CHEM 125a: Freshman Organic Chemistry I
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Freshman Organic Chemistry I
CHEM 125a - Lecture 26 - Van't Hoff's Tetrahedral Carbon and Chirality
Chapter 1. Interpreting the Rotations of Light for Optically Active Compounds [00:00:00]
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.
Chapter 2. Van’t Hoff’s Proof of the Existence of Chiral Allenes [00:09:25]
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?
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.
Chapter 3. Superimposition, Mirror Images and Handedness: Chirality in Alice’s Looking Glass [00:19:57]
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?
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.
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 “χєiρ”, which means hand; it’s handedness. So there’s a right hand. Now let’s talk about… and Lord Kelvin coined the word. He said, “I call any geometric figure, or group of points, chiral, and say it has chirality, if its imagine in a plane mirror, ideally realized…” (so don’t take into account moles or a fingernail that hasn’t been trimmed or something like that) “…ideally realized, cannot be brought to coincide with itself.” (By rotation and so on.) Okay?
So let’s consider x, y, z coordinate systems. So there are points for every point on the surface of the hand. And I could make an image of it by changing some of the signs of some of these things. For example, I could leave all the z and y coordinates identical, but change the sign of x, which would move things from being on that side to being on this side. Got the idea? Okay, so I’m going to make a new hand, that looks like the original one, except every x coordinate has changed its sign. Change all the x coordinates and we get that — everyone see it? — ideally realized. The shadow is a little different and so on; but ideally realized, those are the ones that have done that, right? Changed one sign. Now is one hand right and the other hand left, or are they both right? Okay?
So what kind of relationship would you say there is between these? Are they superimposable or are they non-superimposable mirror images? Can you rotate and put one on top, exactly to coincide with the other? No, because they’re a right hand and a left hand. But that operation, changing the sign of x, corresponds to reflecting in a mirror, which is yz, in the yz plane. Everybody got it? Leaves y and z. That’s like leaving top, top and right, right, but changing in and out, this way. Okay? So that’s a mirror. Now, what would happen if we changed all the y coordinates — can you see? — but left x and z the same? Then you’d get this. Okay? And what does that correspond to? Is that a rotation or a mirror?
Student: It’s a rotation of your left hand.
Professor Michael McBride: So are they both left hands? This one, right? And this is a right hand, incidentally, not a left hand.
Student: That one and that one are left hands.
Professor Michael McBride: And if I rotate it, it would look like that, right? Is that the way it looks? No, it looks like that. Right? So what was the operation that did that? Mathematically it’s changing the sign. But how would you describe it, in terms of mirrors and things like that?
Student: Horizontal mirror.
Professor Michael McBride: It’s a horizontal mirror, that leaves right/left, in/out the same, but changes up/down, top/bottom. Okay, so that’s reflection in an xz mirror. Now suppose we changed the sign of all the z coordinates. Can you guess what that’s going to do?
Professor Michael McBride: Not rotation. Change the sign of z. So that’s going to give that one. Change in and out, but leave right/left and back — change right/left and top — pardon me. Leave right/left, leave top/bottom, but change in/out. That gives the one in front, this one, right? Okay, so that’s reflection in the xy mirror. Now, there’s some — we’ve occupied now four of the octants. But we can occupy the other four as well. For example, we can change the sign of all x and y, but leave z the same. Can you see what that’s going to do? Change x, change y, but leave z the same. There. And what operation was that? Was that a mirror?
Professor Michael McBride: Rotation about what? About z axis, the one that didn’t change. Right? How about if we — that’s rotation around the z axis. How about if we change all the x and z’s, but leave y the same? What’s that going to do? That’s easy, once you know the previous one. That’s going to rotate about the y axis. Right? And how about if we change the sign of y and z, and leave x the same? Sophie do you see? So we’re going to change the sign of y and change the sign of z, from the original one, back here. We’re going to change y, up and down, and we’re going to change — z did I say? — yes, z, in and out, from this one. There’s that one, right? That changes in and out and it changes up and down. Right? And what it is, is rotation around the x axis. Now there’s one octant that hasn’t been occupied yet; the one that’s out front, top left. Can you see how you get there? What haven’t we done yet? Kate?
Student: You have to try and change all three.
Professor Michael McBride: If you change all three, x and y and z, then you come up there and get the eighth one. Okay? Now what operation is that? It’s inversion through the center of symmetry. It’s what I tried to do by pffff, like that, but I couldn’t change myself inside out. Right? So there’s the center of symmetry there. And every point on the back has one the same distance and along the same vector, to the front; right there, or to the base of my thumb. Okay? So here there are — we looked at three mirrors, three rotations, and an inversion. Some of them changed right to left, and some of them didn’t. Some of them were superimposable. Right? Can you see, in terms of changing signs, what determines whether it’s going to be the same hand or the other hand? Angela?
