Anal. Chem. 1988, 60, 2055-2059 (15) Bonilha, J. B. S.; Chiericato, G.; Martins-Franchettl, S. M.; Rlbaldo, E. J.; Quina, F. H. J . fhys. Chem. 1982, 8 6 , 4941-4947. (16) Bunton, C. A.; Romsted, L. S. I n Solufbn Behavior of Surfactants; Mlttal, K. L., Fendler, E. J., Eds.; Plenum: New York, 1982; Vol. 2, pp 975-991. (17) Chaimovlch, H.; Bonilha, J. B. S.; Pollti, M. J.; Quina, F. H. J . fhys. Chem. 1979, 8 3 , 1851-1854. (18) Stadler, E.; Zanette, D.; Rezendo, M. C.; Nome, F. J . fhys. Chem. 1984, 8 8 , 1892-1896. (19) Abuln, E. B.; Llssi, E.; Araujo, P. S.; Aleixo, R. M. V.; Chalmovich, H.; Blanchi, N.; Mlola, L.; Quina, F. H. J . Colloid Interface Sci. 1983, 9 6 , 293-295. (20) AI-Lohedan, H. A. Tetrahedron 1987, 43, 345-350. (21) Veazy, R. L.; Nleman, T. A. Anal. Chem. 1979, 5 7 , 2092-2096. (22) Ehrllch, S. H.; Capone, S. M. Res. Disc/. 1982, 275, 64. (23) Llanos, P.; Zana, R. J . fhys. Chem. 1983, 8 7 , 1289-1291. (24) Hashimoto, S.; Thomas, J. K.; Evans, D. F.; Mukherjee, S.; Ninham, B. W. J . Colloid Interface Sci. 1883, 9 5 , 594-596. (25) Chaimovich, H.: Cuccovia, I.M.: Bunton. C. A.: Moffatt. J. R. J . Phvs. Chem. 1983, 8 7 , 3584-3586. Sepulveda, L.; Cortes, J. J . fhys. Chem. 1985, 8 9 , 5322-5324. Bunton, C. A.; Gan, L. H.; Moffatt, J. R.; Romsted, L. S.; Savelll, G. J . fhys. Chem. 1981, 8 5 , 4118-4125. Riley, T.; Long, F. A. J . Am. Chem. SOC. 1962, 8 4 , 522-526. Nath, N.; Singh, M. P. J . fhys. Chem. 1885, 6 9 , 2038-2043. Veazey, R . L.; Nekimken, H.; Nieman, T. A. Talenta 1984, 37. 603-606. Brady, J. E.; Evans, D. F.; Warr, G. G.; Grieser, F.; Nlnham, B. W. J . Phys. Chem. 1988, 9 0 , 1853-1859. Athanassakis, V.; Moffatt, J. R.; Bunton, C. A.; Savelli, G.; Nicoli, D. F. Chem. fhys. Lett. 1985, 715, 467-471. Paredes, S.; Trlbout, M.; Sepulveda, L. J . fhys. Chem. 1984, 8 8 , 1871-1875. Maskiewicz, R.; Sogah, D.; Bruice, T. C. J . Am. Chem. SOC. 1879, 701, 5347-5359. Veazey, R.; Nieman, T. A. J . Chromatogr. 1880, 200, 153-158. Lai, Y. Z.Carbohyd. Res. 1973, 2 8 , 154-157.
