Hey, everyone. So here it says, calculate the EE, which is our enantiomeric excess, and observe rotation for the following chiral mixtures where the S enantiomer has a specific rotation of plus 20 degrees. Alright, let's take a look at these two images.

In the first image, we're dealing with a racemic mixture because it has an equal amount of R enantiomer versus S enantiomer. So here, they would be 0 for our enantiomeric excess. Remember, the formula for enantiomeric excess is we subtract the larger percentage enantiomer by the lower percentage enantiomer. Since they're both 50%, they cancel out to 0. And remember, with the racemic mixtures, since the R and S enantiomers are completely neutralizing each other, there is no observed rotation. So, it'd be 0.

Over here though, we're no longer dealing with a racemic mixture because the R and S enantiomers are not equal in terms of percentages. So, in this case, let's calculate what our enantiomeric excess will be. Again, our enantiomeric excess is the higher percentage enantiomer; S here is 70%, minus the lower percentage enantiomer, which is R at 30%. So here, our enantiomeric excess would be 40%.

Next, they need us to find the observed rotation. So remember, your observed rotation is just α = σ ⋅ △, where △ is the enantiomeric excess in its decimal form. To find the decimal form, you just divide your percentage by 100. So that would be times 0.4. Here we have our specific rotation which is 20. Positive 20. So now you multiply the positive 20 degrees times the 0.4. So your observed rotation here should be 8 degrees.

Now, does this answer make sense? It does make sense because remember, when we're dealing with pure enantiomer, its full rotation is 20 degrees. We're no longer dealing with a pure enantiomer; we have a mixture. 30% of it is R. And if we want to think about it like this, out of the 70%, we had 30% originally, that was S. Over here we said that these percentages are equal, so they completely cancel one another out. The same thing happens here too. 30% of this R, which is all of it, cancels out with 30% of this S. So they're completely taken out. And what we have left here is this 40%. That is the enantiomeric excess. So, this 40% that's remaining, that's the observed rotation we're seeing. We're seeing it of that remaining 40%. So that's why we wouldn't expect a full positive 20 degree; we'd expect something much lower than that. We expect a positive 8 degree. So again, we're observing this portion, the portion that hasn't been canceled out by this 30% of R. Right? So, keep that in mind when dealing with the enantiomeric excesses. If you're dealing with a racemic mixture, there is no enantiomeric excess, and the observed rotation is 0. Once the percentages of the R and S enantiomers are not equal, there's going to be some type of observed rotation. And here, to determine that, it's important to be able to calculate your enantiomeric excess beforehand.