With his tetrahedral carbon models van't Hoff explained the mysteries of known optical isomers possessing stereogenic centers and predicted the existence of chiral allenes, a class of molecules that would not be observed for another sixty-one years. Symmetry operations that involve inverting an odd number of coordinate axes interconvert mirror-images. Like printed words, only a small fraction of molecules are achiral. Verbal and pictorial notation for stereochemistry are discussed.

Transcript



November 5, 2008



Professor Michael McBride: At the end last time we saw this intemperate quote from Hermann Kolbe on the young van't Hoff: "The fancy trifles in it" (his book about the arrangement of atoms in space) "are totally devoid of any factual reality." The reason he thought so, Kolbe, was he knew there could be no way of knowing about the arrangement of atoms in space; they were just too small. But he was wrong. There was plenty of factual reality. What van't Hoff had done was to collect information about isomerism; in particular about optically active compounds, those that rotated the plane of polarized light, or twisted it.



In looking at the Wiki, I noticed some people talk about "bending" it. Bending would be like this. Right? That's not what happens to the plane of light as it goes. It goes and it twists. Right? It rotates; it doesn't bend. Bending is refractive index; you know, light goes into the surface of water and then bends. But this is twisting the direction that the electric vector oscillates.



Okay, so these optically active compounds that would do that, when in solution, were numerous, and van't Hoff was able to cite a number of examples; for example, lactic acid. But you remember who discovered lactic acid? Scheele already -- close to 100 years before this, Scheele had isolated it from sour milk. But Liebig then found the same analysis of the acid he got from meat… isolated it from meat. And Wislicenus, at this same time that van't Hoff is working -- in fact, the guy who had one of his helpers translate the work of van't Hoff into German for that publication and was therefore castigated by Kolbe -- Wislicenus showed that these things had the same connectivity, by chemical transformation; these two acids, the one from milk and the one from meat. Right?



If you look forty years later, in the Encyclopedia Britannica -- so this is a long time afterwards, right? -- about lactic acid, it says it's hydroxypropionic acid. "Two lactic acids are known, differing from each other in the position occupied by the hydroxyl group in the molecule; they are known respectively as α-hydroxypropionic acid." You remember what α means? It means on the carbon adjacent to a carbonyl group. Okay, so there's α-hydroxypropionic acid, which came from fermentation and is called inactive lactic acid. Why would they call it inactive; in what sense inactive? Can you think what active versus inactive would mean? It means whether it's able to rotate, to twist the plane of polarized light; whether it's optically active. Okay, inactive lactic acid -- and they give the formula, with an OH on the carbon next to the carbonyl of the acid group -- and 3-hydroxypropionic acid, or hydracrylic acid, which has the OH on the terminal carbon. Okay? Now these are clearly constitutional isomers. It's a different sequence of bonds. Okay?



But they go on to say, "Although on structural grounds there should be only two hydroxypropionic acids" (these two) "as a matter of fact four lactic acids are known. The third isomer" (in addition to the inactive one and the one that has the OH on the last carbon) "the third is sarcolactic acid." Sarco means from flesh. Okay, so that's the one that Liebig found in meat extract. In fact, Liebig was so interested in meat extract that he patented bouillon cubes, and they were known for a long time as Liebig's material or whatever, I forget exactly. But I once looked at a train menu from the late 19th century, in the restaurant car of the train, and they were serving Liebig's extract. Okay? So there's the third one is Liebig's, the sarcolactic acid, "and may be prepared by the action of Penicillium glaucum on the solution of ordinary ammonium lactate. It is identical with α-hydroxypropionic acid in almost every respect, except with regard to its physical properties." That's sort of an interesting statement, isn't it? That it's identical in every respect, except it's all different. Right? What was similar about it, do you think? In what way was it identical, if it had all -- its boiling point, everything was different; melting point, crystal form, everything was different, all the physical properties. But how could they possibly say "it is identical in almost every respect"? Kevin?



Student: Its formula.



Professor Michael McBride: What about its formula? Obviously they're isomers. So they have the same composition.



Student: The constitution's the same.



Professor Michael McBride: But the constitution is the same, the sequence of bonds. Right? "The fourth isomer, formed by the action of Bacillus laevolacti on cane sugar resembles sarcolactic acid in every respect, except in its action on polarized light." So one rotated it to the right, the other rotated it to the left, and in every other respect they were identical. So there were four -- [and of a] right, left and inactive. Okay? But here, forty years after, they don't give any explanation of why that should be so. Okay, tartaric acid we've seen a lot. Right? Scheele; Berzelius coined the name isomer to talk about it; Pasteur; Wislicenus again showed the constitution; which meant nothing to Pasteur. Why would the constitution mean nothing to Pasteur, the nature and sequence of bonds? Yeah?



