Articles Anal. Chem. 1994, 66, 1378-1384
Quantitative Determination of Sulfur-Oxygen Anion Concentrations in Aqueous Solution: Multicomponent Analysis of Attenuated Total Reflectance Infrared Spectra David A. Holman, Alan W. Thompson, and Dennis W. Bennett' Department of Chemistry, University of WisconsivMilwaukee, Milwaukee, Wisconsin 5320 1 James D. Otvos Department of Biochemistry, North Carolina State University, Raleigh, North Carolina 27695
The multicomponent analysis of FT-IR attenuatedtotal internal reflectancespectra of mixturesof sulfur-oxygen anionsprovides an accurate noninvasive method for their quantitation. The use of spectral artifact basis functions obtained from the singular value decomposition of a difference spectra matrix results in a marked increase in accuracy. Further improvements in accuracy are attained with the use of multicomponent spectra as basis functions. The analysis of a series of solutions of sulfur-oxygen anions ranging in concentrationfrom 0.0005 to 0.0323 M resulted in a root-mean-squareerror of 0.0002 M. In an in situ experiment in which the anaerobic decomposition of aqueous sodium dithionite was observed in ca. 1.5-min intervals over a 30-min period, the method was shown to account continuously for total sulfur and average oxidation state while simultaneously measuring the concentrations of seven components at each interval. Despite the ubiquitous nature of compounds containing oxygen bonded to sulfur, the SO, functional group has been especially resistive to quantitative spectroscopic analysis. The electronic spectra of sulfur-oxygen compounds have been used quantitatively,' but the broad, nondescript nature of the spectra, as well as the tendency of the bands to undergo spectral shifts, has limited their effectiveness in quantitative analysis. In complex mixtures of ephemeral sulfur-oxygen anions, such as Wackenroder's solution,2 the lack of other chromophores presents an especially challenging analytical problem. Titrimetric3 and electrochemical4 techniques have provided ( 1 ) (a) Dixon, M. Biochim. Biophys. Acta 1971,226,241-258. (b) Connick. R. E.; Tam, T. M.; von Deuster, E. Inorg. Ckem. 1982, 21, 103-107. (c) Badri. B. Analysr 1988, 118. 351-353. (2) Nickless. G. The Lower Oxyacids of Sulfur. In InorganicSulfur Chemistry; Nickless, G., Ed.; Elsevier: Amsterdam, 1968; p 509. (3) (a) Kilroy, W. P. J . Inorg. Nucl. Chem. 1980, 42, 1071-1073. (b) Rinker, R. G.; Lynn, S.; Mason, D. M.; Corcoran, W. H. lnd. Eng. Chem. Fundam. 1965,4,282-288. (c) Spencer, M. S. Trans. Faraday Soc. 1967,63,25102515. (d) Kilroy, W. P. Talanfa 1983, 30, 419-422. (e) Danehy, J . P.; Zubritsky, C. W. Anal. Chem. 1974,46, 391-395. (f)Lister, M. W . ; Garvie, R . C . Can J . Chem. 1959,37.1567-1574. (g) Jouan,R. J . Chim. Pkys. 1959, 56, 327-357. (4) (a) Cermak, V.; Smuteck, M. Collect. Czech. Chem. Commun. 1975, 40, 3241-3264. (b) Benayada, A.; Bessiere, J. Electrochim. Acra 1985,30, 593596. (c) Reynolds, W. L.; Yuan, Y . Polyhedron 1986, 5 , 1467-1473.
