1 00:00:00,030 --> 00:00:02,400 The following content is provided under a Creative 2 00:00:02,400 --> 00:00:03,830 Commons license. 3 00:00:03,830 --> 00:00:06,850 Your support will help MIT OpenCourseWare continue to 4 00:00:06,850 --> 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 --> 00:00:17,490 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,490 --> 00:00:18,740 ocw.mit.edu. 8 00:00:21,050 --> 00:00:22,700 PROFESSOR: Settle down. 9 00:00:22,700 --> 00:00:25,160 Settle down. 10 00:00:25,160 --> 00:00:27,780 Settle down. 11 00:00:27,780 --> 00:00:31,890 All right, first announcement is the 12 00:00:31,890 --> 00:00:32,960 celebration of learning. 13 00:00:32,960 --> 00:00:36,460 Reminding you that the celebration of learning is a 14 00:00:36,460 --> 00:00:37,710 week from today. 15 00:00:40,190 --> 00:00:47,340 Go to your assigned rooms. A through Ha will write in here. 16 00:00:47,340 --> 00:00:49,530 This group will go into 26-100. 17 00:00:49,530 --> 00:00:54,060 And the last group over to 4-270. 18 00:00:54,060 --> 00:00:56,810 And you will take with you your periodic table, table of 19 00:00:56,810 --> 00:01:02,720 constants, aid sheet, something to write with. 20 00:01:02,720 --> 00:01:04,430 And we'll give you paper. 21 00:01:04,430 --> 00:01:07,760 You'll write on the exam paper itself. 22 00:01:07,760 --> 00:01:12,840 And I'll say more about test taking strategies on Monday. 23 00:01:12,840 --> 00:01:15,330 Coverage will be right up through Monday. 24 00:01:15,330 --> 00:01:18,810 With emphasis obviously on the material that you've had some 25 00:01:18,810 --> 00:01:24,790 time to digest. And there will be no weekly quiz next week. 26 00:01:24,790 --> 00:01:26,510 So let's get right into the lesson. 27 00:01:26,510 --> 00:01:30,440 Last day we looked at Louis, who gave us the notion of 28 00:01:30,440 --> 00:01:34,210 achieving octet stability by electron sharing. 29 00:01:34,210 --> 00:01:39,790 And that led to the concept of covalent bonds. 30 00:01:39,790 --> 00:01:42,860 And then Pauling helped us understand the energetics of 31 00:01:42,860 --> 00:01:47,680 covalent bonding by putting forth the idea in a 32 00:01:47,680 --> 00:01:49,640 heteronuclear molecule there's unequal 33 00:01:49,640 --> 00:01:51,330 sharing of the electrons. 34 00:01:51,330 --> 00:01:55,180 And out of that emerged the concept of polar covalency and 35 00:01:55,180 --> 00:01:56,930 the definition of electronegativity. 36 00:01:56,930 --> 00:02:03,180 And on the slide you see how electronegativity varies 37 00:02:03,180 --> 00:02:04,840 across the periodic table. 38 00:02:04,840 --> 00:02:08,470 Electronegativity being a measure of the pull an atom 39 00:02:08,470 --> 00:02:11,840 has for electrons within a covalent bond. 40 00:02:11,840 --> 00:02:15,000 And as you would expect, the non metals which are good 41 00:02:15,000 --> 00:02:18,960 electronic receptors are also the ones that have the highest 42 00:02:18,960 --> 00:02:19,960 electronegativity. 43 00:02:19,960 --> 00:02:23,300 And the metals, over here, which are good electron donors 44 00:02:23,300 --> 00:02:26,280 are those that have the the lowest value of 45 00:02:26,280 --> 00:02:27,430 electronegativity. 46 00:02:27,430 --> 00:02:30,860 And Pauling was quantitative in his formulation and gave us 47 00:02:30,860 --> 00:02:35,280 this equation that tells us how to measure the energy of 48 00:02:35,280 --> 00:02:37,490 the x-y covalent bond. 49 00:02:37,490 --> 00:02:40,580 If x is not equal to y, then axiomatically this is going to 50 00:02:40,580 --> 00:02:43,100 be a polar covalent bond. 51 00:02:43,100 --> 00:02:45,760 And you take the geometric mean of the 52 00:02:45,760 --> 00:02:46,980 homonuclear bond energies. 53 00:02:46,980 --> 00:02:50,110 This is x-x bond energy in x two. 54 00:02:50,110 --> 00:02:52,460 This is the y-y bond energy in y two. 55 00:02:52,460 --> 00:02:54,840 You take the product square root of which. 56 00:02:54,840 --> 00:02:58,610 And then the partial ionic character, this is the 57 00:02:58,610 --> 00:03:00,840 contribution to unequal sharing of the electrons. 58 00:03:00,840 --> 00:03:03,080 You take the square of the difference in the 59 00:03:03,080 --> 00:03:05,100 electonegativities of the two elements. 60 00:03:05,100 --> 00:03:09,350 And the 96.3 is a factor that allows you to get the overall 61 00:03:09,350 --> 00:03:11,700 quantity in kilojoules per mole. 62 00:03:11,700 --> 00:03:14,480 So you need these numbers in kilojoules per mole. 63 00:03:14,480 --> 00:03:18,750 And we further had a formula for the percent ionic 64 00:03:18,750 --> 00:03:22,370 character, which you can get by looking at the difference 65 00:03:22,370 --> 00:03:24,030 in electronegativity. 66 00:03:24,030 --> 00:03:28,690 And then through this formula, you end up with a scale that 67 00:03:28,690 --> 00:03:32,180 runs from 0 to 100%. 68 00:03:32,180 --> 00:03:37,090 And just by way of example, we had a look at H-F. 69 00:03:37,090 --> 00:03:38,670 We spent a fair bit of time on that. 70 00:03:38,670 --> 00:03:41,240 Obviously, it's a heteronuclear molecule. 71 00:03:41,240 --> 00:03:43,770 We calculated its bond energy and so on. 72 00:03:43,770 --> 00:03:46,640 And then to indicate polar covalency, we 73 00:03:46,640 --> 00:03:48,470 use the dipole notation. 74 00:03:48,470 --> 00:03:50,160 The dipole shown here. 75 00:03:50,160 --> 00:03:51,150 It's just an oval. 76 00:03:51,150 --> 00:03:52,400 It's net neutral. 77 00:03:52,400 --> 00:03:56,020 But the charge is not uniformly distributed. 78 00:03:56,020 --> 00:03:58,220 You see one end is a little more negative. 79 00:03:58,220 --> 00:03:59,920 The other end is a little more positive. 80 00:03:59,920 --> 00:04:02,890 Sometimes people write lowercase Greek delta, 81 00:04:02,890 --> 00:04:07,530 indicating little bit negative here, a little bit positive 82 00:04:07,530 --> 00:04:08,940 here, net neutral. 83 00:04:08,940 --> 00:04:12,200 There's the arrow indicating the dipole. 84 00:04:12,200 --> 00:04:17,880 And furthermore, we argue that this is a polar bond. 85 00:04:20,610 --> 00:04:25,620 And since this is just a molecule with the two atoms, 86 00:04:25,620 --> 00:04:29,370 then this is also a polar molecule. 87 00:04:29,370 --> 00:04:33,805 Which means it has a net dipole moment. 88 00:04:33,805 --> 00:04:37,260 And I made some observations about dipole moments and the 89 00:04:37,260 --> 00:04:39,790 ability to store energy capacitively. 90 00:04:39,790 --> 00:04:43,940 And how you'd go about finding a really good capacitor. 91 00:04:43,940 --> 00:04:48,870 And so that all came out of the desire to find something 92 00:04:48,870 --> 00:04:50,540 that has a net dipole moment. 93 00:04:50,540 --> 00:04:53,600 And I want to continue that conversation. 94 00:04:53,600 --> 00:04:58,570 And so I want to look at some other elements. 95 00:04:58,570 --> 00:05:02,130 And what I want to look at in particular is 96 00:05:02,130 --> 00:05:04,150 the compound methane. 97 00:05:04,150 --> 00:05:08,760 Let's look at methane from this new found appreciation of 98 00:05:08,760 --> 00:05:09,780 polar covalency. 99 00:05:09,780 --> 00:05:12,870 So first thing I want to do is to put it's structure up. 100 00:05:12,870 --> 00:05:15,770 We've gone through the Louis notation and the structure. 101 00:05:15,770 --> 00:05:17,980 It forms sp3 hybrids. 102 00:05:17,980 --> 00:05:19,950 And you end up with a structure 103 00:05:19,950 --> 00:05:20,930 that looks like this. 104 00:05:20,930 --> 00:05:24,700 These are all at a 109 degrees, symmetrically 105 00:05:24,700 --> 00:05:26,520 disposed in space. 106 00:05:26,520 --> 00:05:30,790 And we know since we have a heteronuclear system here, 107 00:05:30,790 --> 00:05:33,290 we're going to have some polar covalency. 108 00:05:33,290 --> 00:05:37,360 You can look up that the electronegativity of carbon is 109 00:05:37,360 --> 00:05:42,945 2.55 electronegativity of hydrogen is less than that 110 00:05:42,945 --> 00:05:44,810 from its position in the periodic table. 111 00:05:44,810 --> 00:05:47,140 But to be quantitative it's 2.2. 112 00:05:47,140 --> 00:05:52,000 So that means if I look at the carbon hydrogen bond, carbon 113 00:05:52,000 --> 00:05:53,930 has the higher electronegativity. 114 00:05:53,930 --> 00:05:55,490 So it's going to pull the electrons. 115 00:05:55,490 --> 00:05:58,180 So that means that the carbon end is going to be a little 116 00:05:58,180 --> 00:05:59,140 bit negative. 117 00:05:59,140 --> 00:06:02,540 And the hydrogen end is going to be a little bit positive. 118 00:06:02,540 --> 00:06:05,500 So that means I've got a dipole moment here. 119 00:06:05,500 --> 00:06:08,510 Polar bond. 120 00:06:08,510 --> 00:06:11,110 Everything is the same as above here. 121 00:06:11,110 --> 00:06:12,200 Polar bond. 122 00:06:12,200 --> 00:06:15,900 But, I want to address the question, is 123 00:06:15,900 --> 00:06:17,680 the molecule polar? 124 00:06:17,680 --> 00:06:23,130 So the way I interpret the question, is it a polar 125 00:06:23,130 --> 00:06:27,060 molecule, I ask is there a net charge displacement? 126 00:06:27,060 --> 00:06:29,970 Well, we're off to a good start here. 127 00:06:29,970 --> 00:06:32,860 We see that we have charge displacement on the bonds. 