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Anal. Chem. 1084, 56, 1188-1192
above 2 h, deviation from linearity becomes pronounced. With a deposition time of 5 min the detection limit (signa1:noise = 31) was found to be 1.2 ng/mL Cu. With a deposition time of 2 h, the detection limit was found to be 0.07 ng/mL. The detection limit was also determined for aqueous copper solutions, by conventional nebulization using the same demountable torch system, and was found to be 23 ng/mL. Therefore, a significant improvement in detection limit is gained by the present technique. To determine the absolute detection limit of the method, an estimate must be made of the fraction of copper which is deposited on the graphite electrode during the electrolysis. From the coulometric studies, it was concluded that approximately 3.0% of the copper was deposited per 5 min during the electrolysis. This is confirmed by the shape of Figure 2. The solid points are the experimental points and the circles are calculated signals normalized so that the highest experimental and calculated signal value are equal. The fit is significantly better than that of either 2.5 or 3.5%. With a sample volume of 40 mL and a deposition time of 5 min, the absolute detection limit was then determined to be 1.9 ng. Direct addition of standard copper solutions to the graphite electrode was carried out, for comparison purposes, by pipetting 20 p L of sample, using an Eppendorf pipet, followed by vaporization of the solvent at a forward power of 30 W for 1 min with an argon flow rate of 18 L/min. The detection limit (signahoise = 3:l) was found to be 0.16 ng. The order of magnitude difference observed in the absolute detection limit is probably due to a higher atom population in the viewing region when the analyte is expelled from the electrode crater rather than from the electrode exterior surface. The RSD of the electrochemical deposition method was 3%, which is significantly better than the direct liquid additions method where an RSD of 12% was obtained for nine determinations carried out on three standard copper solutions (1260,126,and 12.6 ng). The precision improvement may be due to a more regular deposition of the analyte on the electrode surface than that which was obtained by placing liquids in the crater. This method should be well suited for the analysis of trace and ultratrace elements that are soluble in Hg (20). Sample pretreatment may be required in cases where direct electrodeposition is not possible; however, the method should provide a good simultaneous separation-preconcentration step prior to the ICP analysis. It should also be pointed out that although small sample volumes (in the order of microliters) cannot be analyzed by the present technique, it may be possible to carry out the electrolysis within the graphite electrode, which would serve as the sample container as well as the working electrode. The use of a flow-through deposition cell may (21) allow the determination of some elements, notably cobalt, nickel, manganese, and chromium even though the anodic stripping voltammetry reduction is irreversible. Their electrochemical irreversibility should not affect their spectrochemical analysis. The use of a cylindrical graphite flow-through cell system should make possible the generation
of a conventional annular shaped plasma by the introduction of an injector gas flow through the tubular electrode. This could eliminate the odd transient signal shape (Figure 1) obtained in these experiments and enhance the ease of automating the data processing. An efficient flow-through cell may also result in a significant decrease in detection limits by increasing the deposition rate as well as introducing the analyte atoms into the central viewing zone of the plasma. We also expect that the technique will be quite capable of simultaneous multielement analysis within the constraints of the electrochemical system. There may be additional improvements to both precision and accuracy by using internal standards or ratioing techniques.