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a useful alternative, but inherent problems in sample handling have often resulted in ambiguous results. 4 graphic case in point is provided by published attempts to establish a rate equation for the decomposition of the dithionite anion in acidic aqueous solution. Depending upon the method of analysis, reaction orders of 1 , 1.5, 2, and "complex" for d [S20d2-] /dt have all been reported,3a along with subsequent proposed mechanisms which differ markedly from one another. Sodium dithionite is a powerful reductant and must be handled in a strictly anaerobic environment. Analytical procedures which require removal or transfer of its solutions are therefore susceptible to serious error, underscoring the need for an in situ analytical technique. Sulfur+xygen compounds have relatively intense vso stretching modes, readily observed in the 750-1 350-cm-' region of the infrared spectrum.j Conventional infrared spectroscopy does not lend itself to quantitative analysis using these bands in aqueous environments, due largely to the dissolution of cell materials and the intense absorption of the solvent in the same region of the spectrum. For such systems, attenuated total internal reflectance spectroscopy (ATR) has resulted in a revolutionary approach to the measurement of infrared spectra. I n ATR the source radiation interacts with thesample mainly at the sample/crystal interface, resulting in a very short and reproducible effective path length.6 It follows that FT-IR/ ATR spectroscopy is an ideal candidate for the quantitative determination of multicomponent mixtures of sulfur4xygen anions. The work reported here was an essential first step in kinetic studies (in progress) designed to determine the mechanism for the decomposition of aqueous dithionite. EXPERIMENTAL SECTION Materials. The following ACS certified reagents were used: Na&Oj(s), Na&04(s), and NaN03(s) (Fischer, Fair ( 5 ) Nakamoto, K. Infrared and Raman Spectra of Inorganic and Coordination Compounds, 4th ed.; Wiley-Interscience: New York, 1986; p 169. (6) (a) Afran,A.Am.Lab. (Fairfield, Conn.) 1993,25,(Feb),40MMM4OQQQ. (b) Marley, N . A , ; Gaffney. J. S.; Cunningham, M. M. Spectroscopy 1992, 7 ( 2 ) . 44-53.
0003-2700/94/0366- 1378$04.50/0
0 1994 American Chemical Society
Lawn, NJ), Na2SzOySHzO (Columbus Chemical Industries, Columbus, WI), NazS04(s) (EM Science, Gibbstown, NJ), and NazSO3(s) (Mallinckrodt, St. Louis, MO). The HSOssolutions were prepared from NazSzOs(s), the anhydride of NaHSOs(aq). Apparatus. All spectra used in this study are aqueous FTIR/ATR spectra obtained on a Perkin Elmer 1800 infrared spectrometer using a Spectra Tech, liquid N~-cooledHgCdTe detector. A Spectra Tech “microcircle” flow-through attenuated total reflectance cell (Part No. 0005-1 32) incorporating a ZnSe crystal was used in the cross-validative study. The flow-through cell, originally designed for HPLC, was bored out slightly to allow for sample aspiration with a syringe. Samples were drawn into the cell, by use of a 60-mL syringe, through Tygon peristaltic pump tubing having l/16-in. internal diameter. The sample compartment remained closed at all times to minimize water vapor peaks in the spectra. A waterheated flow-through cell constructed of glass and silicone glue was constructed for kinetic studies at elevated temperatures. Software was written to perform Q-matrix LLS, partial least squares (PLS), and two variations of PRESS. The PLS algorithm used is given by Geladi.7 The Q-matrix LLS and PLS programs were tested by analyzing calibration spectra. Q-Matrix LLS produced virtually identical results by both Gauss-Jordan and SVD methods only when performed in double precision. Procedures. All solutions were made as dilutions of five stock solutions. Volumetric errors can be expected to be 0.5% or less. All solutions were made and sampled under nitrogen purging. A 60-mL plastic syringe was connected to the circle cell in the sample compartment via Tygon tubing. Samples ( 5 mL) were drawn into the cell and were aspirated continuously as they were scanned. All analyte spectra were recorded as differences from the pure water absorbance spectrum. Water spectra were obtained frequently to minimize baseline drift. Spectra were collected in the single-beam mode between 820 and 1500 cm-l in 1-cm-l increments at a resolution of 2 cm-l. No apodization was used. Absorbance was calculated as the root mean square of the sine and cosine contributions to the spectrum at a given frequency. This treatment is applied after the Fourier transformation. Baseline Characterization. A basis set describing baseline variations was constructed from 118 scans collected over an 8-month period representing pure baseline variation in the absence of analyte peaks. Half of these were obtained as differences between a water absorbance spectrum and another water spectrum taken minutes later. The remaining half of the baseline variation spectra were obtained as solution/ solution difference spectra. Some of the solution/solution spectra were collected after the solution had remained in the cell for several minutes. Other solution/solution spectra were collected quickly after pure water had been present. These were intended to measure broad baseline features that grow in when a salt solution is introduced into the cell after pure water. NaNO3 produces varying broad features similar to those produced by a NaCl solution. The spectral features present in the 118 baseline artifact spectra were extracted (7) Geladi, P.; Kowalski, B. Anal. Chim. Acta 1986, 185, 1-17.