128 00:06:32,860 --> 00:06:35,580 But, is there a net dipole for the molecule. 129 00:06:35,580 --> 00:06:39,090 So the way I think about that is to say, where is the center 130 00:06:39,090 --> 00:06:41,010 of positive charge for the molecule? 131 00:06:41,010 --> 00:06:42,500 Where's the center of negative charge? 132 00:06:42,500 --> 00:06:46,430 So I know all the hydrogens are a little bit positive. 133 00:06:46,430 --> 00:06:49,480 And they're all the same distance from the nucleus. 134 00:06:49,480 --> 00:06:52,140 And I can draw a circle that will 135 00:06:52,140 --> 00:06:54,860 capture all four hydrogens. 136 00:06:54,860 --> 00:06:57,750 Or more appropriately, it's a sphere, right? 137 00:06:57,750 --> 00:07:00,300 These three on the bottom don't lie in the plane. 138 00:07:00,300 --> 00:07:03,880 So the corners of the tetrahedron lie on a sphere. 139 00:07:03,880 --> 00:07:06,920 So where is the center of positive charge? 140 00:07:06,920 --> 00:07:09,870 The center positive charge is right here at the center of 141 00:07:09,870 --> 00:07:11,130 the molecule. 142 00:07:11,130 --> 00:07:13,900 And where's the center of local negative charge? 143 00:07:13,900 --> 00:07:17,630 It's on the carbon because the carbon is the negative end of 144 00:07:17,630 --> 00:07:18,420 all the bonds. 145 00:07:18,420 --> 00:07:22,290 So the centers of positive and negative charge for the entire 146 00:07:22,290 --> 00:07:26,560 molecule are colocated at the center of the molecule. 147 00:07:26,560 --> 00:07:31,750 So this means no net dipole moments. 148 00:07:31,750 --> 00:07:35,625 No net dipole moment for the molecule. 149 00:07:39,890 --> 00:07:42,740 So this is a non polar molecule. 150 00:07:42,740 --> 00:07:47,950 It's a non polar molecule consisting of polar bonds. 151 00:07:47,950 --> 00:07:50,670 Non polar molecule. 152 00:07:50,670 --> 00:07:53,770 So there's two ways that I can get a non polar molecule. 153 00:07:53,770 --> 00:07:57,340 One way is to have a homonuclear molecule, right? 154 00:07:57,340 --> 00:07:59,890 So, homonuclear molecule. 155 00:08:02,860 --> 00:08:04,100 Homonuclear molecules 156 00:08:04,100 --> 00:08:09,250 axiomatically must be non polar. 157 00:08:09,250 --> 00:08:10,500 Because they have equal sharing. 158 00:08:13,190 --> 00:08:15,580 So if I give you anything that's homonuclear trivially, 159 00:08:15,580 --> 00:08:16,830 it's non polar. 160 00:08:16,830 --> 00:08:24,240 So you can look at things like H2, P4, S8. 161 00:08:24,240 --> 00:08:25,570 These things are all non polar. 162 00:08:25,570 --> 00:08:26,730 I don't care what their structures 163 00:08:26,730 --> 00:08:29,090 are, it doesn't matter. 164 00:08:29,090 --> 00:08:31,640 This one here is definitely polar. 165 00:08:31,640 --> 00:08:37,330 And then the last one here that we're looking at, the the 166 00:08:37,330 --> 00:08:42,800 methane, is non polar because we have spatially symmetric 167 00:08:42,800 --> 00:08:46,360 disposition of identical polar bonds. 168 00:08:46,360 --> 00:08:53,210 So spatially symmetric, that means there's three 169 00:08:53,210 --> 00:08:54,260 dimensional symmetry. 170 00:08:54,260 --> 00:09:00,670 Spatially symmetric disposition of identical polar 171 00:09:00,670 --> 00:09:14,450 bonds leads to non polar molecule. 172 00:09:14,450 --> 00:09:18,340 Because the centers of positive and negative charge 173 00:09:18,340 --> 00:09:21,290 are colocated. 174 00:09:21,290 --> 00:09:24,990 So, now it's time to move on. 175 00:09:24,990 --> 00:09:27,900 Now I want to look at covalent bonding from an energetic 176 00:09:27,900 --> 00:09:28,430 standpoint. 177 00:09:28,430 --> 00:09:33,120 I want to go back to energy level diagrams. We've looked 178 00:09:33,120 --> 00:09:37,240 at energy level diagrams in the past for atoms, single 179 00:09:37,240 --> 00:09:40,500 atoms. But now, what I want to do is build energy level 180 00:09:40,500 --> 00:09:42,150 diagrams for molecules. 181 00:09:42,150 --> 00:09:45,590 So, for that we're going to go back to 182 00:09:45,590 --> 00:09:47,610 the Schrodinger equation. 183 00:09:47,610 --> 00:09:53,370 I want energy level diagrams for molecules. 184 00:09:57,750 --> 00:10:04,660 And for that I'm going to call upon the Schrodinger equation. 185 00:10:04,660 --> 00:10:07,640 And we're not going to go through the quantum mechanics 186 00:10:07,640 --> 00:10:09,360 in mathematical detail. 187 00:10:09,360 --> 00:10:12,490 We're going to do quantum mechanics pictorally. 188 00:10:12,490 --> 00:10:14,160 We've got a long way. 189 00:10:14,160 --> 00:10:17,620 And in particular, what I want to do with regard to the 190 00:10:17,620 --> 00:10:20,890 Schrodinger equation is to recognize that we can move 191 00:10:20,890 --> 00:10:25,560 from atomic orbitals to molecular orbitals by 192 00:10:25,560 --> 00:10:29,550 exploiting the fact that the Schrodinger equation is a 193 00:10:29,550 --> 00:10:31,980 linear equation. 194 00:10:31,980 --> 00:10:42,160 Using the linearity property of Schrodinger equation. 195 00:10:42,160 --> 00:10:44,390 All right, what do I mean by linearity? 196 00:10:44,390 --> 00:10:51,170 Well, I'm going to do just a little bit of math. 197 00:10:51,170 --> 00:10:55,480 Just enough to make you sit up in your math classes and find 198 00:10:55,480 --> 00:10:57,660 out that there's some utility there. 199 00:10:57,660 --> 00:11:00,280 Here's what I mean. 200 00:11:00,280 --> 00:11:02,670 Let me talk about what the linearity principal is. 201 00:11:02,670 --> 00:11:07,860 So if I have some equation, f of x, y, and z. 202 00:11:07,860 --> 00:11:09,790 It's a three variable equation. 203 00:11:09,790 --> 00:11:13,730 And the equation is f of x, y, z is k1. 204 00:11:13,730 --> 00:11:16,670 k1 could be a constant, it could be a function, it could 205 00:11:16,670 --> 00:11:17,630 be anything. 206 00:11:17,630 --> 00:11:21,040 And let's say that it has as its solution, 207 00:11:21,040 --> 00:11:23,360 the solution is s1. 208 00:11:23,360 --> 00:11:28,160 And then I've got a second variant of this x, y, z. 209 00:11:28,160 --> 00:11:31,140 And it equals k2. 210 00:11:31,140 --> 00:11:33,450 So it's the same function but it equals k2 here. 211 00:11:33,450 --> 00:11:35,350 It could be a constant, it could be something else. 212 00:11:35,350 --> 00:11:37,910 And it has as its solution, s2. 213 00:11:40,700 --> 00:11:46,230 If this f of x, y, z is a linear equation, then if I'd 214 00:11:46,230 --> 00:11:53,050 give you f of x, y, z equals k1 plus k2, you don't have to 215 00:11:53,050 --> 00:11:55,320 go and solve the equation with impunity. 216 00:11:55,320 --> 00:11:57,920 You can write that the solution is 217 00:11:57,920 --> 00:12:00,330 equal to s1 plus s2. 218 00:12:00,330 --> 00:12:03,730 And that doesn't hold if it's a non linear equation. 219 00:12:03,730 --> 00:12:06,150 Just put y equals x squared. 220 00:12:06,150 --> 00:12:10,300 And if I tell you y equals one, y equals two, and then I 221 00:12:10,300 --> 00:12:15,180 give you y equals 1 plus 2, it doesn't equal the sum of the 222 00:12:15,180 --> 00:12:16,185 solution to that. 223 00:12:16,185 --> 00:12:17,560 You can prove it to yourself. 224 00:12:17,560 --> 00:12:22,560 So this is the fact that superposition holds. 225 00:12:22,560 --> 00:12:26,860 You can superpose solutions and build a library. 226 00:12:26,860 --> 00:12:31,470 So superposition holds when you have a linear equation. 227 00:12:31,470 --> 00:12:35,320 And that's all we're going to use in order to make equations 228 00:12:35,320 --> 00:12:37,810 for the molecular orbital. 229 00:12:37,810 --> 00:12:41,490 So that way I can write that the wave function of a 230 00:12:41,490 --> 00:12:44,600 molecular orbital then is a linear combination of the 231 00:12:44,600 --> 00:12:45,450 atomic orbitals. 232 00:12:45,450 --> 00:12:46,630 That's all this is doing. 233 00:12:46,630 --> 00:12:49,670 This is setting the stage for, if you take quantum mechanics 234 00:12:49,670 --> 00:12:51,440 later, you'll go through this in gory detail. 235 00:12:51,440 --> 00:12:54,290 But I'm saying that you know enough now to appreciate that 236 00:12:54,290 --> 00:12:57,350 we can do what we're about to do so. 237 00:12:57,350 --> 00:13:02,220 That means I'm just going to sum the wave functions of the 238 00:13:02,220 --> 00:13:05,440 atomic orbitals. 239 00:13:05,440 --> 00:13:08,250 In this case, i goes from 1 to 2 because there's only two 240 00:13:08,250 --> 00:13:09,930 orbitals in a bond. 241 00:13:09,930 --> 00:13:15,350 And there will be some pre factor here, a sub i times ci. 242 00:13:15,350 --> 00:13:20,000 And this whole business is called linear combination of 243 00:13:20,000 --> 00:13:22,990 atomic orbitals into molecular orbitals. 244 00:13:22,990 --> 00:13:26,010 So it's an SLI, it's a six letter initialization. 245 00:13:26,010 --> 00:13:28,960 You know like FBI is a TLI, it's a three letter 246 00:13:28,960 --> 00:13:30,350 initialization. 247 00:13:30,350 --> 00:13:33,400 This is an SLI, in 3L91 we go big. 248 00:13:33,400 --> 00:13:36,360 This is an SLI, six letter initialization. 