1 00:00:00,030 --> 00:00:02,400 The following content is provided under a Creative 2 00:00:02,400 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,860 Your support will help MIT OpenCourseWare continue to 4 00:00:06,860 --> 00:00:10,510 offer high-quality educational resources for free. 5 00:00:10,510 --> 00:00:13,390 To make a donation or view additional materials from 6 00:00:13,390 --> 00:00:16,190 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:16,190 --> 00:00:16,600 ocw.mit.edu. 8 00:00:16,600 --> 00:00:25,720 PROFESSOR NELSON: Well, so last time we did a little bit 9 00:00:25,720 --> 00:00:28,810 more work on thermodynamic cycles, and basically went 10 00:00:28,810 --> 00:00:31,420 around a cycle and looked at some state functions, delta u 11 00:00:31,420 --> 00:00:34,910 and delta H. Saw that around a closed cycle those zero 12 00:00:34,910 --> 00:00:35,940 because they're state functions. 13 00:00:35,940 --> 00:00:38,530 So if you start and end at the same place, they've got end at 14 00:00:38,530 --> 00:00:39,860 the same place that they started. 15 00:00:39,860 --> 00:00:42,870 There's no change in them, and then we also looked at some at 16 00:00:42,870 --> 00:00:48,020 non-state functions, work and heat, and saw that those 17 00:00:48,020 --> 00:00:49,720 aren't zero going around a cycle. 18 00:00:49,720 --> 00:00:53,030 Of course you can do work in a cyclic process, and heat can 19 00:00:53,030 --> 00:00:55,200 be exchanged with the environment at the same time. 20 00:00:55,200 --> 00:00:57,040 So we calculated those values too. 21 00:00:57,040 --> 00:01:01,770 And we also looked at this other funny function that's 22 00:01:01,770 --> 00:01:03,590 our special function. 23 00:01:03,590 --> 00:01:10,070 We looked at this integral dq over T. It's so special that 24 00:01:10,070 --> 00:01:14,170 we called this derivative dS, and saw that at least for the 25 00:01:14,170 --> 00:01:16,960 cycle we looked at, it also behaved as a 26 00:01:16,960 --> 00:01:17,840 state function behaves. 27 00:01:17,840 --> 00:01:22,120 That is, going around the cycle, it had no net change, 28 00:01:22,120 --> 00:01:25,210 and we'll see this come back later on. 29 00:01:25,210 --> 00:01:27,540 Then we went on to look at thermochemistry, and that's 30 00:01:27,540 --> 00:01:30,220 what I want to continue today. 31 00:01:30,220 --> 00:01:44,020 So really, the main result that we saw last time is that 32 00:01:44,020 --> 00:01:52,990 we can describe the enthalpy of reaction, so if we have 33 00:01:52,990 --> 00:02:04,750 reactants going to products, and we'd like to know our heat 34 00:02:04,750 --> 00:02:07,800 of reaction or enthalpy of reaction, remember it's a 35 00:02:07,800 --> 00:02:10,540 constant pressure as we're considering it, so it's 36 00:02:10,540 --> 00:02:14,690 equivalent to heat of reaction, than the way we can 37 00:02:14,690 --> 00:02:20,840 do this is construct a cycle where we're going to express 38 00:02:20,840 --> 00:02:23,230 these in terms of their constituent elements. 39 00:02:23,230 --> 00:02:25,810 We're going to all the way back to the atoms. 40 00:02:25,810 --> 00:02:28,430 Right, so if we have the elements in their standard 41 00:02:28,430 --> 00:02:32,310 states, that is their most stable forms at room 42 00:02:32,310 --> 00:02:46,600 temperature and pressure, then what we're really doing is 43 00:02:46,600 --> 00:02:48,900 we're saying let's take the reactants and let's pull them 44 00:02:48,900 --> 00:02:51,110 all apart into their separate elements, 45 00:02:51,110 --> 00:02:52,490 they're separate atoms. 46 00:02:52,490 --> 00:02:55,200 And then put them back together this way, and we'll 47 00:02:55,200 --> 00:02:58,440 calculate the enthalpy of this process, the 48 00:02:58,440 --> 00:02:59,670 enthalpy of this process. 49 00:02:59,670 --> 00:03:02,090 It's a cycle, so that'll give us the enthalpy of 50 00:03:02,090 --> 00:03:04,300 reaction, all right? 51 00:03:04,300 --> 00:03:16,390 So this delta H is our sum for delta H of formation for the 52 00:03:16,390 --> 00:03:18,440 reactants, right. 53 00:03:18,440 --> 00:03:25,580 And this is our sum of the quantity for 54 00:03:25,580 --> 00:03:32,350 the products, right. 55 00:03:32,350 --> 00:03:34,850 And in this way, then we can express our delta H of 56 00:03:34,850 --> 00:03:43,970 reaction is just going to be given a sum of the heats of 57 00:03:43,970 --> 00:03:46,140 formation or the difference between the heats of formation 58 00:03:46,140 --> 00:03:49,320 of the products and the reactants, right? 59 00:03:49,320 --> 00:03:52,210 Now, of course, we have to weight this by the number of 60 00:03:52,210 --> 00:03:55,330 moles of each reactant to each product 61 00:03:55,330 --> 00:03:56,840 involved in the reaction. 62 00:03:56,840 --> 00:03:59,720 So to write this a little more carefully, it's, you want to 63 00:03:59,720 --> 00:04:09,700 write the sum over i of nu i delta H naught of formation of 64 00:04:09,700 --> 00:04:17,200 i summed over the products. 65 00:04:17,200 --> 00:04:25,040 This is per mole minus sum over i, nu i here over the 66 00:04:25,040 --> 00:04:28,940 reactants in the same quantity. 67 00:04:28,940 --> 00:04:34,070 Delta H per mole f i, right? 68 00:04:34,070 --> 00:04:36,830 So in other words, were taking each of the products and we're 69 00:04:36,830 --> 00:04:40,470 going to weight them by their stoichiomeric coefficients, 70 00:04:40,470 --> 00:04:45,660 and we're going to have in this delta H of reaction their 71 00:04:45,660 --> 00:04:47,490 heats of formation, and then we're going to have the 72 00:04:47,490 --> 00:04:50,950 negative heats of formation of the reactants, because that's 73 00:04:50,950 --> 00:05:07,950 being subtracted, okay? 74 00:05:07,950 --> 00:05:11,320 So, just to go through a basic example, let's just look at 75 00:05:11,320 --> 00:05:19,240 the burning of methane. 76 00:05:19,240 --> 00:05:26,440 So we've got methane gas, combining with oxygen gas, so 77 00:05:26,440 --> 00:05:36,070 you have carbon dioxide gas and liquid water, and we'll 78 00:05:36,070 --> 00:05:40,260 consider the whole thing at room temperature 79 00:05:40,260 --> 00:05:43,810 and pressure, right. 80 00:05:43,810 --> 00:05:46,690 So let's just undertake this set of processes. 81 00:05:46,690 --> 00:05:49,460 Let's decompose these to the elements. 82 00:05:49,460 --> 00:05:55,820 So in other words, our methane gas, we're going to write the 83 00:05:55,820 --> 00:06:01,540 chemical equilibrium between this and the solid carbon. 84 00:06:01,540 --> 00:06:05,890 That is to say let's specify graphite, it's not diamond, 85 00:06:05,890 --> 00:06:08,390 right, graphite is the stable form of carbon at room 86 00:06:08,390 --> 00:06:15,260 temperature and pressure. 87 00:06:15,260 --> 00:06:22,460 And then, hydrogen gas two moles of hydrogen gas and 88 00:06:22,460 --> 00:06:27,100 we're going to have a delta H of formation. 89 00:06:27,100 --> 00:06:34,000 This is for CH4 in the gas phase, right? 