qNMR Calculator

(Quantitative Nuclear Magnetic Resonance)

Theoretical Introduction and Practical Guide

Quantitative Nuclear Magnetic Resonance (qNMR) is a powerful analytical technique used to determine the purity or concentration of a sample. As a primary method of measurement, signal intensity is directly proportional to the number of nuclei, eliminating the need for calibration curves with identical standards to the analyte.

The principle is based on adding an internal standard of known purity and mass. By comparing the integral of an analyte signal with that of the standard, the amount of analyte can be precisely calculated.

The internal reference method is generally preferred over external methods due to its higher precision and lower uncertainties. Once materials are weighed into the same vial, the ratio of analyte and reference remains constant, and the amount of added solvent is not critical for quantification.

The qNMR Formula

The purity of the analyte (\(P_{an}\)) in percentage (\%) is given by:

\[ P_{an} [\%] = \frac{I_{an}}{I_{std}} \times \frac{N_{std}}{N_{an}} \times \frac{MW_{an}}{MW_{std}} \times \frac{m_{std}}{m_{sample}} \times P_{std} [\%] \]

\(I_{an}\): Integral of the analyte signal.
\(I_{std}\): Integral of the standard signal.
\(N_{an}\): Number of protons of the analyte signal.
\(N_{std}\): Number of protons of the standard signal.
\(MW_{an}\): Molecular Weight of the analyte (g/mol).
\(MW_{std}\): Molecular Weight of the standard (g/mol).
\(m_{sample}\): Mass of the sample containing the analyte (mg).
\(m_{std}\): Mass of the internal standard (mg).
\(P_{std}\): Purity of the internal standard (%).

Guide to Preparation and Acquisition

For accurate analysis, follow these recommendations:

Choice of Standard: The standard should be highly pure (≥99.5%), stable, non-volatile, non-hygroscopic, free of residual water, highly soluble in common deuterated NMR solvents, and have few signals that minimize overlap with the analyte.
Compatibility Checks: After selecting a suitable reference standard, check the mixture for chemical stability and inertness to avoid reactions between the sample, reference, or solvent. Perform NMR experiments at t=0 and a later time (e.g., 5, 12, or 24h) to measure tolerance. The relevant signals must not overlap with each other or with impurities.
Metrological Weighing: Reliable weighing values are mandatory as they directly influence the result. Use a micro-balance or similar high-precision balance (e.g., readability of 100 ng). Weighing errors are the main source of uncertainty. Weigh sample and reference into an HPLC vial, not directly into the NMR tube. Ensure consistent units (e.g., both masses in mg).
NMR Parameters: The most critical parameter is the relaxation time (\(d1\)). Set \(d1 \geq 7 \times T_1\), where \(T_1\) is the longest relaxation time among the signals to be integrated. If \(T_1\) is unknown, use a conservative value (e.g., 30-60 seconds) to ensure accurate quantification. Ensure an S/N > 250. It is crucial to determine \(T_1\) in the mixture before the experiment starts. No spinning should be applied to avoid spinning sidebands.
Processing: Perform meticulous manual phase and baseline correction before integrating to obtain accurate integrals. Always perform integration consistently for both signals, either including or excluding C-satellites.
Uncertainty Budget: The biggest contributions to overall measurement uncertainty often come from repeatability and the purity of the reference standard. Weighing values also contribute, depending on the balance used.

Table of Common Internal Standards for ¹H-qNMR

Standard	Molecular Weight (g/mol)	Reference ¹H Signal (in CDCl₃ or typical solvent)
Dimethyl sulfone (DMSO₂)	94.13	~3.0 ppm (singlet, 6H)
1,3,5-Trimethoxybenzene	168.19	~6.1 ppm (s, 3H, Ar-H) and ~3.75 ppm (s, 9H, OMe)
1,4-Dinitrobenzene	168.11	~8.4 ppm (singlet, 4H)
Dimethyl terephthalate	194.19	~8.1 ppm (s, 4H, Ar-H) and ~3.9 ppm (s, 6H, OMe)
Maleic acid	116.07	~6.3 ppm (singlet, 2H)
Ethylene carbonate	88.06	~4.5 ppm (singlet, 4H)
Calcium formate	130.11	~8.4 ppm (singlet, 2H)
Benzoic acid	122.12	~8.1 ppm (multiplet, 2H, ortho-H)
Duroquinone	164.2	~2.0 ppm (singlet, 12H)
Potassium hydrogen phthalate	204.22	~7.5-7.9 ppm (multiplet, 4H)
1,2,4,5-Tetrachloro-3-nitrobenzene	260.88	~7.8-8.4 ppm (singlet, 1H)
Ethyl 4-(dimethylamino)benzoate	193.24	~3.0 ppm (singlet, 6H, N(CH₃)₂)
Thymol	150.22	~2.3 ppm (singlet, 3H, CH₃)
Benzyl benzoate	212.24	~5.3 ppm (singlet, 2H, CH₂)
1,2,4,5-Tetramethylbenzene	134.22	~2.18 ppm (singlet, 12H, CH₃)
Dimethylmalonic acid	132.11	~1.3-1.4 ppm (singlet, 6H, CH₃)
Methyl 3,5-dinitrobenzoate	226.14	~4.1 ppm (singlet, 3H, OCH₃)

Purity Calculator

Analyte Integral (\(I_{an}\))

Analyte No. Protons (\(N_{an}\))

Analyte M.W. (\(MW_{an}\))

Standard Integral (\(I_{std}\))

Standard No. Protons (\(N_{std}\))

Standard M.W. (\(MW_{std}\))

Sample Mass (mg)

Standard Mass (mg)

Standard Purity (\(P_{std}\)) [%]