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Anal. Chem. 198S958,544-547
Determination of Sub-Nanogram-per-Liter Levels of Mercury in Lake Water with Atmospheric Pressure Helium Microwave Induced Plasma Emission Spectrometry Yukihiro Nojiri,* Akira btsuki, and Keiichiro F u w a National Institute for Environmental Studies, 16-2 Onogawa, Yatabe, Ibaraki 305, Japan
A hldhly sensltlve method for the analysis bf Hg Was dkveloped utlllzlng atmospheric pressure He microwave induced plasma (He-MIP) emlssion spectrometry. Mercury vapor was generated from water samples by reduction and purglng and was collected with a gold amalgamation trap. The Hg vapor, removed by heating the trap, was introducdd into thb He-MIP. The atomlc emission line of 153.7 nm was used for the determlnatlon of Hg. The detedlon ilmlt, defined as 3 times the standard deviation of the blank operatlons, was 0.5 pg in 50 mL of hater sample, corresponding to 0.01 ng/L. The method was applled to the determination of ultratrace levels of Hg in lake water samples. The Inorganic Hg concentration In subsurface water from unpolluted Lake Mashu was found to be 0.3 ng/L.
Although there has been much interest in the analysis of environmental Hg, it has been very difficult to establish reliable background levels of Hg in natural waters because of their extremely low concentrations. The difficulty has been due to lack of analytical sensitivity and contamination during sampling and analysis. Great efforts by many researchers have revealed that the natural background levels of Hg in unpolluted seawaters are in the nanogram-per-lite; range or less (1-3). Freshwaters in Japan also contain Hg in the nanogram-per-liter range ( 4 ) . Atomic absorption spectrometry using a cold vapor generation technique (CVAAS) has generally been used for the determination of low concentrations of Hg in solution. Detection limits for CVAAS are almost between l and 0.05 ng with ordinary instrumentation (5-8). Analysis of Hg in natural waters at sub-nanogram-per-liter levels with CVAAS requires large sample volumes (nearly 1L per analysis (9)). Detection limits better than 10 pg have only been achieved with some novel instrumentation, e.g., dc mode operation of the light source and double beam compensation by Ingle et al. (10)or vacuum ultraviolet spectrometry by Haraguchi et al. (11,12). While plasma emission spectrometry using various types of plasma has high sensitivity for Hg comparable to or better than that of improved CVAAS (13-191, generally, detection limits better than 10 pg were reported. These reports are classified with the plasma source: dc discharge plasmas (13, 14), microwave-induced plasmas (15-18), hnd low-pressure ring discharge plasmas (19). A convenient sample volume for natural water analysis is less than about 100 mL per analysis, when ease of sample handling and the necessity for repeat analyses are taken into consideration. This implies that the necessary detection limit for analysis of sub-nanogram-per-liter levels of Hg is better than 10 pg. Plasma emission spectrometry thus offers a more useful approach for the analysis of sub-nanogram-per-liter levels of Hg in natural water samples than does CVAAS. In this study, an atmospheric pressure He-MIP excitation source, that has high excitation capabilities for many metallic and nonmetallic elements (20), and a cold vapor generation technique were used. This excitation source has already been
Table I. Instrumentation microwave cavity
Model 218L (EMS, U.K.), TMolo, Beenakker type plasma torch 7 mm o.d., 1 mm i.d., quartz microwave generator Model MR-301 (Ewig Shokai Co., Japan), 2450 MHz focusing lens quartz, 50 mm diameter, 75 mm focal length monochromator Model HR-320 (ISA, U.S.A.), Czernv-Turner mounting focal length, 0.32 m grating, 1200 grooves/mm, holographic dispersion, 2.5 nm/mm high-voltage supplfi one part of JY38P (Jobin Yvon Co., France) photomultiplier tube Model R-955 (Hamamatsu Photonics Co., Japan) dc amplifier laboratory constructed Model U228 (Nippon Denshi Kagaku Co., chart recorder L
JaDan)
applied to the analysis of Hg in solution samples by Tanabe et al. (171, and a good detection limit (8 pg) was obtained. However, their method was more suitable for the analysis of biological tissues than natural waters. The detection limit represented as the concentration in solution was no better than 4 ng/L because of the small applicable solution volume. The method described here improved the sensitivity and the analytical feasibility for sub-nanogram-per-liter levels of Hg in natural water samples by use of an original amalgamation apparatus suitable for the He-MIP excitation source.