Student: He believed the positions in space mattered, rather than the sequence of bonds.



Professor Michael McBride: Would Pasteur have written, at the time he did this work, "we don't know anything about the position of bonds"? I don't think he would've written that. You know why? Bonds wouldn't be invented for another ten years. There was no such thing as bonds, when Pasteur did his work in 1848. Bonds came in 1858. Right? So Pasteur didn't have the tools to think about this. Okay? So aspartic acid was an example of something that was optically active. Amyl alcohol could rotate light. Glucose could rotate light. Notice that this didn't mean they had both the one that could rotate one way and the one that could rotate the other way. They had something that could rotate light. In the case of lactic acid they had things that would rotate either way. Right? In the case of tartaric acid, after Pasteur, they had that. Okay? And also laevulose and lactose were another two that were known but were not cited by van't Hoff. Malic acid -- you know what that comes from? Where's the root, mal? It's apples, right? So it's sour apples. Okay, and most of the derivatives of these compounds, most things you could get by chemical transformations from these compounds were optically active, but not the stuff you got by dehydrating malic acid. If you got the double bond, so you got maleic and fumaric acid, two isomers, but they didn't -- neither of them rotated light, neither right or left. Right? So that was destroyed in this case. And also there was another example, which was replacing the OH by a hydrogen. So you have CH2CH2 in the middle, instead of CH(OH)CH2. And that particular experiment, van't Hoff was involved in; he was involved in by suggesting it to his fellow student, Bremer, who did it by treating it with hydriodic acid and phosphorous, which was a way of removing OHs and changing them to hydrogen, in those days. We'll see later that that's called reduction.



But at any rate there were these two derivatives of malic acid that were not optically active, although most derivatives were. Okay? Now, van't Hoff, as I said, was involved at least in suggesting these experiments. And, as we said, those two were inactive. In van't Hoff's obituary, a former student of his, Bancroft, who was by this time a professor at Cornell, wrote: "In his whole life he never made what would be called a very accurate measurement, and he never cared to. I remember his saying to me eighteen years ago, 'How fortunate it is there are other people who will do that sort of work for us.'" Right? So it's great to do experiments, but in some sense it's even greater if you can talk somebody else, who's competent, into doing them for you. Okay? And that was van't Hoff's approach.



Now, what van't Hoff noticed was that these compounds, that were optically active, all had something in common. They all had these red atoms in common. What's special about the carbons that are red, that exist in the ones that are optically active, but don't exist in the ones that are not optically active? What's special about the ones that are in italics in red? What makes them different? This is what van't Hoff noticed. Chris?



Student: Are they chiral carbons?



Professor Michael McBride: Well they are, but what did van't Hoff notice? Chiral didn't exist then, as a name. Yeah Andrew?



Student: They have four bonds [inaudible].



Professor Michael McBride: They all have -- they use their four bonds to bond to different groups. No two things are the same. Down here, this carbon that was red here, has two hydrogens on it. Here it has two bonds to another carbon. Right? But in the other cases they're all, these red carbons are unique in bonding to four different things. This one, for example, this carbon is bonded to hydrogen, to OH, to another carbon that goes out on this chain, and another carbon that goes out on that chain. And those two chains are different. This one has a carbonyl group; that has an OH. So the difference can be quite remote. But they're different. Okay, so that's what he noticed. And we now call these chiral carbons; or stereogenic, because they give rise to special stereo arrangement in space. So what he said was, "Every carbon compound which in solution can rotate the plane of polarized light contains one or more asymmetric carbon atoms." That's what he called these, that had four different things.



And he made models of carbon. This particular set he folded up, colored, pasted together, and gave to this friend, Bremer, who had done the experiment. And they're in the Museum Boerhaave in Leiden now. Now look at these things and see if you can figure out what some of them are. Here are tetrahedra, whose faces are colored. So you could make… if you had four different colors, that would denote being associated with four different things, and each face would correspond to a substituent. Okay? This one has colored vertices. So instead -- you could use a tetrahedron either way. You could use the faces to denote a neighbor, or you could use the points to denote where a bond is to the neighbor. And he did it both ways. What are these here? What are those models? Those aren't tetrahedra. Can you see why he might have made those models? Kevin, what do you say?



Student: To show pentavalence?.