90 00:06:34,000 --> 00:06:46,990 And then over here, we have our oxygen but 2 O2 gas going 91 00:06:46,990 --> 00:06:53,840 to, well 2 O2 gas -- the point is oxygen already is in it's 92 00:06:53,840 --> 00:06:55,820 stable form at room temperature 93 00:06:55,820 --> 00:06:56,760 and pressure, right? 94 00:06:56,760 --> 00:06:59,500 That is the elemental form of oxygen, of course, is as 95 00:06:59,500 --> 00:07:08,770 oxygen molecules in the gas so there's no delta H formation 96 00:07:08,770 --> 00:07:12,200 for oxygen. 97 00:07:12,200 --> 00:07:17,260 The gas is zero, right. 98 00:07:17,260 --> 00:07:20,160 And then second phase of this, now we're going to take the 99 00:07:20,160 --> 00:07:23,810 elements that we've produced, and we're going to put them 100 00:07:23,810 --> 00:07:26,320 back to make products, right? 101 00:07:26,320 --> 00:07:36,380 So there we've got carbon as graphite, and a solid plus an 102 00:07:36,380 --> 00:07:43,600 oxygen gas goes to make CO2 gas, right. 103 00:07:43,600 --> 00:07:47,450 And we've got our positive delta H of formation 104 00:07:47,450 --> 00:07:52,140 associated with that. 105 00:07:52,140 --> 00:08:03,580 And finally we've got hydrogen gas plus oxygen gas giving us 106 00:08:03,580 --> 00:08:08,180 two water molecules and this is in the liquid phase, and 107 00:08:08,180 --> 00:08:12,140 there's some delta heat of formation associated with 108 00:08:12,140 --> 00:08:19,260 that, okay. 109 00:08:19,260 --> 00:08:23,030 So there is our set of individual processes that's 110 00:08:23,030 --> 00:08:25,690 going to constitute our cycle, right. 111 00:08:25,690 --> 00:08:29,150 If we take the combination of all those, which is to say we 112 00:08:29,150 --> 00:08:33,910 just take both steps in this cycle, then we'll have our net 113 00:08:33,910 --> 00:08:36,790 reaction, which is to say we'll have this, right. 114 00:08:36,790 --> 00:08:43,890 So what that says is our heat of reaction is our heat of 115 00:08:43,890 --> 00:08:53,340 formation per mole of CO2 gas, right. 116 00:08:53,340 --> 00:09:00,410 Plus 2 times the heat of reaction or heat of formation 117 00:09:00,410 --> 00:09:14,790 per mole of liquid water minus heat of formation per mole of 118 00:09:14,790 --> 00:09:17,880 methane, right. 119 00:09:17,880 --> 00:09:22,430 And things we can easily look up. 120 00:09:22,430 --> 00:09:26,220 So in a simple way, we can determine, we can calculate 121 00:09:26,220 --> 00:09:27,520 what the heat of reaction is for 122 00:09:27,520 --> 00:09:29,530 something like this, right. 123 00:09:29,530 --> 00:09:32,900 And you'll see in the back of your book, you'll see 124 00:09:32,900 --> 00:09:36,260 moderately extensive tables of heats of formation, and if you 125 00:09:36,260 --> 00:09:39,690 go online you'll see, you can find extremely extensive 126 00:09:39,690 --> 00:09:41,840 tabulated values of heats of formation, that have been 127 00:09:41,840 --> 00:09:45,160 measured for an enormous number of compounds. 128 00:09:45,160 --> 00:09:48,510 And from that, then you can look at enthalpies of reaction 129 00:09:48,510 --> 00:09:52,050 for countless numbers of reactions, right. 130 00:09:52,050 --> 00:09:55,140 So by using the tabulated data, we can really determined 131 00:09:55,140 --> 00:09:57,970 heats of formation for most reactions that you might 132 00:09:57,970 --> 00:10:04,070 contemplate, OK? 133 00:10:04,070 --> 00:10:09,500 Of course, the cyclic steps that we've taken to do this 134 00:10:09,500 --> 00:10:13,580 apply not just for breaking down reactants and product 135 00:10:13,580 --> 00:10:15,580 into the elements in their standards states, but of 136 00:10:15,580 --> 00:10:19,600 course we could also look at whole sets of reactions and 137 00:10:19,600 --> 00:10:22,580 write cycles as well, right. 138 00:10:22,580 --> 00:10:27,900 So for example, if we wanted to look at the reaction of 139 00:10:27,900 --> 00:10:38,190 something like carbon graphite plus oxygen gas to make carbon 140 00:10:38,190 --> 00:10:42,620 monoxide gas, well normally this isn't the way the 141 00:10:42,620 --> 00:10:43,700 reaction would work. 142 00:10:43,700 --> 00:10:46,810 Normally if you just tried to make this happen what you 143 00:10:46,810 --> 00:10:52,580 would wind up with the CO2, not CO, right. 144 00:10:52,580 --> 00:10:55,860 But one way to approach this is you could look at the 145 00:10:55,860 --> 00:11:00,710 individual reactions of going, you could go to CO2 and then 146 00:11:00,710 --> 00:11:05,240 you can go with CO2 and oxygen and combine, or combine CO and 147 00:11:05,240 --> 00:11:08,630 oxygen to get CO2, right? 148 00:11:08,630 --> 00:11:17,630 So normally, CO2 is formed, but you could calculate the 149 00:11:17,630 --> 00:11:18,330 heat of reaction. 150 00:11:18,330 --> 00:11:21,470 Of course you could go back to the elements, but you can also 151 00:11:21,470 --> 00:11:25,080 say well, let's just take a known heat of reaction for, or 152 00:11:25,080 --> 00:11:29,390 heat of formation for CO2, and then also combine that with 153 00:11:29,390 --> 00:11:33,890 the heat of reaction for CO plus oxygen forming CO2 and 154 00:11:33,890 --> 00:12:04,640 determine this that way, all right, OK, so once you have 155 00:12:04,640 --> 00:12:07,860 done this, once we've got the heat of reaction then there 156 00:12:07,860 --> 00:12:10,050 are a few simple results that are useful. 157 00:12:10,050 --> 00:12:13,370 One is we know immediately whether when we run a reaction 158 00:12:13,370 --> 00:12:16,890 heat is going to be released in the process out to the 159 00:12:16,890 --> 00:12:18,660 environment, or whether heat is going to 160 00:12:18,660 --> 00:12:19,950 be taken in, right. 161 00:12:19,950 --> 00:12:24,220 So, and of course if you ever used a hot pack or a chemical 162 00:12:24,220 --> 00:12:27,180 hot pack or cold pack, you've seen examples of the two of 163 00:12:27,180 --> 00:12:30,250 those, where the constituents are selected to give you 164 00:12:30,250 --> 00:12:33,850 either heat released or heat taken up, right. 165 00:12:33,850 --> 00:12:42,930 So in particular delta H of reaction less than zero, that 166 00:12:42,930 --> 00:12:47,580 means a negative amount of heat, which means that heat is 167 00:12:47,580 --> 00:12:56,270 released, right. 168 00:12:56,270 --> 00:13:08,230 Yes, that is it's exothermic. 169 00:13:08,230 --> 00:13:13,720 Positive enthalpy of reaction, which is to say a heat of 170 00:13:13,720 --> 00:13:15,270 reaction is positive. 171 00:13:15,270 --> 00:13:18,630 Remember the way we define heat is positive it means that 172 00:13:18,630 --> 00:13:22,540 there is heat that is coming from the environment into the 173 00:13:22,540 --> 00:13:24,320 system, right. 174 00:13:24,320 --> 00:13:31,010 In other words heat is absorbed or taken up by the 175 00:13:31,010 --> 00:13:39,870 reacting system. 