from the noise by use of singular value decomposition. Of the resulting 118 singular value decomposition vectors, the first 11 contained spectral features that were significant compared to the noise. They were retained as a basis set capable of describing the baseline variations in the 118 baseline artifact spectra. Two important baseline variations known to be present in the data are “tilting” and “raising and lowering”of the spectra. It is not necessary to measure these variations experimentally because they can be represented ideally by a constant and a sloping line.8 The variations were removed from all spectra by including two lines as additional basis functions in the linear least-squares procedure described below. Singular value decomposition of the artifact spectra was performed after removal of constant- and sloping-line variations. This was accomplished by fitting a sloping line to each spectrum and then subtracting the line from the spectrum. The water vapor spectrum, which differs markedly from the spectrum of liquid water, was also included as an additional basis spectrum.
THEORETICAL SECTION The linear least-squares procedure used is described by McClure, who called it the Q-matrix method to distinguish it from the K-matrix method.9 We have extended this method to accommodate variations in the baseline by employing singular value decomposition for noise filtering and data reduction, an approach which is commonly used in principle component regression.1° The spectrum to be analyzed, hk, is fit as a linear combination of calibration standard spectra and baseline variation functions, both of which are the column vectors of matrix A: The linear least-squares solution for q is q = (ATA)-’ATaok The coefficient vector, q, is transformed into the predicted concentration vector, ccalc:
=cq The transformation matrix, C, is the matrix of experimentally determined calibration standard concentrations. If p is the number of discrete frequencies where an absorbance is measured, then hb is p X I, A is p X m,q is m X I, C is n X m, and ccalcis n X I, where m is the number of calibration spectra plus baseline variation functions and n is the number of chemical components. The baseline variation functions are obtained by singular value decomposition (SVD) of a matrix of 118 baseline variation spectra. The baseline variation spectra have noisy broad features and no analyte peaks. SVD serves to extract these spectral features from the noise in the form of a small number of low-noise principle vectors. These extracted baseline variation vectors are then included in the basis set. They are treated as calibration standard spectra in matrix A corresponding to zero molar concentrations in transformation matrix C. C,lC
(8) Tyson, L. L.; Ling, Y.;Msnn, C . K.Appl. Spectrosc. 1984, 38, 663668. (9) Osten, D.W.;Kowalski,B. R.In ComputerizedQuantitativeInfraredAnalysls; McClure,G. L., Ed.;AmericanSocictyforTcstingandMaterials:Philadelphia. 1987; p 6. (10) Beebe, K..R.; Kowalski, B. R. Anal. Chem. 1987,59, 1007A-1017A.