EXPERIMENTAL SECTION Instrumentation. The instrumentation for this experiment is summarized in Table I. The operating coaditions (the plasma gas flow rate, the microwave power, and the position of observation) were fixed so as to observe a sufficient signal to background ratio (SBR) for the atomic emission line of Hg at 253.7 nm. Usually, the plasma gas flow rate and the microwave power were adjusted to 300 mL/min and 80 W, respectively. The 1:l image of the plasma, axially observed, was focused on the entrance slit of the monochromator. The position of observation was usually adjusted at the center of plasma. As the widths of the entrance and the exit slits of the monochromator were both adjusted to 20 km, the spectral resolution was about 0.05 nm. The output current of the photomultiplier tube was filtered with a circuit in the dc amplifier (time constant of 0.3 s). The amplified signal was recorded by a Strip chart recorder. The peak height of the Hg emission signal was used for the calculation of the amount of Hg. Reagents. A stock standard solution of Hg2+(I mg/L) in 0.1 N nitric acid was prepared from a commercial standard solution (100 mg/L) for atomic absorption spectrometry (Kanto Chemical Co., Japan). The working standard solutions of 1 and 10 kg/L in (1.1N nitric acid were prepared daily. Sulfuric acid used was the atomic absorption spectrometric grade reagent (Wako Pure Chemical Co., Japan), A reducing reagent of 10% tin(I1) chloride solution in 1 N sulfuric acid was prepared from the atomic absorption spectrorhetric grade reagent (Wako Pure Chemical Co., Japan). As these commercial reagents contained appreciable quantities of Hg, a purification procedure, outlined in the following
0003-2700/86/0358-0544$01.50/00 1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 3, MARCH 1986
Figure 1. Schematic diagram of sample introduction system for Hg analysis: VA1, four-way valve; VA2, eight-way valve; R, reaction vessel; A, He gas line for sample purging; B, He gas line for carrier of Hg vapor into MIP; C, He gas line for plasma sustenance; P, gas purifiers of silver columns; F, flow control valves; VT1, VT2, vents; T, amalgamation trap; V, variable transformer; M, connection to He-MIP.
seciton, was necessary. Nitric acid for the preservation of samples was purified in a clean laboratory by subboiling distillation with a quartz still. Water samples of Lake Mashu (Hokkaido, Japan) were collected with a Teflon coated Go-Flo sampler (General Oceanic Co., Florida) in June 1984. The water depth at the sampling station was 210 m, close to the deepest point of the lake. The samples were taken in HARIO borosilicate glass bottles (Shibata Glass Co., Japan) with transparent glass joint cups. Purified nitric acid (4 mL) was added to the sample water (500 mL) for preservation. Human hair, (10-20 mg), a certified reference material (CRM) from the National Institute for Environmental Studies (NIES), Japan (21),was digested by use of purified nitric acid in a closed sample digestion vessel (22),to avoid loss by vaporization and contamination, and diluted (400-fold). One hundred microliters of the solution was used for the analysis of Hg. Apparatus for the Introduction of Hg Vapor into the MIP. Because the introduction of air or a large amount of water mist was not acceptable for He-MIP, it was necessary to construct an apparatus for the introduction of only the Hg vapor. It is shown schematically in Figure 1. Teflon (FEP) tubes of 2 mm i.d. were used for all tubing. Stainless steel connectors with Teflon (TFE) inserts were used for all connections. Sample purging He (A in Figure 1)and He for carrying the trapped Hg to the MIP (B in Figure 1) were purified by passing through glass columns (4 mm i.d., 30 cm length) packed with grained silver (elemental analysis grade reagent, Nakarai Kagaku Co., Japan). The flow rates were adjusted to 300 mL/min. The two valves (four way and eight way) were made of stainles steel and Teflon TFE. The reaction vessel was made of Pyrex of inner volume 80 mL. The amalgamation trap was prepared from a 4 mm i.d. quartz tube packed with 100 mg of grained pumice (12/20 mesh) coated with gold (Nakarai Kagaku Co., Japan) and held in place with quartz wool. The gold content was 15% (w/w). Imaeda and Osawa reported the preparation method and the properties (23). Extremely fine gold particles (0.5-2.5 pm) dispersed on the surface of pumice were observed by a electron microscope (23). The tube was electrically heated with a constant voltage. By the operation of a switch, the temperature in the trap was increased at the rate of 24 K/s in the first 30 s. Finally, the temperature was increased to 900 "C after 90 s of heating time. Mercury trapped on the surface of the adsorbent was vaporized midway through the temperature increase. The trap was cooled by a fan when the heater was not operating. Procedure. The plasma was ignited and allowed to stand for about 1h for thermal stabilization of the system. A wavelength adjustment to the emission line of 253.7 nm was performed using a Hg hollow cathode lamp. First, to reduce Hg in the reagents, 3 mL of the reducing reagent and 3 mL of sulfuric acid (10 N) were added to the reaction vessel. The vessel was connected to the vent port (VT2 in Figure 1)to carry off volatilized Hg by He gas purging. Usually, the operation was carried out during the previous sample analysis. The initial positions of the valves are represented in Figure
