So now what I want to do is I want to talk about enantiomeric excess, 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% enantiomers would produce. So if I had a 100 percent enantiomer, 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 enantiomer, meaning that this would be, let's say, the R. But let's say that I have the S enantiomer 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 ten rotation, maybe I get a negative ten, something like that. Basically, it would be the same absolute value, just a different sign. So that's the first thing that you guys need to know.

The second thing is that we can mix enantiomers. 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 going to mix it up and give you guys some kind of mixture and you're going to have to figure out what the optical activity is at the end of the mixture. Okay. So a perfect one-to-one ratio of enantiomers, meaning that I have 50% S and 50% R is called racemic. That's very important. That's such an important word for organic chemistry. You can never forget that. Okay? A non one-to-one ratio, that it's not pure but it's also not 50/50 is called scelemic. This one is not used quite as frequently, but it's still something that you should be aware of.

So now what I want to do is I want to take our polarimeter tubes, our sample tubes and I want to do some experiments. We're just going to make up some numbers and we're just going to see what happens. Alright. So for this first one, as you can see, I have my S enantiomer and it has a specific rotation, that means the alpha in brackets, of 20. Okay? And I want to know if I took a 100%, if I had a 100% of S in this tube, what would be the observed rotation? The answer is that the observed rotation would just be the same thing. It would be positive 20. I'm going to explain why in a second. Okay. Then the R enantiomer, let's say that my S enantiomer is positive 20, but let's say that I have a 100% of my R enantiomer in here. So now I just mixed it up, then what would that be? What that would give me is negative 20 because it has an opposite configuration, so my observed would also be opposite.

Now what I want to do is let's say that I had in this one, I had 50% of S and then I had 50% of R. 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 it 20 degrees to the right. I have 50% rotating it 20 degrees to the left. What would be the observed rotation? The observed rotation or just the alpha symbol, not the alpha with the brackets, would be 0. Okay? Because they would cancel each other out and this is what we would call racemic. Okay. So a racemic concentration is always going to have an optical activity of 0 because it's going to perfectly cancel out. Does that make sense so far? Cool.

So now what I want to do is I want to talk about something called the enantiomeric excess. And what the enantiomeric excess says is it's just basically you take your highest percentage enantiomer and subtract it from your lowest percentage enantiomer. You only have 2 enantiomers, so you would take your highest minus your lowest and whatever you have at the end of that, that's going to be your enantiomeric excess and that's the amount that is actually optically active. So if we ever want to calculate observed rotation, it's actually really easy. All we do is say observed rotation or alpha equals the specific rotation, meaning the amount that that molecule would produce at 100%, times the enantiomeric excess, which is actually the optically active part because it's the part that isn't cancelled out by anything else.