176 00:13:39,870 --> 00:13:47,320 That's endothermic, okay. 177 00:13:47,320 --> 00:13:53,200 All right, one more important aspect of this that we need to 178 00:13:53,200 --> 00:13:56,670 be able to deal with, and that is the heats of formation that 179 00:13:56,670 --> 00:13:59,350 you'll find tabulated typically are going to be 180 00:13:59,350 --> 00:14:02,210 given for room temperature and pressure. 181 00:14:02,210 --> 00:14:05,080 And it's very common that you might want to know the 182 00:14:05,080 --> 00:14:07,480 thermodynamic condition for reactions, especially at other 183 00:14:07,480 --> 00:14:10,750 temperatures, very common, of course. 184 00:14:10,750 --> 00:14:14,960 And it's not hard to see how the heat of reaction at room 185 00:14:14,960 --> 00:14:19,420 temperature can be related to they heat of reaction at other 186 00:14:19,420 --> 00:14:20,470 temperatures. 187 00:14:20,470 --> 00:14:31,830 So let's just look at that. 188 00:14:31,830 --> 00:14:38,700 So remember your fundamental relation, dH, if you write 189 00:14:38,700 --> 00:14:42,460 that as a function of temperature and pressure, 190 00:14:42,460 --> 00:14:48,990 partial of H with respect to T, constant pressure, dT, plus 191 00:14:48,990 --> 00:14:54,850 partial of H with respect to p at constant temperature, dp. 192 00:14:54,850 --> 00:14:56,690 But if we're working at constant 193 00:14:56,690 --> 00:15:02,750 pressure then dp is zero. 194 00:15:02,750 --> 00:15:06,680 So we just got the derivative with respect to temperature. 195 00:15:06,680 --> 00:15:14,890 That's our heat capacity, right, Cp. 196 00:15:14,890 --> 00:15:18,880 And we may have tabulated values of Cp for an enormous 197 00:15:18,880 --> 00:15:23,240 number of materials. 198 00:15:23,240 --> 00:15:27,530 So now, if we look at the temperature dependence of 199 00:15:27,530 --> 00:15:31,240 delta H for reaction, really what we're going to need to do 200 00:15:31,240 --> 00:15:34,540 is look at how that heat capacity changes going from 201 00:15:34,540 --> 00:15:37,850 reactants to products, right? 202 00:15:37,850 --> 00:15:45,320 So in other words, d delta H of reaction, with respect to 203 00:15:45,320 --> 00:15:45,630 temperature. 204 00:15:45,630 --> 00:15:46,860 That's what we want to find out, right? 205 00:15:46,860 --> 00:15:51,830 So how does delta H change if we change the temperature? 206 00:15:51,830 --> 00:15:59,730 Well, it's just given by Cp dT for the reactants and the 207 00:15:59,730 --> 00:16:01,490 products, right? 208 00:16:01,490 --> 00:16:04,680 For the products minus the reaction, that is it's delta 209 00:16:04,680 --> 00:16:15,350 Cp, we need the sum over the products. 210 00:16:15,350 --> 00:16:26,940 Nu i, Cp i minus same sum over reactants, 211 00:16:26,940 --> 00:16:33,920 i, nu i Cp i, right. 212 00:16:33,920 --> 00:16:37,000 Similar to what we saw before. 213 00:16:37,000 --> 00:16:44,840 Now we need to integrate, right. 214 00:16:44,840 --> 00:16:50,730 So if we integrate between some pair of temperatures, T1 215 00:16:50,730 --> 00:16:56,470 and T2, we do this and we have this quantity, d delta H of 216 00:16:56,470 --> 00:17:01,870 reaction with respect to temperature, dT, all this is 217 00:17:01,870 --> 00:17:05,950 at constant pressure, right. 218 00:17:05,950 --> 00:17:11,300 Let's just be careful to specify that. 219 00:17:11,300 --> 00:17:21,710 Well, so of course, this is then just delta H of reaction 220 00:17:21,710 --> 00:17:27,430 at T2 minus delta H of reaction at T1. 221 00:17:27,430 --> 00:17:28,380 This is looking good. 222 00:17:28,380 --> 00:17:30,890 This is what we want to get, is our heat of reaction at 223 00:17:30,890 --> 00:17:33,020 some new temperature T2. 224 00:17:33,020 --> 00:17:35,900 If we already know it at some initial temperature, usually 225 00:17:35,900 --> 00:17:37,150 room temperature, T1. 226 00:17:40,950 --> 00:17:44,720 And it's just given by the integral from T1 to T2 of 227 00:17:44,720 --> 00:17:47,510 delta Cp dT. 228 00:17:50,250 --> 00:17:55,400 Now in general, this is as far as we can go, but at least if 229 00:17:55,400 --> 00:17:59,810 the temperature change isn't too big, for most materials 230 00:17:59,810 --> 00:18:02,850 that heat capacities doesn't depend very strongly on 231 00:18:02,850 --> 00:18:04,920 temperature, right. 232 00:18:04,920 --> 00:18:08,270 If you take some material, and you measure its heat capacity, 233 00:18:08,270 --> 00:18:10,510 right, how much heat do I have to put into it in order to 234 00:18:10,510 --> 00:18:14,490 change its temperature by a degree, right. 235 00:18:14,490 --> 00:18:17,120 And I make that measurement at room temperature. 236 00:18:17,120 --> 00:18:20,530 And then maybe I raise the temperature to whatever, room 237 00:18:20,530 --> 00:18:23,780 temperature, maybe 20 degrees hotter than room temperature. 238 00:18:23,780 --> 00:18:27,290 And I again say OK, now how much heat do I need to raise 239 00:18:27,290 --> 00:18:30,170 this thing's temperature by 1 degree? 240 00:18:30,170 --> 00:18:33,350 The amount of heat I need to put in to do that is not very 241 00:18:33,350 --> 00:18:36,210 different from what it was at room temperature right. 242 00:18:36,210 --> 00:18:37,300 In other words the heat capacity 243 00:18:37,300 --> 00:18:39,780 didn't change very much. 244 00:18:39,780 --> 00:18:45,340 So, the result of that is that at least for modest 245 00:18:45,340 --> 00:18:49,250 temperature excursions, it may be the case that we can 246 00:18:49,250 --> 00:18:53,470 simplify this and simply say it's just the difference in 247 00:18:53,470 --> 00:18:56,870 heat capacities times the temperature change. 248 00:18:56,870 --> 00:18:59,550 Again, we can't always be assured of that, but it's 249 00:18:59,550 --> 00:19:05,940 often the case. 250 00:19:05,940 --> 00:19:14,930 Any questions on any of this so far? 251 00:19:14,930 --> 00:19:19,030 OK, now what I want to do is just describe a little bit of 252 00:19:19,030 --> 00:19:22,070 how do you measure all this stuff, right? 253 00:19:22,070 --> 00:19:26,030 So what we've done so far is just lay out in principle how 254 00:19:26,030 --> 00:19:29,360 we should describe heats of reaction, and of course 255 00:19:29,360 --> 00:19:31,340 assuming that we've got everything in tables we can 256 00:19:31,340 --> 00:19:34,090 always look them up, but sometimes you want to make new 257 00:19:34,090 --> 00:19:36,740 compounds, right. 258 00:19:36,740 --> 00:19:39,400 Sometimes you'd like to know what the energetics are 259 00:19:39,400 --> 00:19:42,725 involved there, right, and so it's useful to be able to 260 00:19:42,725 --> 00:19:46,710 actually measure something. 261 00:19:46,710 --> 00:19:48,130 So how do we do It? 262 00:19:48,130 --> 00:20:15,390 This is what's called calorimetry. 263 00:20:15,390 --> 00:20:26,040 So we're going to make measurements to determine heat 264 00:20:26,040 --> 00:20:27,950 of reaction values. 265 00:20:27,950 --> 00:20:30,130 Actually, calorimetry is used for all sorts of things. 