249 00:13:36,360 --> 00:13:38,770 So we're going to do some examples here. 250 00:13:38,770 --> 00:13:42,590 And all you need to do in order to run the examples is 251 00:13:42,590 --> 00:13:46,310 use two ideas in LCAO-MO. 252 00:13:46,310 --> 00:13:49,130 First of all, conservation of states. 253 00:13:49,130 --> 00:13:52,805 Conservation of orbital states. 254 00:13:55,540 --> 00:14:01,040 And the second one is, we're going to fill the newly 255 00:14:01,040 --> 00:14:02,940 created molecular orbitals according 256 00:14:02,940 --> 00:14:04,730 to the Aufbau principle. 257 00:14:04,730 --> 00:14:10,620 Fill MOs by Aufbau. 258 00:14:10,620 --> 00:14:13,230 If we do that, we're in good shape. 259 00:14:13,230 --> 00:14:14,020 So let's take a look. 260 00:14:14,020 --> 00:14:15,920 So first think I want to do is just 261 00:14:15,920 --> 00:14:17,840 rationalize this one here. 262 00:14:17,840 --> 00:14:21,330 H plus H goes to H2. 263 00:14:21,330 --> 00:14:23,050 I want to demonstrate that there's a 264 00:14:23,050 --> 00:14:24,280 rational basis for this. 265 00:14:24,280 --> 00:14:27,620 So what I'm going to do is make energy level diagrams. So 266 00:14:27,620 --> 00:14:30,100 there's an energy coordinate here. 267 00:14:30,100 --> 00:14:32,900 Energy goes up in the vertical direction. 268 00:14:32,900 --> 00:14:36,770 And out here is zero. 269 00:14:36,770 --> 00:14:40,460 And what I'm going to draw for you is energy level diagrams 270 00:14:40,460 --> 00:14:44,120 for two atomic hydrogen gas atoms. 271 00:14:44,120 --> 00:14:46,330 So if this is the zero, we know that somewhere 272 00:14:46,330 --> 00:14:49,300 down here is the 1s. 273 00:14:49,300 --> 00:14:51,820 And I'm going to be complete in my label. 274 00:14:51,820 --> 00:14:54,430 This is the 1s atomic orbital of hydrogen. 275 00:14:54,430 --> 00:14:58,570 And over here there's a 1s atomic 276 00:14:58,570 --> 00:15:02,890 orbital of atomic hydrogen. 277 00:15:02,890 --> 00:15:08,570 And furthermore, I've got an electron sitting in 1s. 278 00:15:08,570 --> 00:15:10,850 Now these are at infinite separation. 279 00:15:10,850 --> 00:15:13,560 These are far apart. 280 00:15:13,560 --> 00:15:14,840 Far, you know what that means. 281 00:15:14,840 --> 00:15:17,910 Far with quotation marks means that they're separate quantum 282 00:15:17,910 --> 00:15:21,050 systems. So I'm not violating the poly exclusion principal 283 00:15:21,050 --> 00:15:23,840 by having both of these electrons sitting in the 284 00:15:23,840 --> 00:15:24,530 ground state. 285 00:15:24,530 --> 00:15:26,540 So they both have the same set of quantum numbers. 286 00:15:26,540 --> 00:15:28,830 1, 0, 0, 1/2. 287 00:15:28,830 --> 00:15:29,680 Both of them. 288 00:15:29,680 --> 00:15:30,720 Same thing. 289 00:15:30,720 --> 00:15:33,290 Let's put it over here, 1, 0, 0, 1/2. 290 00:15:33,290 --> 00:15:35,120 So they're very, very far apart. 291 00:15:35,120 --> 00:15:38,290 Now if I bring them close enough together to make the 292 00:15:38,290 --> 00:15:43,160 molecule H2, what happens is I'm going to violate the poly 293 00:15:43,160 --> 00:15:47,410 exclusion principal if I have both of these atomic orbitals 294 00:15:47,410 --> 00:15:48,250 at the same level. 295 00:15:48,250 --> 00:15:50,590 Because I start filling them according to Aufbau principal 296 00:15:50,590 --> 00:15:53,300 I'm going to end up with more electrons than 297 00:15:53,300 --> 00:15:54,510 two at the same state. 298 00:15:54,510 --> 00:15:57,960 So what happens is this splits. 299 00:15:57,960 --> 00:16:01,630 One orbitals ends up at a lower energy and one orbital 300 00:16:01,630 --> 00:16:05,170 ends up at a higher energy than the ground state energy 301 00:16:05,170 --> 00:16:07,990 in the atom itself. 302 00:16:07,990 --> 00:16:12,730 And so now this is called the sigma 1s molecular orbital. 303 00:16:15,640 --> 00:16:20,300 And the one above it is called sigma star 304 00:16:20,300 --> 00:16:23,040 1s molecular orbital. 305 00:16:23,040 --> 00:16:25,110 And sigma is at a lower energy. 306 00:16:25,110 --> 00:16:28,820 So if electrons populate this orbital, the system's energy 307 00:16:28,820 --> 00:16:31,370 will decrease and a bond will form. 308 00:16:31,370 --> 00:16:35,690 So this is called a bonding orbital. 309 00:16:35,690 --> 00:16:39,390 If electrons populate the upper orbital, they will raise 310 00:16:39,390 --> 00:16:41,910 the energy of the system, destabilizing it. 311 00:16:41,910 --> 00:16:45,000 And so this orbital denoted with the star is called 312 00:16:45,000 --> 00:16:46,500 antibonding. 313 00:16:46,500 --> 00:16:49,670 It's an antibonding orbital. 314 00:16:49,670 --> 00:16:52,000 So now I've got the energy level diagram 315 00:16:52,000 --> 00:16:55,460 for molecular hydrogen. 316 00:16:55,460 --> 00:16:57,500 So now let's go and populate according 317 00:16:57,500 --> 00:16:58,520 to the Aufbau principal. 318 00:16:58,520 --> 00:17:03,280 I've got two electrons and they go in spin up spin down. 319 00:17:03,280 --> 00:17:07,260 And now you can see that this occupancy put the electrons at 320 00:17:07,260 --> 00:17:12,060 lower energy than they were by being in the energy state of 321 00:17:12,060 --> 00:17:13,490 the atoms. 322 00:17:13,490 --> 00:17:16,460 And so I can argue that by this diagram, I haven't 323 00:17:16,460 --> 00:17:19,050 predicted anything, but I can use this diagram to 324 00:17:19,050 --> 00:17:23,980 rationalize that for this reaction delta E is negative. 325 00:17:23,980 --> 00:17:25,330 And we know how negative it is. 326 00:17:25,330 --> 00:17:29,260 It's minus 435 kilojoules per mole. 327 00:17:29,260 --> 00:17:31,620 It's hugely negative. 328 00:17:31,620 --> 00:17:36,970 Minus 435 kilojoules per mole. 329 00:17:36,970 --> 00:17:38,150 All right. 330 00:17:38,150 --> 00:17:40,590 So, that's good. 331 00:17:40,590 --> 00:17:43,930 In fact I think I've got some pictures. 332 00:17:43,930 --> 00:17:45,940 You can go through the whole quantum mechanics. 333 00:17:45,940 --> 00:17:53,950 And just as is the case for a single atoms, you can use the 334 00:17:53,950 --> 00:17:57,920 product of the wave function and it's complex conjugate and 335 00:17:57,920 --> 00:18:01,050 so on and make plots. 336 00:18:01,050 --> 00:18:03,940 Oh by the way, this was just making the point that you can 337 00:18:03,940 --> 00:18:07,100 pull out the electronegativity off of the periodic table. 338 00:18:07,100 --> 00:18:08,210 It's given here. 339 00:18:08,210 --> 00:18:10,540 And the periodic table is pretty good. 340 00:18:10,540 --> 00:18:13,480 But obviously somebody got a little bit ahead of himself. 341 00:18:13,480 --> 00:18:16,490 They called this the first ionization potential, which is 342 00:18:16,490 --> 00:18:18,970 the potential you'd put across the plates in a 343 00:18:18,970 --> 00:18:20,610 gas discharge tube. 344 00:18:20,610 --> 00:18:23,390 But the unit is not the electronvolt. 345 00:18:23,390 --> 00:18:24,900 If it's a potential, it's a volt. 346 00:18:24,900 --> 00:18:27,470 Somebody here that put this together seemed to think the 347 00:18:27,470 --> 00:18:29,320 electronvolt is a unit of potential. 348 00:18:29,320 --> 00:18:30,880 And I want to make sure that nobody in this 349 00:18:30,880 --> 00:18:34,020 class believes that. 350 00:18:34,020 --> 00:18:37,260 You got to get a little bit of nail polish or something and 351 00:18:37,260 --> 00:18:39,790 cover up the little e there. 352 00:18:39,790 --> 00:18:43,660 Or take the nail polish, paint over potential and write first 353 00:18:43,660 --> 00:18:44,990 ionization energy. 354 00:18:44,990 --> 00:18:48,980 One or the other, but not this. 355 00:18:48,980 --> 00:18:51,230 This was a plot if percent ionic characters. 356 00:18:51,230 --> 00:18:55,830 You can see that the strongly covalent compounds down here 357 00:18:55,830 --> 00:18:58,200 have very very low electronegativity differences 358 00:18:58,200 --> 00:19:00,270 and therefore very low ionic character. 359 00:19:00,270 --> 00:19:02,470 And way up here are the ionics. 360 00:19:02,470 --> 00:19:03,970 And in between is HF. 361 00:19:03,970 --> 00:19:05,860 It's almost at the cusp. 362 00:19:05,860 --> 00:19:07,980 But, can you see that there must be a 363 00:19:07,980 --> 00:19:09,160 mistake on this diagram? 364 00:19:09,160 --> 00:19:11,690 Because this thing has got a greater electronegativity 365 00:19:11,690 --> 00:19:14,350 difference than lithium iodide and yet lithium iodide has a 366 00:19:14,350 --> 00:19:16,450 higher percent ionic character. 367 00:19:16,450 --> 00:19:19,110 How can this function zigzag like that? 368 00:19:19,110 --> 00:19:20,870 Something's wrong. 369 00:19:20,870 --> 00:19:24,470 So when you look at something, you go wait a minute, that 370 00:19:24,470 --> 00:19:25,080 doesn't make sense. 371 00:19:25,080 --> 00:19:28,930 So I go back and I say, do I trust anything here? 372 00:19:28,930 --> 00:19:30,250 Trust, but verify. 373 00:19:30,250 --> 00:19:31,950 Read critically. 374 00:19:31,950 --> 00:19:32,700 It's a good book. 375 00:19:32,700 --> 00:19:34,500 But, it's a big book and there's 376 00:19:34,500 --> 00:19:35,710 going to be some mistakes. 