545
1 by the continuous line for VA1 (four-way valve) and the dotted line for VA2 (eight-way valve). The reaction vessel containing the purified reagents was connected to VAL After the addition of 50 mL of sample water, VA1 was turned to the position represented by the dotted line. The Hg vapor generated was trapped with the cooled amalgamation trap. After 5 min of reaction, VA1 was turned to the position represented by the continuous line. A 10-s interval then allowed the water mist transported from the reaction vessel to be ventilated. Next, VA2 was turned to the position represented by the continuous line. As this operation caused a shock to the plasma by gas pressure fluctuation, a 50-9 stabilization period was allowed before heating the trap. The heating time was usually 90 s including a cleanup period for the trap. The Hg signal appeared 17 s after the start of heating. Then VA2 was turned to the position represented by the dotted line and the trap was cooled. The next operation could be performed after 120 s. The time required for the analysis of one sample was thus about 10 min. For calibration,a small amount of the working standard solution was added by a micropipet to the reaction vessel containing the already purged reducing reagent and purified water. For the human hair sample analysis, the same method of calibration was used. R E S U L T S AND DISCUSSION Optimization. Major operating parameters for He-MIP are the plasma gas flow rate, the power of microwave generator, and the position of observation. In emission spectrometry, the signal to background ratio (SBR) is a decisive factor for the sensitivity when the background emission intensity is sufficieritly high (24). With the plasma gas flow rate within 300-500 mL/min and the microwave power within 60-100 W, stable operation of the plasma and a sufficiently high SBR were obtained. From the spatial distribution of the emission intensity, the maximum for Hg emission was observed a t nearly the same position as the maximum of the plasma backpound, close to the center of the plasma. The maximum SBR, however, appeared at an off axis position. The results were different from the earlier work by Tanabe et al. (17), where the emission maximum appeared at an off axis position in a plasma torch having wider inside diameter (3 mm). As a precise optimization of the position of observation was a time-consuming procedure for routine operation, the position of observation was adjusted to the center of the plasma. This meant a small loss of sensitivity compared with fully optimized conditions. The cold-vapor generation procedure was optimized so as to obtain a complete reduction of inorganic Hg in lake water samples. The repeated reactions gave measurable peaks of Hg when the reaction times were 1 or 2 min. No measurable peak was observed by the repeated reaction when the reaction time was more than 4 min. The reaction time of 5 min was used for routine analysis. Mercury standard solution spiked in the lake water sample gave a quantitative recovery, compared with that spiked in purified water. Stannous chloride reduction procedure used in this study is accepted as a measurement method of inorganic or easily reducible Hg in natural water samples (1-4, 9). Emission Signal Profile a n d Blank Problem. Typical emission signal profiles are shown in Figure 2. The large negative peaks were due to changing the gas flow with VA2. The small negative peak was observed 8 s after switching on the heater. It is most likely to be the vapor of water trapped on the gold-coated pumice. When the reaction vessel contained only purified water, the same negative peak was observed. The Hg peak was observed 17 s after switching on the heater. The time corresponded to the trap temperature of 380 "C. The half-width of the peak was 2.4 s. The sharpness of the Hg peak was dependent on the heating voltage, i.e., the temperature increase rate. T o improve the sensitivity by sharpening the peak shape, the applied voltage
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 3, MARCH 1986 Hg concentration (ng/L)
0
2 min
0
1
2
3 1
"i \
Figure 2. Typical chart recording of Hg emission signal: A l , A2, blank operations: B, standard containing 50 pg of Hg; C, standard containing 100 pg of Hg; D, 50 mL of lake water sample (the calculated amount of Hg was 23 pg).
