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here we have a proton NMR spectrum for a molecule that has a molecular formula of c 5h 1002 let's start by calculating the hydrogen deficiency index so if we have five carbons we can have a maximum of two times five plus two hydrogen's and so that's equal to 12 so 12 hydrogen's is the maximum number for five carbons here we have only 10 hydrogen's and so we're missing two hydrogen's we're missing one pair of hydrogen so therefore we can say the HDI is equal to one and when the HDI is equal to one I immediately think a double bond is present in this molecule or a ring is present in this molecule next you go to the integration values so for this signal and integration value of 33 point two for this one forty eight point four for this one 33 point three and then forty eight point seven and you divide all for integration values by the lowest one so the lowest one would be 33 point two so 33 point two divided by 33 point two is obviously equal to 148 point four divided by 33 point two is approximately 1.5 thirty-three point three divided by 33 point two is obviously very close to one and then finally forty eight point seven divided by 33 point two gives us approximately one point five and these numbers tell us the relative the relative ratio of protons that are giving us these four signals but we need to think about 10 protons right so we have 10 hydrogen's here and so this is only relative to get the to get the absolute number of hydrogen's we need to multiply these numbers in this rate in this ratio by two if we multiply one by two we obviously get two so this signal represents two protons multiply one point five by two and we get three so this signal represents three protons multiply one by two the signal is two protons multiply one point five by two this signal is three protons all right let's go through and look at each signal one ball one we start with the signal that has two protons on the left over here so two protons so we're talking about a ch2 group so I go ahead and draw in a ch2 group over here how many neighboring protons for this ch2 group we can find that by thinking about the n plus one rule if we have n neighboring protons we would expect to see n plus one Peaks so how many Peaks do we have one two three so three peaks so to find the number of neighbors just subtract one so three minus one is two so these two ch2 protons have two neighboring protons next let's think about the chemical shift so this signal the signal has a chemical shift of approximately four parts per million and that's the highest value for the chemical shift out of all four of these signals and that's the region that's the region for a proton that's connected to a carbon that's bonded to an electronegative atom and if we look at our molecular formula right we have two oxygens here so I'm going to take one of those oxygens and put that oxygen put that oxygen on that carbon because once again when you're thinking about the signal for a proton on a carbon that's bonded to an electronegative atom you get a chemical shift is somewhere in this case close to four parts per million because the oxygen is D shielding those protons right the oxygen is withdrawing electron density all right so that's one piece of the puzzle and let's move on to our next signal so this will be the next piece of the puzzle we have three protons so that's a methyl group so let me go ahead and draw in a methyl group here so CH 3 how many neighboring protons for those methyl protons well we see we see one peak here so one minus one is zero so zero neighboring protons let's think about the chemical shift right so the chemical shift is just past two parts per million and that's in the region for a proton that's next to a carbonyl all right so let's go ahead and draw in a carbonyl here and we're assuming that the carbonyl carbon is bonded to another carbon over here that makes sense in terms of numbers of neighbors all right so let's use blue for for this right so the signal for these three protons right zero neighbors and so if we go to this carbon right if there's a carbon over here there are no protons on this carbonyl carbon and so that explains that explains this piece of the puzzle next next signal a ch2 right so we draw in a ch2 here how many neighbors a little bit hard to see one two three four five six Peaks 6 minus 1 is 5 so we would expect 5 neighbors using using the oversimplified n plus 1 rule and we'll come back to we'll come back to that ch2 and finally we have a signal with 3 protons so a ch3 how many neighbors for these methyl protons well we have 1 2 3 Peaks so 3 minus 1 is 2 so 2 neighbors alright let's put all of the pieces of the puzzle together and let's draw the final dot structure so let's let's start let's start with with this piece of the puzzle right here so we have a carbonyl so I'm going to draw on my carbonyl here and then we have a methyl group bonded to that carbon eel so I'm a draw in our methyl group like that and we used blue for these methyl protons so the signal for these methyl protons appears right here next let's think about a possible functional group right well we have a carbonyl and then over here right we have an oxygen so if we put the oxygen next to the carbonyl that gives us an ester so let's go ahead and do that let's put the oxygen next to the carbonyl and then bonded to that oxygen we had a ch2 so I draw on my ch2 there and let's identify those protons so the protons in magenta are giving us this signal over here alright next let's think about let's think about let's use red and let's think about these protons these methyl protons right here those methyl protons have two neighbors and it makes sense that there would be these two neighbors right here right so these chemical shifts are under two so those are those are Altaf are away from the oxygens so let's draw in the methyl protons next so we have our methyl protons right here and let's make them red so let's highlight those so these methyl protons right here are giving us this