Professor Michael McBride: No. We talked about van't Hoff last time, last lecture. Do you remember what he was talking about? Lucas?



Student: Ladenburg Benzene.



Professor Michael McBride: Pardon me?



Student: Ladenburg.



Professor Michael McBride: Ladenburg Benzene. A triangular prism. That's what these are. And you remember this is 1,2; 3,5; 4,6; or whatever it is, that are this way. If you color these two it's not superimposable on one where you color this one and this one. Or this case. That was AB or AB the other way. Those he said were absolutely different. So those are models he made with regard to this argument with Ladenburg. Okay, now here are his models of these two things you get by removing water -- pardon me -- from tartaric acid. So what he has is tetrahedra for the carbons. And what does he mean when he puts their edges together, like this? What's he using to denote a bond? There we go. What's denoting a bond? A shared vertex. Right? So here's a single bond, right? What's this? A double bond. That's like what Lewis did later -- remember when he brought cubes together to share an edge -- or a little bit like that at least. But now when you do that, when you share an edge, of the other two things on each carbon, they're different; this one red and not red. Right? You could put them together this way, but you could also put them together this way. And you can't get from one to the other without pulling them apart and putting them back together again. Right? So that would explain why they're two different isomers; maleic acid and fumaric acid. Right? That you get -- when you start with tartaric acid and pull off the water. Or start with malic acid. I was saying tartaric. You start with malic acid, pull off water, and you get either this or this. Okay, so he could explain that with his tetrahedral models. The red denotes a red vertex, obviously. Okay? Or if you have a single bond you could count isomers. Now what he says here is you don't get all that many isomers because it can freely rotate about the bond between the two. So the carbon atom is in the center of a tetrahedron, and its substituents are on the vertices. Right? So the top carbon has three things, R1, R2, R3. And what he shows here is you can rotate that freely. You don't count all these as separate isomers. Who would've thought you did count them as separate isomers? You may not remember the name. Where was he? What?



Student: The guy from [inaudible].



Professor Michael McBride: The guy from Palermo. Right? Paternó was his name, right? He tried to explain the existence of isomers. But van't Hoff says no, that's not true; you can freely rotate, so you can't count that. But you could have -- if you looked down on R1, R2, R3, you could look down and see them clockwise, from one to two to three, or you could see them counterclockwise from one to two to three. And you can't go back and forth between those by rotating, because they're in a certain order. So you do get isomers.



So he made this diagram to show that free rotation about the central bond results in rapid inter-conversion, and thus inseparability and irrelevance of the isomers that Paternó talked about. And they can be arranged clockwise or counterclockwise, which is not affected by the rotation about the central bond. And you can then count how many isomers there are, depending on whether R1, R2, R3 are the same as four, five, six, or are different from four, five, six. Okay?



But maybe the most spectacular thing he showed was that if you put three tetrahedra together like that, you get these forms, which -- what's the relationship between these two? Can you superimpose them and have them be exactly the same? Is there any relationship between them? Obviously if you just slid them together, R1 would be on top of R1 and two on two, but four and three -- this is a four here, it looks like a one -- four and three would not be on top of one another when you slid them together. And there's no way of twisting it so it'll be right. Right? But there's a special relationship between those. They're not completely unrelated. What symmetry relates them? Do you see? Zack?



Student: Right handed and left handed?



Professor Michael McBride: Yeah, they're mirror images, like right-handed and left-handed. Okay? So he predicted that if you had two double bonds in a row, with a common carbon in the middle, then you could get right and left-handed, where you can't get it with just a double bond, as in the maleic and fumaric acid. Those aren't "chiral", as we now say. But this wasn't shown until 1935. That's probably the longest that there's been a correct theory proposed, until the time that it was confirmed. Or at least I don't know of anything longer than that; sixty-one years after he predicted it, before it was demonstrated to be true. And it was proved, you see, in the labs of E.P. Kohler, the same guy we talked about last time. And here's the molecule he used, down on the bottom left. And we can enlarge it here. So there it is.



Now, that molecule, as you look at it, would be superimposable on its mirror image. It looks planar. Right? Now let's think about that. The bonds at that carbon should be tetrahedral. So one bond should be coming in and out, or one pair of bonds, and the other pair of bonds should lie in the plane. But if that's true, then the one on the right would have its four bonds coplanar -- right? -- all in the plane of the paper. So there's something wrong here. And you can see what's wrong if you think about the p orbitals that go into making a double bond. Right? What's wrong with that arrangement? Why don't the p orbitals like it?



Student: They're orthogonal.



