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15. Analytical Techniques:IR, NMR, Mass Spect

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in this video, we're going to cover the role of isotopes in mass spectrometry. So before we go any further, let's just all remember that an isotope would be an atom that has the same number of protons, meaning it's the same element. But it has a different number of neutrons. So what that means is that isotopes are gonna have different ways from each other, depending on which Isis hope it iss. Now, why would that be important for mass spectrometry? Because guys we're analyzing Wait. So I need to know if there's Adams that out there, that is the same Adam with different weights. I need to take that into consideration, right? So we're gonna talk about a few different types of peaks that results purely on the because there's isotopes present. So the first one is the M plus one peak. So we've talked a lot about and minus one and minus a lot of numbers, but we haven't talked yet about the pluses. Plus has happened because of isotopes, okay. And the M plus one peak is probably the most famous situation where this happens, and it's due to the isotope of carbon 13. Remember that carbon is usually 12 but it turns out that 1.1% of all the carbon in the universe in fact, 1% of all the carbon that's making up your body has an extra neutron in it. It's carbon 13. So what this is going to do is it's gonna add a small, very small, because it's so. It's such only 1% but distinctive M plus one peak that's proportional in size. The number of carbons in your compound. Remember in our intro video how we were looking at methane and methane Haddon mtz of 16. But you sold this tiny little peek at 17 and I told you, Don't worry about it yet. That is where it was coming from. Was coming from the carbon 13 isotope. Well, guys, it turns out that this isn't something that you just have to mentally. No, it's also something you need to build to make do some calculations based on because it's such a consistent ratio that we can actually build equations to solve problems with this. So, um, the equations that we're gonna cover today are one calculating the height of an M plus one, so sometimes you're going to be asked to estimate How tall would this M plus one be based on what the structure is and we're never You're not expected to get it perfectly right, because this is an approximation, but we can get pretty darn close. The second equation we're gonna cover is using the M plus one peak, the height of it to go back and look at how maney, Carbon City originally having a molecule. So let's go ahead and start off with the first, Okay? The first equation says that if I want to try to calculate how tall my M plus one is gonna be, I'm going to need to multiply the number of carbons I have times the percentage 1.1. Now you might be saying, Johnny, if the chances of having carbon 13 or 1.1% doesn't that mean that the M plus one is always going to be 1.1% of the original and that's not true at all. Actually, the M plus one peak gets bigger and bigger and bigger, depending on the number of carbons we have in our structure. And the reason guys is simple, something like methane something like methane, where it has only one carbon in it. What are the chances of having a carbon 13 and methane exactly 1.1%. So we would be multiplying one carbon times 1.1, and we would get an estimated height of the M plus one peak at 1.1%. Makes sense. But how about a molecule like decade? Guys, remember, Decade has 10 carbons in it, right? So doesn't have a higher chance of having a carbon 13 in it. Sure, because now any of those carbons could be a carbon 13 not just one of them. It could be any of them. And it's gonna increase the wait for the whole molecule. So that's why you have to multiply that 1.1% by the total number of carbons in the molecule. So in this case, 10 times 1.1, guess how tall that peak is gonna be. Well, you do the math, you could type it into your phone or your calculator is fine. It's gonna be 11%. And the guys That's what's seen and observed in the mass spectrum for methane. Look how tiny that M plus one peak is for decades. Look how much bigger it iSS. Why is it so much bigger? I'm sorry I'm right in the way. Why is it so much bigger, guys? Because now there's all those different chances. Basically, what it's saying is that 11 out of 100 times, one of your carbons is gonna be a carbon 13. Right? Because you have so many different carbons there that the chances the probability of one of those carbons being heavier just increased by 10 versus the first one. Making sense so far. Thankfully, it's a super easy equation to use. It's always just gonna be 1.1, which is the odds by number of carbons. Okay, now I do want to just say one thing for all of you guys that air reading the textbook line by line, Um, which is awesome, by the way. But I wanted to say that this is an approximation because there are other isotopes that will increase the wait for a M plus one. For example, nitrogen has a nitrogen, 15 isotope sulfur has an isotope. Phosphorus has isotopes. So what that means is that the bigger the molecule gets, the less accurate. This is if we're talking about 100 carbon molecule that has a bunch of oxygen and nitrogen and sulfur Z. This approximation probably isn't gonna work very well. But for a small molecule or pretty much any that you're going to get in your textbook that you're having to do this, we're going to use reasonably sized molecules where this where this works reasonably well, Awesome. So that is the end of the first equation. Now it's going to the second one, which looks more confusing, but it's actually not bad at all because the M Plus one peak is going to continue to grow. The more carbons that we have in our structure, couldn't we also go backwards and say, Well, based on the height of the M plus one, I could make a guess of how maney carbons I have, and that's exactly what this equation lets us do. So what the equation says is that you put your M plus one, which is your small peek over your molecular ion, which is the one that scale to 100. So you would say this is how tiny this is my tiny and plus one, I'm putting that over 100 because that's my molecular ion. Now you're molecular. Ion isn't always 100 because sometimes your molecular ion will be smaller than your base peak. But I'm just basically saying you're comparing them against each other. You're saying m plus one over M. Then you multiply by, ah 100 to bring up the percentage to like 100% and then you divide by 1.1, which is the likelihood of finding a carbon. And what this is going to do is it's going to give you the total number of carbons in your structure. Again, it's an approximation. It's not perfect, but it works really well. So for this first one, I felt I put some blanks in there so that we could do it together. Okay, so what should be the number that I'm putting here? Well, the top number should be the value of my M plus one, which in this case we just calculated is 1.1, right, Cool. So it's 1.1, by the way, it's also visible in my mass spectrum that it's 1.1 cool. What's the number that I should put at the bottom. Well, the number I should put at the bottom is the height of the molecular ion, which in this case, the height of the molecular ion goes right upto 100. It's my base peak. So I'm gonna put 100. Okay. But again, you're molecular Ion isn't always 100. Sometimes it could be 30. Or it could be 50 depending on where it is compared to the base peak. Great. So, guys on just a quick glance at this shows you that all the numbers we're gonna cancel out, right 1.1 cancels out with 1.100 with 100. So this is just gonna basically told me that there's one carbon present, which is exactly right, right? We know that methane has one carbon, so it seems like a big exercise just to find that number, but it's going to get more complicated. So this is gonna be a very helpful equation when the molecules get bigger and when you're peaks are different sizes. So let's move on to the next one. What should be the number that I put in my M plus one at the top? I should put 11 because 11 is the height of my M plus one. What should I put it? The bottom. Once again, my molecular ion is all the way to 100. So I'm gonna put 100 okay. And guys, this time I'm actually gonna use my calculator. So just to make sure everyone's following, I'm gonna do 11 divided by 100. That's giving me 0.11 Okay, now I'm gonna multiply that by hundreds, so I'm gonna say 0.11 times 100 is giving me 11. So I'm at 11. Because they just multiplied by 100 and I have to divide by 1.1 divided by 1.1. And the number I got was 10. So, guys, I just use this equation to determine that I have 10 carbons. Is that the correct number? Totally. We nailed it. Okay. So, again, this isn't always going to give you like the perfect number. Sometimes it will give you 9.9 or 10.1, but then you can round you would round to the nearest whole number, and you say, that's the number of carbons I likely have in my structure. Cool. Awesome, guys. So that's it for the M plus one peak. Now let's move on to the M plus to peak