Student: If there’s been reflection then it would be the other hand.
Professor Michael McBride: Reflection changes hands. So if you change x or y or z. Any other way to change hands?
Student: Or you can invert.
Professor Michael McBride: If you change everything, x and y and z. So if you change an odd number, then you change the hand. Okay? So chirality, handedness, is non-superimposable mirror images, and it involves an odd number of changes of coordinates. Now notice the right hand has only one mirror image; the right and the left are mirror images of one another. I can put the mirror image here, or I can put it here, or I can put it here. Right? So which mirror I use determines where the new hand is going to be. But it’s always the same mirror image. Okay? Just generates it in different locations and orientations.
Chapter 4. How Special Is Chirality? [00:36:24]
Now, this is a special property, handedness. Right? Or is it an everyday property. Right? We’ve looked at molecules. Van’t Hoff was able to come up with what? about less than a dozen examples from all the molecules that had been known up to that time. So what do you think? Do you think most molecules are chiral, or do you think most organic molecules are not chiral? Well we had an exciting night last night and learned about the democratic process. So the way to settle such a question is to vote. Okay, so how many — we’re going to vote on how special is chirality. First, very special, right? only unusual molecules will have it. Or, on the other hand… like these carbons that have four different things. Or the alternative, it’s very general, and what’s unusual is ones that are achiral, not like hands. So here we go. How many people think that chirality is pretty special? Okay. It’ll be a little like Indiana. How many people think chirality is not so special? Ah, not very many. That’s what I anticipated. It’s pretty special. The class voted overwhelmingly [Laughter] there should be more achiral than chiral molecules. And the voice of the people is the voice of God. Right? So let’s look at words. “You can use words,” Alice said, holding up her book to a mirror. Okay, so here’s a message: LET’S DECODE AT NOON BUT KEEP IT MUM. Okay? Now let’s make the — change the sign of x, so we get the mirror image of this. Okay? It looks like nonsense. Is there anything special?
Professor Michael McBride: MUM; MUM is its own mirror image. Thus it’s not handed, it’s achiral. Right? But it’s the only word that has — that when you change the sign of x it stays the same. It’s pretty special to be achiral; to be MUM, at least, okay, here. Now any other words look interesting?
Professor Michael McBride: NOON looks sort of interesting. Is it superimposable on its mirror image? No. So it’s chiral, handed, like most words. You can have a right or a left-handed NOON. It does have symmetry though. Watch what happens if we, instead of using a mirror, rotate the message on the right. So change both x and y. And now you notice what? NOON is the same. So it has symmetry. It has rotational symmetry — right? — but not mirror — okay? — in two-dimensions. So it has rotational symmetry, but that doesn’t keep from being chiral. Like a propeller is chiral; it has rotational symmetry. Okay, now let’s mirror by changing the sign of y. Anything special here? What?
Professor Michael McBride: DECODE is the same. So DECODE is a meso-word. Right? It’s achiral. But it’s harder to recognize because we’re not accustomed to dealing with mirrors that are horizontal. We’re much more familiar with mirrors that are vertical. So it’s much easier to see it in MUM than to see it in DECODE. So you can amaze your roommates with that. Okay, so how special is chirality? In the case of words it’s not at all special. Right? What’s special is to be achiral, to have some kind of special symmetry. Almost all words are chiral. But there are certain achiral, or meso-words, such as MUM and DECODE. But they’re very rare. Okay? It’s the same with molecules. Almost all molecules are chiral. But if you work with very, very simple ones, as you do when you begin to do chemistry, then a lot of them are achiral. But it’s a very atypical example. Essentially every molecule in you is chiral. All your amino acids, all the sugars, everything; almost everything. Fatty acids aren’t chiral, but when they’re parts of fats they are chiral. Okay? But when we deal with very simple molecules, we often encounter achiral or meso ones.