266 00:20:30,130 --> 00:20:34,340 It can be used to determine, for example, the energetics of 267 00:20:34,340 --> 00:20:35,340 phase transitions. 268 00:20:35,340 --> 00:20:37,370 Maybe you're not looking at a reaction, but you've got some 269 00:20:37,370 --> 00:20:40,280 new compound, and you're looking at it go from liquid 270 00:20:40,280 --> 00:20:42,140 to solid or to gas. 271 00:20:42,140 --> 00:20:45,330 And you can see what the heat involved in a process like 272 00:20:45,330 --> 00:20:48,080 that is as well. 273 00:20:48,080 --> 00:20:50,000 So what happens? 274 00:20:50,000 --> 00:21:01,280 Well, the objective in the case of a reaction, we have 275 00:21:01,280 --> 00:21:09,210 reactants at some temperature going to products at that 276 00:21:09,210 --> 00:21:14,010 temperature, and that is our heat of reaction at that 277 00:21:14,010 --> 00:21:14,390 temperature. 278 00:21:14,390 --> 00:21:16,480 That's how it's defined, right, at constant 279 00:21:16,480 --> 00:21:18,940 temperature. 280 00:21:18,940 --> 00:21:23,640 OK? 281 00:21:23,640 --> 00:21:25,720 What do we actually measure? 282 00:21:25,720 --> 00:21:31,150 Well, what we can really do is we can put the reactants in 283 00:21:31,150 --> 00:21:37,270 some container, put the whole thing in an insulated place, 284 00:21:37,270 --> 00:21:40,310 you know, hold things in a big insulated box. 285 00:21:40,310 --> 00:21:42,190 Run the reaction. 286 00:21:42,190 --> 00:21:44,620 Maybe it produces heat. 287 00:21:44,620 --> 00:21:47,810 If it does, then the whole thing will heat up, right? 288 00:21:47,810 --> 00:21:52,290 The stuff that's inside the reacting volume, and 289 00:21:52,290 --> 00:21:55,445 whatever's right around it there inside the big box, it's 290 00:21:55,445 --> 00:21:56,990 all going to heat up. 291 00:21:56,990 --> 00:21:58,600 So I'll start at some initial temperature, T1. 292 00:21:58,600 --> 00:22:01,170 I won't end up at the same temperature. 293 00:22:01,170 --> 00:22:02,570 It'll be hotter. 294 00:22:02,570 --> 00:22:03,480 How much hotter? 295 00:22:03,480 --> 00:22:06,740 Well, that depends on how much heat was produced. 296 00:22:06,740 --> 00:22:08,640 So in principle, if I measure how much hotter, I can 297 00:22:08,640 --> 00:22:11,430 determine how much heat was produced, and from that, I 298 00:22:11,430 --> 00:22:15,670 should be able to calculate delta H at T1. 299 00:22:15,670 --> 00:22:24,950 So let's think about how that's really working. 300 00:22:24,950 --> 00:22:35,640 I've really got reactants at T1, plus a calorimeter at T1, 301 00:22:35,640 --> 00:22:39,650 and I'm going to end up with products -- well let's let me 302 00:22:39,650 --> 00:22:46,140 just write that's over. 303 00:22:46,140 --> 00:22:48,260 In fact, let's start by just putting a little sketch of the 304 00:22:48,260 --> 00:22:50,430 whole thing up. 305 00:22:50,430 --> 00:23:00,750 So here's my reacting stuff, maybe it's a liquid. 306 00:23:00,750 --> 00:23:02,440 It's going to take place in there. 307 00:23:02,440 --> 00:23:04,410 It's going to be a constant pressure, it might be open to 308 00:23:04,410 --> 00:23:06,960 the air, or even if it isn't, there might be plenty of room, 309 00:23:06,960 --> 00:23:09,280 and it's a liquid anyway, so the pressure isn't going to 310 00:23:09,280 --> 00:23:11,380 change significantly. 311 00:23:11,380 --> 00:23:18,490 I want to measure the temperature. 312 00:23:18,490 --> 00:23:23,520 And the whole thing is insulated right. 313 00:23:23,520 --> 00:23:26,300 I don't want to have to deal with heat escaping to the 314 00:23:26,300 --> 00:23:28,920 outside environment in a way that might be difficult or 315 00:23:28,920 --> 00:23:32,190 complicated to measure or calculate. 316 00:23:32,190 --> 00:23:36,640 OK, so this, what I've sketched here would be a 317 00:23:36,640 --> 00:23:39,440 constant pressure calorimeter. 318 00:23:39,440 --> 00:23:40,360 There's a reaction. 319 00:23:40,360 --> 00:23:42,600 Normally this is used for a reaction in the condensed 320 00:23:42,600 --> 00:23:45,300 phases and liquid usually. 321 00:23:45,300 --> 00:23:58,620 So this is a constant pressure calorimeter. 322 00:23:58,620 --> 00:24:00,020 It's set up to be 323 00:24:00,020 --> 00:24:03,320 well-insulated so it's adiabatic. 324 00:24:03,320 --> 00:24:04,580 That's the set up. 325 00:24:04,580 --> 00:24:06,750 We're going to run the reactants, the reaction. 326 00:24:06,750 --> 00:24:08,860 The reactants are going to turn into products. 327 00:24:08,860 --> 00:24:31,420 Let's look at what happens. 328 00:24:31,420 --> 00:24:41,270 So what happens is my reactants at T1 plus 329 00:24:41,270 --> 00:24:52,460 calorimeter at T1 turn into products at T2 plus my 330 00:24:52,460 --> 00:24:57,030 calorimeter at T2, right. 331 00:24:57,030 --> 00:24:57,980 That's my process. 332 00:24:57,980 --> 00:24:59,180 That's what really happens. 333 00:24:59,180 --> 00:25:03,470 Now that, the enthalpy of that process isn't what I want, 334 00:25:03,470 --> 00:25:07,110 right, because the temperature has changed, also the 335 00:25:07,110 --> 00:25:09,360 calorimeter is heated up. 336 00:25:09,360 --> 00:25:12,850 So I need to relate this to what I do want. 337 00:25:12,850 --> 00:25:17,520 Let's label this one. 338 00:25:17,520 --> 00:25:18,600 It is adiabatic. 339 00:25:18,600 --> 00:25:23,790 It is taking place inside this thing, and it's a constant 340 00:25:23,790 --> 00:25:29,420 pressure, and we'll do it reversibly, right. 341 00:25:29,420 --> 00:25:30,850 So that's what we've got. 342 00:25:30,850 --> 00:25:39,010 Now, we can always take these things the products and the 343 00:25:39,010 --> 00:25:43,040 calorimeter at temperature T2 and cool them or warm them to 344 00:25:43,040 --> 00:26:07,480 get to products plus calorimeter at T1, right. 345 00:26:07,480 --> 00:26:10,620 Let's label that two. 346 00:26:10,620 --> 00:26:14,650 It's still at constant pressure. 347 00:26:14,650 --> 00:26:16,090 It's reversible. 348 00:26:16,090 --> 00:26:19,650 It's a temperature change. 349 00:26:19,650 --> 00:26:22,100 Now to make that happen, it's not adiabatic, right. 350 00:26:22,100 --> 00:26:24,750 If I wanted to do that, I'd need a heating element or 351 00:26:24,750 --> 00:26:28,370 something to cool, so I could make that temperature change 352 00:26:28,370 --> 00:26:31,870 happen, right. 353 00:26:31,870 --> 00:26:33,980 Well, so now I can complete the cycle. 354 00:26:33,980 --> 00:26:36,490 I've got reactants and calorimeter at T1. 355 00:26:36,490 --> 00:26:40,770 Fewer products and calorimeter at T1, right. 356 00:26:40,770 --> 00:26:44,260 Calorimeter doesn't change in this process. 357 00:26:44,260 --> 00:26:51,380 So here I've got some delta H associated with changing the 358 00:26:51,380 --> 00:26:52,360 temperature. 359 00:26:52,360 --> 00:26:55,690 This delta H though, this is what I want. 360 00:26:55,690 --> 00:27:02,000 This is delta H of reaction at T1, right? 