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alright, guys. So why would we ever get a nem plus to peak? What turns out that there's two atoms that because of their isotopic ratios, they happen to give very distinctive M plus two peaks. And those two atoms are the halogen, chlorine and bromine. Okay, now why do they give em plus two? Because the way they naturally occur in the universe is in isotopes that have a difference of two in weight. So let's see what chlorine first. So guys, you might remember from well from your periodic table, whatever that the atomic weight or the molecular weight of chlorine is actually 35.5, about 35.5 Okay, but the reason that it's 35. is the Mike Laurie is because about 3/4 of it is chlorine 35 and about 1/4 of it is chlorine 37. So about 75% 35 on about 25% 37. So if you average those together, you get 35.5. Okay, now you don't have to do that math. It's fine. But the interesting thing is that on a mass spectrum, this is going to give us a very interesting ratio where it's gonna look like an approximate 3 to 1 ratio on, um, aspect on a mass spectrum. So that means wherever your molecular ion is, if you add to to that molecular ion, you're likely to see a peak. That's about one third of the size of the of the Winkler I am. So we're just going to do this molecule as an example. I'm not gonna write mass to charge numbers, because it doesn't matter. But let's say that this is your molecular ion here, so I'm just gonna put that this is my molecular ion. Um, right, So this is my molecular ion. Well, then I would expect to find an M plus two that is about a third of the size. This would be my M plus two. And why is that? Well, once again because about 75% of my chlorine atoms we're chlorine and about 25% are giving it the extra plus to wait of 37. Now, the reason that this is helpful for us guys is because when you see that very distinctive, um 3 to 1 ratio that simples to you automatically know that there's a chlorine in your molecule, so it's like it's a It's a really easy read. It's like, Oh, I know there's a chlorine here because I have this pattern and this pattern on Lee happens with chlorine. Awesome. That's chlorine. And it turns out bro mean also has an M plus, too. But it's different because the isotopic abundances different. It turns out that bro mean on the periodic table, has a weight of about 80. Okay, but it's not really 80. What it really is about 50% is 79 and about 50% is 40. About 50% is 81. I'm sorry. So basically about half of it is 79. About half of it is 81 so they blend that together to get the number 80. So what this means is that for, bro mean we're going to get an M plus to about a 1 to 1 ratio. Now, I do see that the percentages are a little bit off. It's like 50.7 49.3. But guys, those air so close that we're just gonna call it one toe one. I hope you're OK. with that. So again, I'm just going to write that. Let's say this is my molecular ion here. Right? So this would be my molecular ion. What I would expect is, if there's a bro mean present, then I should have, um, in m plus two. That is about the same exact height. And it's two units over on. This would be due to the bro means this would be my m plus two. And I know that there's a Brahmin there because that means that about half of it was bro me in 79. And about half of it was bro me in 81. Okay, now, really quickly. I know that I drew them differently. So actually feel weird about that. I'm going to change it. I hope you brought your eraser. Because what I'm trying to show is that the 81 increased by two units. That's why I'm putting em. Plus two. This is your M plus one that I'm not really drawing that part. But over here, we should move this peak to be right here. Okay? So you can see how it's two units shifted. Not just one. Okay? What? I'm trying to show you is that your M plus two should be about a third of the size with chlorine, and it should be about the same exact size with bro means. So if you see this pattern, you know Brahman is present. If you see that pattern, you know, chlorine is present. And by the way, I'm ignoring the M plus one. I'm not even worrying about that because this I'm not talking about m plus one right now. I'm just talking about them. Plus two. Would there be some M plus one? Sure, but we're not talking about that right now. Cool. Awesome. So now we're done with M plus to. The biggest thing is that you know how to identify it, whether it's chlorine or bromine. Let's move on to the nature General.