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(37) Singh, M. P.; Singh, A. K.; Tripathi, V. J . fhys. Chem. 1978, 8 2 , 1222-1 225. (38) Garrett, E. R.; Young, J. F. J . Org. Chem. 1970, 3 5 , 3502-3509. (39) Lange’s Handbook of Chemistry; Dean, J. A,, Ed.; McGraw-Hill: New York, 1973; pp 5-18, 5-27, and 5-39. (40) Handbook of Chemistry and fhysics; Weast, R. C., Ed.; CRC Press: Cleveland, OH, 1974; pp D-129, and D-130. (41) The Merck Index; Wlndholz, M., Ed.; Merck 8 Co., Inc.: Rahway, NJ, 1976; pp 111 and 549. (42) Pfeiderer, W. Justus Liebigs’ Ann. Chem. 1974, (12), 2030-2045. (43) Bunton, C. A.; Savelli, G.; Sepulveda, L. J . Org. Chem. 1978, 43, 1925-1929. (44) Seno, M.; Kousaka, K.; Klse, H. Bull. Chem. SOC. Jpn. 1879, 52, 2970-2974. (45) Ortega, F.; Rodenas, E. J . fhys. Chem. 1887, 9 1 , 837-840. (46) Nlnham, B. W.; Evans, D. F.; Wie, G. J. J . Phys. Chem. 1983, 8 7 , 5020-5025.
RECEIVED for review January 12, 1988. Accepted June 14, 1988. Support of this work by the National Science Foundation (Chemical Analysis Program, Grant CHE-8215508)and the North Carolina Board of Science and Technology (Grant 3125) is gratefully acknowledged. Thanks are also due to the Alcoa Foundation for providing an Alcoa Undergraduate Summer Research Fellowship to J.M.W. and to the R. J. Reynolds Foundation for providing a Wake Forest University Reynolds Research Leave Grant to W.L.H. A.I. was a 1983 participant in the Swedish CHUST Program. This work was presented at the 36th Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, New Orleans, LA, Feb 28, 1985 [Abstract No. 9511.
Study of Equilibria in 0.03 mM Molybdate Acidic Aqueous Solutions by Factor Analysis Applied to Ultraviolet Spectra Toru Ozeki* and Hiroshi Kihara Hyogo University of Teacher Education, Shimokume, Yashiro-cho, Kato-gun, Hyogo 673-14, Japan
Shigero Ikeda Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan
Ultravlolet (UV) spectra of 25 solutlons of 0.03 mM sodium molybdate wRh pH values in the range 5.38-1.97 were analyzed by factor analysis. The presence of three mononuclear molybdate specles-monomer, monoprotonated monomer, and dlprotonated monomer-Is proposed. The UV spectrum of each species was obtalned. The formation constants of the two protonated specles are log @ = 3.773 and 7.707, respectively. It is also demonstrated that the combination of these three species and three other lsopolymoiybdates (heptamer, protonated heptamer, and octamer) accounts for all of the equlllbrla In solutions of 0.1 M to 0.03 mM total molybdate concentratlon from pH 7 to 2.
The dissolved states of the isopolymolybdates have been the subject of much research (2-14). Species such as Moot-, HMo04-, H2M004,M%07”, HM03O1l3-, MqO,&, HMqOU6, H ~ M O & ~H, ~ M o ~ OMOg0x4-, S ~ ~ , HM0g0s3-, H7M0&gb, M03601128-etc. have been proposed. Potentiometry, ultraviolet (UV) spectroscopy, Raman spectroscopy, etc., have been used for the research and potentiometry has been especially widely used. The potentiometric curve, however, is essentially a
superposition of the contributions of each component. Thus the analysis of the curve is difficult and several different equilibria models have been proposed. Furthermore, for solutions of low molybdate concentration and low pH values, potentiometry may be subject to large uncertainties, because the amount of the protons consumed by formation of a new species is very small compared to the amount of total acid. On the other hand, Raman or UV spectroscopy give a distinguishable change in spectra because each species has its own characteristic spectrum. Furthermore, the application of factor analysis to the overlapped spectra of multicomponent systems aids in interpretation of the data (15-25). We applied it previously to the analysis of the overlapped Raman spectra of some isopolymolybdate ions (24); the presence of heptamer, protonated heptamer, and octamer was proposed. In order to check the equilibria of the isopolymolybdate species in solutions of low molybdate concentration, UV spectra of 25 solutions with pH ranging from 5.38 to 1.97 and containing 0.03 mM molybdate ions have now been measured and again factor analysis has been employed. As a result, a model for the equilibria that is consistent with the results of the Raman study, has been obtained. The presence of the monoprotonated monomer and diprotonated monomer is proposed.