ACKNOWLEDGMENT The authors acknowledge the assistance of Jitka Kirchnerova during the conceptual stage of this project and W. C. Purdy during the evaluation phase. Registry No. Cu, 7440-50-8. LITERATURE CITED ( I ) Salin, E. D.;Horlick, G. Anal. Chem. 1978, 5 1 , 2284-2286. (2) Sommer, D.;Ohls,K. Fresenlus' 2.Anal. Chem. 1980, 97, 304. (3) Horlick, G.; Pettii, W. E.; Todd, B. Presented at Annual Conference of the Spectroscopy Society of Canada, September 26-29, St-Jovite, Quebec, Canada, 1982; Paper No. 10. (4) Kirkbrlght, G. F.; Walton, S.J. Ana&st(London) 1982, 107, 276-281. (5) Volland, G.; Tschopel, P.; Tolg, 0 . Spectrochlm. Acta, Part 6 1981, 36, 901-917. (6) Brandenberger, H. Chlmia 1988, 22, 449. (7) Brandenberger, H.;Bader, H. At. Absorpt. Newsl. W67, 6 , 101. (8) Lund, Walter; Larsen, Bjorn. V. Anal. Chlm. Acta 1974, 70, 299-310. (9) Lund, Walter: Larsen, Bjorn. V. Anal. Chim. Acta 1974, 72, 57-62. 10) Falrless, Charles; Bard, Allen. J. Anal. Left. 1972, 5 , 433-438. 11) Falrless, Charles; Bard, Allen. J. Anal. Chem. 1975, 45, 2289-2291. 12) Jensen, B. 0.;Dolezal, Jan; Langmyhr, F. J. Anal. Chlm. Acta 1974, 72, 245-250. 13) Batley, Graeme E.; Matousek, Jaroslav. P. Anal. Chem. 1977, 4 9 , 203 1-2035. 14) Edwards, Lawrence L.; Oreglonl, Beniamino Anal. Chem. 1975, 47, 23 15-2316. (15) Matuslewicz, H. Presented at Annual Plttsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 9-13, Atlantic City, NJ, 1981; Paper No. 237. (16) Jagner, Daniel; Granell, Anders Anal. Chlm. Acta 1976, 83, 19-26. (17) Jagner, Daniel Anal. Chem. 1078, 50, 1924-1929. (18) Jagner, Daniel; Aren, Kerstin Anal. Chlm. Acta 1978, 100, 375-388. (19) Jagner, Danlel Anal. Chem. 1979, 5 1 , 342-345. (20) Lundell, G. E. F.; Hoffman, J. I. "Outlines of Methods of Chemical Analysls"; Why: New York, 1938; p 94. (21) Long, S. E.; Snook, R. D. Analyst (London) 198% 108, 1331-1338.
Eric D. Salin* Magdi M. Habib Department of Chemistry McGill University 801 Sherbrooke St. West Montreal, Quebec H3A 2K6, Canada RECEIVED for review November 18, 1982. Resubmitted October 7, 1983. Accepted February 3, 1984. This work was made possible by grants from the Natural Sciences and Engineering Research Council of Canada (Grant A1126) and the Government of Quebec (Fonds F.C.A.C. EQ1642).
Standard Addition Method in Flow Injection Analysis with Inductively Coupled Plasma Atomic Emission Spectrometry Sir: The introduction of sample solutions to various detectors by flow injection analysis (FLA) is a valuable approach and is utilized for rapid routine analysis employing diverse instrumental techniques (1,2). Tyson and Idris (3) suggested that flow injection sample introduction offers more than re-
producible passage of sample to instruments. Tyson et al. (3-6) devised a simplified model for the dispersion effects observed in FIA with atomic absorption spectrophotometry (AAS), which enabled the development of a novel flow injection analogue of the standard addition method. This ap-
0 1984 American Chemical Society 0003-2700/84/0356-118S$01.50/0
ANALYTICAL CHEMISTRY, VOL. 56, NO. 7 , JUNE 1984
proach was applied from the determination of calcium in the presence of phosphate and aluminum ( 3 , 4 ) and for the determination of chromium in standard steels (6). Greenfield (7) demonstrated the feasibility of applying the same technique for the determination of calcium in Portland cement by combining FIA with inductively coupled plasma atomic emission spectrometry (ICP-AES). In Tyson’s method the analyte was pumped continuously through the carrier stream into the AAS nebulizer to obtain a steady-state absorbance signal. Discrete volumes of standards were injected into the analyte stream, resulting in transient absorbances, which were positive when the concentrations of the standards were higher than the concentration of the analyte, and vice versa. This is essentially an “inverse” FIA method as the functions of the carrier and the sample streams in conventionalFIA are reversed. A graphical interpretation was employed to compute the analyte concentration when the transient equaled zero. This approach may be necessitated by the limited dynamic range of AAS, but for other detectors with wide dynamic range such as ICP-AES it is somewhat tedious. Alternatively a conventional FIA standard addition method could be developed which enables a straightforward analytical determination of the concentration of the analyte. The main aspect of employing a standard addition method is to compensate for some matrix effects arising from the analyte’s peculiar composition. To achieve this goal best, the measurement of the standard contribution to the overall signal must be secured at the same dilution as the analyte proper. FIA is ideally suited for introducing solutions to detectors at a preselected dilution without the need for sample preparation. For the particular FIA combination with ICP-AES, a rapid FIA standard addition method would also be effective in obviating short- and long-term instabilities arising from variations of torch efficiency, power, wavelength, or argon gas flow rate. However, the standard addition method is not expected to compensate for spectral or chemical interferences. In the present study a rapid, “inverse” FIA method was developed based on the measurement of two flow injection transient signals relating to the concentrations of the analyte and the added standard under identical dilutions. A simple model is devised for the derivations of interest, which is applied for the FIA-ICP-AESdetermination of silicon. The same method is expected to be applicable directly (except for notation) with various detectors exhibiting linear signal-concentration dependence and should be adaptable for use to a whole range of other signal-concentration dependencies.
