Specific rotation [α] is the rotation that 100% pure enantiomers produce.

Opposite enantiomer = opposite rotation.

Racemic:A perfect 1:1 ratio of enantiomers

Scalemic:A non-1:1 ratio of enantiomers

1

concept

How to calculate enantiomeric excess.

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So now what I wanna do is I want to talk about an anti American access, which is actually one of the most important concepts of optical activity. Okay, so remember that I told you guys the specific rotation is the rotation that 100% in anti MERS would produce. Okay, So if I had a 100% Nancy murder, let's say my specific rotation is 10 degrees. Then I would get 10 degrees. Well, it turns out that if I have the opposite and anti or meaning that this would be, let's say that the are. But let's say that I have the S Indian tomorrow over here. Then what would I get? I would just get the opposite rotation. Okay, So then that means that instead of getting a positive 10 rotation, maybe I get a negative 10. Something like that. Basically, it be the same absolute value, just a different sign. So it's the first thing you guys need to know. Second thing is that we can mix and anti MERS. It doesn't always have to be a 100% pure solution. And in fact, for most of these questions, it never will be your professor is gonna mix it up and give you guys some kind of mixture, and you're gonna have to figure out what the optical activity is at the end of the mixture. Okay, So a perfect 1 to 1 ratio of any answers meaning that have 50% us and 50% are is called Rosie Mick. And that's very important. Like that's such an important word for again in chemistry. You can never forget that. Okay, A non 1 to 1 ratio. Meaning that it's not pure, but it's also not 50. 50 is called Scully. Mick Scully, Mick. Okay. And this one is not used quite as frequently, but it's still something that you should be aware of. Okay, so now what I wanna do is I want to take our polar emitter tubes are sample tubes, and I want to do some little I want to do some experiments. We're just gonna make up some numbers, and we're just gonna see what happens. All right, so for this first one is, you can see I have my s and and summer, and it has a specific rotation. That means the Alfa in brackets of 20. Okay, and I want to know if I took 100%. If I had 100% of s in this tube, what would be the observed rotation? Okay. And the answer is that the observed rotation would just be the same thing. It would be positive. 20. Okay, I'm gonna explain why in a second. Okay, then the Iranian steamer, let's say that my s and anti was positive. 20. But let's say that I have 100% of my Iranian team are in here. Okay, so I just mixed it up. Then what would that be? Okay, what that would give me is negative. 20. Okay? Because it has an opposite configuration, so my observed would also be opposite. Okay, Now, what I wanna do is, let's say that I had in this one, I had 50% of s. And then I had 50% of our okay. What would be my observed rotation in that case? Well, just intuitively, the way you can think of it is well, I have 50% rotating at 20 degrees to the right. I have 50% rotating at 20 degrees to the left. What would be the observed rotation, the observed rotation or just the Alfa symbol, Not the Alfa with the brackets would be zero. Okay, because they would cancel each other out. And this is what we would call Rosie. Mick. Okay, so a receive it. Concentration is always gonna have an optical activity of zero because it's gonna perfectly cancel out. Does that make sense? So far? Cool. So now what I wanna do is I want to talk about something called the an anti American excess. And with the in anti American excess says is it's just basically you take your highest percentage in an summer and subtract it from your lowest percentage in Nancy, where you only have to an anti MERS, so you would take your highest minus your lowest. And whatever you have at the end of that, that's gonna be your in anti American excess. And that's the amount that is actually optically active. Okay, so if we ever want to calculate observed rotation, it's actually really easy. All we do is you say, observed rotation or Alfa equals the specific rotation, meaning the amount that that molecule would theoretically produce at 100% times the an anti American excess, which is actually the optically active part because it's the part that isn't canceled out by anything else.

2

example

Calculating Enantiomeric Excess and Observed Rotation

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So my equation says that my observed rotation equals my specific rotation times my e. Okay, well, in this case, what was my specific rotation equal to? It was equal to positive. 20. Okay, so I just have to figure out what was e equal to e is equal to my highest and answer minus my lowest in anti mark. In this case, it was 50 minus 50 which meant that I had a Nancy America excess of zero. So that means that my e equals zero. So it was 20 times zero. Which means that even though I have this awesome specific rotation of 20 all of the Ananta MERS air getting canceled out, so there's no overall rotation at the end. So that is why my observed rotation zero.

Calculate the observed rotation when given the following ratio of enantiomers in solution.

3

example

Calculating Enantiomeric Excess and Observed Rotation

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All right. So I'm gonna go ahead and take myself out of this videos that you guys can see the full image. So first of all, we had to figure out the Indians America access. The way we figure that out is by saying 70 minus 30% equals What percentage? 40% e. Okay, so that means that my e e is 40%. So what's my equation when my equation says that my observed rotation should be equal to my specific rotation, which is still positive 20 times my e, which is now gonna be 40%. Okay, Now, we don't really wanna work with percentages if we're multiplying. So we would turn this into 0.4, which is just I'm turning my my percentage into a decimal, which is very common. Okay, So now I would just multiply these together, and what I'm going to get is that 20 times 200.4 is gonna equal positive eight. Okay, so my Nancy America excess here should have been 40% and my observed rotation, instead of being positive 20 which is what it would be if it was 100. It's gonna be positive eight. Now, how does that intuitively make sense? Well, actually, it makes a lot of sense if you think about it. Remember what I said about Rosie mc Richy mc isn't optically active. Well, if I were to look at my tube as broken up into parts, what I would see is that the 70% is actually broken up into two parts. There's 30%. Here s that is perfectly canceled out by. 30% are. So what that means is that this entire area right here is Rosie. Mick, Okay. And the race Emmick portion adds up to I'm just gonna put here, Rossi, Mick, The race emmick portion adds upto what it adds up to 60% because I have 30 and 30. That means that the Onley part of this that's optically active. Let's put that back. That means that the only part of this that's optically active is the extra remaining s or the an anti American excess, and that part equals 40%. Okay, So that means that even though my s would love to rotate this positive 20 there's only 40% of it available that can actually rotate it because the other 30% is being canceled out by 30% of our Okay, So what that means is that Onley 40% is functional, and that's why it's only 40% of the total rotation is pop. That's happening out of the total rotation that I could have only 40% of that is actually taking place, so it's positive eight.

We can also use these equations to calculate specific and observed rotation when other variables are given to us. Just plug the numbers in! Let's try a few.

4

Problem

Calculate the observed rotation of a chiral mixture that contains 65% (S)-stereoisomer where the [α] of pure (S)-stereoisomer = -118.

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5

Problem

An optically pure (R)-stereoisomer of a molecule has a specific rotation of – 20°. What specific rotation would be observed for a mixture of the (R) and (S) stereoisomer where there is an enantiomeric excess equal to (S) 60%.