377 00:19:35,710 --> 00:19:38,130 All right, so here's some pictoral stuff of what we were 378 00:19:38,130 --> 00:19:39,060 just doing over here. 379 00:19:39,060 --> 00:19:42,730 So here are the two spherical 1s orbitals and now they come 380 00:19:42,730 --> 00:19:45,210 closer and closer together and they overlap. 381 00:19:45,210 --> 00:19:48,970 And this is what the shape of the sigma 1s 382 00:19:48,970 --> 00:19:50,765 orbital looks like. 383 00:19:50,765 --> 00:19:54,670 It's like an oval with the two nuclei inside. 384 00:19:54,670 --> 00:19:56,690 Here's taken from a different text book. 385 00:19:56,690 --> 00:20:00,560 The overlap of atomic 1s atomic and now here's the 386 00:20:00,560 --> 00:20:02,240 molecular orbital. 387 00:20:02,240 --> 00:20:06,660 Now you can also look at what the shape of the antibonding 388 00:20:06,660 --> 00:20:07,350 orbital would be. 389 00:20:07,350 --> 00:20:10,030 This is what the shape of the antibonding orbital would be. 390 00:20:10,030 --> 00:20:12,580 It would have two lobes with a nodal plane in between. 391 00:20:16,400 --> 00:20:19,510 I think this is taken from yet another book. 392 00:20:19,510 --> 00:20:20,960 Oh this is our book. 393 00:20:20,960 --> 00:20:21,340 There we go. 394 00:20:21,340 --> 00:20:23,850 1s, 1s, as there we go. 395 00:20:23,850 --> 00:20:25,380 Hydrogen molecular orbitals. 396 00:20:25,380 --> 00:20:28,160 Now look, suppose we do the same thing for helium. 397 00:20:28,160 --> 00:20:31,310 If we do the same thing for helium, helium starts with two 398 00:20:31,310 --> 00:20:32,620 electrons in 1s. 399 00:20:32,620 --> 00:20:34,610 And now it's going to have four electrons. 400 00:20:34,610 --> 00:20:37,240 Two will go in the bonding and two will go in the 401 00:20:37,240 --> 00:20:38,560 antibonding. 402 00:20:38,560 --> 00:20:41,740 And the two that go in the antibonding raise the energy 403 00:20:41,740 --> 00:20:45,430 of the system more than the two that go into bonding 404 00:20:45,430 --> 00:20:46,980 decrease the energy of the system. 405 00:20:46,980 --> 00:20:48,470 There's a net increase in energy. 406 00:20:48,470 --> 00:20:52,190 And this is the way you could rationalize that helium exists 407 00:20:52,190 --> 00:20:55,130 as the atom in the gas phase. 408 00:20:55,130 --> 00:20:57,860 You don't see He2 gas molecules. 409 00:20:57,860 --> 00:21:01,230 So using this energy level diagram you can go through an 410 00:21:01,230 --> 00:21:01,940 rationalize. 411 00:21:01,940 --> 00:21:03,820 I would never ask you to predict. 412 00:21:03,820 --> 00:21:11,100 I would say, fact, helium is found as the atomic species in 413 00:21:11,100 --> 00:21:13,160 the gas phase. 414 00:21:13,160 --> 00:21:17,710 With the use of energy level diagrams, rationalize. 415 00:21:17,710 --> 00:21:19,450 And that's what I would expect you to do. 416 00:21:19,450 --> 00:21:23,930 Take this and show that the two are 417 00:21:23,930 --> 00:21:26,950 of different stability. 418 00:21:26,950 --> 00:21:32,160 One other point to to make, the level of 1s. 419 00:21:32,160 --> 00:21:35,270 If I wanted to put helium on this board here. 420 00:21:35,270 --> 00:21:37,560 Not the scale, but just roughly. 421 00:21:37,560 --> 00:21:42,330 Where would helium 1s be relative the hydrogen 1s. 422 00:21:42,330 --> 00:21:43,760 We got three choices. 423 00:21:43,760 --> 00:21:51,480 Same level, closer to zero energy, or more negative. 424 00:21:51,480 --> 00:21:52,880 How do you think about the problem? 425 00:21:52,880 --> 00:21:56,280 What determines what this energy is? 426 00:21:56,280 --> 00:21:58,820 It's the electrostatic force of attraction. 427 00:21:58,820 --> 00:22:01,640 Is the electrostatic force of attraction on the 1s electron 428 00:22:01,640 --> 00:22:07,490 in helium greater than or less than it is in hydrogen? 429 00:22:07,490 --> 00:22:08,230 It's greater. 430 00:22:08,230 --> 00:22:11,570 So that means that the energy is going to be more negative. 431 00:22:11,570 --> 00:22:15,170 And so if I were to put over here helium, I'd put down here 432 00:22:15,170 --> 00:22:19,510 this would be 1s atomic orbital for helium and then we 433 00:22:19,510 --> 00:22:21,090 go through the analysis. 434 00:22:21,090 --> 00:22:22,410 And why does that come into play? 435 00:22:22,410 --> 00:22:25,450 Well you might want to do a heteronuclear molecule. 436 00:22:25,450 --> 00:22:28,030 Suppose you wanted to do the bonding diagram 437 00:22:28,030 --> 00:22:29,530 for hydrogen fluoride. 438 00:22:29,530 --> 00:22:32,390 So we'd have hydrogen here and the fluorine 439 00:22:32,390 --> 00:22:33,820 and would be here. 440 00:22:33,820 --> 00:22:36,410 And all the fluorine orbitals would be much lower and then 441 00:22:36,410 --> 00:22:39,760 they'd combine to make the molecular orbitals. 442 00:22:39,760 --> 00:22:42,710 And I think there's something opportunities to practice that 443 00:22:42,710 --> 00:22:44,980 in the homework. 444 00:22:44,980 --> 00:22:46,410 OK let's do one more. 445 00:22:46,410 --> 00:22:47,280 Let's do one more. 446 00:22:47,280 --> 00:22:49,940 How about lithium. 447 00:22:49,940 --> 00:22:50,800 Let's do lithium. 448 00:22:50,800 --> 00:22:54,985 I want to ask, is dilithium stable? 449 00:22:58,220 --> 00:22:58,780 Li2. 450 00:22:58,780 --> 00:23:01,040 And this is all gas phase. 451 00:23:01,040 --> 00:23:02,210 Is dilithium stable? 452 00:23:02,210 --> 00:23:05,982 So I'll start off with here's the zeroes. 453 00:23:05,982 --> 00:23:10,360 The zero of energy for infinite separation. 454 00:23:10,360 --> 00:23:15,330 So this'll be a lithium gas atom. 455 00:23:15,330 --> 00:23:18,610 And this is the putative dilithium gas atom. 456 00:23:18,610 --> 00:23:20,280 We're going to figure out if it's stable or not. 457 00:23:20,280 --> 00:23:23,870 So it's going to have bonding and antibonding orbitals. 458 00:23:23,870 --> 00:23:29,690 And then this is the 1s, 2s. 459 00:23:29,690 --> 00:23:37,130 And this will be sigma 1s, sigma star 1s, and so on. 460 00:23:37,130 --> 00:23:44,660 And then we'll have 2s atomic orbital splitting into sigma 461 00:23:44,660 --> 00:23:48,030 and sigma star of 2s. 462 00:23:48,030 --> 00:23:52,000 And now lithium is 1s2, 2s1. 463 00:23:52,000 --> 00:23:54,640 So there's one, two, three. 464 00:23:54,640 --> 00:23:57,270 And one, two, three. 465 00:23:57,270 --> 00:23:59,260 And so now let's use the Hund rule. 466 00:23:59,260 --> 00:24:02,900 So I've got four electrons in the n equals one shell, and 467 00:24:02,900 --> 00:24:05,000 they populate in this manner. 468 00:24:05,000 --> 00:24:08,600 And then I've got two electrons that go only into 469 00:24:08,600 --> 00:24:09,620 the bonding orbital. 470 00:24:09,620 --> 00:24:13,700 And according to this it appears that lithium 2 is 471 00:24:13,700 --> 00:24:16,020 favored over atomic lithium. 472 00:24:16,020 --> 00:24:17,930 And that in fact is the case. 473 00:24:17,930 --> 00:24:21,960 That in fact is the case and so that applies to all of the 474 00:24:21,960 --> 00:24:25,080 all of the alkalide metals. 475 00:24:25,080 --> 00:24:29,010 Because they all have the ns1 configuration. 476 00:24:29,010 --> 00:24:32,780 So when you're driving down the highway and you see those 477 00:24:32,780 --> 00:24:36,390 orangey yellow low pressure sodium vapor lamps. 478 00:24:36,390 --> 00:24:39,070 What you're looking at is emission not from atomic 479 00:24:39,070 --> 00:24:42,560 sodium but from Na2 vapor. 480 00:24:42,560 --> 00:24:45,210 And you've got the energy level diagram to convince 481 00:24:45,210 --> 00:24:46,720 yourself of that. 482 00:24:46,720 --> 00:24:50,680 So next time you see those, just smile, knowing that 483 00:24:50,680 --> 00:24:54,850 you're looking at disodium, not sodium. 484 00:24:54,850 --> 00:24:57,290 OK, well so far we've only looked at single bonds. 485 00:24:57,290 --> 00:24:59,820 Now I want to look at multiple bonds. 486 00:24:59,820 --> 00:25:00,820 Double and triple bonds. 487 00:25:00,820 --> 00:25:03,210 So let's look at nitrogen now. 488 00:25:03,210 --> 00:25:03,730 N2. 489 00:25:03,730 --> 00:25:06,440 Remember that gave us the the triple bond? 490 00:25:06,440 --> 00:25:10,340 We had nitrogen, one, two, three, four, five. 491 00:25:10,340 --> 00:25:13,890 Second nitrogen, one, two, three, four, five. 492 00:25:13,890 --> 00:25:16,880 So in order to get octet stability, we had three pairs 493 00:25:16,880 --> 00:25:17,990 of electronic sharing. 494 00:25:17,990 --> 00:25:21,430 Which then give us a triple bond here. 495 00:25:21,430 --> 00:25:25,680 And so what's that going to look like? 496 00:25:25,680 --> 00:25:29,670 what's that going to look like pictorally? 497 00:25:29,670 --> 00:25:32,600 And the way to think about that is first of all these are 498 00:25:32,600 --> 00:25:34,940 all p orbitals. 499 00:25:34,940 --> 00:25:40,520 If we look at, this is 2s2, 2p3. 500 00:25:40,520 --> 00:25:44,420 So 2s and these are the 2d orbitals. 501 00:25:44,420 --> 00:25:48,740 So I've got s is filled first and then I've got the lone 502 00:25:48,740 --> 00:25:50,930 electrons in each of the p orbitals. 503 00:25:50,930 --> 00:25:54,050 And these things are shaped like figure eights. 