to the heater was adjusted as high as possible. This condition (heating rate of 32 K/s a t the Hg appearance temperature, and maximum temperature of 900 "C) was the optimal after heat resistance of the apparatus was taken into consideration. A relatively long (1.5 m) tube from VA2 to the MIP was preferable for stable operation of the plasma, as it minimized the shock due to changing the carrier gas flow. By the flow rate and the volume of tube, it was calculated that transfer of Hg vapor from the trap to MIP took 1s. No effect of carrier gas flow rate on peak sharpness was observed within 300-500 mL/min. The diffusion of Hg vapor in carrier gas was not as effective for peak width in such short transfer time. Small blank signals were observed even after purification of the reagents. These signals were obtained after the reduction of Hg in purified water (Milli-Q water purifier, Millipore Co., Bedford, MA) containing 0.29 ng/L of Hg, without the addition of any sample. This may have been due to the residual material of the reaction vessel, as it was influenced by the cleaning procedure. The vessel was used after heating in a drying oven at 400 OC to minimize contamination by Hg. A typical blank corresponded to 3 pg of Hg. Sensitivity, Precision, and Dynamic Range. The detection limit was calculated from three times the standard deviation of the blank signals. The detection limit varied little day to day, because the daily optimization of the system was impossible. The best observed was 0.5 pg, corresponding to 0.01 ng/L of Hg, as the sample volume was 50 mL. The background equivalent concentration (BEC), a decisive factor for the detection limit in emission spectrometry, was 2 1 pg. The detection limit of 2.4% of BEC would be a reasonable value for the detection method using a peaked emission signal. The range in daily variation of the sensitivity was from 0.5 to 3 pg. The reproducibility of a standard solution was 4.5% at 25 pg (n = 5). A straight line with a correlation coefficient of 0.9999 was obtained as the calibration curve with the standard of 10,25,50,100,200, and 400 pg Hg. Up to 20 ng, the linear calibration range was confirmed. Thus, a dynamic range of more than lo4was acquired. The wide dynamic range is one of the merits of emission spectrometry, compared with CVAAS. Accuracy. The analytical result for the reference material (human hair, NIES CRM No. 5 ) was 4.4 pg of Hg/g (4% relative standard deviation (RSD), n = 8). The certified value is 4.4 i= 0.4 pg of Hg/g (21). The accuracy and precision of this method were, therefore, confirmed. Compared with the CVAAS method used for the certification procedure, only a small quantity of sample was required for analysis. Analytical Result for Lake Water Samples. Lake Mashu is an oligotrophic lake, where we have been studying the background levels of pollutants in the Japanese freshwater environment. The water characteristics of Lake Mashu have been reported elsewhere (25,26). Similar to other trace metals
Figure 3. Vertical profile of Hg concentration in Lake Mashu.