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The estimated standard error, cri, in the predicted concentration, talc i, from vector ccalcis given by"
where x2 is thesum of squared residuals between thecalculated and observed spectra, acalcand Bobs;p and m are the number of observed frequencies and calibration standards, respectively; ci, (from matrix C) is the concentration of species i corresponding to calibration spectrumj; and Ujk is an element of the variance-covariance matrix, V,
v = (A'A)-' Selection of Least-SquaresMethods. Calibrated methods that employ two least-squares regressions are commonly employed in multivariate analysis.12 An optional calibration regression can be used to increase the precision of the calibration model. However, some calibration methods should not be used if idealized single-component spectra cannot model the data. In addition, if unknown spectral features arise, the inevitable error in an optional regression may compound the overall error. The simplest calibrated method is the K-matrix method. The K-matrix method assumes that baseline variations can be separated from analyte spectra, and that the spectra of n-component mixtures are simple linear combinations of n ideal single-component spectra. Application of the K-matrix method involves solving for a basis set, K, whose column vectors are idealized single-component spectra, A=KC where A and C are the matrices of experimental spectra and experimental concentrations defined previously. Because of experimental error, A differs from KC. K is the linear regression of the overdetermined number of experimental spectra onto n single-component spectra, where n is the number of observed chemical components:1°
K = AC'r(CCT)-l The n column vectors of K then become an idealized basis set used in place of the original basis set A. The Q-matrix method employed in the data analysis described here simply omits the calibration step and uses the original data, A, as the basis set for fitting the prediction spectra. The K-matrix method cannot be used in the analysis of the data in this study since a valid treatment demands a basis set of more vectors than the number of chemical components, n, for two reasons: (1) Baseline drift cannot be eliminated from the FT-IR/ATR spectra of aqueous solutions. Therefore, baseline drift is necessarily included in the model. (2) There are slight inconsistencies in the band shapes of individual components due to interactions between components. It follows that idealized single-component spectra cannot model changes due to these interactions; Le., single-component basis spectra do not span the multicomponent space. The same comments apply to principle component regression, which differs from the K-matrix method in that SVD is ( I I ) Gans, P. Data Fitting in the Chemcial Sciences; John Wiley & Sons: New York, 1992; Chapter 3. (12) Nyden, M.; Forney, G.; Krishnan, C. Appl Spectrosc. 1988, 42, 588-594.
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used for noise filtering.1° SVD has been similarly incorporated here to reduce a large baseline variation data matrix into 11 low-noise basis spectra. The method of partial least squares is a more flexible and popular modification of principle component regression.' If there are more spectroscopic variations than chemical components, then PLS will produce an extended basis set having as many vectors as needed to account for all significant spectroscopic data variations. However, a comparative analysis between PLS and the more straightforward method described here (which does not require a calibration regression) produced virtually identical results. Data Reduction of the 118 Baseline Variation Spectra. As mentioned previously, the use of SVD to filter noise is a method employed in principle component regression.1° In a similar manner, SVD can provide a noise-filtered basis set to model baseline variations in a Q-matrix analysis as follows: Let B be a matrix of mt, baseline variation spectra. Singular value d e c o m p ~ s i t i o n reduces '~~ B to a product of two orthogonal matrices, U and W, and a diagonal matrix, S: B = USW' where B is p X mb and S and W are mb X mb. This is accomplished by employing Householder reflections followed by the QR a1g0rithm.I~~Matrix W contains concentration information. It is not used since baseline variations represent zero molar concentrations. The first few column vectors of U represent the majority of recurring spectral features in matrix B while the remaining vectors of U represent noise and redundant spectral features. Use of SVD as a noise filter requires a judicious selection of the number of leading SVD vectors to retain. Determining the optimum number to retain is equivalent to determining the rank of an experimental data matrix, excluding noise.14 To find this optimum number, cross-validative least-squares analyses were performed on mixtures MI1-MI6 (Tables 1 and 2), by varying the number of SVD vectors retained in the basis set. For each set of six cross-validative analyses for which a number, d, of SVD vectors were retained in the basis set, there are 30 predicted concentrations which are used to calculate the PREdiction Error Sum of Squares (PRESS).' Thus we have PRESS(d) = (nd)-'
F,r(&j d
n
j
i
-
where d&j is the predicted concentration using d SVD vectors in the basis set and cu is the actual concentration. As d is increased, the value of PRESS(d) reaches a minimum and then increases slowly as SVD vectors consisting mostly of noise and redundant spectral variations are added to the basis set. Figure 1 shows PRESS(d) for the baselinevariation data in this study. An estimate of the rank in the range 10-12 is obtained readily from this analysis. Originally, the same estimate was obtained simply by inspecting a log plot of the singular values, and by a different (13) (a) Hager, W. W. Applied Numerical Linear Algebra; Prentice Hall: EnglewdCliffs,NJ, 1988;p294. (b)Pre-ss,W.H.; Flannery,B.P.;Teukolsky, S. A.; Vetterling, W. T.Numerical Recipes; Cambridge University Press: New York, 1989; p 60. (14) Jolliffe. I. T. Principle Component Analysis; Springer-Verlag: New York, 1986: Chapter 8.