504 00:25:57,410 --> 00:26:02,630 And the p orbital, this is the p atomic orbital. 505 00:26:02,630 --> 00:26:04,830 It has two lobes. 506 00:26:04,830 --> 00:26:07,020 Each of these zones are just called lobes. 507 00:26:07,020 --> 00:26:09,070 Same word is earlobe. 508 00:26:09,070 --> 00:26:14,460 And this zone in the middle, this one point in the middle, 509 00:26:14,460 --> 00:26:15,710 is called a node. 510 00:26:18,650 --> 00:26:21,990 And that's a sight of zero electron density. 511 00:26:21,990 --> 00:26:24,980 Zero electronic density. 512 00:26:24,980 --> 00:26:27,290 And remember the electron, even if it only has one 513 00:26:27,290 --> 00:26:30,100 electron here, the electron can be in either a lobe. 514 00:26:30,100 --> 00:26:32,990 It can move from lobe to lobe even though it can never be at 515 00:26:32,990 --> 00:26:33,660 the nucleus. 516 00:26:33,660 --> 00:26:36,850 And how does it get from one lobe to the other while never 517 00:26:36,850 --> 00:26:39,110 crossing the nucleus because it's never supposed to be in 518 00:26:39,110 --> 00:26:40,380 the nucleus? 519 00:26:40,380 --> 00:26:43,630 By behaving as a wave. The same way that you can have a 520 00:26:43,630 --> 00:26:47,420 jump rope and you can have a fixed point of zero motion, 521 00:26:47,420 --> 00:26:52,530 yet you can transmit energy down the rope passed the node. 522 00:26:52,530 --> 00:26:54,730 So, let's draw these things. 523 00:26:58,150 --> 00:27:00,570 A word about how you draw, you have to use 524 00:27:00,570 --> 00:27:02,140 the right hand rule. 525 00:27:02,140 --> 00:27:03,320 Have to use the right hand rule. 526 00:27:03,320 --> 00:27:06,830 So when I put the coordinate system up, it's going to have 527 00:27:06,830 --> 00:27:10,630 to conform so that the thumb is x and they go y and z. 528 00:27:10,630 --> 00:27:13,000 And if you don't use the right hand rule later on if you get 529 00:27:13,000 --> 00:27:16,740 into electromagnetics, you start looking at forces and 530 00:27:16,740 --> 00:27:18,920 vectors, you're going to end up with things moving in the 531 00:27:18,920 --> 00:27:19,650 wrong direction. 532 00:27:19,650 --> 00:27:21,540 So we conform to the right hand rule. 533 00:27:21,540 --> 00:27:22,690 And the other thing, and it's kind of 534 00:27:22,690 --> 00:27:24,260 nice, it's not mandatory. 535 00:27:24,260 --> 00:27:28,150 But chemists generally like to have atoms 536 00:27:28,150 --> 00:27:30,110 bond along the z-axis. 537 00:27:30,110 --> 00:27:33,425 So that means we start with the z-axis here, if I'm going 538 00:27:33,425 --> 00:27:36,650 to put my second nitrogen, have them bond on the z-axis. 539 00:27:36,650 --> 00:27:40,580 And so that means if z is in the plane of the board 540 00:27:40,580 --> 00:27:44,340 pointing to the right, then pointing up must be y, and 541 00:27:44,340 --> 00:27:46,830 then pointing into the board must be x. 542 00:27:46,830 --> 00:27:51,930 So I'll have, here's my px orbital, then the py orbital, 543 00:27:51,930 --> 00:27:53,710 and the pz orbital. 544 00:27:53,710 --> 00:27:57,740 And the three of these are all symmetrically disposed around 545 00:27:57,740 --> 00:27:59,990 the nucleus. 546 00:27:59,990 --> 00:28:02,540 And next to it at the same kind of floral arrangement. 547 00:28:02,540 --> 00:28:09,070 I'll start with px, py, and pz. 548 00:28:09,070 --> 00:28:10,450 And now these are going to come close 549 00:28:10,450 --> 00:28:12,360 together and overlap. 550 00:28:12,360 --> 00:28:14,590 So I want to figure out what those orbitals are 551 00:28:14,590 --> 00:28:15,670 going to look like. 552 00:28:15,670 --> 00:28:17,970 So let's start along the z-axis. 553 00:28:17,970 --> 00:28:19,910 The z-axis is the easy one. 554 00:28:19,910 --> 00:28:23,130 So I've got two of these things lying on their sides 555 00:28:23,130 --> 00:28:24,740 like infinity signs. 556 00:28:24,740 --> 00:28:26,970 We're going to do quantum mechanics pictorally. 557 00:28:26,970 --> 00:28:27,700 Why? 558 00:28:27,700 --> 00:28:30,420 Because it's a linear equation. 559 00:28:30,420 --> 00:28:33,300 So I can add pictural. 560 00:28:33,300 --> 00:28:36,140 So this is 2pz of one of them. 561 00:28:36,140 --> 00:28:38,340 And a 2pz of the other. 562 00:28:38,340 --> 00:28:42,410 And this is the nitrogen atomic orbital. 563 00:28:45,190 --> 00:28:46,780 And I'm going to smear these things and what are they going 564 00:28:46,780 --> 00:28:47,930 to look like? 565 00:28:47,930 --> 00:28:51,510 The nucleus is here, the nucleus is where I'm 566 00:28:51,510 --> 00:28:52,790 indicating the dot. 567 00:28:52,790 --> 00:28:55,580 These two combine, very simply, it's going 568 00:28:55,580 --> 00:28:56,830 to look like this. 569 00:28:59,650 --> 00:29:01,360 So there's one nitrogen. 570 00:29:01,360 --> 00:29:03,010 Here's the other nitrogen. 571 00:29:03,010 --> 00:29:04,780 And what's this thing? 572 00:29:04,780 --> 00:29:06,570 This is electronic density. 573 00:29:06,570 --> 00:29:11,550 And so this is our sigma bond. 574 00:29:11,550 --> 00:29:15,820 Looks a little bit different from the case of of hydrogen, 575 00:29:15,820 --> 00:29:19,330 because hydrogen was the blending of two s orbitals and 576 00:29:19,330 --> 00:29:21,280 s orbitals are spherically symmetric. 577 00:29:21,280 --> 00:29:23,620 In this case, we've got two lobes. 578 00:29:23,620 --> 00:29:27,500 But what's characteristic about this one and hydrogen, 579 00:29:27,500 --> 00:29:29,930 hydrogen looked like this, remember? 580 00:29:29,930 --> 00:29:31,020 This was hydrogen. 581 00:29:31,020 --> 00:29:32,570 This was H2. 582 00:29:32,570 --> 00:29:35,080 And this was a sigma bond. 583 00:29:35,080 --> 00:29:39,780 The characteristic of a sigma bond is that when you start 584 00:29:39,780 --> 00:29:44,020 from one nucleus and you go to the other nucleus, you move 585 00:29:44,020 --> 00:29:47,240 through unbroken electron density. 586 00:29:47,240 --> 00:29:51,420 So there are no nodes, no holidays, between the nitrogen 587 00:29:51,420 --> 00:29:54,940 nucleus on the left and the nitrogen nucleus on the right. 588 00:29:54,940 --> 00:29:57,460 There is a node here, but that's different. 589 00:29:57,460 --> 00:30:00,240 I can go from one nitrogen to the other with unbroken 590 00:30:00,240 --> 00:30:01,170 electron density. 591 00:30:01,170 --> 00:30:02,680 That's what makes this a sigma bond. 592 00:30:08,790 --> 00:30:09,760 So that's good. 593 00:30:09,760 --> 00:30:12,390 So this thing here is going to be called stigma 594 00:30:12,390 --> 00:30:15,710 2p molecular orbital. 595 00:30:15,710 --> 00:30:21,370 Sigma 2p molecular orbital And I think I've got the slide 596 00:30:21,370 --> 00:30:22,230 that shows this. 597 00:30:22,230 --> 00:30:23,780 There's some art work. 598 00:30:23,780 --> 00:30:27,710 People really get excited about this. 599 00:30:27,710 --> 00:30:28,960 OK there's dilithium. 600 00:30:28,960 --> 00:30:31,060 Or dipotasium, disodium. 601 00:30:31,060 --> 00:30:31,920 OK so here we are. 602 00:30:31,920 --> 00:30:37,790 This is the smearing of two pz atomic orbitals to make the 603 00:30:37,790 --> 00:30:41,080 sigma 2p bonding orbital. 604 00:30:41,080 --> 00:30:43,020 And there just for grins and chuckles is what the 605 00:30:43,020 --> 00:30:44,200 antibonding would look like. 606 00:30:44,200 --> 00:30:48,640 But we don't care, because it doesn't form. 607 00:30:48,640 --> 00:30:49,980 Well this is the book. 608 00:30:49,980 --> 00:30:50,980 And you know what I'm going to say. 609 00:30:50,980 --> 00:30:52,350 I've got my little hobby horse here. 610 00:30:52,350 --> 00:30:55,810 I don't know why they change color on the lobes. 611 00:30:55,810 --> 00:30:58,680 Because when I look at that, it starts conjuring up to me 612 00:30:58,680 --> 00:31:01,900 the image that one electron stays in the blue lobe and one 613 00:31:01,900 --> 00:31:03,730 electron stays in the yellow lobe. 614 00:31:03,730 --> 00:31:06,190 Besides, I've seen them and they're not different colors. 615 00:31:06,190 --> 00:31:07,440 They're the same color. 616 00:31:13,830 --> 00:31:17,800 So now let's look at what happens when we blend off of 617 00:31:17,800 --> 00:31:18,420 the z-axis. 618 00:31:18,420 --> 00:31:22,300 So let's blend the two py orbitals. 619 00:31:22,300 --> 00:31:24,660 See what that goes like. 620 00:31:24,660 --> 00:31:26,460 OK so let's do that one. 621 00:31:26,460 --> 00:31:28,450 And that one is going to look like this. 622 00:31:28,450 --> 00:31:32,650 We're to start with, again figure eights. 623 00:31:32,650 --> 00:31:35,140 But now they're their side by side, they're lateral. 624 00:31:35,140 --> 00:31:38,300 So this is 2py atomic orbital. 625 00:31:38,300 --> 00:31:40,190 2py atomic orbital. 626 00:31:40,190 --> 00:31:45,350 And then we're going to blend them along the z-axis to give 627 00:31:45,350 --> 00:31:48,680 us, and I'm going to do this stylized, OK? 628 00:31:48,680 --> 00:31:52,590 So there's the the two nitrogen nuclei. 629 00:31:52,590 --> 00:31:54,340 So I put the nuclei up. 630 00:31:54,340 --> 00:31:56,880 And I'm going to smear the upper lobes. 631 00:31:56,880 --> 00:31:58,850 So these two lobes are going to smear. 