(26), the concentration of Hg in Lake Mashu water was very low. Analytical results for Hg are shown in Figure 3. The results for the samples of 0 and 30 m depth were obtained from three independent sample bottles. About 20% RSD was obtained for the lake water sample below nanogram-per-liter levels. The vertical profile was consistent with the limnological data. The surface enrichment showed atmospheric input of Hg similar to some other trace metals (26). The increase below 100 m, also observed for Fe, appeared to be due to input from the lake sediment or groundwater. The value for inorganic Hg reported here is one of the lowest values obtained for unpolluted freshwaters (4, 27-29). Comparison with Other Analytical Methods for Hg Using Atomic Spectrometry. CVAAS for Hg analysis may be classified into the two groups according to the method of introduction of Hg vapor. First, direct introduction from the reaction vessel into the absorption cell (8, 10-12). Second, the use of a Hg trap between the reaction vessel and the absorption cell (1-7,9). Because the solution volume for the former is limited by the absorption peak broadening, the detection limit cannot be improved below the nanogramper-liter limit. Although the absolute amount of detectable Hg is not so decreased by preconcentration using a Hg trap, the detection limit of the latter represented in the unit of concentration is improved with the larger sample volume. Furthermore, spectral interferences from the absorption of concomitants (water mist, nitric acid vapor, etc.) and chemical interference in the reduction stage from coexisiting substances are reduced. Nevertheless, it is necessary to consume a large amount of sample for determination of Hg in sub-nanogramper-liter levels by usual CVAAS technique, because of the poorer, no better than 50 pg, Hg detection ability of this method. To substitute AAS by plasma emission spectrometry as a detection method for Hg analysis with cold vapor generation technique improves the sensitivity in terms of the absolute amount of Hg, because it has picogram level detection ability. However, the determination at sub-nanogram-per-liter levels with direct Hg vapor introduction is impossible because of the smallness of the applicable sample volume. The detection limit of Hg reported previously employing direct Hg vapor introduction to He-MIP was 8 pg in a 2-mL water sample (17). In this study, an amalgamation technique for Hg analysis in natural water sample was successfully applied to He-MIP. It took some modification from the usual amalgamation apparatus for CVAAS. As the introduction of a large amount of water vapor into MIP extinguished the plasma, a combination of gas flow switching valves shown in Figure 1 was necessary. The merit of the amalgamation technique was the same as in CVAAS, Le., the improvement of the detection limit
Anal. Chem. 1988, 58. 547-551
in terms of the concentration and the elimination of interference. Moreover, an improvement of absolute detection limit of 1 order of magnitude, compared with previously reported work (In,was achieved by use of the amalgamation apparatus. The reasons for this improvement are likely to be as follows. (A) Separation of the large amount of water mist from the Hg vapor by the amalagamator might enhance the Hg emission in the plasma. (B) Separation of dissolved concomitants and gases might reduce the spectral interference at the Hg emission line, where nitrogen-containing compounds, especially, give a NO band emission (17). (C) Sharpening of the peak might give a higher concentration of Hg in the plasma excitation source. (D)The removal of contaminating Hg in the reducing reagent might reduce the blank. Contamination from marketing reagents corresponded to about 100 pg without purification. The detection limit obtained in this study (0.5 pg) was of the same order as that of methylmercury(I1) chloride by the gas chromatography-MIP system (24, 28). MIP emission spectrometry may have the detection capability of this order with gas-phase Hg introduction. Hg analysis a t levels below nanogram-per-liter was established with a suitable sample volume for natural water analysis, in this study. Research is continuing into the application of the technique reported here to the analysis of various kinds of environmental water samples.
ACKNOWLEDGMENT The authors thank K. Okamoto and T. Uehiro of the NIES, Japan, for their offering of CRM and valuable discussion. We also thank J. Edmonds of Marine Research Laboratories of Western Australia for his valuable comments. Registry No. Hg, 7439-97-6;water, 7732-18-5. LITERATURE CITED (1) Matsunaga, K.; Nlshimura, M.; Konishi, S. Nature (London) 1975, 258, 224-225.
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(2) Mukherjl, P.; Kester, D. R. Science 1979, 204, 64-66. (3) Olafsson, J. "Trace Metals In Sea Water"; Wong, C. S.,Boyle, E., Bruland, K. W., Burton, J. D., Goldberg, E. D., Eds.; Plenum Press: New York, 1983;pp 475-485. (4) Matsunaga, K. Jpn. J . Limnol. 1976, 37, 131-134. (5) Fltzgerald, W. F.; Lyons, W. B.; Hunt C. D. Anal. Chem. 1974, 46,
iaa2-ia85. ( 6 ) Nishimura, M.; Matsunaga, K.; Konishi, S . Bunseki Kagaku 1975, 24,
655-658. (7) Yoshida, Y.; Murozuml, M. Bunseki Kagaku 1977, 26, 789-794. (8) Chou, H. N.; Naleway, C. A. Anal. Chem. 1984, 56, 1737-1738. (9) Bloom, N.; Crecelius, E. A. Mar. Chem. 1983, 74, 49-59. (10) Hawley, J. E.; Ingle, J. D., Jr. Anal. Chem. 1975, 47,719-723. (11) Tanabe, K.; Takahashi, J.; Haraguchi, H.; Fuwa, K. Anal. Chem. 1980, 52,453-457.
