Sodium Determination by Nuclear Magnetic Resonance Spectrometry Anthony L. Van Geet’ and Gareth J. Templeman Department of Chemistry, State University College, Oswego, NY 13 126, and Research and Development Laboratory, The Pillsbury Company, Minneapolis, MN 554 14
Several good instrumental methods are available for the determination of sodium. Flame photometry, atomic absorption, and atomic fluorescence are commonly used. X-Ray spectrography, induced emission spectroscopy and ion-selective electrodes are non-destructive methods. We have used the magnetic resonance of the sodium nucleus (1, 2 ) . This method is suitable for any solution. I t is specific, not subject to interference, and no calibration curve is required. I t is rather fast, but the sensitivity is poor.
THEORY The 23Na nucleus has a good NMR sensitivity and, although it has an appreciable electric quadrupole moment, its resonance in dilute aqueous solution is only 10 Hz wide (3). However, in more concentrated solutions, the resonance may be appreciably broadened (3, 4 ) . As a result, the peak heights are not necessarily proportional to the concentration, nor are the integrals, that is, the area under the peak ( 5 ) . Furthermore, the peak height depends on the amplitude yH1 of the radiofrequency radiation used to excite the sample. This dependence is given by the Bloch equations (6, 7) which describe the motion of the nucleus in the combined magnetic field Ho HI, that is, the constant and the radiofrequency fields. The peak height, that is, the signal strength a t resonance, follows from the Bloch equation for the absorption mode by the resonance condition w = y Ho, where w is the angular frequency of the exciting radiation. The result is
+
where 2 is the saturation factor. The magnetization Mo is proportional to the number of nuclei per cm3, that is, the sodium Concentration. The full width of the peak a t half ~ .\/z: The form of Equation 1 is height (5) is u1/2 = l / Tz the asymmetric Lorentz distribution, and a plot of u vs. yH1 has the same shape as the dispersion, or u-mode NMR signal, with a maximum a t ~ H , ( T , T , ) ~=/ ~1
( 2)
The peak height a t this maximum is
If the relaxation times T1 and Tz are equal, as they nearly always are in solution, the maximum peak height is always proportional to the concentration c, regardless of the value of Tz. Z’,%
=
(-1/*,M0
= ac
(4)
The proportionality constant a depends only on temperature and instrumental parameters, such as sample tube diAuthor to whom correspondence should be addressed. 1448
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ANALYTICAL CHEMISTRY, VOL. 47, NO. 8, JULY 1975
ameter and the field strength Ho; and is independent of the line width. In dilute aqueous solution T I = Tz = 0.048 sec, corre9.4 Hz (3).This sponding to a line width u1/2 = ~ T T = Z is the full width a t half height when y H ~ ( T ~ T =Z 1. )~/~
EXPERIMENTAL Equipment. Sodium NMR spectra were obtained a t 15.871 MHz by sweeping the magnetic field, using sample tubes with an outside diameter of 5 mm, and an inside diameter of 4.20 mm ( 3 ) . The sweep rate was calibrated from the side bands obtained by applying a frequency of 100 Hz or higher to the linear sweep coil. Although the magnetic field was not locked, the sweep rate varied less than 1%during a series of measurements (3). The homogeneity of the magnetic field was adjusted for protons a t 60.000 MHz. The frequency was then changed to 15.871 MHz, using an almost identical probe. No further homogeneity adjustment was needed. The peak height as well as the line width depend on the radiofrequency power, ? H I . At maximum peak height, u, a 3.00M NaCl solution had a line width of 10.4 Hz (theoretical 9.4 Hz). Thus, the contribution of the inhomogeneous broadening t o the line width is only 1.0 Hz, and the observed line shape is essentially the natural one. It is also possible to tune the homogeneity directly, using a 3M NaCl solution, but the inhomogeneous broadening will be more than 1.0 Hz. The signal-to-noise ratio was 13 for a 0.1M NaCl solution. Analysis by NMR. The peak height urnaxof the unknown and a 3.00M NaCl solution are compared, and the concentration of the unknown solution is calculated by Equation 4.It is usually necessary to readjust the R F power yH1 when the sample is changed. This was done by slowly sweeping the field until the pen deflection was maximum. Keeping the pen on top of the resonance, the pen deflection is further maximized by changing yH1 in steps of 1 db. In this, strong filtering is used to suppress noise. T o verify that the spectrometer has not drifted off the center of resonance, a small sweep through the top of the peak is made. Next, the base line is drawn, either by removing the sample or by sweeping far away from the resonance. The peak height is measured in mm. Since the output potentiometer (sensitivity) is not calibrated, it should be kept in the same position throughout a series of measurements.
