# Calculating purity from NMR spectrum

I just started organic chemistry in university. I have no idea what I'm doing — it's wonderful.

My assignment was to produce $\pu{10g}$ of fluorescein, the theoretical yield is $70~\%$ — I need at least $60~\%$ yield. I've made $\pu{11.07g}$ of product and my lab instructor analysed a sample of my product on the NMR spectrometer, which gave us the following result:

There are some impurities in my product (I know that f.e. $1.12$ is from the impurity and $3.42$ is from the fluorescein, same with $1.00$ and $3.46$) and I have no idea how to use that data to compute purity or actual yield.

Can somebody help?

• Your question can't be answered without more information. We don't know what the side products are. The aryl region of the spectrum is not particularly helpful in any case... – Zhe Mar 29 '17 at 19:47
• @Zhe That's actually helpful. Would you mind telling me why this question can't be answered? That should help me when I'll turn my paper in tomorrow - maybe my lecturer didn't provide enough information to solve the task. – Michał W Mar 29 '17 at 19:54
• Impurities could also include reactants and intermediates. Be sure to review all the information about this exercise for clues. If you know what the impurities are and they have distinct NMR signals you can identify and integrate, you can calculate purity. – iad22agp Mar 29 '17 at 20:51
• Beside proper identification and attribution of signals related to the product; remaining starting material(s), reagent(s), and intermediate(s); watch-out if there is evidence for the presence of remaining solvents from reaction / extraction / recrystallization. There should be no signal in the NMR without reasonable attribution. Conversely, say you know ethyl acetate still is present in the sample, than all three expected signals should be consistently present in the spectrum (along $\delta$, in mulitplicity and relative integration). The original question contains just too many unknowns. – Buttonwood Mar 29 '17 at 21:05
• Identifying the purity of your substance is a non-trivial task, even for a seasoned chemist. Figuring out exactly what the other substances are and quantifying how much is even more difficult. You are in this latter camp, if you've provided all of the information you have. Because we don't know what impurities are present, we can't quantity the mass of material that is not your product in your final sample. Your best bet is actually to purify the sample and isolate only the desired product. Then the whole mass of the sample determines the experimental yield. – Zhe Mar 30 '17 at 2:37

A couple of points for starters:

• to say anything about impurities you need to show the entire spectrum, typically from $0$ to $\pu{10ppm}$ for $\ce{^1H}$. Merely describing the existence of peaks is not enough.

• you also need to make sure your baseline is a proper baseline as you need to use the integrals to calculate purity if you even can. Here again, $n_\mathrm{t} = 8$ is absolutely too little.

However, it still needs to be said that determining the purity in percent just from NMR spectra is a very non-trivial task. It can only be done, if you know exactly which impurities you have, if they all contain the corresponding NMR-active nucleus, if the NMR-active nucleus is sufficiently predominant for the read to be quantitative and if there is no mechanism by which a non-NMR-active nucleus may be introduced into your impurity. Especially the predominance of NMR active nuclei along with another few requirements for ‘nice’ NMR spectra means that purity via NMR can in practice only be measure for $\ce{^1H, ^19F, ^31P}$ and a few much less common elements.

The main deal breaker is typically the requirement to contain the NMR-active nucleus. You can have a beautifully clean $\ce{^1H}$ NMR spectrum but the actual substance can be as little as $1~\%$ pure: most notably if the impurities are inorganic salts and do not contain any hydrogen. In most non-carbohydrate organic chemistry, this is not so much of a problem, though.

For any substances that contain the NMR-active nucleus and are impurities, the first step is to find out exactly what the substance is. To be able to calculate anything from an NMR spectrum, you need to know the impurity’s molar mass as NMR readings can only give you relative amounts.

Finally, you also need to make sure that your impurity does not lose its NMR-active nucleus. For example, if you are measuring in $\ce{CD3OD}$ and the impurity happens to be $\ce{C3F7OH}$ (1,1,1,2,3,3,3-heptafluoropropan-2-ol), the reading of the final remaining signal (if it even remains) will not be accurate due to proton/deuterium exchange:

$$\ce{C3F7OH + CD3OD <=>> C3F7OD + CD3OH}\tag{1}$$

(The equilibrium is shifted towards the products due to the abundance of methanol as the solvent.)

This is why NMR analysis is typically only used to determine relative purity, e.g. if two diastereomers form during a reaction. These will have the same molar masses allowing for an easy comparison.

To actually perform this, you need to:

• Identify the peaks belonging to an impurity, the impurity’s structure and the signals’ integrals.

• Normalise the impurity’s integrals to a single proton equivalent (i.e. if your impurity is cyclohexane, divide the integral by $12$ since you have $12$ magnetically equivalent protons.)

• Normalise your desired compound’s integrals so that a single proton has the integral 1.

• Determine a ratio of amounts in moles. (e.g. $\pu{8mol}:\pu{2mol}$)

• Calculate the corresponding masses of desired product and impurity.

• Add up the masses you calculated to a total mass.

• Divide your desired product’s mass by the total mass to get your purity. Multiply by $100~\%$ to get a percentage.

From the information you give and the spectrum you show it is absolutely impossible to tell you anything about the purity of your compound. Signal integrals themselves are also not helpful; if your impurity is huge in molar mass but only has few protons, or if it has multiple magnetically identical protons a simple integral reading will be way off.

The practical approach for an organic chemist to determine purity is to use chromatography (either flash or HPLC) until no signals can be detected that do not belong to the compound in question and then label it ‘pure’.