Chapter 5. Conclusion: Exploring Stereochemistry [00:41:04]
Now, we’re going to go beyond constitution into stereochemistry. So we’ve talked about composition. We’ve talked about constitution, the nature and sequence of bonds. And now we’re going to go into configuration and conformation, the other two Cs. These last three Cs all have to do with isomers, but there’s a difference in that the last two have to do with arrangement in space; what the traditional chemists warned the young folks not to think about, in the third-quarter and the early fourth-quarter of the 19th century, and what the Encyclopedia Britannica still didn’t know about by 1911. Okay? But what’s the difference between configuration and confirmation? The distinction is based on the model we make. Right? And because configurational isomers relate to one another by breaking a bond. You have to break a bond to go from one to the other and reassemble the pieces. Right? But when you’re talking about conformation, you can do it by rotating from one to the other. So Paternó was talking about isomers that related by rotation. His particular ones rotate so easily that it’s very hard to see different isomers, in his case. Right? Although you can get information about that kind of thing. Right? But the ones that require breaking a bond, to go from one to the other, those are much easier to deal with. Right? And so we have different names for them. But it relates only to the model we use, talking about bonds, whether you break them or not. And you won’t be surprised to hear that there are some bonds that are so easy to break that it’s easier to convert those configurational isomers than it is to convert certain conformational isomers; where formally all you have to do is rotate about a bond, but in the process other things run into one another and make it very difficult.
So configuration and conformation relates to the models we draw of the molecules, not to something the molecule itself fundamentally knows about. So that one’s hard to get back and forth, and that one’s easy, typically; but it doesn’t have to be that way. Okay? So all isomers represent local energy minima; that is, if you were at a low enough temperature, the molecule could sit in that structure and just vibrate; have a zero-point amplitude of vibration around that particular structure. But then you can get from one to another. You don’t take every possible structure, as Paternó tried to do, and say that all these structures are isomers. Because then there’d be an infinite number and they wouldn’t last any time, because they’re always vibrating. But you can vibrate within a little well here, or a little well here, or a little well here. And those are different isomers, not just different phases of vibration.
Now, the words of stereochemistry often involve relationships. For example, two molecules that have exactly the same constitution, nature and sequence of bonds, can be identical. Okay? They’re superimposable. And if you wanted a name for that you would call them homomers. But no one needs to use that because it’s always the same thing. So that word doesn’t really exist. But if they’re just completely different, then you call them diastereomers, which has the same root as diameter; things that are as far apart as you can get, right? They’re just plain different. Those are diastereomers. But they have the same constitution, the same nature and sequence of bonds, but they’re just completely different in their arrangement in space. Or there can be a very special relation in space. You know what that is?
Students: Mirror image.
Professor Michael McBride: They could be mirror images, which are not the same thing, but they’re going to be very similar, in many respects. Right? So that one has a special name. Diastereomer just means different. But enantiomer means mirror image. Right? Okay, so these are relationships between two molecules. You say this molecule is the enantiomer of this molecule. Okay? Now we need to talk about things like this, as Lavoisier told us. We need to think about the facts, the ideas, and the words. And when we come to words, now we need to convey such complicated ideas, we need pictures, not just written letters. Okay, so we need pictures for our notation that will show this third dimension. Now, there are a number of tricks that you can use to do that. Can you see what’s being used here, in this particular picture of — which is an old-fashioned picture when laptop computers were new and they had very simple programs. Yeah.
Student: Relative size.
Professor Michael McBride: I can’t hear.
Student: Relative size.
Professor Michael McBride: Relative size is one, right. The hydrogens that are far back are small. Anything else? Any other clues that show the three dimensions? Yeah.
Professor Michael McBride: Can’t hear very well.
Student: Slender lines for bonds.
Professor Michael McBride: The lines for the bonds. They are thinner in the back and notice that some of them are wedges, showing that they are coming in and out. Anything else? Corey?
Student: Some things are in the front and some in the back.
Professor Michael McBride: How do you know whether they are in the front or the back?
Professor Michael McBride: Like this one
Professor Michael McBride: How do you know it’s in front of this one?
Student: You can’t see part of it.
Professor Michael McBride: Because it hides it, right? That’s a way you can tell. There’s another one, which is if you look at this one with the left eye and that one with the right eye, your brain is able to put it together in three dimensions. It will be hard for you to do. I don’t expect you to; you usually use glasses to do that, ok. But you can see that they are different. Look at this hydrogen here. There you see the bond and there it’s being a little bit obscured, right? So, there are different images that your left and right eye see which is why Tenniel might have had trouble with the third dimension.
Now, there’s another way, which is motion. So, here’s a complicated picture, right? It’s hard to tell what’s in and out. But if I grab it, and do this, then you can perceive what’s in and what’s out, right? So, if you have a picture that moves, which didn’t used to be possible, of course, until you had computers that can do this kind of thing. So, that’s another way – motion. There’s that same molecule.
There’re other ways. What’s new in this one? Shadows. Or here. More obscuring and shadowing of the balls. Or here, even better, right, depending on what you want to show. So, there are lots of conventions or tricks that are used to convey the third dimension. Ok, and next time we’ll go on to simple notation that you can write on an exam, like showing tetrahedral carbons.
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