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## Organic chemistry

### Unit 14: Lesson 3

Proton NMR- Introduction to proton NMR
- Nuclear shielding
- Chemical equivalence
- Chemical shift
- Electronegativity and chemical shift
- Diamagnetic anisotropy
- Integration
- Spin-spin splitting (coupling)
- Multiplicity: n + 1 rule
- Coupling constant
- Complex splitting
- Hydrogen deficiency index
- Proton NMR practice 1
- Proton NMR practice 2
- Proton NMR practice 3

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# Chemical shift

The formula for calculating chemical shift based on a TMS reference signal and spectrophotometer frequency. Created by Jay.

## Video transcript

- [Voiceover] In the previous video, we looked at the protons on benzene. And we said all six protons
were in the same environment, therefore all six protons
were chemical equivalents, and should give us only one
signal on an NMR spectrum. And so here's the one signal on a spectrum due to the protons on benzene. If we compare benzene to this compound, this is tetramethylsilane or TMS. And the protons on TMS are
all in the same environment and so therefore we would
expect one signal for TMS. And here's the signal for TMS right here. In an earlier video we said that as you go to the right on an NMR spectrum you're talking about a
lower frequency signal. So a lower frequency signal
as you move to the right on an NMR spectrum. And so if you move to the
left on an NMR spectrum, you're talking about a
higher frequency signal. And so therefore, the protons on benzene have a higher frequency signal than the protons on TMS. TMS is actually our standard because the protons on
TMS are more shielded than almost all organic compounds. And so therefore it's our reference. And so instead of talking about frequency, we could talk about
chemical shift values here. And the chemical shift would be, would be a similar idea to the frequency. So as you go to the right, you're talking about a
lower chemical shift. And as you move to the
left on an NMR spectrum, you're talking about a
higher chemical shift. So a higher shift as you move to the left. So the protons on benzene
have a higher chemical shift than the protons on TMS. Actually we set this equal to zero. So this is our standard. So how do we figure out
what the chemical shift is? For example for the protons on benzene, it looks like the signal appears a little bit past seven here. So how do we get this
number for a chemical shift? Well again, everything is compared to TMS. And so let's look at the formula for calculating chemical shift. And so if I move down here we can see the formula for chemical shift. Chemical shift is equal to the observed shift from TMS in hertz, times 10 to the sixth, divided by the spectrometer
frequency in hertz. For example, let's say that we
are using an NMR spectrometer operating at 300 megahertz. So we're using a 300
megahertz spectrometer here. If you're using a 300
megahertz spectrometer, the protons on benzene absorb a frequency 2181 hertz more than the protons on TMS. And so once again TMS is
our standard, our reference. So this difference, if you're thinking about frequency, this difference between our two signals, is 2181 hertz, if we are using a 300
megahertz spectrometer. And so let's go ahead and figure out the chemical shift for
the protons on benzene. So let's get some more room down here. And so here's a symbol for chemical shift, so chemical shift is equal to the observed shift from TMS that was 2181, so that's 2181 hertz, and we need to multiply
that by 10 to the sixth, and the reason we multiply
that by 10 to the sixth is because the spectrometer
is in megahertz here. So 300 megahertz is 300 times 10 to the sixth hertz. And so we can cancel out, we can cancel out the hertz, we can cancel out 10 to the sixth, and so we have a simple calculation here to figure out the chemical shift. And so let's go ahead and do that, so we turn the calculator on, 2181 divided by 300 gives us 7.27. So this is equal to 7.27. Notice how the hertz will cancel out. And we have right here ppm or parts per million because these signals are reported as a fraction of the operating
frequency of the spectrometer. And so there's a reason why we do that. So we got this number 7.27 here. Let's do this calculation again, let's say we did this, we ran the spectrum on a
different spectrometer. Let's say we're using a
60 megahertz spectrometer. So let's change it up a little bit. So a 60 megahertz spectrometer, if you use a 60 megahertz spectrometer, the protons on benzene absorb a frequency 436 hertz more than the protons on TMS. So to calculate the chemical shift now, the difference would be 436 hertz, times 10 to the sixth, divided by, now we're using a 60
megahertz spectrometer, so 60 times 10 to the sixth hertz, once again the hertz cancels, the 10 to the sixth cancels, and we can do that calculation. So we take a 436, we divide that by 60, and we get 7.27 again. So we get 7.27. Notice we got the same
value we did up here right? So 7.27 is a constant, no matter what kind of
spectrometer you're using. So you could be using a
300 megahertz spectrometer, or a 60 megahertz spectrometer, you're gonna get the same
value for the chemical shift. And so that's why we go
through this calculation here. So we get a constant value
for the chemical shift. So the protons on benzene have a chemical shift of 7.27. And we'll talk much more
about chemical shifts in the next few videos.