THEORY Inverse FIA was employed, similar in approach to that used by Tyson et al. (3-6). The carrier stream is used to pump the analyte continuously into the nebulizer of an ICP-AES apparatus, displaying a steady-state emission intensity signal, I,” (see linear sections of Figure 1). A discrete volume, Vi, of distilled water, or other solvent matrix of the standard solution, is injected into the analyte stream, in plug form, depicted by the minimum transient, P,of Figure la. This is followed by the injection of the same volume of a standard solution to give rise to the transient peak, P,of Figure lb. The latter was positive only because the concentration of silicon in the standard solution exceeded that of the analyte. The model used for deriving the relationships pertaining to standard addition is based on the following assumptions: (1) A linear emission intensity-concentration relationship prevails throughout the range of measurements for standard addition. (2) The emission intensity profile follows the time-dependent concentrationprofile of the active ingredient reaching the detection zone. The overall concentration profile is due
1189
+25 pg SVrnL(177 pL)
48
72 96 120 Time, s Flgure 1. FIA determination of 10 pg of Si/mL in aqueous solutions. Steady-state and transient ICP-AES signals were obtained in the determination of silicon by injection of 177 pL of (a)water and (b) 25 pg of SilmL into the steady stream of 10 bg of Si/mL. I, indicates the 24
background signal level for Si-free carrier solution. to the following two-stage processes occurring in series: (a) The well-known dispersion phenomenon in flow injection takes place in the first stage. Mixing of the injected plug with the carrier stream proceeds throughout the tube connecting the injection port to the nebulizer as the result of the concentration gradient between the two solutions usually controlled by convection-diffusionmass transfer processes. Dispersion is dependent on length and diameter of the connecting tube, flow rate, and volume of the injected plug (1,2,8,9). (b) The dispersed plug streaming from stage (a) is nebulized by the argon carrier gas. The dispersion layers cross the nebulizer within a finite time, in which discrete layers are detached continuously in the nebulizer-spray chamber path to the plasma and transported, in part, as an aerosol of tiny droplets. To assume that the concentration profile of the first stage persists through the second stage as well is tempting. However, owing to the turbulence exerted by the high carrier flow rate, the microstructure of the droplets in the aerosol is expected to undergo some localized redistribution. (3) The time-dependent concentration profile reaching the detector is a direct result of the volume distribution profile of the injected plug into the analyte stream and vice versa. Hence the instantaneous concentration can be evaluated for both the minimum and peak emission intensities in terms of the initial concentration of the analyte and the instantaneous dilution. This approach is not restricted to minimum and peak emissions and is valid for inverse as well as direct FIA. (4)For any discrete volume injection, the volume distribution is the same for minimum and peak transients. The above model exploits volume distribution explicitly for the derivation of relationships for standard addition with inverse FIA. This approach is novel and deals with a specific case and therefore requires the definition of new terms, when necessary. To avoid ambiguity, the dispersion for inverse FIA, Dinv,is related solely to the special case of distilled water injection when a transient minimum is depicted. The approach adopted for the definition of Dinvin terms of the concentrations (not the signals) is consistent with the conventions used for the definition of “dispersion” for normal FIA (1,2), or
C: is the initial concentration of the analyte and C,” is the concentration at the transient’s minimum obtained by the injection of the distilled water plug, Vi. The steady-state
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 7, JUNE 1984
intensity, I,", is related by the proportionality constant, k , to C,O in the carrier stream before the injection. In accordance with the first assumption of the model described above, mainly the prevalence of a linear dynamic range
I," = kC,O
(2)
Similarly, the emission intensity a t the transient minimum,
I,", is proportional to the concentration of the diluted analyte, C,", at t = tm,the residence time a t the transient's minimum
