You can determine purity by quantitative NMR without a reference standard of your own compound, because the NMR signal is proportional to the number of nuclei and not to the identity of the molecule. What you need instead is a certified internal standard of known purity, accurate weighing, acquisition parameters that keep every signal fully relaxed, and an uncertainty budget that shows how good the number is. With those four in place, qNMR gives a purity value traceable to SI units, typically with an expanded uncertainty well below 1 %.
That is why qNMR is the method of choice for new intermediates, early API batches and in-house working standards: the situation where chromatographic assay would need exactly the reference material you do not yet have.
Why does qNMR not need a reference standard of the analyte?
In chromatography the detector response depends on the molecule. A UV detector sees absorptivity, so you need the same compound at known purity to convert peak area into mass. In 1H NMR, under the right conditions, the integral of a signal depends only on how many protons produce it. One proton of your analyte gives the same integral as one proton of any other molecule in the same tube.
The internal standard method uses that directly. Weigh analyte and standard into the same tube, integrate one signal of each, and the purity of the analyte follows:
P(a) = (I(a) / I(std)) × (N(std) / N(a)) × (M(a) / M(std)) × (m(std) / m(a)) × P(std)
I is the integral, N the number of protons behind the signal, M the molar mass, m the weighed mass and P the purity. The certified purity of the standard carries the traceability. USP general chapter <761> and Ph. Eur. 2.2.33 both describe this approach.
What do you need instead of a reference standard?
A certified internal standard.
Maleic acid, dimethyl sulfone, 1,4-bis(trimethylsilyl)benzene and 3,5-bis(trifluoromethyl)benzoic acid are common choices, each available as certified reference material. Pick one whose signal sits in an empty region of your spectrum, that dissolves completely in your solvent and that does not react with your analyte.
A balance you can trust.
Weighing usually dominates the uncertainty after integration. A microbalance with 0.001 mg readability, weighing at least 10 mg of each component and correcting for buoyancy where the densities differ strongly keeps this term small.
Fully relaxed signals.
The relaxation delay plus acquisition time should be at least five times, better seven times, the longest T1 of the signals you integrate. Measure T1 by inversion recovery once per method. A 90° pulse and a delay set from a guessed T1 is the most common reason a qNMR result is biased low.
Enough signal.
A signal-to-noise ratio of at least 250 to 1 for the integrated signals is a common target if the integration error is to stay below 1 %. Add scans rather than increasing the receiver gain beyond the linear range.
Clean processing.
Careful phase and baseline correction, integration ranges wide enough to include the 13C satellites (or consistently excluded for both signals), and no overlap with impurities, water or residual solvent.
A worked example
A new batch of paracetamol (M = 151.163 g/mol) without an in-house reference standard, measured in DMSO-d6 against certified maleic acid (M = 116.072 g/mol, certified purity 99.94 %). The illustrative numbers below show the arithmetic.
| Quantity | Analyte (paracetamol) | Internal standard (maleic acid) |
|---|---|---|
| Weighed mass | 20.12 mg | 10.05 mg |
| Integrated signal | aromatic doublet, 7.3 ppm | olefinic singlet, 6.3 ppm |
| Protons in signal | 2 | 2 |
| Integral ratio I(a)/I(std) | 1.526 |
P(a) = 1.526 × (2/2) × (151.163/116.072) × (10.05/20.12) × 99.94 % = 99.21 %
How good is the number? The uncertainty budget
A purity without uncertainty is not a result. The budget for the example, with relative standard uncertainties:
| Source | Relative standard uncertainty |
|---|---|
| Integral ratio (repeatability over five spectra) | 0.30 % |
| Mass of analyte (0.0058 mg on 20.12 mg) | 0.03 % |
| Mass of standard (0.0058 mg on 10.05 mg) | 0.06 % |
| Purity of the internal standard (certificate) | 0.03 % |
| Molar masses | negligible |
| Combined | 0.31 % |
Expanded uncertainty with k = 2: 2 × 0.31 % × 99.21 % = 0.61 percentage points. The result is reported as 99.2 % ± 0.6 % (k = 2).
The budget also tells you where to improve. Here integration dominates by a factor of five. Better signal-to-noise or a second, independent signal pair reduces it; a better balance would change almost nothing.
When is an internal standard not the right choice?
Sometimes nothing suitable dissolves in your solvent, or every free spectral region is occupied. Two alternatives avoid putting a standard in the tube:
- External calibration (PULCON). The standard is measured in a separate tube under identical conditions, and the pulse length difference between the two tubes is corrected. It needs very stable spectrometer conditions and careful matching of tubes and temperature.
- Electronic reference (ERETIC). A synthetic signal calibrated once against a certified standard serves as the reference. Useful for routine series once the calibration is verified regularly.
Both are valid but put more demands on instrument qualification and system suitability than the internal standard method.
Limits of the statement
- qNMR gives the mass fraction of the molecule behind the integrated signal. It does not tell you what the impurities are; that needs chromatography or MS.
- An impurity hidden under the integrated signal inflates the result. Check with a second signal of the analyte: two signals that disagree by more than the repeatability point to overlap.
- Inorganic salts, water and residual solvents count as "not analyte" without appearing as signals. That is correct for an assay but means qNMR purity and chromatographic purity (area %) are different numbers and should not be compared one to one.
- The method rests on the acquisition parameters. A changed probe, solvent or temperature means checking T1 and system suitability again.
Frequently asked questions
Can qNMR replace a reference standard for assay?
qNMR can assign the purity of a material that then serves as an in-house reference or working standard, and it can determine assay directly. Whether it replaces a pharmacopoeial reference standard in a registered method depends on the method and the regulatory context; for development batches and new intermediates it is routinely the first traceable value.
Which internal standard should I use for qNMR?
One with a certified purity, a sharp signal in an empty region of your spectrum, good solubility in your solvent and no reactivity with the analyte. Maleic acid and dimethyl sulfone in DMSO-d6 or D2O, and 1,4-bis(trimethylsilyl)benzene in CDCl3, cover many cases.
How long should the relaxation delay be in qNMR?
Relaxation delay plus acquisition time should be at least five times the longest T1 of the integrated signals for about 99.3 % recovery of magnetisation, and seven times for better than 99.9 %. Measure T1 instead of assuming it; aromatic protons in small molecules can exceed 5 s.
What uncertainty is realistic for qNMR purity?
With a microbalance, a certified standard and good signal-to-noise, an expanded uncertainty of 0.5 to 1 percentage point (k = 2) is typical. In the example above it was 0.6 percentage points, dominated by integration repeatability.
Is qNMR described in the pharmacopoeias?
Yes. USP general chapter <761> and Ph. Eur. chapter 2.2.33 cover NMR spectrometry including quantitative use, and USP <1761> gives application guidance.