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guys. The Nigerian rule actually has nothing to do with isotopes. I'm just throwing it in here because it's another very helpful form of structure determination for mass spec. And it's usually taught in the same area as isotopes, so we might as well just learn it here. So, guys, nitrogen has a property that's different from carbon. That makes it helpful for mass spec, which is that carbon always likes to form for bonds, right? So since it likes to form for bonds, if a molecules made just out of carbon or hydrogen carbon and hydrogen, you know that it's gonna be an even number for the molecular weight because you always have those four bonds. So it's always going to be ch four or, UH, C two h six. There's always multiples of two or four, But nitrogen likes to form three bonds, meaning that, um, the molecular weight could be odd, or it could be even, and that's going to tell us how maney nitrogen zehr present. So what the nitrogen rule says is that and even molecular weight of our parent ion basically the molecular ion right indicates an even number of nitrogen present. Okay, whereas an odd molecular weight of a parent I on indicates an odd number of nitrogen is present. So, for example, the number one odd number being one right. If there's one nitrogen present, that means that nitrogen wants to have three bonds, meaning that when I piled together my molecular weight, I'm gonna always have to add three at the end or some odd number of bonds. So my entire molecular weight is that is likely to be odd if there's one nitrogen present, whereas if there's an even number. So, for example, to bonds, Well, now we've got to nitrogen. I'm sorry. To nitrogen. Those two nitrogen is like to form three bonds each, so three plus three equal six. So it's an even number again. So one of the easiest ways to look at this is just these two molecules. We've got butane, which we saw earlier has an emcee of 58. But if you take the butane and you replace one of the carbons with an N H. Two, what's gonna happen is that your molecular weight now turns odd because this nitrogen likes to form three bonds. So what's happening is that now you're just adding one. You're adding a molecular weight of one to it. Okay, now you might be saying, Johnny, how does that math work? Um, well, first of all, you can calculate yourself. You'll see that I'm right. What's happening, guys, is that carbon weighs 12 right? Nitrogen weighs 14. So by turning one of the carbons into nitrogen, how much molecular weight should I be adding to? I should be adding to. But then there's a difference. Carbon likes to have. How maney h is it like step four, right? Nitrogen likes have how maney, ages three. Right. So what that means is that when you add it all together, every carbon you add should be adding something around 16. If you were toe do a ch four. But every nitrogen you add should be adding about 17 because it's a little bit heavier, but it likes to have less hydrogen. So basically, that's the gist of it. But what you should know is that if you have an odd number of molecular weight, then it should be an odd number of nitrogen. Um, and then if you haven't even number, then you haven't even number of nitrogen. Even if that means zero zero is also a even number. So it just could mean I don't have any. Nitrogen is present. Awesome guys. So let's go ahead and flip the page and do some practice.