I," = kC,"
(3)
By combination of eq 1-3, inverse dispersion can be defined in terms of emission intensities
Dinv= I," /I,"
(4)
One of the discrepencies between inverse and normal FIA is revealed in eq 4, for in the latter the denominator is the transient's signal rather than I," (the emission intensity corresponding to the transient's concentration, Cxm).Furthermore, Dinvincreases upon increasing the volume of the injected plug, contrary to the behavior of "D" for normal injection. Invoking assumption 3 of the above model, C", can be redefined in terms of C,O and a dilution factor, d, at a time
t" C,"
= C,Od
(5)
Rearranging eq 5 and comparing it with eq 1, d is the reciprocal of Dinv and can be defined in terms of the volumes of the analyte, Vxm,and distilled water, Vim, prevailing at the transient's minimum, a t time tm
d = Vx"/(Vx" + Vi")
(6)
Vxmand Vimmust be distinguished clearly from the volumes V, and Vi. The emission intensity of the transient's minimum, I", is given by I" = I,"
- I,"
(7)
As indicated by eq 7, Imis the difference between two signals and is measured from the steady-state emission intensity signal. This is equivalent to the "A" terminology used by Tyson et al. (6). Combining eq 7 with eq 2 , 3 , and 5, P" can be redefined in terms of C,O and d
P
= kC,O(l- d )
(8)
Upon the injection of a volume, Vi, of a standard solution (with an initial concentration C,O) to the analyte stream, a transient peak, IP, results when C,O exceeds C: (see Figure lb). The net contribution of the added standard to the emission intensity singal, I,, can be expressed in terms of C; and the volumes at the residence time, tP, of the transient's peak, as demonstrated by eq 9.
I , = kC,OViP/(V,P + Vi')
(9)
Invoking assumption number 4 of the above model and using the same Vi for both transients, we can assume that tm = tP, Vxm= VxP, and Vim = Vip. At these conditions, eq 9 can be rewritten as eq 10
I s = kC,O(l - d )
(10)
Combining eq 8 and 10 gives
c,O = PC,O/I,
(11)
I, is the peak-to-peak distance between the two transients as in eq 12
Is=P+Ip
(12)
Substituting for I , in eq 11 leads to eq 13
c,O = I"C,O/(P + Ip)
(13)
Equation 13 is the FIA standard addition method equation. In each determination, Vi must be kept the same for the injection of both the distilled water and the standard solution, so long as FIA and ICP parameters are held constant. The transient's emission intensity peak can be expressed in terms of the difference between the total emission intensity at the transient's peak, I$, and the steady-state emission intensity signal
P
= I+' - I,"
(14)
The transient's peak is measured again by difference of two emission intensity signals, one of which is the steady-state signal. This situation gives rise to three different cases: 1. ITP = I,": at which P = 0 and eq 13 reduces into C,O = .C : This is the special case which was dealt with by Tyson et al. (3-6). 2. ITP < I,', then IP < 0 and eq 13 gives C,O > C,O. 3. ITP > I,",then IP > 0 and eq 13 gives C,O < C,O. To calculate the analyte concentration, only the two transients, P" and P,from the steady-state emission intensity signal need be measured. Implicit in the above treatment is that the emission intensities I,", IXm, and ITp are net values corrected for the background current, Ib. However as indicated in eq 13 the results obtained by the standard addition method are independent of the background signal, the flow rate, or the volume of injection. This does not imply that for various experimental reasons optimum conditions cannot be influenced by the above parameters. When actual samples are involved, this is only true when P" and P are free from spectral and chemical interferences. Inverse dispersion, Din",can be easily computed from the ratio
Dinv= I," / (I,"
- P)
(15)
In the derivation of eq 13, the constant, k , was assumed to be the same for both the steady state and the transients. If this condition does not prevail, a correction factor, f, must be introduced f = (1- d ) / [ ( k ' / k ' ' ) - d ]
(16)
in which k'and k"are the constants for the steady state and the transients, respectively. Equation 13 can be rewritten in a more general form taking into consideration discrepencies between the constants
C,O = (1 - d ) P C , O / ( P + P)[(k'/k'?- d ]
(17)
Equation 17 would be employed whenever the results of eq 13 are reproducible but are either high or low, or for empirical corrections with some actual samples.