Tabk 1. Exporhontal and Calculated Concentrationr of 8unur4xygen Anion Solutknr MIl-MI6’ errors ( X W M) concn (x102M)
Exper
Calcl
Calcz
3.229 2.571 2.566 2.620 0.973
3.615(9) 2.545(7) 2.495(5) 2.646(5) 1.084(8)
3.33(1) 2.526(8) 2.603(6) 2.589(6) 1.099(6)
3.23(1) 38.6 10.6 0.2 2.524(6) 2.6 -4.5 -4.7 2.541(6) -7.0 3.8 -2.4 2.593(5) 2.6 -3.1 -2.7 0.988(6) 11.1 12.6 1.5
0.065 2.571 2.566 0.105 0.973
0.082(8) 2.455(7) 2.533(4) 0.106(5) 0.967(7)
0.051(5) 2.590(4) 2.518(2) 0.127(3) 0.916(3)
0.043(6) 2.570(3) 2.551(3) 0.109(3) 0.946(3)
0.807 0.643 0.641 0.656 0.243
0.716(4) 0.597(3) 0.662(2) 0.644(2) 0.238(4)
0.836(3) 0.644(2) 0.649(2) 0.646(2) 0.241(2)
0.827(4) 9.2 2.9 2.0 0.642(2) 4.6 0.1 -0.1 0.663(2) 2.0 0.7 2.2 0.649(2) -1.2 -0.9 -0.6 0.254(2) -0.5 -0.3 1.1
0.161 2.699 0.128 0.131 0.049
0.152(3) 2.652(2) 0.123(1) 0.171(2) 0.045(3)
0.161(4) 2.659(2) 0.127(2) 0.135(2) 0.067(2)
0.150(5) 1.0 0.0 -1.2 2.674(3) 4.1 -4.0 -2.5 0.129(3) -0.5 -0.1 0.0 0.146(2) 4.0 0.4 1.5 0.051(3) -0.4 1.8 0.3
0.161 0.129 0.128 0.131 0.049
0.126(2) 0.139(1) 0.1413(9) 0.152(1) 0.040(2)
0.152(2) 0.151(1) 0.130(1) 0.143(1) 0.045(2)
0.126(3) -3.6 -1.0 -3.5 0.135(2) 1.1 2.2 0.7 0.129(2) 1.3 0.2 0.1 0.138(2) 2.1 1.2 0.7 0.037(2) -0.9 -0.4 -1.2
0.161 0.129 1.155 2.751 0.049
0.49 1(1) 0.240(7) 1.189(5) 2.902(5)
0.211(1) 0.185(8) 1.2446) 2.790(6) 0.090(8) 0.087(8)
Calca
Err1 Err2 Err3
14.6 -1.3 11.6 1.9 -3.2 -4.7 0.1 2.2 -0.6 -5.7
0.137(7) 32.9 0.129(4) 11.2 1.169(4) 3.4 2.795(3) 15.1 0.015(4) 4.1
-2.2 -0.1 -1.5 0.4 -2.7
5.0 -2.5 5.6 0.1 9.0 1.5 3.9 4.4 3.9 -3.4
Exper refers to experimental concentrations prepared gravimetrically. Calcl refers to least-squares fit with single-component basis only. Calcz refers to leastsquares fit with multiple-component basis spectra. Calc3 refers to least-squares fit with multicomponent basis spectra and baseline artifact functions. Errl, Errz, and Err3 refer to difference between calculated and measured concentrations for corresponding fib, Calcl, Calcz, and Calca. Estimated standard deviations (in parentheses) refer to the last significant figure. a
T a m 2. Composition of Standards and Tost Sdutlons
concn (M) . . SOln
[HSOs-I
[SzOa~I [ S O r ~ I [SOs”I
[NOa-l
MI1 MI2 MI3 MI4 MI5 MI6 SN BIS FATE FITE NIT THIO
0.032 29 O.Oo0 65 0.008 07 0.001 61 0.001 61 0.001 61 0 0.016 14 0 0.016 14 0 0
0.025 71 0.025 71 0.00643 0.026 70 0.001 29 0.001 29 0 0 0 0 0 0.025 71
0.025 66 0.025 66 0.00641 0.001 28 0.001 28 0.011 55 0.025 66 0 0.025 66 0 0 0
0.026 20 0.001 05 0.006 55 0.001 31 0.001 31 0.027 51 0 0
0.00973
0.026 20 0 0
0 0.048 67 0
0.009 73 0.002 43 o.Oo0 49 o.Oo0 49 o.Oo0 49 0.024 33 0
”PRESS” analysis employing only the baselinevariation data.I4 The PRESS statistic described above is more standard.