(12) Haraguchi, H.; Takahashi, J.; Tanabe, K.; Fuwa, K. Specfrochirn. Acta, P a r t s 1981, 368,719-726. (13) Braman, R. S.; Johnson, D. L. Environ. Sci. Techno/. 1974, 8, 996-1003. (14) Bricker, J. L. Anal. Chem. 1980, 52, 492-496. (15) Talmi, Y. Anal. Chim. Acta 1975, 74, 107-117. (16) Watling, R. J. Anal. Chim. Acta 1975, 75, 281-268. (17) Tanabe, K.; Chiba, K.; Haraguchl, H.; Fuwa, K. Anal. Chem. 1981, 53, 1450-1453. (18) Chiba, K.; Yoshida, K.; Tanabe, K.; Haraguchi, H.; Fuwa, K. Anal. Chem. 1983, 55, 450-453. (19) Wrembel, H. 2 . Specfrochlm. Acta, Part 8 1982, 378,937-946. (20) Estes, S. A.; Uden, P. C.; Barnes, R. M. Anal. Chem. 1981, 53,
1829-1837. (21) Okamoto, K.; Morita, M.; Quan, H.; Uehiro, T.; Fuwa, K. Clin. Chem. (Winston-Salem, N.C.) 1965, 37, 1592-1597. (22) Okamoto, K.; Fuwa, K. Anal. Chem. 1984, 56, 1758-1760. (23) Imaeda, K.; Ohsawa, K. Bunseki Kagaku 1974, 28, 239-244. (24) Boumans, P. W. J. M.; de Boer, F. J.; Witmer, A. W.; Bosveld, M. Specfrochim. Acta, Part B 1978, 338, 535-544. (25) Furuta, N.; Otsuki, A. Anal. Chem. 1983, 55, 2407-2413. (26) Nojiri, Y.; Kawai, T.; Otsuki, A.; Fuwa, K. Wafer Res. 1985, 79, 503-509. (27) Minagawa, K.; Takizawa, Y.; Kifune, I. Anal. Chim. Acta 1980, 775, 103-1 10. (28) Olafsson, J. Limnol. Oceanogr. 1980, 25, 779-788. (29) Yamamoto, J.; Kaneda, Y.; Hikasa, Y. Int. J. Environ. Anal. Chem. 1983, 76,1-16.
RECEIVED for review August 8, 1985. Accepted October 7, 1985.
X-ray Diffraction Spectrometry for Analysis of Lamellar Ion Exchangers of the a- and y-Zirconium Phosphate Type Ricardo Llavona, Marta Sulrez, Jose R. Garcia, and Julio Rodriguez*
Departamento de Quimica Inorgcinica, Facultad de Qutmica, Uniuersidad de Ouiedo, CICaluo Sotelo sln, Ouiedo, Spain
X-ray dlffraction in the quantltative analysis of crystalllne solld phases was used. The evolution of y-tltanium phosphate in the H+/M+ (M = Na, K) ion exchange and the best condltions for the quantitative determination to be carried out are reported. The areas of each phase with dlfferent ionic composltlon were obtained. The use, in materials of the CY- and y-zirconium phosphate type, of a linear relationship between intensity and concentration for mixtures of phases with different counterlon contents is proposed.
The ion-exchange properties of lamellar inorganic materials have been widely studied (1, 2). a-Zirconium bis(monohydrogen orthophosphate) monohydrate (a-ZrP) and its isomorphic titanium compound (3,4) belong to this group. Both have an interlayer distance of 7.6 8,, which restricts their
capacity for exchanging ions with a large diameter. In both compounds, the dihydrated form shows a different structure (5-8) known as the y variety (5) with a basal spacing quite higher than that of the cy form (12.2 8, for y-ZrP and 11.6 8, for T-TiP), which allows large ions to diffuse through it. Thus, in acidic media, cy-TiP retains Li+ and Na+ while K+ is only retained at pH >7 and with a high degree of hydrolysis (9-14). However, y T i P possesses a larger affinity for K+ than for Na+ ions reaching in acidic media 50 and 25%, respectively, of its exchange capacity ( 7 , 1 5 ) . Control of the degree of saturation of ion-exchange materials must be reproducible and should be done quickly and accurately and with small amounts of sample. In an earlier paper (16)a nonconventional method of calibration for mixtures of materials with the same chemical composition and isomorphic structure was described. The solution was possible by assuming a linear relationship between the intensity of a re-
0003-2700/86/0358-0547$01.50/0 @ 1986 American Chemical Society
