a little bit about the relationship between delta h 517 00:31:32,970 --> 00:31:33,920 and delta e. 518 00:31:33,920 --> 00:31:38,440 And they're actually pretty similar. 519 00:31:38,440 --> 00:31:45,070 A delta h usually equals delta e plus a change in p v. So, 520 00:31:45,070 --> 00:31:50,920 for gases it's about 1% or 2% difference, and for solids, 521 00:31:50,920 --> 00:31:52,840 there's really negligible difference between 522 00:31:52,840 --> 00:31:54,150 delta e and delta h. 523 00:31:54,150 --> 00:31:58,570 So, they're pretty similar types of values. 524 00:31:58,570 --> 00:32:01,995 So, we can we can think about what delta e really is, and so 525 00:32:01,995 --> 00:32:05,830 delta e in terms of activation energy is going to be equal to 526 00:32:05,830 --> 00:32:09,880 the activation energy for the forward reaction minus the 527 00:32:09,880 --> 00:32:13,220 activation energy for the reverse reaction. 528 00:32:13,220 --> 00:32:17,650 And in this particular case, we have 226 kilojoules per 529 00:32:17,650 --> 00:32:24,440 mole is our delta e, and for our forward reaction, we have 530 00:32:24,440 --> 00:32:33,060 132 kilojoules per mole, and for the reverse reaction, the 531 00:32:33,060 --> 00:32:38,700 activation energy for the reverse reaction is 358 532 00:32:38,700 --> 00:32:43,730 kilojoules per mole, and so these should all equal up to 533 00:32:43,730 --> 00:32:44,640 each other. 534 00:32:44,640 --> 00:32:47,010 And so, if you know two of these values, you can 535 00:32:47,010 --> 00:32:48,250 calculate the third. 536 00:32:48,250 --> 00:32:50,270 And this is one of the equations that you have to 537 00:32:50,270 --> 00:32:53,760 memorize for the final, because it has, its sort of a 538 00:32:53,760 --> 00:32:56,540 conceptual thing that you need to understand what this 539 00:32:56,540 --> 00:33:01,050 diagram says, that this plus that is equal to that, that 540 00:33:01,050 --> 00:33:02,940 these all add up to each other. 541 00:33:02,940 --> 00:33:05,950 And if you have a negative value here, that means it's an 542 00:33:05,950 --> 00:33:07,990 exothermic reaction. 543 00:33:07,990 --> 00:33:12,030 So, this delta e is a change in internal energy of the 544 00:33:12,030 --> 00:33:16,330 system, and you can determine that value experimentally, 545 00:33:16,330 --> 00:33:21,030 say, with a calorimetry experiment. 546 00:33:21,030 --> 00:33:27,800 OK, so let's keep this in mind and go on and take a look at 547 00:33:27,800 --> 00:33:31,060 how this connects back with some other things that we have 548 00:33:31,060 --> 00:33:34,020 already talked about in this course. 549 00:33:34,020 --> 00:33:37,730 So, for an elementary reaction, and I think for all 550 00:33:37,730 --> 00:33:40,060 of us, there's always some activation 551 00:33:40,060 --> 00:33:42,510 energy barrier to overcome. 552 00:33:42,510 --> 00:33:46,090 There's always some positive activation energy to overcome. 553 00:33:46,090 --> 00:33:49,050 And because there's always this activation energy to 554 00:33:49,050 --> 00:33:52,680 overcome, increasing the temperature is always going to 555 00:33:52,680 --> 00:33:56,150 increase the rate of an elementary reaction. 556 00:33:56,150 --> 00:33:59,120 It's always going to make it easier to get over that 557 00:33:59,120 --> 00:34:01,930 activation energy barrier. 558 00:34:01,930 --> 00:34:06,350 But for an overall reaction, increasing the temperature may 559 00:34:06,350 --> 00:34:09,140 not increase the rate of the reaction. 560 00:34:09,140 --> 00:34:14,480 So let's consider why that would be true. 561 00:34:14,480 --> 00:34:17,580 So, here is a reaction that we've talked about before, we 562 00:34:17,580 --> 00:34:20,950 talked about this proposed mechanism where we have a fast 563 00:34:20,950 --> 00:34:26,530 reversible step and a slow second step. 564 00:34:26,530 --> 00:34:28,800 So we learned last time that we can write the rate of 565 00:34:28,800 --> 00:34:33,000 product formation from the second step, there are two 566 00:34:33,000 --> 00:34:36,340 molecules of n o 2 being formed, so we have 2 times k 567 00:34:36,340 --> 00:34:39,790 2, the concentration of n 2 o 2, and the 568 00:34:39,790 --> 00:34:43,310 concentration of o 2. 