361 00:27:02,000 --> 00:27:12,370 It's isothermal, constant pressure, reversible. 362 00:27:12,370 --> 00:27:13,370 Just what I want. 363 00:27:13,370 --> 00:27:17,880 That's how I've defined delta H of reaction. 364 00:27:17,880 --> 00:27:19,410 This is what I'm after. 365 00:27:19,410 --> 00:27:24,050 All right, so now let's see how we execute it, and do the 366 00:27:24,050 --> 00:27:26,690 calculations that allow us to calculate this. 367 00:27:26,690 --> 00:27:43,840 So, one, what's delta H in step one? 368 00:27:43,840 --> 00:27:50,790 Yes, exactly, it's adiabatic, right constant pressure. 369 00:27:50,790 --> 00:27:51,800 it's zero. 370 00:27:51,800 --> 00:27:58,980 Delta H1 is zero, right. 371 00:27:58,980 --> 00:28:01,940 What we're really going to do in practice is we're going to 372 00:28:01,940 --> 00:28:05,610 measure, we're going to use our thermometer and say great, 373 00:28:05,610 --> 00:28:09,750 how much did the temperature change, right. 374 00:28:09,750 --> 00:28:13,350 So now, then we're going to use what we're going to learn 375 00:28:13,350 --> 00:28:16,840 from step two in order to calculate this part, what we 376 00:28:16,840 --> 00:28:20,840 could call step three. 377 00:28:20,840 --> 00:28:29,040 OK, so two, that's the crucial part. 378 00:28:29,040 --> 00:28:30,370 It's constant pressure. 379 00:28:30,370 --> 00:28:34,730 It's just given by the corresponding heat, and it's 380 00:28:34,730 --> 00:28:36,640 just a temperature change, right. 381 00:28:36,640 --> 00:28:46,440 So we know how to do this, integral from well it's T1 to 382 00:28:46,440 --> 00:28:52,530 T2, depending on which way we go of Cp for the 383 00:28:52,530 --> 00:28:56,470 whole system dT. 384 00:29:04,390 --> 00:29:05,590 OK? 385 00:29:05,590 --> 00:29:09,050 It's just how much heat is involved when we change the 386 00:29:09,050 --> 00:29:09,450 temperature. 387 00:29:09,450 --> 00:29:13,370 Now, the products have some heat capacity associated with 388 00:29:13,370 --> 00:29:16,750 them right, it takes a certain amount of heat if we make 389 00:29:16,750 --> 00:29:19,060 their temperature change, to either put it in or take it 390 00:29:19,060 --> 00:29:21,030 away, depending on which direction the 391 00:29:21,030 --> 00:29:22,070 temperature is changing. 392 00:29:22,070 --> 00:29:29,050 Same with the calorimeter, OK. 393 00:29:29,050 --> 00:29:33,050 In actual practice though, the calorimeter, is going to be 394 00:29:33,050 --> 00:29:35,910 this big hunk of metal, and really what's going to, 395 00:29:35,910 --> 00:29:38,610 there's going to be some stuff in here, right, they'll be a 396 00:29:38,610 --> 00:29:42,390 fluid, it will usually be some sort of oil. 397 00:29:42,390 --> 00:29:46,340 There's a pretty big thermal mass. 398 00:29:46,340 --> 00:29:50,260 Now we run the reaction and it produces heat. 399 00:29:50,260 --> 00:29:55,310 Most of the heat is going to warm up or cool off all that 400 00:29:55,310 --> 00:29:57,200 oil and stuff. 401 00:29:57,200 --> 00:29:59,390 There's a moderate amount of material 402 00:29:59,390 --> 00:30:00,570 in the actual reaction. 403 00:30:00,570 --> 00:30:04,180 You want to design the calorimeter to fulfill that 404 00:30:04,180 --> 00:30:05,100 condition, 405 00:30:05,100 --> 00:30:08,560 Of course, you can't make it so enormous that even for, 406 00:30:08,560 --> 00:30:11,310 that for any ordinary reaction there's not even a measurable 407 00:30:11,310 --> 00:30:13,310 temperature change, right, because if you have your 408 00:30:13,310 --> 00:30:15,860 enough oil to fill up this room, it would take a huge 409 00:30:15,860 --> 00:30:18,340 amount of heat to change it by even a tiny, it's temperature 410 00:30:18,340 --> 00:30:19,900 but even a tiny amount. 411 00:30:19,900 --> 00:30:25,200 So the calorimeter is designed sort of to scale to match the 412 00:30:25,200 --> 00:30:29,490 maybe the ordinary volume of reactants that you'll put in 413 00:30:29,490 --> 00:30:34,950 there, such that, pretty much all the heat's just going to 414 00:30:34,950 --> 00:30:39,430 heat up the calorimeter, and there's only a small amount 415 00:30:39,430 --> 00:30:43,510 that's going toward heating up the products, right. 416 00:30:43,510 --> 00:30:49,510 So in general, or at least usually it'll be the case, 417 00:30:49,510 --> 00:31:01,450 that this is approximately equal to integral from T1 to 418 00:31:01,450 --> 00:31:09,180 T2 Cp of just the calorimeter dT. 419 00:31:22,950 --> 00:31:27,100 And that generally is just given by the heat capacity the 420 00:31:27,100 --> 00:31:31,220 calorimeter times delta T, right.. 421 00:31:31,220 --> 00:31:34,620 Because the heat capacity of the calorimeter just like this 422 00:31:34,620 --> 00:31:41,170 thing is not strongly temperature dependent, OK. 423 00:31:41,170 --> 00:31:44,950 So the point is we can calculate delta H associated 424 00:31:44,950 --> 00:31:52,280 with this process pretty readily, OK. 425 00:31:52,280 --> 00:32:00,700 That leaves three, right. 426 00:32:00,700 --> 00:32:07,400 But delta H for step three must just be the opposite of 427 00:32:07,400 --> 00:32:10,930 this delta H because this was zero and we know that were 428 00:32:10,930 --> 00:32:23,910 going around a cycle, right. 429 00:32:23,910 --> 00:32:28,750 And that's our heat of reaction. 430 00:32:28,750 --> 00:32:44,010 So we're going to be able to do this, right? 431 00:32:44,010 --> 00:32:50,120 OK, now this is one way to do calorimetry, and it's 432 00:32:50,120 --> 00:32:53,480 practical as long as all the materials are in condensed 433 00:32:53,480 --> 00:32:56,630 phases, solids and liquids. 434 00:32:56,630 --> 00:33:01,700 If gases are involved it can work, but it can be tricky to 435 00:33:01,700 --> 00:33:06,070 keep the pressure constant, right, because that means that 436 00:33:06,070 --> 00:33:10,290 now the moles of gas might be changing, and that means in 437 00:33:10,290 --> 00:33:12,670 some way the volume has to be adjustable. 438 00:33:12,670 --> 00:33:14,760 You'd need some sort of balloon or membrane that will 439 00:33:14,760 --> 00:33:16,910 allow that to happen. 440 00:33:16,910 --> 00:33:20,760 Could be done, but easier is to just do the whole thing at 441 00:33:20,760 --> 00:33:25,010 constant volume, right, and just run the reaction that way 442 00:33:25,010 --> 00:33:29,550 and redo the calculation to be a constant volume rather than 443 00:33:29,550 --> 00:33:32,200 constant pressure calorimeter, right. 444 00:33:32,200 --> 00:33:33,950 And it's not hard to do that. 445 00:33:33,950 --> 00:33:37,240 So let's just look at what happens in that case. 446 00:33:37,240 --> 00:34:02,150 It's almost the same. 447 00:34:02,150 --> 00:34:06,700 So let's see, just to finish the job here though, all this 448 00:34:06,700 --> 00:34:11,700 says is delta H of reaction is just negative Cp for the 449 00:34:11,700 --> 00:34:18,880 calorimeter times delta T, all right. so that's what we think 450 00:34:18,880 --> 00:34:29,780 we know in constant pressure calorimetry. 