632 00:31:58,850 --> 00:32:00,690 And I'm going to get really stylized. 633 00:32:00,690 --> 00:32:04,990 I feel like it's France and it's the late 1800s. 634 00:32:04,990 --> 00:32:06,430 So there it is. 635 00:32:06,430 --> 00:32:08,720 And I'm going to smear the two bottom ones. 636 00:32:08,720 --> 00:32:12,120 And it's going to look like this. 637 00:32:12,120 --> 00:32:13,820 So what do I have here? 638 00:32:13,820 --> 00:32:20,660 Now I have two lobes as before. 639 00:32:20,660 --> 00:32:25,340 But if I look at the second nucleus from the first 640 00:32:25,340 --> 00:32:30,480 nucleus, not only do I fail to have unbroken electron 641 00:32:30,480 --> 00:32:32,990 density, I have zero electron density. 642 00:32:32,990 --> 00:32:35,880 See, this was a nodal point in the atom. 643 00:32:35,880 --> 00:32:39,170 With the two atoms together, the plane orthogonal to the 644 00:32:39,170 --> 00:32:40,740 board is a nodal plane. 645 00:32:40,740 --> 00:32:43,370 There's no electron density in the plane 646 00:32:43,370 --> 00:32:45,800 orthogonal to the board. 647 00:32:45,800 --> 00:32:47,500 Nodal plane. 648 00:32:47,500 --> 00:32:52,630 So this is definitely not a sigma bond, this is a pi bond. 649 00:32:52,630 --> 00:32:53,860 This is a pi bond. 650 00:32:53,860 --> 00:32:57,160 And it's characterized by smearing of atomic orbitals, 651 00:32:57,160 --> 00:32:58,740 just as the sigma bond is. 652 00:32:58,740 --> 00:33:02,290 But it has a nodal plane that separates the two lobes. 653 00:33:06,080 --> 00:33:10,590 I think I've got some cartoon illustrations from other books 654 00:33:10,590 --> 00:33:13,440 Here OK this is from one book. 655 00:33:13,440 --> 00:33:15,030 This is good. 656 00:33:15,030 --> 00:33:17,460 They call the px, I call it py. 657 00:33:17,460 --> 00:33:20,270 There it is. 658 00:33:20,270 --> 00:33:23,200 And I'd go further and I'd say that if I were to slice this 659 00:33:23,200 --> 00:33:28,610 and look at it from angle, if we were to cut this and look 660 00:33:28,610 --> 00:33:31,470 from here, I'd venture that you'd see something that's 661 00:33:31,470 --> 00:33:32,720 sort of figure eightish. 662 00:33:35,730 --> 00:33:40,870 Oh here's our book, bless them with two colors. 663 00:33:40,870 --> 00:33:43,370 But anyway, there's what it looks like. 664 00:33:43,370 --> 00:33:44,620 That's the pie. 665 00:33:47,630 --> 00:33:50,040 And then the same thing happens with the x. 666 00:33:50,040 --> 00:33:53,426 So this is this is going to be pi 2py. 667 00:33:56,040 --> 00:33:58,830 This is pi 2py. 668 00:33:58,830 --> 00:34:00,480 And it's a molecular orbital. 669 00:34:00,480 --> 00:34:02,000 And there's going to be a pi 2px. 670 00:34:02,000 --> 00:34:05,120 And it's going to blend front and back. 671 00:34:05,120 --> 00:34:07,320 So we can make a catalog. 672 00:34:07,320 --> 00:34:09,710 So we're going to do quantum mechanics in pictures here. 673 00:34:09,710 --> 00:34:15,510 So I know that s plus s must always make a sigma bond. 674 00:34:15,510 --> 00:34:16,370 There's no other way. 675 00:34:16,370 --> 00:34:19,570 Because I've got electron density all around. 676 00:34:19,570 --> 00:34:20,820 Let's do it pictorally. 677 00:34:26,230 --> 00:34:27,020 That's easy. 678 00:34:27,020 --> 00:34:28,610 And this is sigma. 679 00:34:28,610 --> 00:34:30,650 We know this has to be sigma. 680 00:34:30,650 --> 00:34:37,290 What about something like HF where the H is an s and the F 681 00:34:37,290 --> 00:34:39,660 is going to have the one last electron 682 00:34:39,660 --> 00:34:41,040 missing in the p orbital. 683 00:34:41,040 --> 00:34:45,270 S plus p must give sigma always. 684 00:34:45,270 --> 00:34:48,720 Because that's this cartoon. 685 00:34:48,720 --> 00:34:52,080 See there's no way that when this smears with this, there's 686 00:34:52,080 --> 00:34:56,360 going to be zero electron holidays from the hydrogen 687 00:34:56,360 --> 00:34:59,060 nucleus to the fluorine nucleus. 688 00:34:59,060 --> 00:35:00,060 So you're going to end up with something 689 00:35:00,060 --> 00:35:01,290 that looks like this. 690 00:35:01,290 --> 00:35:03,860 It starts around and gives you something that's going to be a 691 00:35:03,860 --> 00:35:06,070 little bit asymmetric. 692 00:35:06,070 --> 00:35:07,810 So this will also be a sigma. 693 00:35:07,810 --> 00:35:11,970 So I'll just put HF here as sort of prototypical of that. 694 00:35:11,970 --> 00:35:22,350 And then if I take p plus p axially, on axis, that also 695 00:35:22,350 --> 00:35:23,600 gives us a sigma. 696 00:35:26,520 --> 00:35:29,790 Because that's this one, the infinity signs. 697 00:35:29,790 --> 00:35:31,630 Two infinity signs give us this. 698 00:35:35,110 --> 00:35:41,335 And then finally, if we get p plus p longitudinally. 699 00:35:45,580 --> 00:35:50,710 So that will give us a pi bond and that's the 88. 700 00:35:50,710 --> 00:35:55,730 8 plus 8 gives me, and this is pi. 701 00:35:55,730 --> 00:35:57,730 So that's quantum mechanics. 702 00:35:57,730 --> 00:36:00,790 The math will follow. 703 00:36:00,790 --> 00:36:04,600 So now what I want to do is go back to this energy level 704 00:36:04,600 --> 00:36:06,530 diagram and show how these energy level 705 00:36:06,530 --> 00:36:09,290 diagrams can work. 706 00:36:09,290 --> 00:36:12,810 So here's the energy level diagram for nitrogen, N2. 707 00:36:12,810 --> 00:36:17,760 There's two f's, two p, and the scaffolding is in place. 708 00:36:17,760 --> 00:36:19,120 There's the energy levels. 709 00:36:19,120 --> 00:36:24,110 Now here's the molecular orbitals and here are the 710 00:36:24,110 --> 00:36:25,830 atomic orbitals. 711 00:36:25,830 --> 00:36:27,390 And now here they are occupied. 712 00:36:27,390 --> 00:36:30,560 So nitrogen has one, two, three, four, five according to 713 00:36:30,560 --> 00:36:31,590 the Hund rule. 714 00:36:31,590 --> 00:36:35,100 And here is the set up for the N2 molecules. 715 00:36:35,100 --> 00:36:39,200 So the 2s's and the 2s's go bonding antibonding. 716 00:36:39,200 --> 00:36:41,420 Now I've got three plus three is six. 717 00:36:41,420 --> 00:36:43,650 Two, two, two. 718 00:36:43,650 --> 00:36:45,230 Everything's paired. 719 00:36:45,230 --> 00:36:49,480 So we get the triple bond, 946 kilojoules per mole. 720 00:36:49,480 --> 00:36:51,730 Enormous energy in nitrogen. 721 00:36:51,730 --> 00:36:54,120 Enormous energy in nitrogen. 722 00:36:54,120 --> 00:36:55,890 Now, let's keep going. 723 00:36:55,890 --> 00:36:57,270 Now let's look at oxygen. 724 00:36:57,270 --> 00:36:59,820 This is the scaffolding for oxygen and fluorine. 725 00:36:59,820 --> 00:37:01,700 And there's a little change here. 726 00:37:01,700 --> 00:37:03,780 A little change, I'm going to draw your attention to it. 727 00:37:03,780 --> 00:37:05,050 And you can't predict this. 728 00:37:05,050 --> 00:37:06,030 We would give you this. 729 00:37:06,030 --> 00:37:10,220 I would tell you what the energy sequence is of the 730 00:37:10,220 --> 00:37:11,050 energy levels. 731 00:37:11,050 --> 00:37:16,260 But look here carefully, you see in the case all nitrogen, 732 00:37:16,260 --> 00:37:18,540 the pi's lie below the sigma. 733 00:37:18,540 --> 00:37:21,580 In the case of oxygen and fluorine the sigma 734 00:37:21,580 --> 00:37:22,730 lies below the pi's. 735 00:37:22,730 --> 00:37:24,850 These are tiny, tiny differences. 736 00:37:24,850 --> 00:37:28,220 But, they are measurable. 737 00:37:28,220 --> 00:37:29,270 That's the little difference. 738 00:37:29,270 --> 00:37:30,520 Now let's see what happens. 739 00:37:30,520 --> 00:37:33,690 Actually here's from out text book and it shows the stigma 740 00:37:33,690 --> 00:37:39,380 2pix slowly meandering down, down, down, down, down. 741 00:37:39,380 --> 00:37:44,540 And somewhere between nitrogen and oxygen it crisscrosses. 742 00:37:44,540 --> 00:37:46,600 All right, so now let's fill oxygen. 743 00:37:46,600 --> 00:37:50,460 So oxygen is two, four, five, six. 744 00:37:50,460 --> 00:37:53,730 So two plus two is four. 745 00:37:53,730 --> 00:37:56,540 There's the two, two, two. 746 00:37:56,540 --> 00:37:59,790 And then these last ones go up into the antibonding. 747 00:37:59,790 --> 00:38:02,220 But look at the antibonding. 748 00:38:02,220 --> 00:38:06,510 We have, according to the Hund rule, not two electrons in the 749 00:38:06,510 --> 00:38:09,330 first orbital, but one and one. 750 00:38:09,330 --> 00:38:12,070 So we end up with unpaired electrons in 751 00:38:12,070 --> 00:38:13,790 the antibonding orbital. 752 00:38:13,790 --> 00:38:17,570 So these offset the three pairs here, and so we end up 753 00:38:17,570 --> 00:38:18,910 with a double bond. 754 00:38:18,910 --> 00:38:22,210 And its energy us 498 kilojoules per mole. 755 00:38:22,210 --> 00:38:25,460 Substantially less then nitrogen. 756 00:38:25,460 --> 00:38:30,190 And this energy level diagram rationalizes that. 757 00:38:30,190 --> 00:38:31,440 And then here's for fluorine. 758 00:38:31,440 --> 00:38:33,960 If you go to fluorine it's the same scaffolding only there's 759 00:38:33,960 --> 00:38:34,890 two more electrons. 