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.
Remember that I told you guys the specific rotation is the rotation that 100% enantiomers
would produce.
If I had a 100% enantiomer, let's say my specific rotation is 10 degrees, then I would get 10
degrees.
It turns out that if I had the opposite enantiomer, meaning that this would be the R, but let's
say I have the S enantiomer over here, then what would I get?
I would just get the opposite rotation.
Then that means that instead of getting a positive 10 rotation, maybe I'd get a negative
10, something like that.
Basically, I'd do the same absolute value, just a different sign.
That's the first thing that you guys need to know.
Second thing is that we can mix enantiomers.
It doesn't always have to be a 100% pure solution.
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.
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.
A non-one-to-one ratio, meaning that it's not pure but it's also not 50/50 is called
scalemic.
This one is not used quite as frequently, but it's still something that you should be
aware of.
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.
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.
I want to know if I took 100%, if I had 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.
Then, the R enantiomer – let's say that my S enantiomer is positive 20, but let's
say that I have 100% of my R enantiomer in here.
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?
Just intuitively the way you can think of it is 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 alpha symbol, not the alpha with the brackets, would be
zero because they would cancel each other out.
This is what we would call racemic.
A racemic concentration is always going to have an optical activity of zero because it's
going to perfectly cancel out.
Does that make sense so far?
Cool.
Now what I want to do is I want to talk about something called the enantiomeric excess.
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 two enantiomers.
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.
That's the amount that's actually optically active.
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 molecule would theoretically produce at 100% times the enantiomeric excess, which
is actually the optically active part because it's the part that isn't canceled out by anything
else.