451 00:34:29,780 --> 00:34:37,990 Yes, and if we have gases involved, it's pretty similar, 452 00:34:37,990 --> 00:34:41,910 but now what will have is something like this. 453 00:34:41,910 --> 00:34:46,300 We'll have a reaction vessel that's sealed, 454 00:34:46,300 --> 00:34:51,280 it's constant volume. 455 00:34:51,280 --> 00:34:55,470 That'll be inside our calorimeter. 456 00:34:55,470 --> 00:35:06,900 It's insulated, and there's still a thermometer, so we can 457 00:35:06,900 --> 00:35:08,170 measure the temperature. 458 00:35:08,170 --> 00:35:10,290 So this is still adiabatic. 459 00:35:10,290 --> 00:35:17,100 It's insulated, but now it's constant volume, OK. 460 00:35:17,100 --> 00:35:21,060 Now, you know with constant volume, now it's not going to 461 00:35:21,060 --> 00:35:23,880 be delta H that's straightforward to measure, 462 00:35:23,880 --> 00:35:27,580 it's going to be dealt u, all right. 463 00:35:27,580 --> 00:35:30,820 But it's going to be almost the same, right? 464 00:35:30,820 --> 00:35:33,900 So let's just think about what happens here. 465 00:35:33,900 --> 00:35:36,480 Now it's the cycle that we've got will still 466 00:35:36,480 --> 00:35:37,780 basically look the same. 467 00:35:37,780 --> 00:35:44,980 That is its reactants at T1 plus calorimeter at T1, going 468 00:35:44,980 --> 00:35:54,310 to products at T2 plus calorimeter at T2, right? 469 00:35:54,310 --> 00:36:04,560 And it's still adiabatic, but now it's constant volume. 470 00:36:04,560 --> 00:36:09,690 And it's also reversal right. 471 00:36:09,690 --> 00:36:14,990 So this is our process one. 472 00:36:14,990 --> 00:36:21,450 Now, process two, we're going to end up here with our 473 00:36:21,450 --> 00:36:29,100 products, again at T1 plus our calorimeter at T1, right. 474 00:36:29,100 --> 00:36:33,520 So now we have a constant volume 475 00:36:33,520 --> 00:36:41,810 reversible temperature change. 476 00:36:41,810 --> 00:36:47,760 And so this part now isn't exactly what we want to 477 00:36:47,760 --> 00:37:00,540 determine delta H, because it's a isothermal constant 478 00:37:00,540 --> 00:37:07,490 volume, reversible products or reversible process that takes 479 00:37:07,490 --> 00:37:11,170 a reactant to T1 to a product of T1. 480 00:37:11,170 --> 00:37:14,440 What these are going to give us are delta u values. 481 00:37:14,440 --> 00:37:20,810 This'll give us delta u of reaction, right, T1, right. 482 00:37:20,810 --> 00:37:25,070 It's a constant volume. 483 00:37:25,070 --> 00:37:28,190 All right, so in the end, we're going to determine delta 484 00:37:28,190 --> 00:37:29,910 u here, and then in the end, we're going to have to relate 485 00:37:29,910 --> 00:37:32,790 that to delta H, but that's straight forward enough to do. 486 00:37:32,790 --> 00:37:38,060 So let's look at how we'll analyze what happens. 487 00:37:38,060 --> 00:37:48,850 So one adiabatic, constant volume process, right. 488 00:37:48,850 --> 00:37:51,290 What's zero in that case? 489 00:37:51,290 --> 00:37:53,260 In this case delta H was zero in the 490 00:37:53,260 --> 00:37:56,170 constant pressure example. 491 00:37:56,170 --> 00:37:59,790 Now we've got a constant volume process. 492 00:37:59,790 --> 00:38:03,410 What's zero? 493 00:38:03,410 --> 00:38:07,880 It's u, because u is to q plus w right, heat and work, but 494 00:38:07,880 --> 00:38:09,250 it's adiabatic. 495 00:38:09,250 --> 00:38:14,050 So there's no heat, exchange with the environment, and it's 496 00:38:14,050 --> 00:38:20,020 constant volume, so there's no p dV work, right. 497 00:38:20,020 --> 00:38:29,320 So q is zero adiabatic. 498 00:38:29,320 --> 00:38:35,000 Work is zero. 499 00:38:35,000 --> 00:38:40,850 Delta u1 is zero. 500 00:38:40,850 --> 00:38:45,390 And again just in the constant pressure case, what happens 501 00:38:45,390 --> 00:38:49,960 that we're going to measure in step one, which is to say in 502 00:38:49,960 --> 00:38:52,650 actually running the reaction is the 503 00:38:52,650 --> 00:38:54,480 temperature's going to change. 504 00:38:54,480 --> 00:38:54,960 Right? 505 00:38:54,960 --> 00:38:57,200 The whole thing's going to come to some new equilibrium 506 00:38:57,200 --> 00:39:00,250 temperature between the products and the oil or 507 00:39:00,250 --> 00:39:04,480 whatever's around it, and we're going to measure that. 508 00:39:04,480 --> 00:39:13,540 OK, two, now it's a temperature change, right? 509 00:39:13,540 --> 00:39:17,490 We know how to calculate delta u for a temperature change. 510 00:39:17,490 --> 00:39:20,420 It's very similar here, but what's going to be different 511 00:39:20,420 --> 00:39:28,870 from the case with constant pressure? 512 00:39:28,870 --> 00:39:32,470 There's a real important detail that's different if you 513 00:39:32,470 --> 00:39:35,790 want to calculate what happens at constant pressure when you 514 00:39:35,790 --> 00:39:36,980 change the temperature? 515 00:39:36,980 --> 00:39:40,220 What happens at constant volume? 516 00:39:40,220 --> 00:39:45,000 Looking at this expression, what's got to be different? 517 00:39:45,000 --> 00:39:45,800 Cv, right. 518 00:39:45,800 --> 00:39:47,240 We're not going to have the constant pressure heat 519 00:39:47,240 --> 00:39:48,860 capacity, we're going to have the constant volume heat 520 00:39:48,860 --> 00:39:50,620 capacity, right. 521 00:39:50,620 --> 00:39:57,800 So delta u for step two, that's our q under constant 522 00:39:57,800 --> 00:40:05,760 volume conditions, integral from T1 to T2 Cv for our 523 00:40:05,760 --> 00:40:08,030 whole system dT. 524 00:40:12,140 --> 00:40:19,030 Integral from T2 to T2, and now I can separate again the 525 00:40:19,030 --> 00:40:24,930 calorimeter from the product, and at least approximately, 526 00:40:24,930 --> 00:40:34,400 again, it'll be Cv for the calorimeter dT, which is to 527 00:40:34,400 --> 00:40:38,700 say then it's Cv of the calorimeter 528 00:40:38,700 --> 00:40:50,290 times delta T. Great. 529 00:40:50,290 --> 00:40:55,310 Three, well delta u1 was zero. 530 00:40:55,310 --> 00:41:03,910 Delta u2 was there Cv delta T, so now all we need since the 531 00:41:03,910 --> 00:41:07,820 whole thing is going around in a cycle, Since we know delta 532 00:41:07,820 --> 00:41:17,410 u3 must be negative delta u2, and that is our delta u of 533 00:41:17,410 --> 00:41:46,560 reaction, right? 534 00:41:46,560 --> 00:41:52,800 So delta u of reaction is approximately equal to 535 00:41:52,800 --> 00:41:59,500 negative Cv for the calorimeter times delta T. So, 536 00:41:59,500 --> 00:42:07,530 this is what we're going to measure, and this is what 537 00:42:07,530 --> 00:42:09,490 we're going to determine. 538 00:42:09,490 --> 00:42:13,100 And now we're almost done, except what we really want is 539 00:42:13,100 --> 00:42:18,530 delta H and not delta V, right. 