0003-2700/88/0360-2055$01.50/00 1988 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 19, OCTOBER 1, 1988
0-
AB1
BK25 BK24 BK2 3
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BK22 BK21 BK20
- AB6
/? -
-
2.83 2.68 2.50
AB22
2.33
AB2 3 AB2 4 AB25
2.11
1.97
I
3.s4
boOQbo
Flgure 2. Compositions of data sets used for the evolving factor
analysis (EFA).
200
250
300
wavelength/nm Figure 1. UV spectra of 0.03 mM molybdate solutions with the indicated pH values.
In addition to information about their concentrations the spectrum of each species has been obtained. The UV studies of the molybdates, which have been reported by other authors, were limited to that of the isopolymolybdate such as the heptamer (I, 9, IO). There have been no reports relating to the UV spectra of the protonated monomer. We think that the UV spectra of the protonated mononuclear molybdates obtained in this work are the first to be reported. EXPERIMENTAL SECTION Preparation of Samples. All reagents were analytical grade chemicals. Sodium molybdate was used for the preparation of molybdate solutions. The final concentration of the molybdate ion was 0.03 mM. The pH values of the sample solutions were adjusted to 25 different values from 5.38 to 1.97 with perchloric acid. The ionic strength was not adjusted. Perchloric acid was used because it has no effective absorption above 200 nm when the concentration is lower than 0.1 M. Measurement of UV Spectra. UV spectra were measured by a double-beam spectrometer (Shimadzu UV-21OA, slit 1 nm); a D, lamp was used as a light source. Two matched quartz cells of 1 cm optical length were used, one for a sample solution and the other for a reference solution; the reference was a perchloric acid solution containing no molybdate salt. Spectra from 200 to 350 nm were measured and a data set of 76 wavelength points with 2-nm interval, was read from the chart and was used for the analysis. RESULTS AND DISCUSSION pH Dependence of t h e UV Spectra of 0.03 mM Molybdate Aqueous Solution. When the pH value of the molybdate solution was varied from 5.38 to 1.97, UV spectra from 200 to 350 nm changed as shown in Figure 1. The changes to the spectra are divided into three regions: (1) pH 5.38-3.90, the maximum at 208 nm decreased and the tail at 270 nm increased with the decrease of pH, two isosbestic points were observed at 223 and 242 nm; (2) pH 3.90-3.54, the absorption intensity at 210 nm decreased but that at 225 nm increased with the decrease of pH; (3) pH 3.54-1.97, the absorption intensity of 225 nm increased and an isosbestic point was observed at 210 nm. Evolving Factor Analysis Applied to UV Spectra. First, the general procedure of factor analysis will be outlined (18,23-25). A data matrix D is formed of absorption intensities, for example, of 76 wavelengths and 25 solutions. In the
case of this example, the matrix D consists of 76 rows and 25 columns. Each column corresponds to the spectrum of each sample solution. A covariance matrix Z is obtained by the multiplication of the transpose tD and the original D
Z = tDD
(1)
An eigenvalue matrix E and an eigenvector matrix Q are obtained by using the Jacobi method
z = QEQ
(2)
Eigenvalues are obtained, equal in number to the number of rows of Z. The number of the factors (pure components) can be selected by examining the IND function introduced by Malinowski (16) or by checking the reproducibility of the data matrix as mentioned below. Now, suppose the system has n factors. The eigenvectors that correspond to the n largest eigenvalues are taken out and are lined up as rows, to get a new matrix C, which is the first expression of a composition matrix. By multiplication of D with the transpose of C, an additional new matrix R is obtained, which is the first expression of a spectral matrix
R=DV: (3) When the spectral matrix R is multiplied with the composition matrix C, a theoretical data matrix D‘ is obtained
D’ = RC
(4)
The reproducibility of the data matrix can be examined by calculating ER