Professor Michael McBride: They're orthogonal. They don't overlap, right? What you need to do is to twist it, like that, so that the groups, C10H7 and C6H5, come in and out of the plane. Right? And that's what then makes it not superimposable on its mirror image. Okay, now if you wanted to convert one mirror image to the other -- notice if you used the plane, something parallel to the screen, as a mirror, what comes out in front of the mirror would be the same on the left. But on the right C10H7 would be back in, and C6H5 would be coming out. Right? So if you want to interconvert these, you have to put ten where six is and six where ten is. You have to rotate around the bond. But to do that you have to break the bond, because it's a double bond. You'd have to go back to where the p orbitals don't overlap and you lose the double bond, and then you can keep rotating and get the other mirror image isomer. Right? But you have to break a bond to do that. So that's very tough.



Okay, now we were counting isomers in homework for today. And this slide goes through and counts them. I'm just going to begin it, and then hustle through the end, rather than go through it in great detail, because you've already worked on it. But this can be thought of as an answer key. Okay, so we want to count how many different mono-substituent positions there are in that compound. There's one. Okay? There's obviously a different one, two. Now about three, is that different, if you have just a mono-substitution. Is the blue different from the red? No, obviously because this thing has rotational symmetry, you could rotate it; put the red on top of the blue. So the blue's not a new one; forget blue. Okay, now how about that blue one, is that a new one? No, because the one in the left front would go, on that same rotation, go the right rear. So that one doesn't count. How about that one? Is that different or the same? Can you rotate it so the one on the front left becomes the one on the front right? No. So now we have a question. Is that something real about the models? Or is that just like the sausages, that Kekulé used, that it suggests a difference, when there's not a real difference? Okay? So, we'll put a question mark on that one. Okay, so there are two isomers, if we don't count the two on the bottom, and there's an additional isomer if we do count it. Okay? So there are either two isomers, or conceivably three isomers, of that one. Okay, and notice that this one, the third one in, has exactly the same arrangement among the hydrogens as the first one.



So the numbers would be the same: two and an additional one, if you count those extras. Now here, you have obviously three different positions you can have for mono -- top, middle, bottom. But also the ones on the right are not superimposable on the ones on the left, if this is three-dimensional. So you could have another three, if they count. And so on. I'll not go through these -- notice -- except to note in this one that there's obviously top here and these three. Now the question is, are those three different or not? And we're following van't Hoff here and saying it rotates rapidly around here. So on time-average you won't be able to put those in separate bottles, right? They're going to interconvert too rapidly to count. So there'll be three. But the two on the top are not really -- they're not superimposable by rotation, in the model. Okay? So the question is whether you have that additional one. And in prismane there's only one.



And then if you go disubstituted, if we start on the left, if you start with one on the top here, you can have the second one here, or here, or here. That's clearly three. But there might -- this one is not superimposable. That is, if you have this one already, this one and this one, as sites for the second, are not superimposable. Right? So maybe we need another one there and another one over here as well. So there might be an additional two. And again, this is the same as that one. And you can go through this -- and presumably you have done. But anyhow these are the answers I got. And if you found something different, let me know. Maybe you saw something I didn't see. Okay, so that's interesting.



Now mirror images. Here's me with a mirror image. Right? Now this is a question. Why does a mirror exchange right and left, but it doesn't exchange top and bottom? How does the mirror know which way gravity points? Or how about if I lay on my side when I looked in the mirror, would it still exchange left and right and not top and bottom? I'm talking about plane mirrors, not funhouse mirrors. That's an interesting problem, right? But notice, it doesn't change either, because top is on top and right is on right. It didn't change right and left. It left right on right. What did it change? Why does the mirror image look different from the real image, if it doesn't change right and left, and it doesn't change top and bottom?



Student: Front.



Professor Michael McBride: It changes front to back, or in and out. Right? Because my original self, you see the back of my head, and in the mirror image you see the front of me. So what a mirror changes is in and out, not right and left. Okay? But our intuition interprets that as rotation. Because if I look like this, and I go like this, you expect it to change, the right hand, because you're accustomed to people rotating. You're not expecting me to go pfff, like that and turn inside out. Right? [Laughter] Okay, so people don't invert. So our mind makes us think that the person we see in the mirror has turned 180°, so that the right should be on the left. Okay? And, of course, this is not a new observation. Through the Looking-Glass -- you know, Lewis Carroll, and Alice going through. And here are successive pictures in that book. There she is looking into the glass, and we turn the page, and here she is coming out, on the other side.