540 00:42:18,530 --> 00:42:25,320 So now we're going to use the fact that H is u plus pV. 541 00:42:27,890 --> 00:42:38,770 Delta H is delta u plus delta pV, and now this is all at 542 00:42:38,770 --> 00:42:40,570 constant temperature in the end, right? 543 00:42:40,570 --> 00:42:46,180 We've determined delta u for some temperature T1, right. 544 00:42:46,180 --> 00:42:49,210 So what happens then we're going to use 545 00:42:49,210 --> 00:42:52,000 the ideal gas law. 546 00:42:52,000 --> 00:42:56,270 So it's approximately delta u plus delta nRT. 547 00:42:59,700 --> 00:43:01,440 That's a constant. 548 00:43:01,440 --> 00:43:03,300 That's a constant. 549 00:43:03,300 --> 00:43:10,050 So it's delta u plus RT, we can say T1 is the temperature 550 00:43:10,050 --> 00:43:15,060 we've used here, delta n of the gas. 551 00:43:15,060 --> 00:43:18,620 In other words, what matters here in changing the pressure 552 00:43:18,620 --> 00:43:19,730 volume product? 553 00:43:19,730 --> 00:43:23,050 What matters is we turned some reactants into some products. 554 00:43:23,050 --> 00:43:26,000 How many moles of gas are there in each case, in 555 00:43:26,000 --> 00:43:27,180 reactants and products? 556 00:43:27,180 --> 00:43:30,840 If that changes, of course you know that the pressure in 557 00:43:30,840 --> 00:43:33,850 there is going to change at constant volume if the amount 558 00:43:33,850 --> 00:43:35,940 of gas in there is changing. 559 00:43:35,940 --> 00:43:37,840 And nothing else is going to make a significant 560 00:43:37,840 --> 00:43:46,560 contribution to it, OK? 561 00:43:46,560 --> 00:43:53,720 So finally, then delta H of reaction for our temperature 562 00:43:53,720 --> 00:44:00,750 T1 is approximately minus Cv of the calorimeter times delta 563 00:44:00,750 --> 00:44:07,680 T plus R T1 delta n of gas. 564 00:44:07,680 --> 00:44:12,450 Change of the number of moles of gas, right. 565 00:44:12,450 --> 00:44:17,400 We're going to measure that, and now we're going to 566 00:44:17,400 --> 00:44:20,850 determine this. 567 00:44:20,850 --> 00:44:25,630 In practice, we'll already know the heat capacity of our 568 00:44:25,630 --> 00:44:29,520 calorimeter, when we buy it, right? 569 00:44:29,520 --> 00:44:32,730 So we don't really need to put in a certain amount of heat 570 00:44:32,730 --> 00:44:34,530 and change the temperature of the products and the 571 00:44:34,530 --> 00:44:35,740 calorimeter and so on. 572 00:44:35,740 --> 00:44:37,450 What we need to do is just measure how much the 573 00:44:37,450 --> 00:44:45,370 temperature changed, OK. 574 00:44:45,370 --> 00:44:48,640 It's worth getting just sort of roughly calibrated how big 575 00:44:48,640 --> 00:44:51,130 is this compared to the rest of this stuff. 576 00:44:51,130 --> 00:44:55,950 That is, how different is delta u from 577 00:44:55,950 --> 00:44:58,120 delta H, all right. 578 00:44:58,120 --> 00:45:00,250 And of course it's straightforward to do this, 579 00:45:00,250 --> 00:45:03,930 and I've written this out in the notes, so I won't re-write 580 00:45:03,930 --> 00:45:05,030 the numbers here. 581 00:45:05,030 --> 00:45:09,490 But I gave an example looking at combining 582 00:45:09,490 --> 00:45:11,690 HCl and oxygen right. 583 00:45:11,690 --> 00:45:18,150 So 4 HCl plus oxygen gas. 584 00:45:18,150 --> 00:45:26,730 This two in the gas going to water and the liquid, plus 585 00:45:26,730 --> 00:45:30,160 chlorine gas at room temperature. 586 00:45:30,160 --> 00:45:38,020 Well, what you find out is delta u of reaction is minus 587 00:45:38,020 --> 00:45:43,960 195 kilojoules for the reaction as written. 588 00:45:43,960 --> 00:45:47,090 And it turns out, as written, if you say OK, how much, what 589 00:45:47,090 --> 00:45:49,100 changed for the pV product? 590 00:45:49,100 --> 00:45:52,720 Well here we've got four moles of gas, five moles of gas. 591 00:45:52,720 --> 00:45:54,880 Here just two, so we changed the number of 592 00:45:54,880 --> 00:45:57,600 moles of gas by three. 593 00:45:57,600 --> 00:46:01,080 All right, how much did it matter, right? 594 00:46:01,080 --> 00:46:02,010 Well it matters. 595 00:46:02,010 --> 00:46:03,130 It's measurable. 596 00:46:03,130 --> 00:46:09,330 So now delta H of reaction turns out to be minus 202 597 00:46:09,330 --> 00:46:12,540 kilojoules. 598 00:46:12,540 --> 00:46:15,815 So, you know, seven out of a couple of a hundred, right, a 599 00:46:15,815 --> 00:46:18,810 few percent, kind of typical. 600 00:46:18,810 --> 00:46:20,920 In other words, if you look at energetics of ordinary 601 00:46:20,920 --> 00:46:23,480 reactions where you're, you know, you're making and 602 00:46:23,480 --> 00:46:26,045 breaking covalent bonds, there's a fair amount of 603 00:46:26,045 --> 00:46:28,660 energy stored in those, right? 604 00:46:28,660 --> 00:46:33,860 The additional change due to changing pressure volume is 605 00:46:33,860 --> 00:46:34,960 certainly measurable. 606 00:46:34,960 --> 00:46:38,510 You don't want to just ignore it, but in cases like that, 607 00:46:38,510 --> 00:46:40,310 it's usually a small fraction of the total. 608 00:46:40,310 --> 00:46:47,560 A few percent is typical, okay. 609 00:46:47,560 --> 00:46:54,190 All right, let me just go through one numerical example 610 00:46:54,190 --> 00:46:58,510 of a calorimetry calculation, OK. 611 00:46:58,510 --> 00:47:02,070 I won't put all the numbers up on the board because our time 612 00:47:02,070 --> 00:47:04,470 is running short, but I just want to outline it. 613 00:47:04,470 --> 00:47:08,870 All I really want to do is calibrate you a little bit for 614 00:47:08,870 --> 00:47:13,760 what happens with ordinary calorimeter heat capacities 615 00:47:13,760 --> 00:47:16,740 that makes the calculation turn out to be relatively 616 00:47:16,740 --> 00:47:18,240 easy, right. 617 00:47:18,240 --> 00:47:22,580 So let's just write it out. 618 00:47:22,580 --> 00:47:30,590 Let's take iron sulfide as a solid, plus 11 halves oxygen 619 00:47:30,590 --> 00:47:40,240 gas to make iron oxide, also a solid, plus 620 00:47:40,240 --> 00:47:43,820 sulphur dioxide gas. 621 00:47:43,820 --> 00:47:46,460 All right. 622 00:47:46,460 --> 00:47:53,060 We'll start at T1 is 298 Kelvin. 623 00:47:53,060 --> 00:47:59,460 T2, maybe we don't know it yet, right. 624 00:47:59,460 --> 00:48:11,740 OK, so we know how to calculate what's going to 625 00:48:11,740 --> 00:48:14,320 happen, delta H and delta u, because we can look up the 626 00:48:14,320 --> 00:48:16,400 heats of formation and so forth of all 627 00:48:16,400 --> 00:48:19,080 the compounds, right. 628 00:48:19,080 --> 00:48:26,200 So if we do that, what we discover is that delta H of 629 00:48:26,200 --> 00:48:30,320 formation whoops, something's wrong here. 630 00:48:30,320 --> 00:48:35,390 This is sulphur -- what am I doing, boy, S and it's a two, 631 00:48:35,390 --> 00:48:40,040 sorry, and the heat of formation is minus 180 632 00:48:40,040 --> 00:48:47,600 kilojoules per mole, that's oxygen, it's zero. 633 00:48:47,600 --> 00:48:52,020 Boy, I'm, I don't know what is about this reaction that's 634 00:48:52,020 --> 00:48:53,980 vexing me but it's not that complicated. 