ER = [CtC,(dtj - d ’ ~ ~ ~ 2 ~ ” 2 / ~ (5) ~ ~ ~ ~ ~ d ~ from the square sum of the difference of each elements of the two matrices D and D’ (25). The number of factors, n, can be selected as the smallest number for which the value of ER converges. Gampp et al. proposed another way to estimate the number of factors, which is called evolving factor analysis (EFA) (26-28). Their method has been adapted in the present work. Twenty-five UV spectra were recorded, producing 25 data sets designated AB-1 to AB-25. Each data set, AB-n, consisted of n spectra. Thus data set AB-1 consists of only one spectrum of the solution with pH 5.38. The second data set AB-2 consists of two spectra of two solutions with pH 5.38 and 5.28. Similarly, AB-n consists of n spectra of n solutions from the first one, pH 5.38, to that of the nth sample (Figure 2). For each data set, factor analysis was applied and the logarithmic values of the obtained eigenvalue (log A) were plotted as the upper panel of Figure 3. Here, the largest eigenvalue was normalized to 10“. A large value of an eigenvalue means that the corresponding factor (species) makes a large contribution
ANALYTICAL CHEMISTRY, VOL. 60, NO. 19, OCTOBER 1, 1988 20
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First Equilibrium Observed for Solutions with pH 5.38-3.98. From the above discussion, the presence of two species is proposed for the data set from pH 5.38 to 3.98. After the treatments corresponding to eq 1-3, a spectral matrix R of 76 rows and two columns and a composition matrix C of two rows and 13 columns were obtained by taking out the eigenvectors corresponding to the two largest eigenvalues. Each column of R corresponds to a spectrum of a single species and each row of the C corresponds to a concentration distribution of a single species. But these matrices have some negative values. Thus, the rotation of the base axes of the matrices R and C is necessary
B
25
R
R* = RTR
(6)
C* = TcC
(7)
The rotation matrices TRand Tc must possess the property
-
WJ 0
TRTc = I
2
4
3
5
6
PH Figure 3. Dependence of eigenvalues upon the size of the data set and the pH. See text for explanation.
to the spectra of the data set. The level of noise in the factors is given by log X = 5.2 (Figure 3). Thus the increase of log X as AB-n increases from 1 to 25 above the 5.2 line indicates the importance of a new species. One species exists in all of the solutions and the corresponding log X value has been normalized to 10; thus it appears as the top most set of points in the upper panel of Figure 3. A second species is inferred for n 1 6 (represented by the second curve) from the top in the upper panel of Figure 3. A third species is important for n 2 12. Subsequent eigenvalues fall below the noise level (log X = 5.2). Thus at AB-25, the total data set, three factors are required, signifying three independent species. As shown in Figure 2, a second series of data sets, from BK-1 to BK-25, were similarly examined. Data-set BK-1 consists of the spectrum of the solution with pH 1.97, only. Analogous to the AB series, data set BK-n consists of n spectra from the (26-n)th sample to the last one, pH 1.97. Namely, AB-n increases from right to left with the increase of n in Figure 3 but BK-n increases from left to right. The corresponding change of the eigenvalues is shown in the mid panel of Figure 3. From BK-1 to BK-5, only one factor is significant. For n 1 6, a second factor becomes important. For n 1 11, a third factor is important. The upper two panels of Figure 3 reveal the generation of new species and their range of existence, as shown in the lower panel of Figure 3. The first species, A, present at pH 5.38, is considered to be the molybdate monomer; it disappears at pH 3.75. The second species, B, appears at pH 5.03 and disappears at pH 2.83. The third species, C, appears at pH 4.08. These descriptions about the appearance and the disappearance are semiquantitative but give useful information about the equilibria. They suggest that there are three species in the solutions with pH 5.38 to pH 1.97 but the consideration of only two species is sufficient for explaining the spectra of the solutions with pH 5.38 to pH 4.