RESULTS AND DISCUSSION ATR Spectroscopyof Sulfur-OxygenAnions. As indicated in the introduction, sulfur-oxygen anions are extremely difficult to analyze with conventionalspectroscopictechniques.
0
-x CI
-
Ln
Ln 2.40 W
R
a
2.20
-
1
2
3
4
5
6
7
E
9 1 0 1 1 1 2 1 3
number o f r e t a i n e d SVD v e c t o r s
Flgure 1. PRESS analysis of baseline varlatlan data.
700
EO0
900
1000
1100
1200
1300
1400
1500
1
wavenumbers
Flgure 2. FT-IR/ATR spectra of analytes in mixtures MI1-MIB.
While sulfur-oxygen compounds often absorb in the ultraviolet region of the electronic spectrum, the bands are usually broad and ill-defined. Raman spectroscopy has been used as an analytical tool for aqueous solutions of sulfur-oxygen anions, but it is most sensitive to vibrations involved in sulfur-sulfur interaction^.^^ Even the strongest Raman scatters are too weak to allow for rapid data collection.16 On the other hand, sulfur-oxygen stretching modes have large infrared extinction coefficients in the 750-1 350-cm-l range. The spectra of the analytes used in the cross-validative study described below are shown in Figure 2. Attenuated total reflectance infrared spectroscopy of aqueous solutions is usable in the 750-1 500- and 1775-3700-cm-l regions of the spectrum. The highly reproducible path length allows the water spectrum to be subtracted out, and accurate concentrations to be determined from measured absorbances without the need for internal standardization. Characterization of Systematic Baseline Error. Because analytes represent only 0.5-10% of the total measured attenuated reflectance at their maximum absorbing frequencies, spectral artifacts with features appearing to arise from the strong water background are always present. In addition, the internal reflectance phenomenon occurs at the solution/ crystal interface in the ATR cell, and subtle changes in temperature, hydrostatic pressure, organization of solvent molecules at the interface, etc., can all contribute to systematic fluctuations in the spectral baseline. (15) Meyer, B.; Ospina, M.; Peter, L. B. A d . Chim. Acta 1980, 117, 301-311. (16) Miliccv, S.; Stergarsck, A. Spectrochim. Acto 1989, ISA, 225-228.
AnaWcal Chemisby, Vol. 66, No. 9, May 1, 1994
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s i ?
1 ,calculated
700
BOO
900
1000
1100
1200
1300
1400
I
1500
J
1600
m
L
,
700
, 800
1
,
,
900
,
1000
,
1100
1200
1300
1400
1500
jf
0
wavenumbers
wavenumbers
Figure 3. Experimentaland calculated FT-IR/ATR spectra of analyte mixture M I 1 using multiple-component basis spectra and baseline artifact functions. The residual is plotted below the spectra.
