Calculations with Enantiomeric Percentages

so we're going to keep talking about optical activity. But it turns out that there's another way that your professor could ask these questions. All right, that's not based on the specific and observed rotations that we talked about already. And it has to do with an anti American percentages. Okay, so another way your professor could ask this type of question is that they give you both the specific and the observed rotation and you have to solve for what? The percentages of each and dance summer. I know that sounds like you should be able to figure it out, and I'm sure a lot of you guys could, but it could get surprisingly tricky. So I want to go ahead and go over this. Now it turns out that there's three equations that we want to use for this two of them you already know. Okay, this one right here is just the shuffled around version off the equation that we're using earlier. Which was that observed equal specific times and anti America access. So that's the same question. I That's the same equation. I just rearranged it so that we're solving for E for any anti American access now. Okay, so that makes sense. The observed over the specific is your Nancy America access. Cool, then another one that, you know, because we've already used it is that the higher and anti murder plus the lower and anti always has to equal to 100%. Okay, Yeah, that's just kind of common sense. But then we've got this one in the middle. That's kind of just a derivation off the definition of an anti MERS. So the way that it works is that if you're given the Ananta America access So let's say that I say that my nan's America excesses 50% and you have to and you're asked to figure out how much each Indian summer represents in that, Then you'd use this equation. What this equation says is that you take your percent highest and Nancy mur, and that would be 100 minus the e over two plus the e, and that's going to give you a percentage higher hiring and summer. All right, then we can use the last equation to figure out what the lower Nancy more percentages. If we know the higher one, we can easily figure out the lower one. All right, so let's go ahead and get started with this question. Um, I'm gonna go ahead and read it for you guys, give you guys some hints, and then I'm gonna have you guys solve it on your own. Okay, So it says that the specific rotation of pure s epinephrine is positive. 50? So I've been given the specific rotation. That would be right here. I'm gonna say it's positive. 50? Okay. Calculate the E, the Indians, America, access of the solution off the following observed value. The following observed value is gonna be this guy right here. So that means I'm gonna put here from my observes what? I'm actually getting out of it. Even though I have a 50% theoretical, I'm only getting a 25%. So it tells you that I have some mixture of an anti MERS in here. It's definitely not 100% off the s. Okay, then we have to calculate the percentage of each and anti um, er from the and anti America access, and then we have to sketch the approximate mixture in our polar emitter tube. What that means is that I want you to actually sketch out like we were doing before, say, like, this part would be the S on this part would be the are whatever based on percentages. So if this is 50 and 50 then I would want you to draw that. Okay, Now, these numbers were obviously wrong, but I just want you to draw something like that. So you guys can kind of understand why we're only getting half of the efficacy from this 50 instead of rotating 50. It's only 25. Why is that? Okay, so go ahead and try toe. Just work with the equations above. So if you get the right answer, fill in those three blanks below right here and then I'll go ahead and sell it for you guys.

All right, so this is a pretty fun problem. First, I'm gonna take my equation that relates specific rotation and observed and solve for E. So what it says is that basically 25. Well, for my observed over 54 my my specific is gonna give you my an anti American excess. When you divide those together, what you're gonna wind up getting is equal to 0.5. Or if you convert that into a percentage, you would just multiplied by 100 that would give you 50%. Okay, so my an anti mark access is 50%. Is that cool? So far. So I'm gonna right here, 50. Okay. And that actually already makes sense to me because notice that I'm on Lee getting half of the rotation that I would expect. I would expect 50% not 50% 50 degree rotation, but getting 25. So that means that it must be half assed effective. So it means that Onley half of it is in excess. Is thean the entire in excess? Okay, now we just have to use that kind of weird equation to figure out what each percentage Indian team, er is. So the way we do this, it says that the percentage highest Indians humor is equal to 100 minus over to. And then all of this plus 50. Okay, when I do this math, what I'm gonna get is 50 divided by two, which is 25 plus 50 equals 75%. Okay, So what this is telling me is that I must have one of my an anti murders in 75%. Okay, then if I want to figure out what the other Nancy Moore is, I just used the equation. That 100 minus 75 is equal to 25. So that means that my other Indian team, er, is 25% cool. So now we have Our percentage is now the only thing we need to do is figure out which letter is which. Okay, The way we do this is by looking at the sign of the rotation. So notice that my specific rotation is Is it positive or is it negative? It's positive, and it's positive. For which letter s or r? Yes, OK, that's something to be very careful about. So I have a positive rotation for the s Indian summer when the S and Ann Summers and in excess then we're gonna have a positive Now, what is my observed? It's also positive. So what that means is that is my excess gonna be is my higher and Nancy more they are or the s. My hiring answer must be the s, because that's the one that would give it a positive rotation. So that means that my 75% must belong to my s in an steamer, and by 25% must belong to my or any consumer. Okay, If I then wanted toe backtrack and calculate to see if I did everything right, I could subtract 25 from 75 I would get back to the 50% that I have. So that's 50% of s, which is my an anti American access. Is that cool? Awesome. Guys, we're gonna do one more same exact concept, just different numbers. So go ahead and try to do it and try to get the right answer