635 00:48:53,980 --> 00:49:00,840 Here it's minus 824 kilojoules per mole minus 297 kilojoules 636 00:49:00,840 --> 00:49:01,920 per mole, right. 637 00:49:01,920 --> 00:49:07,340 So that's our input thermodynamic data. 638 00:49:07,340 --> 00:49:16,030 So first of all, let's just do a heat of reaction 639 00:49:16,030 --> 00:49:16,950 calculation, right. 640 00:49:16,950 --> 00:49:20,930 Taking the product minus the reaction, right. 641 00:49:20,930 --> 00:49:29,890 So it's minus 824 plus 4 times minus 297 minus 642 00:49:29,890 --> 00:49:33,450 2 times minus 180. 643 00:49:33,450 --> 00:49:34,120 Right? 644 00:49:34,120 --> 00:49:36,540 In other words I've got the stoichiometric coefficients in 645 00:49:36,540 --> 00:49:39,840 there and the values, and I'm subtracting the reactants from 646 00:49:39,840 --> 00:49:49,370 products wind up with minus 1652 kilojoules per mole. 647 00:49:49,370 --> 00:49:52,440 Well, it depends on what we write, what we consider mole, 648 00:49:52,440 --> 00:50:04,150 right, maybe I should just write kilojoules as written. 649 00:50:04,150 --> 00:50:16,010 OK, I'm going to skip the delta and get the change in 650 00:50:16,010 --> 00:50:18,055 moles of gas calculation. 651 00:50:18,055 --> 00:50:19,530 It's straightforward to do. 652 00:50:19,530 --> 00:50:21,680 What I really want to do is just give an example of what 653 00:50:21,680 --> 00:50:24,900 happens when you throw the thing, the material into a 654 00:50:24,900 --> 00:50:26,930 calorimeter and see how much the temperature changes. 655 00:50:26,930 --> 00:50:38,340 So let's imagine we start with 0.1 moles of our iron sulfide, 656 00:50:38,340 --> 00:50:40,250 and then we have a stoichiometric amount of 657 00:50:40,250 --> 00:50:43,200 oxygen, and the whole thing is done in a constant volume 658 00:50:43,200 --> 00:50:45,010 calorimeter, and we see what happens. 659 00:50:45,010 --> 00:50:47,870 Now the crucial element is what is the heat capacity of 660 00:50:47,870 --> 00:50:49,930 the calorimeter, right? 661 00:50:49,930 --> 00:50:53,320 And it's, again it's a macroscopic pretty big thing, 662 00:50:53,320 --> 00:50:58,540 so typical might be 10 kilojoules per Kelvin, and 663 00:50:58,540 --> 00:51:00,820 that's pretty big, right? 664 00:51:00,820 --> 00:51:02,880 Noticed that's not per mole, right. 665 00:51:02,880 --> 00:51:05,820 I mean the calorimeter is a big thing filled the little 666 00:51:05,820 --> 00:51:08,370 oil or whatever is inside it, right? 667 00:51:08,370 --> 00:51:11,180 And it's for that whole unit that you've 668 00:51:11,180 --> 00:51:12,400 got some heat capacity. 669 00:51:12,400 --> 00:51:14,780 How much heat does it take the warm the entire thing up or 670 00:51:14,780 --> 00:51:18,140 the insides of the thing up by a degree? 671 00:51:18,140 --> 00:51:20,480 It's that number right. 672 00:51:20,480 --> 00:51:24,230 Ordinary heat capacities are in Joule's per Kelvin mole, 673 00:51:24,230 --> 00:51:25,690 not kilojoules, right. 674 00:51:25,690 --> 00:51:28,865 And what that's telling you is probably your reactants and 675 00:51:28,865 --> 00:51:30,850 products, so the amount of heat that's involved in 676 00:51:30,850 --> 00:51:32,820 changing the air temperature is going to be negligible 677 00:51:32,820 --> 00:51:36,610 compared to what happens to the whole calorimeter. 678 00:51:36,610 --> 00:51:39,530 OK? 679 00:51:39,530 --> 00:51:46,000 So now if we say, OK, we we've done this calculation starting 680 00:51:46,000 --> 00:51:48,980 with 2 moles of this, but now we're going to be at 0.1 mole, 681 00:51:48,980 --> 00:51:51,830 so we're going to need to divide by 20, right. 682 00:51:51,830 --> 00:51:57,950 So instead of minus 1652, it's going to turn out delta u is 683 00:51:57,950 --> 00:52:07,980 minus 1648 kilojoules, so, and then divide by twenty, we end 684 00:52:07,980 --> 00:52:17,250 up with minus 82.4 kilojoules, that is, that's the delta u of 685 00:52:17,250 --> 00:52:21,620 reaction for what happens if you'd put in not two moles of 686 00:52:21,620 --> 00:52:24,400 this, but 0.1 mole of this, right. 687 00:52:24,400 --> 00:52:26,860 Practical amounts is the reason I'm using numbers like 688 00:52:26,860 --> 00:52:28,970 this, right. 689 00:52:28,970 --> 00:52:32,050 So now, what's delta T? 690 00:52:32,050 --> 00:52:41,060 Well here's Cv, right, so delta T is just our minus 10 691 00:52:41,060 --> 00:52:50,640 kilojoules per degree oh sorry, it's our minus 82.4 692 00:52:50,640 --> 00:52:59,930 kilojoules. 693 00:52:59,930 --> 00:53:06,280 That's the heat released, divided by minus 10 or 10 694 00:53:06,280 --> 00:53:11,630 kilojoules per Kelvin, right. 695 00:53:11,630 --> 00:53:14,070 It's 8.2 Kelvin. 696 00:53:14,070 --> 00:53:18,450 In other words, how much does the temperature of the whole 697 00:53:18,450 --> 00:53:21,060 thing change when you put an ordinary amount of material in 698 00:53:21,060 --> 00:53:22,940 there and run a reaction, right. 699 00:53:22,940 --> 00:53:23,620 Well, what do you do? 700 00:53:23,620 --> 00:53:27,300 You calculate how much heat is released in the reaction. 701 00:53:27,300 --> 00:53:29,800 And then what's going to matter is what's the heat 702 00:53:29,800 --> 00:53:32,420 capacity of the whole, of the calorimeter? 703 00:53:32,420 --> 00:53:35,750 I didn't even need to know that heat capacity of the 704 00:53:35,750 --> 00:53:38,100 product, right. 705 00:53:38,100 --> 00:53:42,110 Because it's effect the thermal mass of the product is 706 00:53:42,110 --> 00:53:44,080 negligible compared to the thermal mass of the 707 00:53:44,080 --> 00:53:46,200 calorimeter. 708 00:53:46,200 --> 00:53:50,650 Now in real practice, I'll do the calculation in reverse. 709 00:53:50,650 --> 00:53:53,870 I'll measure how much the temperature changed in the 710 00:53:53,870 --> 00:53:56,040 calorimeter, right. 711 00:53:56,040 --> 00:53:58,740 I'll know the heat capacity, and what I'll really be 712 00:53:58,740 --> 00:54:02,440 calculating is OK, how much heat must have been released 713 00:54:02,440 --> 00:54:06,080 in the reaction to make that temperature change happen? 714 00:54:06,080 --> 00:54:09,100 And that in the case of constant volume, in this case 715 00:54:09,100 --> 00:54:12,305 that's my delta u, and then I'll add my little delta n 716 00:54:12,305 --> 00:54:16,360 term to get delta H. 717 00:54:16,360 --> 00:54:20,260 Any questions on calorimetry? 718 00:54:20,260 --> 00:54:20,950 OK. 719 00:54:20,950 --> 00:54:21,710 See you Friday. 720 00:54:21,710 --> 00:54:26,670 We'll finish on calorimetry and thermochemistry and then 721 00:54:26,670 --> 00:54:30,670 we'll start in on one of the really most difficult topics 722 00:54:30,670 --> 00:54:33,020 that we'll deal with all semester, which is a second 723 00:54:33,020 --> 00:54:36,550 law and our special function that we've seen just a little 724 00:54:36,550 --> 00:54:38,110 bit so far.