Now notice something about this. That's her right arm. Right? And in the previous picture it was also her right arm. That's not the way the mirror image should look. It should've changed the way it looks, when you go from back to front. Okay? Now, Lewis Carroll was a smart guy. He taught mathematics at Oxford. Right? But of course he didn't draw the picture. The picture was drawn by John Tenniel. And it turned out that John Tenniel was blind in one eye; a fact I only discovered yesterday, on Wikipedia. [Laughter] So is that the reason that he's unable to perceive depth, and draws the wrong thing? No, it's much more subtle than that. Notice that the name of the book is Through the Looking-Glass. She moved through the looking-glass and her right arm stayed right. But if she had been reflected in the looking-glass, if the title had been chosen to be In the Looking Glass, rather than Through the Looking-Glass, then when you looked at the mirror image it would've been the left arm. That's sort of cute. So Carroll is more subtle than you might give him credit for; or John Tenniel, or both. Okay? Or look even further in the book. This was, notice, 1872. What was going on in chemistry in 1872? Wislicenus was studying these isomers of lactic acid, the Scheele and the Liebig, and showing that they had the same constitution but were different. Okay? So look what happens here when she's talking to her kitty.



"Now, if you'll only attend Kitty, and not talk so much, I'll tell you all my ideas about Looking-glass House… Well then the books are something like our books, only the words go the wrong way. I know that because I've held up one of our books to the glass, and then they hold up the one in the other room… How would you like to live in a Looking-Glass House, Kitty? I wonder if they'd give you milk, there? Perhaps Looking-glass milk isn't good to drink."



Because in the college Carroll knew Vernon Harcourt, who was a chemist who was involved in this work, with Wislicenus. So almost certainly they'd had conversations about lactic acid, the mirror image form. Right? So there's a lot of stuff in Alice. So was he referring maybe to sarcolactic acid, the one that comes from meat instead of from sour milk? Anyhow, chirality comes from the Greek word "χÑ

1. How Do You Know?
2. Force Laws, Lewis Structures and Resonance
3. Double Minima, Earnshaw's Theorem, and Plum-Puddings
4. Coping with Smallness and Scanning Probe Microscopy
5. X-Ray Diffraction
6. Seeing Bonds by Electron Difference Density
7. Quantum Mechanical Kinetic Energy
8. One-Dimensional Wave Functions
9. Chladni Figures and One-Electron Atoms
10. Reality and the Orbital Approximation
11. Orbital Correction and Plum-Pudding Molecules
12. Overlap and Atom-Pair Bonds
13. Overlap and Energy-Match
14. Checking Hybridization Theory with XH3
15. Chemical Reactivity: SOMO, HOMO, and LUMO
16. Recognizing Functional Groups
17. Reaction Analogies and Carbonyl Reactivity
18. Amide, Carboxylic Acid and Alkyl Lithium
19. Oxygen and the Chemical Revolution (Beginning to 1789)
20. Rise of the Atomic Theory (1790-1805)
21. Berzelius to Liebig and Wohler (1805-1832)
22. Radical and Type Theories (1832-1850)
23. Valence Theory and Constitutional Structure (1858)
24. Determining Chemical Structure by Isomer Counting (1869)
25. Models in 3D Space (1869-1877); Optical Isomers
26. Van't Hoff's Tetrahedral Carbon and Chirality
27. Communicating Molecular Structure in Diagrams and Words
28. Stereochemical Nomenclature; Racemization and Resolution
29. Preparing Single Enantiomers and the Mechanism of Optical Rotation
30. Esomeprazole as an Example of Drug Testing and Usage
31. Preparing Single Enantiomers and Conformational Energy
32. Stereotopicity and Baeyer Strain Theory
33. Conformational Energy and Molecular Mechanics
34. Sharpless Oxidation Catalysts and the Conformation of Cycloalkanes
35. Understanding Molecular Structure and Energy through Standard Bonds
36. Bond Energies, the Boltzmann Factor and Entropy
37. Potential Energy Surfaces, Transition State Theory and Reaction Mechanism

This is the first semester in a two-semester introductory course focused on current theories of structure and mechanism in organic chemistry, their historical development, and their basis in experimental observation. The course is open to freshmen with excellent preparation in chemistry and physics, and it aims to develop both taste for original science and intellectual skills necessary for creative research.

Course Structure: This Yale College course, taught on campus three times per week for 50 minutes, was recorded for Open Yale Courses in Fall 2008.

Original Course Title: CHEM 125: Freshman Organic Chemistry