EXPERIMENTAL SECTION Apparatus. The commercial FIA instrument utilized (Fiatron Systems, Model SHS-200) included an all-Teflon, dual-channel sample injector consisting of electronically driven, microminiature solenoid values. Two four-way valves are microprocessor controlled, which provides various solution handling modes. A multiroller, variable speed pump is situated before the valves and can be operated in continuous-flowor in stop-flow modes. For the present work, a continuous-flowmode was operated mainly according to the following cycle: (1)The analyte stream is pumped into the nebulizer through the carrier tube, and simultaneously the sample tube is primed either with distilled water or with a standard solution. The excess is led to waste. (2) A preprogrammed volume of either the distilled water or the standard solution is injected, and simultaneously the analyte is diverted to waste. (3) Step (1) is repeated.
ANALYTICAL CHEMISTRY, VOL. 56, ~~
Table I ICP-AES Operating Conditions for Si at 251.61 nm power, kW outer gas flow, L/min nebulizer gas flow, L/min intermediate gas flow, L/min observation height, mm slit height, mm monochromator slit widths, mm
0.51 16.00 0.55 0.17 16 5 0.05
Each cycle can be repeated at will by preprogramming the microprocessor. In another mode which becomes useful for the preliminary assessment of the optimum volumes to be used for injection, three different volumes can be successivelyinjected in step (2). Clearly a complete FI determination by the standard addition method requires two of the above cycles alternating between distilled water and a standard solution injection. Linking an automatic sampler with the FIA system enables preprogramming the whole arrangementto perform both cycles automatically. Utilizing such a setup should enable each determination to be carried out within 160-200 s. Two sizes of manifold tubing (Fisherbrand Accu-Rated PVC) were used for the pump with flow rates of 1.06 mL/min and 2.02 mL/min at 90% motor speed. However, the same size tubing served for both the analyte and the standard solution stream in each experiment. The injection time (or the injected volume) was varied to give dispersion,Dhv, from 1.3 to 4.8, which was estimated from the negative transients resulting from distilled water injections (see Theory section). Instrumentation for ICP-AES was described in a previous work (IO). In addition to the 3abington nebulizer, a homemade concentric-impact nebulizer was used. A BASIC program was employed to smooth intensity measurements with time using a Keithley 411 Picoammeter interfaced with Digital PDP 11/23 computer. Intensity-time curves were plotted with a HewlettPackard 7221B plotter. Operating conditions were determined for silicon by simplex optimization (11) and are listed in Table I. Some minor adjustments of the power and the nebulizer gas flow rate were often necessary to reduce the noise level at the steady-state signal. Certified reagents (Fisher Scientific) were used. A standard stock solution of 2000 wg of Si/mL was prepared by dissolving 10.1171 g of sodium metasilicate, Na2Si03.9H20,in distilled water to a final volume of 500 mL. Diluted standard solutions, 0.4-400 Fg of Si/mL, were made by dilution with distilled water. The effect of the viscosity on the results obtained by the FIA standard addition method was examined for the determination of Si in concentrated (85%)phosphoric acid (Fisher A-242, ACS certified). Three solutions were prepared, ca. 57.8 g/L, 100 g/L, Table 11. Determination of Si in Aqueous Standard Solutions expt C', taken, C,O added, no. pg/mL Si ,ug/mL Si DhV 1 2 3 4 5 6 7 8 9
a
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1191
and 289 g/L with kinematic viscosities of 1.105, 1.187, and 1.707 cS, respectively,by dissolving the weighed acid sample in distilled water, cooling to ambient temperature, and making up to volume in a volumetric flask with distilled water.