760 00:38:34,890 --> 00:38:37,070 These are paired and you have a single bond. 761 00:38:37,070 --> 00:38:39,960 160 kilojoules per mole. 762 00:38:39,960 --> 00:38:43,470 Now there's a property that we get from the fact that we have 763 00:38:43,470 --> 00:38:44,700 these unpaired electrons. 764 00:38:44,700 --> 00:38:46,490 We're going back oxygen now. 765 00:38:46,490 --> 00:38:48,950 We have unpaired electrons in the antibonding orbitals. 766 00:38:48,950 --> 00:38:50,770 We saw unpaired electrons. 767 00:38:50,770 --> 00:38:53,350 What did they do in the Stern-Gerlach experiment? 768 00:38:53,350 --> 00:38:55,960 Changed the magnetics substantially, right? 769 00:38:55,960 --> 00:39:01,370 We ended up with the splitting of the silver bean. 770 00:39:01,370 --> 00:39:03,610 So this will also have an impact. 771 00:39:03,610 --> 00:39:06,190 An impact known as a paramagnetism. 772 00:39:06,190 --> 00:39:07,320 What's paramagnetism? 773 00:39:07,320 --> 00:39:09,110 It's shown in this little cartoon. 774 00:39:09,110 --> 00:39:13,950 If you have a substance here that's balanced and it is 775 00:39:13,950 --> 00:39:18,380 paramagnetic, if you engage the magnetic field, the 776 00:39:18,380 --> 00:39:22,480 magnetic field will pull on a substance that's paramagnetic. 777 00:39:22,480 --> 00:39:24,920 And oxygen is paramagnetic. 778 00:39:24,920 --> 00:39:28,410 Not only in a gas state, but paramagnetic as liquid. 779 00:39:28,410 --> 00:39:30,520 And here's an illustration from your text book. 780 00:39:30,520 --> 00:39:32,870 You may have seen this and said, yeah a guy is pouring 781 00:39:32,870 --> 00:39:35,170 liquid oxygen, wow. 782 00:39:35,170 --> 00:39:37,720 Look carefully now. 783 00:39:37,720 --> 00:39:40,410 The boiling point of oxygen at one atmosphere 784 00:39:40,410 --> 00:39:42,550 pressure is 90 Kelvin. 785 00:39:42,550 --> 00:39:45,030 So room temperature is substantially higher. 786 00:39:45,030 --> 00:39:49,930 This is the equivalent of taking water and putting it in 787 00:39:49,930 --> 00:39:53,750 an oven at about 300 degrees celsius and watching it pour. 788 00:39:53,750 --> 00:39:55,770 It would still be liquid, but it would be 789 00:39:55,770 --> 00:39:57,020 liquid trying to boil. 790 00:39:57,020 --> 00:39:58,910 Why doesn't it all turned to gas? 791 00:39:58,910 --> 00:40:02,220 Because there's a time to heat everything. 792 00:40:02,220 --> 00:40:06,180 So this is sitting at 90 Kelvin, he pouring it down, or 793 00:40:06,180 --> 00:40:09,220 she's pouring it down, and these are the jaw of a 794 00:40:09,220 --> 00:40:10,870 permanent magnet. 795 00:40:10,870 --> 00:40:12,920 And it's in a gravity field, it doesn't 796 00:40:12,920 --> 00:40:14,940 keep falling, it stops. 797 00:40:14,940 --> 00:40:18,400 And it continues to boil away and as fast as you can pour 798 00:40:18,400 --> 00:40:21,310 it, it sits between the jaws of the magnet. 799 00:40:21,310 --> 00:40:22,660 Because it's paramagnetic. 800 00:40:22,660 --> 00:40:24,300 You can think of this as the liquid 801 00:40:24,300 --> 00:40:27,090 equivalent of iron filings. 802 00:40:27,090 --> 00:40:30,020 If I told you that were these were iron filings you'd say, 803 00:40:30,020 --> 00:40:32,400 yeah the iron filings go and they stick to the magnet, 804 00:40:32,400 --> 00:40:34,670 that's what magnets do to iron filings. 805 00:40:34,670 --> 00:40:36,250 They do the same thing to liquid oxygen. 806 00:40:39,520 --> 00:40:40,290 And why? 807 00:40:40,290 --> 00:40:41,700 Because of this. 808 00:40:41,700 --> 00:40:44,640 This explains this. 809 00:40:44,640 --> 00:40:50,870 So we can do a lot with these primitive little diagrams. 810 00:40:50,870 --> 00:40:51,950 Let's do one more. 811 00:40:51,950 --> 00:40:54,436 I want to do one more of these things. 812 00:40:54,436 --> 00:40:58,010 I want to go to hybridized systems. I want to go to a 813 00:40:58,010 --> 00:40:59,010 hybridized system. 814 00:40:59,010 --> 00:41:03,560 And I want to look at ethylene. 815 00:41:03,560 --> 00:41:08,740 C2H4 is ethylene. 816 00:41:08,740 --> 00:41:12,250 OK, so if I told you give me the Louis structure of 817 00:41:12,250 --> 00:41:15,500 ethylene, you just start going according to the rule. 818 00:41:15,500 --> 00:41:22,090 So I'm going to have carbon, carbon, hydrogen, hydrogen. 819 00:41:22,090 --> 00:41:27,680 And carbon has one, two, three, four electrons. 820 00:41:27,680 --> 00:41:30,610 The hydrogen has one electron. 821 00:41:30,610 --> 00:41:32,890 I'll put the one electron from hydrogen. 822 00:41:32,890 --> 00:41:34,870 And then the other carbon over here, I'm 823 00:41:34,870 --> 00:41:36,630 going to give it dots. 824 00:41:36,630 --> 00:41:38,470 One, two, three, four. 825 00:41:38,470 --> 00:41:41,000 And then these hydrogen each have one. 826 00:41:41,000 --> 00:41:42,770 And now let's see what I have here. 827 00:41:42,770 --> 00:41:46,230 These hydrogens are all isoelectronic with helium, so 828 00:41:46,230 --> 00:41:47,210 they're happy. 829 00:41:47,210 --> 00:41:52,340 And the carbon now has two, let's see, what does he got? 830 00:41:52,340 --> 00:41:53,410 Yeah, carbon is happy. 831 00:41:53,410 --> 00:41:55,190 Two, four, six, OK good. 832 00:41:55,190 --> 00:41:56,070 So now carbon is. 833 00:41:56,070 --> 00:41:57,350 Happy as well. 834 00:41:57,350 --> 00:41:58,580 So what do we have here? 835 00:41:58,580 --> 00:42:02,906 This is the equivalent to a carbon carbon double bond. 836 00:42:06,320 --> 00:42:10,510 So what have I learned with the nitrogen example? 837 00:42:10,510 --> 00:42:13,900 What I learned with the nitrogen example was, that if 838 00:42:13,900 --> 00:42:17,650 I want to make more than one bond, I have to have a 839 00:42:17,650 --> 00:42:20,210 combination of a stigma and a pi. 840 00:42:20,210 --> 00:42:23,210 You can only make one sigma bond because there's no room. 841 00:42:23,210 --> 00:42:27,050 Once you've got zero electron density between the two nuclei 842 00:42:27,050 --> 00:42:29,430 you're going to violate the Pauli exclusion principle if 843 00:42:29,430 --> 00:42:31,140 you have another orbital cutting 844 00:42:31,140 --> 00:42:32,800 through that same domain. 845 00:42:32,800 --> 00:42:39,200 So this means that multiple bonds require a mix 846 00:42:39,200 --> 00:42:42,080 of sigma and pi. 847 00:42:42,080 --> 00:42:53,770 Multiple bonds require a mix of sigma and pi. 848 00:42:53,770 --> 00:42:58,390 If you have a single bond, all you need is the sigma. 849 00:42:58,390 --> 00:43:04,050 So let's go back to how we got the original hybridization. 850 00:43:04,050 --> 00:43:08,020 Remember, we started with carbon, with the box notation 851 00:43:08,020 --> 00:43:09,330 looking like this. 852 00:43:09,330 --> 00:43:15,190 Here's the 2s and the 2p's and we started with just native 853 00:43:15,190 --> 00:43:17,240 carbon off the periodic table. 854 00:43:17,240 --> 00:43:18,470 And we have this. 855 00:43:18,470 --> 00:43:22,590 Just if we go according to the 2s2, 2p2. 856 00:43:22,590 --> 00:43:26,640 And then in order to get hybridization to rationalize 857 00:43:26,640 --> 00:43:31,070 methane, where we've got four equivalent bonds. 858 00:43:31,070 --> 00:43:35,810 In that case, we hybridize the s and all of the p's. 859 00:43:35,810 --> 00:43:39,500 We took the s and all three of the p's to make 860 00:43:39,500 --> 00:43:43,000 the sp3 hybrid orbitals. 861 00:43:43,000 --> 00:43:45,800 And then we were able to take these electrons and put them 862 00:43:45,800 --> 00:43:47,820 in one at a time. 863 00:43:47,820 --> 00:43:50,620 And then bring in the four hydrogens and we end up with 864 00:43:50,620 --> 00:43:52,480 something that is 865 00:43:52,480 --> 00:43:54,250 symmetrically disposed in space. 866 00:43:54,250 --> 00:43:57,700 The carbon, hydrogen and so. 867 00:43:57,700 --> 00:44:01,290 So now I give to you ethylene I say, well 868 00:44:01,290 --> 00:44:02,500 how do I make ethylene. 869 00:44:02,500 --> 00:44:08,010 Well, if I started with this sp3 thing maybe I could bring 870 00:44:08,010 --> 00:44:10,620 another carbon over here. 871 00:44:10,620 --> 00:44:14,820 And I'd have three hydrogen sticking out. 872 00:44:14,820 --> 00:44:16,250 So there's my sigma bond. 873 00:44:16,250 --> 00:44:17,670 So I'm off to the races. 874 00:44:17,670 --> 00:44:18,180 This is good. 875 00:44:18,180 --> 00:44:20,390 But now I need to build a second bond. 876 00:44:20,390 --> 00:44:22,760 I'm going to throw away a couple of hydrogen. 877 00:44:22,760 --> 00:44:25,490 So i'll throw this hydrogen away and this hydrogen away. 878 00:44:25,490 --> 00:44:28,290 So I'm going to have now C2H4. 879 00:44:28,290 --> 00:44:29,590 I'm almost there. 880 00:44:29,590 --> 00:44:32,890 The only problem is, this orbital is sticking out this 881 00:44:32,890 --> 00:44:34,810 way, this orbital is sticking out this way. 882 00:44:34,810 --> 00:44:38,240 And I don't have the license to bend these orbitals. 883 00:44:38,240 --> 00:44:39,920 And build a double bond. 884 00:44:39,920 --> 00:44:43,460 Because they're 109 degrees apart and they're inflexible 885 00:44:43,460 --> 00:44:45,010 and they won't bend. 886 00:44:45,010 --> 00:44:50,460 So this hybridization technique will not work as 887 00:44:50,460 --> 00:44:56,210 such to give me what I need to build ethylene. 