Concentration Determination by Standard Addition

In quantitative NMR (qNMR), an analytical method that some chemists are averse to whilst others celebrate is standard addition. As the name implies, standard addition is a procedure where you prepare a series of samples (two or more), each having the same volume and the same amount of the unknown analyte but vary in the amount of known concentration stock solution (the standard) added to each vial or flask. The concentration range of these standard addition standards should reflect a reasonable approximation of the unknown concentration.

In NMR analysis, finding a suitable internal calibrant can be challenging due to solubility issues, chemical reactivity, and/or signal overlap with the analyte(s) of interest. The standard addition method offers a practical alternative because it involves simple sample preparation and enables quantitative analysis without the need to add an internal calibrant or any other compound to the sample. Owing to these advantages, standard addition is widely applied across industries such as pharmaceuticals¹, food analysis², and forensic science.²

We conducted the standard addition procedure to determine the unknown concentration of sodium acetate in an organic sample. The sample was transferred to an NMR tube and a T₁ experiment was acquired to optimize the scan delay of the sodium acetate signal. After which incremental amounts of a 200 mM solution of sodium acetate in deuterium oxide were added so that the final amount of sodium acetate added ranged from 0 mM to 50 mM (Figure 1). Note that all NMR experiments were conducted using the Nanalysis-100 and the acquisition parameters used remained the same for all samples.

Figure 1. Sample preparation for the standard addition method using an NMR tube.

For data analysis, the 1D ¹H NMR spectra were stacked as shown in Figure 2, where we observed the signal that corresponds to sodium acetate (δ = 2.0 ppm). As the concentration of sodium acetate increases, the intensity of the signal of interest also increases. Consequently, these signals can be viewed as steps. These steps can be tabulated by comparing the concentrations of each sample to the absolute integral of each of their respective signals. If the data is integrated, tabulated, and then plotted, a linear calibration curve is generated (Figure 3).

Figure 2. Stacked ¹H NMR (100 MHz) plot of analyte with successive additions of the sodium acetate solution.

Figure 3. Calibration curve of the analyte (a) with the successive additions of sodium acetate (s). The general standard addition equation is given by S = kC + b, where S is the integral area, k is the slope, b is the y-intercept, and C is the concentration. By extrapolating the slope, the unknown concentration of sodium acetate can be determined by taking the negative of the x-intercept. The concentration of the sodium acetate in the organic sample was determined to be 42.4 mM.

Standard addition can look deceptively easy but can prone to error if you use the wrong concentrations. Therefore, before commencing on your analytical journey ensure that you are using the right concentration and consider any dilutions!

If you are interested in learning more about this experiment, or other ways to incorporate a benchtop NMR spectrometer into your undergraduate teaching curriculum please see our sample experiments page or contact us directly!

[1] Diehl, B.; Malz, F.; Holzgrabe, U. Spectroscopy Europe. 2007, 19, 15-19

[2] Brinson, R. G. Molecules. 2021, 26, 7091

[3] Bharti, S. K.; Roy, R. Trends. Anal. Chem. 2012, 35, 5

[4] Harris, D. C. ‘Quantitative Chemical Analysis’, 5th Ed.; W.H. Freeman and Company: New York, 1999

[5] Rajabzadeh, M. J. Chem. Educ. 2012, 89, 1454

[6] Bruce, G. R.; Gill, P. S. J. Chem. Educ. 1999, 76, 805