(8)
where I is the unit matrix. The conditions for getting the proper rotation matrices, based on the pure wavenumber assumption or on the pure composition sample assumption, have been reported elsewhere (25). When the rotation matrices were selected so as to avoid negative absorbances (pure wavenumber assumption) and when the rotation matrices were selected so as to avoid negative concentrations (pure composition sample assumption), two different kinds of R and C were obtained. This means that the true spectra and the true composition distribution cannot be obtained by assuming such conditions. The formation reaction of the second species (A,H,) can be assumed to be nA
+ mH = A,H,
(9)
where monomer is denoted by A and proton by H. The formation constant, /3, is expressed as follows:
P = [A,H,I/[Aln[Hl"
(10)
(For the symbol to denote a cumulative formation constant (stability constant), K was used in the previous paper (24) but in this paper, /3 is used to follow an international convention.) If the value of /3 is known, the true concentration of each species in each solution, namely, all elements of a true composition matrix C*, can be calculated, neglecting activity coefficients. Then the matrix C* can be related to C with eq 7, by using a proper rotation matrix Tc. In other words, five parameters, one the equilibrium constant /3 and four, the four elements of the Tc, can be obtained by iterative refinement while applying the nonlinear least-squares method to eq 11 so as to obtain a minimum LSM
In this case, the stability constant /3 is the only adjustable parameter and the elements of Tc are automatically selected by the nonlinear least-squares method. The details of this procedure can be found in the paper of Gampp et al. (22). Furthermore, the spectral matrix R* is also obtained by using the inverse of Tc and R. This procedure should result in the true spectra and the true composition distributions. The study of the Raman spectra of the 0.1 M molybdate solution showed that the chemical species appearing after the monomer was the heptamer (24). Pungor and Halasz also have reported that the first formed species next of the monomer was the heptamer, even at a low molybdate concentration (9, IO). On the other hand, Sasaki and Sillen have proposed the existence of the protonated monomer (5, 7). We must distinguish between these two proposals. In order to do this, data from 13 solutions, from pH 5.38 to 3.98, were analyzed, independent of the total data set AB-25. We applied the
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 19, OCTOBER 1, 1988
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I PH
MOO:-
I
Flgure 4. Comparison of the concentration distribution (circles)with the simulated curves calculated by using formation constant (lines): (A) the case of the protonated monomer (log P(1,l) = 3.77), (B) the case of the heptamer (log p(8,7) = 62.53).
least-squares method to two cases, one assuming the heptamer and the other assuming the protonated monomer, as the second chemical species of molybdate. From this analysis values of (3 and species concentrations were obtained. In Figure 4, the circles are the concentrations obtained after the rotation of the composition matrix C and the lines are the results of the theoretical calculation using the formation constant obtained by the above least squares method. For the case of the protonated monomer, lines and circles are consistent with each other. But for the case of the heptamer, there are differences, especially around pH 5. Furthermore, the formation constant of the heptamer was obtained as log p(8,7) = 62.53 and this value is much larger than those already reported; 52.81 (6), 53.1 ( 2 4 ) , and 53.18 (24) (note that the formation constant is expressed as (the number of protons, the number of monomers))
Flgure 5. Dependence of log 6 values on the sum of squares of the error (LSM): (A) monoprotonatedmonomer, (B) diprotonated monomer. 1
C
.-0 +I
u
F
rc
.-u
E 0
CI
a
! H2M004
