Determining concentration from NMR spectra

One of the strengths of NMR is that the signal is directly proportional to the amount of material present. This makes it possible to measure concentrations without having a sample of the pure material. This post describes how to use the residual protonated solvent signal as an internal standard to determine concentration.

The signals in an NMR spectrum are directly proportional to the number of nuclei that produce them. This means that if you know the concentration of one molecule you can use it as an internal standard to determine the concentration of another molecule that produces signals in the same spectrum. The internal standard can be an extra compound that produces a clearly resolved signal, like TMS or DSS, but most users don't like adding extra compounds to their samples. For this reason several groups have suggested using residual solvent signals to measure concentration^1,2,3.

The residual solvent signal is the signal due to the small fraction of solvent that is not deuterated. Most NMR solvents have at least 99.9% of the protons replaced with deuterons. The concentration of the solvent that has not been deuterated can be calculated from the density of the solvent, its molecular weight, and the level of deuteration. For example, 99.9% DMSO-d6 has a density of 1.1 g/ml and a molecular weight of 78.13 g/mol. Taking into account that only 0.1% of the DMSO gives a signal, the concentration of the protonated DMSO is 14 mM.

The figure below shows the 1D ¹H spectrum of lophotoxin in DMSO-d₆. All the lophotoxin peaks and the residual protonated DMSO peak have been integrated. The integral of the residual DMSO peak was set to 84, or 6 x 14 mM, since it is due to six protons. The four left most peaks in the spectrum are all due to one proton each, so their integrals give the concentration of the lophotoxin, 220-240 mM. From the molecular weight and the volume, the mass of natural product can be calculated. In this case it was 9-10 mg.

The above example gives only a rough estimate of the concentration. The variation in the integrals prevented a more accurate measurement. For more precise integrations a long relaxation delay (60 seconds) should be used to ensure that all nuclei are fully relaxed for each scan. In the figure above the relaxation delay was 0.5 seconds. Also, the actual level of deuteration should be determined from spectra of the solvent spiked with a known concentration of a reference compound. This can be done once for each bottle of solvent.

Determining concentration by NMR is especially useful for small quantities that cannot be accurately weighed. Even when there is enough material to accurately weigh, HPLC-purified compounds often have contaminants, like water, formic acid, trifluoroacetic acid or ammonium salts, that make the amount of material appear larger than it really is. Look at Table 3 in reference 2 for an eye-opening comparison of masses measured on an analytical balance and those determined by NMR.

References

1. Solvent Signal as an NMR Concentration Reference
Huaping Mo and Daniel Raftery
Anal. Chem. 2008, 80, 24, 9835–9839

2. Determination of Analyte Concentration Using the Residual Solvent Resonance in ¹H NMR Spectroscopy
Gregory K. Pierens, Anthony R. Carroll, Rohan A. Davis, Meredith E. Palframan, and Ronald J. Quinn
J. Nat. Prod. 2008, 71, 5, 810–813

3. NMR Quantitation of Natural Products at the Nanomole Scale
Doralyn S. Dalisay and Tadeusz F. Molinski
J. Nat. Prod. 2009, 72, 4, 739–744

Acknowledgments
The sample used to record the spectrum in this post was purified in the Fenical lab and kindly provided by Xi Zhang of the Taylor lab.