Flgure 4. Residuals for least-squares fits of mixture MI 1: (a) singlecomponent basis, (b) multicomponent basis included, and (c) multicomponent basis and spectral artifact basis included.
Baseline drift cannot be removed from the calibration model. This problem was resolved by producing a basis set for baseline variations. Baseline variation functions actually constitute the majority of the components in the basis set employed in this study, introduced as zero molar calibration standard spectra. Fortunately, baseline drift can be modeled as a linear combination of a manageable number of factors, making it unnecessary to model baseline drift as a function of time. Cross-ValidativeTest of the Method. In order to evaluate this method, we analyzed six mixtures each containing five components. The compositions of the solutions used as test solutions and standards are listed in Table 2. For each analysis, one of the mixtures, MI1-MI6, was treated as a test solution, and the remaining solutions were used as calibration standards. For each analysis, the basis set for fitting the test solution spectrum consisted principally of baseline functions in addition to the spectra of the 11 calibration standards. The baseline functions consisted of a sloping line, a horizontal line, a water vapor spectrum, and 11 principle vectors resulting from SVD of 118 baseline variation spectra. The results using the full basis set just described are listed in Table 1 under columns Calc3 and Err3. Figure 3 illustrates the calculated and experimental spectra for mixture MI1 using the full basis set. The columns Calcl and Calc2 and their corresponding error columns illustrate the significance of certain groups of calibration standards by omitting them from the basis set. The group of mixtures, MII-MI6 and SN, represent component interactions. The group of 11 SVD vectors represent baseline variations. Calcl results when both of these groups, the mixtures and the SVD baseline variations, are omitted. Calc2 results when only the SVD baseline variations are omitted. In going from Calcl to Calc2 to Calc3 there is approximately a 2-fold improvement in accuracy with each step. The overall root-mean-square errors for Errl, Err2, and Err3 are 0.0009, 0.0004, and 0.0002 M, respectively. Correlation coefficients are given in Table 3. Spectroscopic residuals for Calcl, Calc2, and Calc3 (mixture MII) are shown in Figure 4. Note the remaining spectral features present in the Calcl residual (Figure 4a) and the substantial improvement when the complete basis set was incorporated in Calc3 (Figure 4c). 1382
AnalyficalChemlstty, Vol. 66,No. 9, May 1, 1994
Table 3. Correlatlon Coefflclents of Least-Squares Flts to Spectra of Mixtures of Sulfur-Oxygen Anlons Calcl calcz Calca
MI1 MI2 MI3 MI4 MI5 MI6 av
0.999 83 0.999 84 0.999 36 0.999 90 0.997 67 0.999 14 0.999 29
0.999 95 0.999 99 0.999 94 0.999 97 0.999 18 0.999 72 0.999 79
0.999 98 0.999 99 0.999 97 0.999 98 0.999 38 0.999 96 0.999 88
Some of the improvement in going from Calcl to Calc2 is due to the representation of baseline variations implicit in the mixture spectra and not solely due to the representation of component interactions. The more interesting experimental result is the 2-fold improvement in accuracy in going from Calc2 to Calc3. This improvement is due solely to the representation of pure baseline variations collected occasionally over an 8-month period. It represents a considerable improvement over an already effective basis set. This illustrates an advantage of the method described here. Baseline variation spectra are much easier