On the other hand, the formation constant of the protonated monomer was found to be log p(1,l) = 3.77 and this value was almost equal to 3.89 (5) or 3.53 (6). These facts suggest that the second species appearing after the monomer as the pH decreases is the protonated monomer, not the heptamer. Total Equilibria in Solutions with pH from 5.38 to 1.97. The proposition that the second species of Figure 3 is the protonated monomer makes the identification of the third species easy. From Raman spectroscopy, we know that three species exist: heptamer, protonated heptamer, and octamer ( 2 4 ) . The concentrations of these species in solutions with 0.03 mM molybdate total concentration were calculated by using fl(L11, P(8,7), P(9,7), and p(l2,8)
7M00b2- + 9H+ = HMo:O~*~+ 4H2O log p(9,7) = 56.0 (13) 8M00~+ ~ -12H+ = M o ~ O + ~ 6~H~2 -0 log p(l2,S) = 69.73 (14) The calculations showed that the heptamer and the protonated heptamer are almost negligible in 0.03 mM solution and the octamer exists below pH 2.5 as the third species. The third species C of Figure 3, however, appears about pH 4. Thus the assumption that the octamer is the third species is not consistent with the E F analysis. On the other hand, Schwarzenbach and Meier have proposed the presence of diprotonated monomer (2). The validity of their proposition was also examined. Factor analysis was applied to the AB-25 data set and three factors were selected. The iterative nonlinear least-squares method was applied with
2
3
4
PH
5
6
7
Figure 6 Comparison of the concentration distribution (circles)with simulation curves calculated by using formation constants (lines):log p(1,l) = 3.773 and log p(2,l) = 7.707.
two formation constants, p(1,l) and p(2,1), and nine rotation matrix elements as parameters. As a result, the following formation constants were obtained:
MOO^^- + H+ = HMo04- log P(1,l) = 3.773 MOO^^- + 2Hf = H2Mo04 log @(2,1)= 7.707
(15) (16)
The dependence of the two p values on the LSM (eq 11) is shown in Figure 5 . The LSM has a minimum when P(1,l) and p(2,l) are 3.773 and 7.707, respectively. In Figure 6, atomic fractions of each species, obtained by the rotation of the composition matrix, are shown as a function of pH by circles and the simulated curves calculated from the formation constants are shown by lines. By the rotation based on Tc, the true spectral matrix R was also obtained. The spectrum of each species is shown in Figure 7. The molar extinction coefficients of the protonated monomer are smaller than those of the monomer and its peak maximum is shifted to a longer wavelength. But its band profile is very similar to that of the monomer. On the other hand, compared to the monoprotonated monomer, the diprotonated monomer has relatively large molar extinction coefficients and a different shape. In the Raman study, the protonated monomer and the diprotonated monomer were not identified. The populations
ANALYTICAL CHEMISTRY, VOL. 60,NO. 19, OCTOBER 1, 1988
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protonated monomer occurs in 0.1 M molybdate solution, as shown in Figure 8A. Thus the result of this work does not conflict with that of the Raman study (24). These facts suggest that six species-monomer, monoprotonated monomer, diprotonated monomer, heptamer, protonated heptamer, and octamer-account for all of the equilibria in solutions with pH 7 and 2 and molybdate concentrations between 0.1 M and 0.03 mM. This conclusion is almost the same as that reached by Tytko et al. (13);the presence of diprotonated heptamer, however, could not be ascertained by our Raman study (24).
A
MOO:-
ACKNOWLEDGMENT We thank K. Yokoi of Osaka Kyoiku University and K. Murata of Naruto University of Teacher Education for their useful suggestions about the dissolved states of molybdate species. We also thank D. E. Irish of University of Waterloo (Canada) for his useful suggestions about the data analysis. Registry No. MOO?-, 14259-85-9; M O , ~ ~ . 12274-10-1; ,~, 12346-58-6. 200 0
250
300
0
LITERATURE CITED
I
wavelengt h/n m Flgure 7. Isolated UV spectra of mononuclear molybdate species.