RESULTS T o test the method, various solutions of known concentration were analyzed. Aqueous solutions of sodium chloride and sodium hydroxide were prepared with concentrations between 1M and saturation. Calibration plots of the analysis result vs. the known concentration gave straight lines through the origin, as shown in Figure 1. The least squares fits gave standard deviations of 0.061 and 0.17M, respectively, not unexpected in view of the signal-to-noise ratio. Sodium hydroxide provides a severe test of the method, since 1ITz is strongly concentration dependent in a non-linear fashion ( 3 ) .A few single determinations are listed in Table I. A solution of sodium methoxide in methanol gives a broad resonance, providing a still more severe test. One might be tempted to use a fixed rather than optimum value of the RF power, y H I , as was done by Jardetzky and Wertz (8) and others (9, 10). This is satisfactory for NaCl and dilute NaOH ( 3 )up to about 3M, but not when the anion is big as in NaC104, NaI, NaSCN, or NaSP04 so-
Table I. Sodium Analysis by NMR Concentration, .N
Solute
Solient
Known
KMR
Line width
'/T2, sec-l
10 22 3.00b same NaCla 76 168 12.00c 12.06 NaOH 9.72 108 240 9.65d NaC10, 3 . 4 l C 3.37 280 630 NaOCH, a Standard for analysis by ?;MR. b By weight. By titration with acid. d From density.
H,O H20 H20 CH,OH
Figure 1. Peak height of
the sodium
NMR resonance in aqueous so-
lution
( 0 )NaCI: (El, M) NaOH; (El) amplitude of y H1 optimized:
constant y H1. The peak height is in arbitrary units (12.3 mm), chosen to make the slope equal to one
lutions, as 1/Tz increases with concentration for these solutions, resulting in a curved calibration plot which has a maximum (8),as shown in Figure 1. Limitations. The method is suitable for solutions only, including nonaqueous solutions. In viscous solutions, the resonance will be broadened; but as long as sufficient RF power is available to reach the maximum peak height, the analysis will be correct. Viscous solutions occur in biological tissues. If the sodium ion is complexed (11-13), the resonance will also be broadened, again requiring more R F power. For extremely high RF power, it is difficult to balance the bridge of a single coil spectrometer perfectly, resulting in increased noise and lower sensitivity. For a cross coil instrument, the same problem obtains in that the adjustment of the paddles becomes very critical. The sensitivity is rather poor. While we have detected solutions as dilute as 0.01M or 230 Mglml (ppm), much higher concentrations are needed if good precision is re-
quired. We prefer solutions with a concentration over 0.3M. However, the sensitivity can be improved by more than an order of magnitude by using larger sample tubes, time averaging, and stronger magnetic fields. A principal advantage of the method is that it is essentially free from interferences. Although a standard is used, it is an absolute method in that urnaxis always directly proportional to the sodium ion concentration. Calibration curves should not be needed except to check the procedure. Furthermore, the method is non-destructive and rather fast, once the spectrometer is adjusted.
LITERATURE CITED (1) A. L. Van Geet and G. J. Templeman in "Abstracts of Papers", 167th National Meeting of the American Chemical Society, Los Angeles, Calif., April, 1974. Abstract No. Anal. 161. (2) G. J. Templeman, Ph.D. dissertation, State University of New York at Buffalo, 1970; Diss. Abstr. lnt. 6,31, 5301 (1971). (3) G. J. Templeman and A. L. Van Geet, J. Am. Chem. Soc., 94, 5578 (1972). (4)M. Eisenstadt and H. L. Friedman, J. Chem. Phys., 44, 1407 (1966). (5) A. L. Van Geet and D. N. Hume, Anal. Chem., 37, 979 (1965). (6) J. A. Pople, W. G. Schneider, and H. J. Bernstein, "High Resolution Nuclear Magnetic Resonance", McGraw-Hill. New York, 1959, p 35. (7) J. D. Roberts, "Nuclear Magnetic Resonance. Applications to Problems in Organic Chemistry", McGraw-Hill, New York. 1959, p 88. (8)0. Jardetzky and J. E. Wertz, J. Am. Chem. Soc., 82, 318 (1960). (9) G. 2 . Mal'tser, G. V. Malinin, V. P. Mashorets, and V. A. Shcherbakor. Zh. Strukt. Khim., 6,353 (1965) (English). (10) C. A. Rotunno, V. Kowalewski. and M. Cereijido, Biochim. Biophys. Acta., 135, 170 (1967). (11) D. H. Haynes, B. C. Pressman, and A. Kowalsky, Biochemistry, IO, 852 (1971). (12) E. Shchori, J. Jagur-Grodzinski, Z. Luz. and M. Shporer, J. Am. Chem. SOC.,93, 7133 (1971). (13) A. M. Grotens. J. Smid, and E. de Boer, Chem. Commun., 759 (1971).
RECEIVEDfor review April 18, 1974. Accepted March 3, 1975.
Determination of Parts per Billion Phosphate in Natural Waters Using X-Ray Fluorescence Spectrometry Donald E. Leyden,' William K. Nonidez, and Peter W. Carr Department of Chemistry, University of Georgia, Athens, GA 30602
The importance of excess phosphate in environmental waters has been of much concern and discussion. The determination of orthophosphate or t$al phosphate converted to orthophosphate is frequently performed by environmental monitoring laboratories. A standard method for the Author to whom all correspondence should be addressed.
determination of orthophosphoric acid involves the formation of 12-molybdophosphoric acid (12-MPA) in a strongly acidic solution. Reduction of the 12-MPA with ascorbic acid or stannous chloride forms the heteropolyblue complex which is measured spectrophotometrically. Because germanium, silicon, and arsenic also form heteropolyacids with molybdate anion in acidic solution, a number of techANALYTICALCHEMISTRY,
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