888 00:44:56,210 --> 00:44:57,180 What do I need? 889 00:44:57,180 --> 00:45:00,380 If I'm going to build a sigma and a pi bond, I'm going to 890 00:45:00,380 --> 00:45:04,440 need to preserve one of the p orbitals so that it can still 891 00:45:04,440 --> 00:45:06,850 be available for lateral smearing 892 00:45:06,850 --> 00:45:08,900 Because how do I make a pi orbital? 893 00:45:08,900 --> 00:45:11,900 I make a pi orbital middle with an 88. 894 00:45:11,900 --> 00:45:17,820 So I need to preserve a p orbital so that in both of the 895 00:45:17,820 --> 00:45:22,590 carbons I still have this pi bonding capability. 896 00:45:22,590 --> 00:45:26,680 So what I'm going do is instead of taking the s and 897 00:45:26,680 --> 00:45:30,610 all three of the p's I'm going to take the s and only two of 898 00:45:30,610 --> 00:45:34,410 the p' s and reserve one of the p' s to be sitting there 899 00:45:34,410 --> 00:45:35,580 for lateral smearing. 900 00:45:35,580 --> 00:45:39,300 So instead what I'm going to do is this. 901 00:45:39,300 --> 00:45:43,720 So this is going to be an unmixed p and this is going to 902 00:45:43,720 --> 00:45:48,430 take the s and not three p' s but only two p 's. 903 00:45:48,430 --> 00:45:49,680 And this would be called sp2. 904 00:45:52,040 --> 00:45:53,090 And now what do I have? 905 00:45:53,090 --> 00:45:55,280 I've one, two, three. 906 00:45:55,280 --> 00:45:57,630 And how do I put three of these in space? 907 00:45:57,630 --> 00:46:03,330 They lie symmetrically in a plane at 120 degrees. 908 00:46:03,330 --> 00:46:06,830 And then this thing is normal to the plane of the board. 909 00:46:06,830 --> 00:46:07,540 It's sticking out. 910 00:46:07,540 --> 00:46:09,780 Actually, I should've maybe drawn it in 911 00:46:09,780 --> 00:46:13,400 perspective like this. 912 00:46:13,400 --> 00:46:15,990 And so now I've got the ability to put 913 00:46:15,990 --> 00:46:17,290 two of these together. 914 00:46:17,290 --> 00:46:19,500 This'll giving me my sigma. 915 00:46:19,500 --> 00:46:23,100 And then these two things lying on their side will smear 916 00:46:23,100 --> 00:46:25,600 with the lobes to give me the pi. 917 00:46:25,600 --> 00:46:28,020 Now that's what gives me the double bond. 918 00:46:28,020 --> 00:46:30,680 And here are the cartoons that show this. 919 00:46:33,480 --> 00:46:36,040 Oh here, I took this from an old text book, it's text book 920 00:46:36,040 --> 00:46:37,920 I had when I was your age. 921 00:46:40,455 --> 00:46:41,590 The wrote great books. 922 00:46:41,590 --> 00:46:43,710 And then I flipped this around see. 923 00:46:43,710 --> 00:46:44,820 I did all this just for you. 924 00:46:44,820 --> 00:46:46,980 So I took this one, I flipped the image around. 925 00:46:46,980 --> 00:46:49,850 So there are the sp2's these are the unmixed p's. 926 00:46:49,850 --> 00:46:51,510 And you bring them close together and bingo. 927 00:46:51,510 --> 00:46:52,870 There's the sigma. 928 00:46:52,870 --> 00:46:55,550 That's this one, p plus p axially, that gives me the 929 00:46:55,550 --> 00:46:56,570 sigma bond. 930 00:46:56,570 --> 00:46:59,540 And then I smear those two and that gives me the pi. 931 00:46:59,540 --> 00:47:01,190 And there's ethylene. 932 00:47:01,190 --> 00:47:03,710 You put the hydrogens here, one, two, three, four. 933 00:47:03,710 --> 00:47:05,040 Two carbons. 934 00:47:05,040 --> 00:47:06,440 Tada. 935 00:47:06,440 --> 00:47:08,640 Isn't that cool? 936 00:47:08,640 --> 00:47:10,740 Here's from another book. 937 00:47:10,740 --> 00:47:14,580 It's looks like a Boston traffic map, doesn't it? 938 00:47:14,580 --> 00:47:17,410 Just crazy. 939 00:47:17,410 --> 00:47:18,850 This is from our book. 940 00:47:18,850 --> 00:47:25,050 So they're showing you there's the sigmas and the pi's. 941 00:47:25,050 --> 00:47:26,300 There we go. 942 00:47:31,360 --> 00:47:32,610 More pictures. 943 00:47:35,670 --> 00:47:38,860 OK, I'm going to take three minutes at the end here and 944 00:47:38,860 --> 00:47:39,960 show you an example of 945 00:47:39,960 --> 00:47:42,000 electronegativity at the extreme. 946 00:47:42,000 --> 00:47:44,990 So if you take a look at the periodic table and look at a 947 00:47:44,990 --> 00:47:47,050 compound like sodium iodide. 948 00:47:47,050 --> 00:47:50,240 If I just told you sodium iodide, covalent or ionic? 949 00:47:50,240 --> 00:47:52,150 You'd say, ionic. 950 00:47:52,150 --> 00:47:54,850 Because you got something from the the most metallic of the 951 00:47:54,850 --> 00:47:56,870 metals and something from the most non 952 00:47:56,870 --> 00:47:58,500 metallic of the non metals. 953 00:47:58,500 --> 00:47:59,180 And you're right. 954 00:47:59,180 --> 00:48:01,520 And the delta chi is 1.73. 955 00:48:01,520 --> 00:48:06,560 And the covalent character is high. 956 00:48:06,560 --> 00:48:09,280 And you end up with something that's very polar and so on. 957 00:48:09,280 --> 00:48:12,640 Now here's a very interesting one, if you compare cesium and 958 00:48:12,640 --> 00:48:14,870 gold, you get 1.75. 959 00:48:14,870 --> 00:48:18,670 Which is greater than what it was for sodium and iodine. 960 00:48:18,670 --> 00:48:21,700 Now no one would argue that sodium and iodine is covalent, 961 00:48:21,700 --> 00:48:22,950 you'd argue that's ionic. 962 00:48:22,950 --> 00:48:26,340 Well by the same metrics, cesium and gold is as ionic. 963 00:48:29,470 --> 00:48:30,970 The plot thickens. 964 00:48:30,970 --> 00:48:35,090 Cesium, if you melt it it's a metal, liquid metal. 965 00:48:35,090 --> 00:48:37,720 If you melt gold, it's a liquid metal. 966 00:48:37,720 --> 00:48:41,020 But if you mix them in equal number. 967 00:48:41,020 --> 00:48:47,200 So you make a alloy of 50 mole percent cesium and 50 mole 968 00:48:47,200 --> 00:48:51,700 percent gold and you've got a delta chi 1.75, you've 969 00:48:51,700 --> 00:48:55,360 essentially made a cocktail with equal numbers of really 970 00:48:55,360 --> 00:48:57,340 good electron donors and really 971 00:48:57,340 --> 00:48:58,690 good electron acceptors. 972 00:48:58,690 --> 00:49:01,660 And guess what happens, electron transfer. 973 00:49:01,660 --> 00:49:05,990 And the melt is not metallic, it turns clear and colorless 974 00:49:05,990 --> 00:49:08,620 just as molten sodium iodide would be. 975 00:49:08,620 --> 00:49:10,810 It turns into a molten salt. 976 00:49:10,810 --> 00:49:12,960 So cesium gives its electron to gold. 977 00:49:12,960 --> 00:49:16,730 And gold becomes the negative gold ion. 978 00:49:16,730 --> 00:49:19,310 And what color is every ion? 979 00:49:19,310 --> 00:49:21,550 It's got stable octet configurations. 980 00:49:21,550 --> 00:49:24,860 It's got be the same color as neon, argon, and helium. 981 00:49:24,860 --> 00:49:26,110 They are clear and colorless. 982 00:49:29,080 --> 00:49:32,190 Big drop in electrical conductivity and a shift from 983 00:49:32,190 --> 00:49:33,910 electronic to ionic conduction. 984 00:49:33,910 --> 00:49:37,710 Metals have electronic conductivity, ions, what do 985 00:49:37,710 --> 00:49:38,800 ionic liquids have? 986 00:49:38,800 --> 00:49:40,110 They have like ionic conductivity. 987 00:49:40,110 --> 00:49:41,940 Here's some data from the literature. 988 00:49:41,940 --> 00:49:44,890 This is the log on the connductivity as a function of 989 00:49:44,890 --> 00:49:45,700 concentration. 990 00:49:45,700 --> 00:49:47,950 So here's pure cesium over here, here's 991 00:49:47,950 --> 00:49:48,900 pure gold over here. 992 00:49:48,900 --> 00:49:50,230 This is 600 degrees C. 993 00:49:50,230 --> 00:49:54,460 So the line stops here because gold melts at about 1060. 994 00:49:54,460 --> 00:49:57,760 So gold is a solid beyond this alloy concentration. 995 00:49:57,760 --> 00:50:01,040 But you can see this is roughly what you'd get. 996 00:50:01,040 --> 00:50:05,320 So electronic conductivity up here at about 10 to the 4 997 00:50:05,320 --> 00:50:08,870 siemens per, this is reciprocal ohms, but siemens 998 00:50:08,870 --> 00:50:09,790 per centimeter. 999 00:50:09,790 --> 00:50:13,000 And down here, this is very low value ionic conductivity. 1000 00:50:13,000 --> 00:50:14,200 So this is a liquid metal. 1001 00:50:14,200 --> 00:50:15,680 And this is a molten solid. 1002 00:50:15,680 --> 00:50:17,170 And it all happens just when you get very 1003 00:50:17,170 --> 00:50:20,260 very close to 50/50. 1004 00:50:20,260 --> 00:50:24,230 So you end up with something called cesium oride. 1005 00:50:24,230 --> 00:50:25,540 And it's sorcery. 1006 00:50:25,540 --> 00:50:28,700 You have one vial of liquid metal. 1007 00:50:28,700 --> 00:50:30,320 You have a second vial of liquid metal. 1008 00:50:30,320 --> 00:50:33,500 You pour then and it turns clear and colorless. 1009 00:50:33,500 --> 00:50:37,010 And the conductivity drops three orders of magnitude all 1010 00:50:37,010 --> 00:50:41,240 because of electron transfer due to this electronegativity 1011 00:50:41,240 --> 00:50:42,860 difference. 1012 00:50:42,860 --> 00:50:44,870 That's so cool. 1013 00:50:44,870 --> 00:50:47,090 That is so cool. 1014 00:50:47,090 --> 00:50:48,680 OK, with that I'll let you go. 1015 00:50:48,680 --> 00:50:50,000 We'll see you on Friday.