RESULTS AND DISCUSSION A preliminary day-to-day experiment was performed to examine the validity of eq 13 of the calculation of the analyte concentration by the standard addition method. Aqueous standard solutions of Si, 0.4 pg/mL to 400 pg/mL, were studied, and the results obtained are given in Table 11. No attempt was made to determine lower or higher concentrations. The recoveries ranged between 96.90% and 104.6% with an average of 99.7%. Usually the results of Table I1 were satisfactory yielding a linear regression between taken and found for 2 to 400 pg of Si/mL with a slope and relative standard deviation of the slope of 0.995 and 0.48%. The intercept was nil (-0.041). These data indicate that the model presented and the relationships developed for the FIA standard addition method are valid. Speculations can be made based on the values of the terms of eq 13 and on signal-to-noise ratios. As a result, the choice of experimental parameters must be directed to increase P/I," and IP/IxOratios to enable the measurement of P" and IP with high accuracy. This dictates the choice of relatively high volume injections (high Dinv). For IP/Ixo to be high, proper values of C,"/C," must be selected. For IP < 0 the ratio of concentrations must be kept low and for IP > 0, high. However, choosing IP < 0 is disadvantageous, since the sum of P" and IP is small, making the ratio P / ( P+ IP) sensitive to small errors in either P or IP. The error in experiment 9 was high because of the choice of low Dinv,which equaled 1.3, corresponding to P/IxO = 0.23 and a measured IP/Ixo = 0.21, which are too low to enable accurate determinations. There seems to be a limitation to the increase of either Dhvand/or CC /:,: for using Dinv= 4.8 (experiment 18) and CC /: : = 4 (experiment 3) yielded errors between 3.0% and 3.5%. Experiments 4 and 5 were performed with different nebulizers, yielding different values of Ixo,P,and IP, but the results of using eq 13 were satisfactory in both cases. Experiment 6 was performed at a ratio of CC /: : = 0.5, hence the resulting negative IP. To supplement the results of Table 11,the determination of 20 pg of Si/mL standard solution was carried out with various C:/C: ratios a t Dinv= 4 and reported in Table 111. The highest deviation was obtained for C,O/C,O = 0.25, while the most adequate result was for C,O/C,O = 2.0, which seems
I m ,nA
0.400 3.0 0.800 0.0835 2.000 3.3 4.000 0.4830 2.000 3.3 8.000 0.4830 10.00 3.1 25.00 2.130 10.00 3.2 25.00 2.820 20.00 4.1 10.00 4.988 20.00 4.1 40.00 4.988 40.00 3.0 80.00 7.150 100.0 1.3 200.0 11.40 10 100.0 1.5 200.0 15.6 11 100.0 1.8 200.0 15.3 12 100.0 1.9 200.0 12.61 13 100.0 2.0 200.0 16.60 14 100.0 2.1 200.0 20.23 15 100.0 2.2 200.0 26.00 16 200.0 2.1 400.0 50.00 17 200.0 2.3 400.0 53.60 18 200.0 4.8 400.0 58.30 19 400.0 2.0 400.0 87.30 No transient was observed. The accuracy of measurement in such cases is low.
I p , nA 0.0870 0.4830 1.388 3.165 4.130 -2.413 5.103 7.300 10.40 15.65 16.00 13.10 16.50 20.20 26.00 51.00 54.20 62.00 0.oa
CXofound, pg/mL Si 0.392 2.000 2.065 10.06 10.14 19.37 19.77 39.56 104.6 99.84 97.76 98.09 100.3 100.1 100.0 198.0 198.9 193.8 400.0
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Anal. Chem. 1984, 56, 1192-1194
Table 111. Determination of 20 pg of Si/mL in Aqueous Standard Solution Addition of Various Concentrations of Si Standard Solutionsa C,O added, pg/mL IP, nA CXofound, fig/mL 5.00 -2.45 f 0.03 18.9 10.0 -1.63 i 0.02 19.6 20.0 -0.1 b 20.6 40.0 3.34 t 0.06 20.0 a Transient intensities are averages of three measurements at Din” = 4.0 and Im = 3.33 i 0.01 nA. This measurement is an approximate value. Table IV. Determination of Si in 85% Phosphoric Acid Sample concn of sample concn of Si in initial concn of in solution, g/L solution, pg/mL Si, in sample, pg/g 57.802 0.341 5.90 * 0.23 100.01 0.565 5.65 f 0.20 289.01 1.350 4.70 z 0.12 to support the above speculations for achieving higher accuracy. It may be concluded that accuracy is enhanced by the choice of high injection volumes, up to a value of Din”of ca. 4, and that a ratio C,O/C,O between 2 and 2.5 is adequate. The precision was examined by running within-day experiment of an aqueous solution containing 20 pg of Si/mL to which 40 pg of Si/mL standard solution was added at D = 3.3. The relative standard deviations for P and IP were 1.2 and 1.9% (two series, 17 measurements each). The mean values were then used to calculate the concentration of the analyte yielding results which deviated by 0.1% and -0.3% for series I and 11. As stated above the standard addition method is not expected to compensate spectral and chemical interferences, such as those that may be exhibited by practical samples. This work mainly examined the validity of eq 13 with standard solutions. However, the influence of viscosity on the results obtained by the present method was also investigated. The
results for the determination of Si a t various dilutions of concentrated phosphoric acid (85%) are summarized in Table IV. The mean values obtained decrease with increasing sample viscosity. This phenomenon reflects the change in nebulization efficiency with sample viscosity which was not compensated for using standard addition method but should be minimized if an internal reference were measured simultaneously with the silicon.