569 00:34:43,310 --> 00:34:46,370 But this is an intermediate, so we need to solve for that 570 00:34:46,370 --> 00:34:49,040 intermediate. 571 00:34:49,040 --> 00:34:54,530 So, in this case, we have a fast reversible first reaction 572 00:34:54,530 --> 00:34:56,730 and a slow second reaction. 573 00:34:56,730 --> 00:34:59,860 So this intermediate is going to build up, and it's going to 574 00:34:59,860 --> 00:35:03,840 be more or less an equilibrium with the reactants, because 575 00:35:03,840 --> 00:35:07,180 this is very fast, and only a little bit of this is siphoned 576 00:35:07,180 --> 00:35:12,270 off to make product, and so this creates an equilibrium 577 00:35:12,270 --> 00:35:13,560 type situation. 578 00:35:13,560 --> 00:35:17,440 So why don't you solve this intermediate for me, this is a 579 00:35:17,440 --> 00:36:13,090 review from the last class. 580 00:36:13,090 --> 00:36:29,150 OK, let's just take 10 more seconds. 581 00:36:29,150 --> 00:36:33,760 Very good. 582 00:36:33,760 --> 00:36:37,250 So, we can solve for this, equilibrium constant for the 583 00:36:37,250 --> 00:36:40,980 first step, products over reactants, and then if you 584 00:36:40,980 --> 00:36:43,770 solved for this, the intermediate here, which is 585 00:36:43,770 --> 00:36:47,440 the product in the first step, then it would be equal to k 1 586 00:36:47,440 --> 00:36:50,150 times n o squared. 587 00:36:50,150 --> 00:36:55,350 We can take that term and we can we can plug it in, so over 588 00:36:55,350 --> 00:36:59,720 here, we can substitute it into this equation, and so we 589 00:36:59,720 --> 00:37:08,160 have 2 k 2, big K 1 times n o squared times o 2. 590 00:37:08,160 --> 00:37:10,740 All right, so here is our rate then. 591 00:37:10,740 --> 00:37:13,810 And if you missed some of this, this was in the notes 592 00:37:13,810 --> 00:37:15,310 from before. 593 00:37:15,310 --> 00:37:19,190 So now let's think about the effect of temperature. 594 00:37:19,190 --> 00:37:23,610 So, k 2 is an elementary rate constant, and so its 595 00:37:23,610 --> 00:37:26,230 temperature -- if you increase the temperature, 596 00:37:26,230 --> 00:37:29,640 its rate will increase. 597 00:37:29,640 --> 00:37:34,980 So here again is our equation, the activation energy is 598 00:37:34,980 --> 00:37:37,260 always positive, there's always positive, there's 599 00:37:37,260 --> 00:37:39,500 always some barrier to overcome. 600 00:37:39,500 --> 00:37:41,850 So if you increase the temperature, you're always 601 00:37:41,850 --> 00:37:46,040 going to increase the elementary rate. 602 00:37:46,040 --> 00:37:49,200 Well, what about equilibrium constant? 603 00:37:49,200 --> 00:37:52,890 So we've talked about this back in chemical equilibrium 604 00:37:52,890 --> 00:37:56,330 that the effect of temperature on the equilibrium constant 605 00:37:56,330 --> 00:37:58,580 depends on whether the reaction is endothermic or 606 00:37:58,580 --> 00:38:01,030 exothermic. 607 00:38:01,030 --> 00:38:05,000 And you told me before, the equation, and that's the Van't 608 00:38:05,000 --> 00:38:06,970 Hoff equation shown here. 609 00:38:06,970 --> 00:38:09,830 And so look how similar those equations are. 610 00:38:09,830 --> 00:38:13,480 So for an elementary rate constant, we had e a, and for 611 00:38:13,480 --> 00:38:18,090 equilibrium constant, we're talking about delta h. 612 00:38:18,090 --> 00:38:23,020 So, if you have, here the reaction is exothermic, and if 613 00:38:23,020 --> 00:38:26,640 you increase the temperature of an exothermic reaction, 614 00:38:26,640 --> 00:38:33,760 what happens to k? 615 00:38:33,760 --> 00:38:36,750 It decreases. 616 00:38:36,750 --> 00:38:40,490 So, again, it would shift, then, to the endothermic 617 00:38:40,490 --> 00:38:42,840 direction, decreasing k. 618 00:38:42,840 --> 00:38:44,270 So let's look at this then. 619 00:38:44,270 --> 00:38:47,760 So we have in this k obs term, we have an elementary rate 620 00:38:47,760 --> 00:38:51,330 constant and an equilibrium constant, so if you if you 621 00:38:51,330 --> 00:38:54,940 increase the temperature, the rate constant increases, but 622 00:38:54,940 --> 00:38:59,950 the equilibrium constant is going to decrease. 