signal and then finally we have we have a ch2 left right here so we draw in our ch2 and let's make these green right so these two protons right here in green are giving us this signal all right let's go through and see if everything makes sense and we'll start with the green protons so we predicted five neighbors right so we look at the carbon the green protons are on we go to the next door carbon one two three neighboring protons we go to the other next door carbon one two so a total of five neighbors and so that's what we predicted using the n plus one rule in reality the magenta and red protons are in different environments and so this oversimplified n plus one rule is it isn't exactly correct but it corresponds to what we see on the NMR spectrum so we can just we can just go with it here it helped us figure out the structure of the molecule all right so this makes sense five neighbors here let's move on to the red protons we predicted two neighbors for the red protons so we go to the carbon that's next door right so this carbon has the red protons we go to the next door carbon and we see two neighbors so this makes sense alright let's look at the magenta protons right so the magenta protons we predicted two neighbors so the magenta protons are on this carbon we go to the carbon next door and I see one two neighbors so this makes sense and then finally finally the blue protons over here we predicted zero neighbors so we go to the carbon that's next door to this carbon and there are no protons on this carbon right so zero neighbors and that's why we got our singlet over here so this makes sense right the chemical shifts make sense the the splitting makes sense that everything seems to make sense for this ester one thing I've noticed when students get a problem with an ester sometimes they reverse the ester let me show you what I mean so I've seen a lot of students do this on exams what they'll do is is they identify the fact they have an ester but in this case they would put like the methyl group on the oxygen and then draw on the rest of the molecule over here is with three carbons so one two three and they'll put this down for their answer on the test so why is this wrong well this is wrong because the signal for these methyl protons right that's right next to this oxygen this oxygen is D shielding so we would get a singlet for these methyl protons but the signal would be closer to four parts per million and not right here not right here at two parts per million and so and so that that's a clue as to as to how to assemble the pieces for an ester so think about what's next to this oxygen here think about the chemical shifts and and you won't make that mistake for this NMR spectrum our molecule has a molecular formula of c4h10 oh and let's calculate the hydrogen deficiency index so if we have four carbons the maximum number of hydrogen's we can have is two times four plus two which is equal to ten and that's how many hydrogen's we have in our molecular formula so this time we're not missing any hydrogen's and so the HDI is equal to zero so we wouldn't expect any double bonds or rings so no double bonds or rings for the dot structure for integration this signal is one proton the signal is three protons and this signal over here is six protons let's focus in on this signal so we have one proton so I'm going to go ahead and draw that proton on a carbon like that let's think about how many neighbors that proton has so look at the peaks I see one two three four five six seven Peaks so 7 minus 1 is 6 so that proton is going to have 6 neighboring protons let me go ahead and give that proton a color so this is the signal for the magenta proton the chemical shift is somewhere around four parts per million and that's the chemical shift that we would expect if that proton was on a carbon bonded to an electronegative atom and we have an oxygen here so I'm going to go ahead and put an oxygen right here bonded to that carbon because the oxygen is withdrawing electron density away from this proton right it's D shielding this proton giving it a higher chemical shift alright let's move on to our next signal so we have three protons so this is B a methyl group so we have three methyl protons how many neighboring protons for those methyl protons we have only one peak here so one minus one is zero so zero neighboring protons and the chemical shift is about 3.5 parts per million so those methyl protons must be really close to that oxygen right we get a higher value for the chemical shift and so we can put the methyl protons over here on the left side of the oxygen alright so that makes sense in terms of the chemical shift it also makes sense in terms of the number of neighbors so these three protons right here give us this signal and we have zero neighbors right so there are no neighbors for these three protons let's move on to the last signal all right so we have six protons so that's like two methyl groups so we have two methyl groups here and the signal is split into a doublet all right so we see these two peaks here so two minus one is one so we expect one neighbor for these two methyl groups and obviously obviously would have to be this proton in magenta because we have these only these two places left right so we put these methyl groups right here and we can see we get one neighbor so those those two methyl groups are further away from the oxygen relatively because of the signal right having a lower value for the chemical shift so let's use red here so red for these six protons it's giving us this signal and we have one neighboring proton it's this proton in magenta right here let's think about the magenta proton right we said that the magenta proton would have six neighbors and that's what we see so three from this methyl and then three from this methyl so six neighbors for the magenta proton and then finally we said their b0 neighbors four for the protons blew and that's what we see for our dot structure and so this this molecule is an ether so this NMR spectrum represents this ether