to obtain than calibration standard spectra, and their zero molar “concentrations” are known with particular accuracy. A Test Case: In Situ Observationof the Anaerobic Aqueous Decomposition of Sodium Dithionite. As mentioned in the introduction, we are interested in the aqueous decomposition of the dithionite ion under anaerobic conditions. In particular, we wish to simultaneously measure the concentrations of reactants and products versus time. This turns out to be a rigorous test of the analytical technique described here, since the reactions are run in a closed system in which the total sulfur concentration and average oxidation state should remain constant over the course of the reaction. Since we cannot verify the results with another method, we have selected a kinetic run with two known experimental constants in addition to total sulfur and average oxidation state. Figure 5 illustrates the decomposition of sodium dithionite is an anaerobic aqueous environment at 55 O C . Spectra were collected at ca. 1.5-min intervals; each spectrum was analyzed for S ~ O A ~ - , S S2052-, ~ O ~ ~S3062-,S032-, -, HS03-,and Sod2-. The analyte anions were represented by a combination of 23 pure and mixture standard solutions. In addition to the
Table 4. Standard Solution Comporltlonr and Temperaturer
concn (M)
T ("C) 58.0 68.0 67.0 67.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0 84.5 73.0 71.5 25.0 25.0 25.0 25.0 58.0 67.0 84.5 86.8
[S2042-1
[HSOd
[S2032-1
[S042-1
[s30S2-l
[SOS"]
[SZOS2-1
0 0 0
0 0 0 0 0 0 0 0 0 0.030 54 0.100 13 0.121 00 0.20375 0.91795 0.113 22 0.065 67 0.013 53 0.028 70 0.010 63 0.003 49 0.068 80 0.216 90 0.592 66
0.046 48 0.046 28 0.044 69 0.04444 0.040 06 0.050 25 0 0 0 0 0 0 0 0 0.03057 0.008 16 0.00260 0.005 00 0.001 88 0.00137 0.021 51 0.002 30 0.006 76
0 0 0 0 0 0 0.046 06 0 0 0.006 00 0.018 15 0.004 30 0.011 52 0.224 10 0.005 66 0.007 24 0.001 79 0.004 24 0.002 80 0.001 67 0.005 11 0.013 72 0.14207
0 0 0 0 0 0 0 0.053 68 0 0 0 0 0 0 0 0 0 0 0 0 O.OO0 23 0,001 50 0.018 09
0
0 0 0 0 0 0 0 0 0 0 0 0 0.001 58 0.13479 0 0 0 0 0 0 0 0.001 63 0.03998
0
0 0
0 0 0 0 0 0 0 0 0 0 0.04640 0.093 47 0.036 53 0.018 64 0.018 02 0.031 11 0
3.15
0 0 0 0 0 0 0 0.059 00 0 0 0 0.006 17 0.033 74 0.003 60 0 O.Oo0 90 0.001 61 0.001 62 0.00656 0.019 26 0.009 83 0.019 39
S3062-, to the point where it was consumed faster than it was produced. The calculated concentrations of S032-and S2OsZbecame very slightly negative at points where they should have been zero, due to a small contamination with these ions in solutions used for basis spectra in which these concentrations were assigned zero values. We elected to allow the leastsquares method to accommodate this rather than constraining these values to be positive, since this would bias the remaining concentrations. The two top lines in the figure illustrate the total sulfur concentration and average sulfur oxidation state, calculated as
-
-SI I
X
I
T
C 0 c1
U
L
U
C
U 0
U
0.9
Statal = 2[s20,2-]
0.x)
+ 2[s2032-] + 2[s,o,2-] + 3[s30,2-] + [SO:-]
0.10
0
4
E
12
16
20
24
28
32
36
minutes Figure 5. In situ multicomponent analysis of sulfur-oxygen anions involved in the anaerobic aqueous decomposition of sodium dithionite (e) versus time: (a) [HS03-], (b) [S2032-],(c) [S2042-],(d) [S~OS~-], [S042-],(f) [S20s2-],(9) [S032-],(OX ) average oxidation state, and [SIT total sulfur. Error bars at 5u above and below each data point are approximatelythe sire of the circles marking the data points and were omitted for clarity.
+ [HSOi] + [SO,"]
and (Sox) = {6[S20,"] 10[S30,"]
+ 4[S20,2-] + 8[S20s2-]+ + 4[S032-] + 4[HSO