623 00:38:59,950 --> 00:39:03,550 So, the magnitude of the increase or decrease depends 624 00:39:03,550 --> 00:39:09,440 on the size of the activation energy or the size of delta h. 625 00:39:09,440 --> 00:39:12,780 So for this particular example, there's no way that 626 00:39:12,780 --> 00:39:14,860 you would know this so I'm telling you, that the 627 00:39:14,860 --> 00:39:17,620 activation energy is a small number, or you might be able 628 00:39:17,620 --> 00:39:21,090 to look it up in your book, and delta h is a very big 629 00:39:21,090 --> 00:39:24,030 number and it's negative, it's an exothermic reaction. 630 00:39:24,030 --> 00:39:27,940 So if you have a very small number for e a, that means 631 00:39:27,940 --> 00:39:30,300 that the rate constant will increase only a little bit, 632 00:39:30,300 --> 00:39:33,250 it's not that sensitive to a change in temperature, because 633 00:39:33,250 --> 00:39:35,280 e a's a very small number. 634 00:39:35,280 --> 00:39:38,920 But if delta h is a big number, then the equilibrium 635 00:39:38,920 --> 00:39:41,940 constant would decrease a lot with temperature because this 636 00:39:41,940 --> 00:39:43,470 is a big number here. 637 00:39:43,470 --> 00:39:46,410 So in this particular example, increasing the temperature 638 00:39:46,410 --> 00:39:50,740 actually decreases the observed rate, because delta h 639 00:39:50,740 --> 00:39:53,690 is, in this particular example, a much bigger thing. 640 00:39:53,690 --> 00:39:56,470 So if you were given either numbers or some information 641 00:39:56,470 --> 00:39:59,350 like that, you should be able to rationalize what might be 642 00:39:59,350 --> 00:40:05,260 true about the rate of the reaction. so, a large 643 00:40:05,260 --> 00:40:08,560 activation energy means that the rate constant is very 644 00:40:08,560 --> 00:40:10,780 sensitive to changes in temperature. 645 00:40:10,780 --> 00:40:14,570 A large delta h means equilibrium constant is very 646 00:40:14,570 --> 00:40:18,620 sensitive to changes in temperature. 647 00:40:18,620 --> 00:40:22,450 And, as we've talked about, e a is always positive, so the 648 00:40:22,450 --> 00:40:26,320 elementary rates always increase with temperature, 649 00:40:26,320 --> 00:40:32,010 whereas delta h can be positive or negative, so 650 00:40:32,010 --> 00:40:36,410 equilibrium constants can increase or decrease with 651 00:40:36,410 --> 00:40:38,240 temperature. 652 00:40:38,240 --> 00:40:42,460 And here, the magnitude of delta h indicates the 653 00:40:42,460 --> 00:40:45,280 magnitude of the change, how much k will change, will it be 654 00:40:45,280 --> 00:40:48,410 a big change or a small change, whereas the sign of 655 00:40:48,410 --> 00:40:55,480 delta h indicates the direction of the change. 656 00:40:55,480 --> 00:40:58,810 So, just want to review one thing and then we'll 657 00:40:58,810 --> 00:41:00,140 stop for the day. 658 00:41:00,140 --> 00:41:04,510 So when a stress is applied to a system, an equilibrium, the 659 00:41:04,510 --> 00:41:08,490 system tends to try to minimize that stress. 660 00:41:08,490 --> 00:41:12,130 So we're back to LeChatelier's principle. 661 00:41:12,130 --> 00:41:14,790 And so, just one more clicker question and we'll 662 00:41:14,790 --> 00:41:15,670 stop for the day. 663 00:41:15,670 --> 00:41:21,130 So increasing the temperature is going to do what again? 664 00:41:21,130 --> 00:41:36,430 Again, thinking back to LeChatelier. 665 00:41:36,430 --> 00:41:51,500 And just 10 more seconds. 666 00:41:51,500 --> 00:41:52,630 Very good. 667 00:41:52,630 --> 00:41:56,750 So, we're going to finish up these notes on Monday. 668 00:41:56,750 --> 00:41:59,840 We're going to think about LeChatelier in a new way, 669 00:41:59,840 --> 00:42:02,920 we're going to think about it in terms of activation energy, 670 00:42:02,920 --> 00:42:06,050 which is really fun, because we tie back what we learned in 671 00:42:06,050 --> 00:42:08,490 the middle of course to what we're seeing now in the end of 672 00:42:08,490 --> 00:42:09,250 the course. 673 00:42:09,250 --> 00:42:11,600 All right, have a great weekend, everybody.