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Problem

Propose the number of carbons for a compound that exhibits the following peak in its mass spectrum:

(M)+• at m/z = 72, relative height = 38.3% of base peak

(M+1)+• at m/z = 73, relative height = 1.7% of base peak

A

3

B

4

C

5

D

7

5

Problem

Predict the approximate height of the (M + 1) peak for the molecule icosane, molecular formula C_{20}H_{42}.

A

11

B

44

C

50

D

22

6

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draw the expected isotope pattern that would be observed in a mass spectrum of ch two br two. In other words, predict the relative heights of the peaks at M, which is molecular ion. So I'm just gonna put plus radical M plus two and the M plus four peaks. Now, this one could definitely catch you off guard. Because where did this come from? I never talked about M plus four. I only talked about M plus one and M plus two. But, guys, it makes sense. That notice we have multiple halogen is in this case. We have to, bro means. So where would an M plus four come from? Well, that would be the version of the molecule where both of the bro means our bro Mean 81 are the bro mean, that's the higher isotope. If both of them are giving us and plus two peaks, then it's gonna add up to an M plus four. So we're looking for is the ratio okay? And I'm actually going to just coach you through this. You can try it one more time on your own, and then I'm gonna tell you the answer, And if it was for me to coach you. What I would say is think about probability. What are the chances that both of the Brahmins are the small isotope, the 79? What are the chances that one is 79 1 is 81? So that being plus two and then what are the chances that both of them are 81? And just so you know, for any question involving two, um, halogen that are on the same Adam weaken, basically use a pun it square system like you would have used in genetics where genetics was used in genetics. You talk about, like, FINA types and Gina types. So you'd say, like, these are the chances of having this genotype. What's the phenotype gonna be? What's the same principle? But for bro means because we're talking about probability. So you would say, What are the chances of having these, bro means together versus these? So I'm gonna let you try to arrange the chemistry pundits square, Um, the way you think is best, and then I'm gonna teach you how to do it. It's very easy. Just have to learn how to do it once and then you'll know it for forever, so hopefully so go ahead and try to do it and then I'll give you the answer.

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