0.03 mM I I
2
3
5
4
6
1
P" Figure 8. Distribution diagram for Moo,", HMo0,-, H&t00,, MO,O,~, HMo,O~,~, and Mo,OaC, calculated by using the formation constants: log p(1,l)= 3.773,log p(2,l)= 7.707,log p(8,7)= 53.18,log @(9,7) = 56.0,and log p(l2,8) = 69.73. Total molybdate concentrations are (A) 0.1 M, (B) 1 mM, and (C) 0.03 mM.
of these molybdate species in three solutions with different total molybdate concentration were calculated by using the formation constants now known. The results are shown in Figure 8. Neither monoprotonated monomer nor di-
(1) Lindqvlst, 1. Acta Chem. Scand. 1951, 5 , 568. (2) Schwarzenbach, G.; Meier, J. J. Inorg. Nucl. Chem. 1958, 8 , 302. (3) Sasaki, Y.; Lindqvist, I.; SiiiOn, L. 0. J. Inorg. Nucl. Chem. 1959, 9 , 93. (4) Cooper, M. K.; Salmon, J. E. J. Chem. SOC. 1982, 2009. ( 5 ) Sasakl, Y.; Sill&, L. 0. Acta Chem. Scand. 1984, 18, 1014. (6) Aveston, J.; Anacker, E. W.; Johnson, J. S. Inorg. Chem. 1964, 3 , 735. (7) Sasaki, Y.; Sill%, L. 0. Ark. Kemi 1987, 29, 253. (8) Griffith, W. P.; Lesniak, P. J. B. J. Chem. Soc.A 1969, 1066. (9) Pungor, E.; Halasz. A. J. Inorg. Nucl. Chem. 1970, 32, 1187. (10) Kiba, N.; Takeuchi, T. J. " r g . "9.Chem. 1974. 36, 847. (11) Tytoko. K. H.; Schonfeld, B. 2.Naturforsch; 8 : Anorg. Chem., Org. Chem. 1975, 308, 471. (12) Johansson, G.; Petersson, L.; Ingri, N. Acta Chem. Scand. 1979, A33, 305. (13) Tytoko, K. H.; Baeth, G.; Hirschfeld, E. R.; Mehmke, K.; Stellhorn, D. 2.Anorg. Allg. Chem. 1983, 503, 43. (14) Murata, K.; Ikeda, S. Spectrochim. Acta., PartA 1983, 39A, 787. (15) Syivestre, E. A.; Lawton, W. H.; Maggio, M. S. Technometrics 1974, 16, 353. (16) Matinowski, E. R. Anal. Chem. 1977. 49, 612. (17) Knorr, F. J.; Futreli, J. H. Anal. Chem. 1979, 51, 1236. (18) Mallnowski, E. R.; Howery, D. 0. Factor Analysis in Chemistry; Wiiey: New York. 1980. (19) Cox, R. A.; Haldna, U. L.; Idler, K. L.; Yates, K. Can. J. Chem. 1981, 59, 2591. (20) Maiinowski, E. R. Anal. Chlm. Acta 1982, 134, 129. (21) Malinowski, E. R.; Cox, R. A.; Haldna, U. L. Anal. Chem. 1984, 56, 778. (22) Oampp, H.; Maeder, M.; Meyer, C. J.; Zuberbuhler, A. D. Talanta 1985, 32, 257. (23) Ozeki, T.; Kihara, H.; Hikime, S. Bunseki Kagaku 1986, 35, 885. (24) Ozeki, T.; Klhara, H.; Hikime, S. Anal. Chem. 1987, 59, 945. (25) Ozeki, T.; Kihara, H.; Hlkime. S.; Ikeda, S. Anal. Sci. 1987, 3 . 285. (26) Gampp, H.; Maeder, M.; Meyer, C. J.; Zuberbuhler, A. D. Talanta 1985, 32, 1133. (27) Gampp, H.; Maeder, M.; Meyer, C. J.; Zuberbuhier, A. D. Chimia 1985, 39. 315. (28) Oampp, H.; Maeder, M.; Meyer, C. J.; Zuberbuhisr, A. D. Talanta 1988, 33, 943.
RECEIVED for review September 22,1987. Accepted June 14, 1988.