ACKNOWLEDGMENT We appreciate the loan of the Fiatron instrument from Baird Corp., Spectrochemical Products Division, Bedford, MA. Registry No. Si, 7440-21-3;phosphoric acid, 7664-38-2.
LITERATURE CITED (1) Ruzicka, J.; Hansen, E. H. “Flow Injection Analysis”; Wiiey: New York, 1981; pp 146-176, pp 15-17. (2) Betteridge, D. Anal. Chem. 1978, 50, 832A. (3) Tyson, J. F.; Idris, A. B. Analyst (London) 1981, 106, 1125. (4) Tyson, J. F. Anal. R o c . 1981, 78, 542. (5) Tyson, J. F.; Appleton, J. M. H.; Idris, A. B. Analyst (London) 1983, 108, 153. (6) Tyson, J. F.; Appleton, J. M. H.; Idris, A. B. Anal. Chim. Acta 1983, 145, 159. (7) Greenfield, S. Spectrochhn. Acta, Parts 1983, 388, 93. (8) Ruzlcka, J.; Hansen, E. H. Anal. Chlm. Acta 1978, 99, 37. (9) Vandersllce, J.; Stewart, K. K.; Rosenfeld, A. G. Talanta 1981, 28, 11. (IO) Mahanti, H. S.;Barnes, R. M. Anal. Chem. 1983, 55, 405. (11) Cave, M.; Barnes, R. M.; Denzer, P. 1982 Winter Conference on Phsma Spectroscopy, Orlando; ICP Information Newsletter: Amherst, MA, 1982; Abstract 23.
‘
On leave from I M I Institute for Research and Development, Inc., Haifa 31002, Israel.
Yecheskel Israel’ Ramon M. Barnes* Department of Chemistry GRC Towers University of Massachusetts Amherst, Massachusetts 01003-0035
RECEIVED for review October 14, 1983. Accepted February 15, 1984. Supported in part by Department of Energy Contract DE-AC02-77EV-0432.
Band Broadening in Solid-Phase Derivatization Reactions for Irreversible First-Order Reactions Sir: The use of solid-phase reactors in flow-through analytical systems has been recently discussed (1). In liquid chromatography, this type of reactor is used to improve the sensitivity and/or selectivity of detection systems. Due to the low concentration of analytes detected, many derivatization reactions obey first-order kinetics with rate constant k,
For a skewed chromatographic peak, an exponentially modified Gaussian (EMG) defined mathematically as a convolution of Gaussian with exponential decay represents a suitable model (4-7). The response curve is given by eq 2
k,
A-D
If a narrow pulse of analyte, A, is introduced into the reactor, separation of derivative, D, from the pulse of A may occur. Therefore,the solid-phase reactor behaves as a so-called chromatographic reactor (2). The resulting peak of D is skewed and fused with the peak of A. This phenomenon, which restricts the use of solid-phase reactor in HPLC and FIA, has been called “reaction band broadening” and treated on the basis of a simple mathematical model (I). Usual band broadening mechanisms are not taken into account in this model derived for first-order kinetics. 0003-2700/84/0356-1192$01.50/0
where the essential parameters are as follows: A , peak area; 7,time constant of the exponential decay; t ~center , of the gravity of Gaussian; and u, standard deviation of Gaussian. The quantity t ’ is a dummy variable of integration. Also the reaction chromatogram of a first-order irreversible reaction is supposed to be a result of two independent processes: Gaussian band broadening and exponential decay. This fact led to the idea of treating the reaction chromatogiam as an EMG. The aim of this paper is to supplement our previous paper (1)and demonstrate that a reaction chromatogram of a.fast 0 1984 Amerlcan Chemical Soclety
