Fernando Pérez-Villaseñor and M. L. Bedolla-Hernández , Gustavo A. Iglesias-Silva. Industrial & Engineering Chemistry Research 2007 46 (19), 6366-6374.
Apr 1, 1978 - Richard S. Fein, Bruce S. Bailey. Environ. Sci. Technol. , 1978, 12 (4), pp 463â465. DOI: 10.1021/es60140a011. Publication Date: April 1978.
Conductimetric and pararosaniline method sulfur dioxide monitoring uncertainties and their significance. Richard S. Fein, and Bruce S. Bailey. Environ. Sci.
Conductimetric and pararosaniline method sulfate monitoring uncertainties and their significance. Reply to comments. Richard S. Fein, and Bruce S. Bailey.
Feb 26, 2014 - Gibbs Energy and Chemical Equilibrium Constants. Francisco ... alternative approach is introduced in which a simple algebraic equation can ...
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Anal. Chem. 1983, 55,567-570
Table 111. Condition K and the (Determinant)'" of K K T for Experimentally Obtained K Matrix wavelength corn hination
10, 25, 28, 34 1 , 3 , 5 , 7)...,55
65.6 20.3 12.1
2.21 x 10' 1.28 X 10' 3.22 X 10"'
the responses and the relative errors in the estimated calibration constants can be multiplied by 65.6 to yield the relative error in no,The worst accuracy and precision were found for the four sensor system. This is reflected both in cond ( K )and the relative errors and the RSDs listed in Table 11. The best accuracy and precision were found when all 36 sensors are used for analysis of the four-component system. This is also expressed in the cond ( K ) shown in Table I11 and the relative errors and the RSD's listed in Table 11. It appears that cond ( K ) can be used as an indication for the stability of the system to noise perturbations while at the same time it can be used for a measure of accuracy and precision. That is, a minimum cond (ac)means minimum relative errors and RSD for no. Kaiser has shown (28) that it is possible to define the total sensitivity of a multicomponent procedure as the absolute value of the determinant of the calibration matrix K. Maximum sensitivity will correspond to a K matrix with large diagonal elements andl low off-diagonal elements. These same circumstances will minimize cond ( K ) . Hence a minimum cond ( K ) should be reflected as a maximum determinant. "he method of Kaiser is limited to the case of p = r. Junker and Bergmann (19)have generalized Kaiser's definition of sensitivity for p 2 r as the square root of the determinant of the product of the K matrix and its transpose. Again, we would expect that for p > r, maximum sensitivity, greatest determinant would also be represented as a minimum in cond ( K ) . This was found to be true for the present study. Shown in Table I11 are the determinants of K p for the three sets of sensors. The sensor set containing all 36 wavelengths is seen to have the minimum cond ( K ) and the maximum sensitivity. Consequently, it appears that the sensitivity of the calibration matrix K compliments the information contained in cond ( K ) . Jochum et al. (5) have also used the cond ( K ) to determine the optimal sensors for multicomponent analysis. This is accomplished by obtaining the minimum cond ( K ) for various combinations of the available sensors. Similarly, Junker and Bergmann (19)have used the sensitivity number as a method of optimization of a multicomponent system. Other methods for the choice of optimal analytical sensors in multicomponent systems exist (8-10); these involve tedious mathematical calculations and necessitate the direct comparison of several numbers rather than the comparison of single numbers as in the methods of the GSAM and Junker and Bergmann. With the cond ( K ) or determinant of K p as criteria for optimal
selection of sensors, all 36 sensors should be used for optimal performance. This agrees with the experimental findings presented in Table 11. These results suggest digitization at a higher resolution for optimal performance. Namely, measurement at 1.0 nm intervals should increase the precision and accuracy accordingly. Other studies have been performed to show the optimal number of standard additions that should be made (20, 21). This paper describes a new approach for using the GSAM to perform analytical multicomponent analysis and ai new interpretation of the condition number of matrix K. It was demonstrated th,at, whenever possible, the best results are obtained when p > r , as expressed by cond (K). This paper is in agreement with a previous study (22)where similar results were found for a series of computer-simulated experiments and real data. The real data were those obtained by Jochum et al. ( 5 ) ,but only consisted of selected wavelength positions in the absorption curves rather than the complete absorption spectra as done here.
LITERATURE CITED (1) Saxberg, B. E.; Kowalski, B. R. Anal. Chem. 1979, 57, 1031--1038. (2) Kaiivas, J.; Kowalski, B. R. Anal. Chem. 1981, 53, 2207-221 2. (3) Gerlach, R. W.; Kowalski, B. R. Anal. Chem. Acta 1982, 734, 119. (4) Moran, M.; Kowalski, B. R., Laboratory for Chemometrlcs, Department of Chemistry, Unlversity of washington, unpublished work, June 1981. (5) Jochum, C.; Jochum, P.; Kowalski, B. R. Anal. Chem. 1961, 53, 85-92. (6) Kalivas, J.; Kowaiski, B. R. Anal. Chem. 1982, 54,560-565. (7) Kalivas, J.; Jochum, C.; Kowalski, B. R. Presented as paper NO. 440 at the Pittsburgh Conference, Atlantic Clty, NJ, March 1982. (8) Sustek, J. Anal. Chem. 1974, 46, 1676-1679. (9) Zscheile, F. P.; Murray, H. C.; Baker, G. A.; Peddicord, R. 0. Anal. Chem. 1962, 3 4 , 1776-1780. (10) Sustek, J.; Llvar, M.; Schiessl, 0. Chem. Listy 1972, 66, 168. (11) Certontaln, H.; Duin, H. 0.J.; Vollbracht, L. Anal. Chem. 196:3, 35, 1005-1007. (12) Milano, M. J.; Kim, K. Anal. Chem. 1977, 49,555-559. (13) Ratzlaff, K. L. Anal. Chem. 1980, 52, 1415-1420. (14) Hirschfeld, T. [email protected] Spectrosc. 1976, 30, 67-69 (15) Neter, J.; Wassorman, W. "Applied Linear Statistical Models"; Rlchard D. Irwln, Inc.: Homewood, IL, 1974;Chapter 6. (16) Naylor, T. H.; Baiintfy, J. L.; Burdlck, D. S.; Chu, K. "Computer Simulatlon Techniques"; Wiley: New York, 1966;Chapter 4. (17) Dahlquist, G.;Bjorck, A.; Anderson, N. "Numerical Methods", Pretntica Hall: Englewood Cliffs, NJ, 1974;Chapter 5. (18) Kaiser, H. Pure Appl. Chem. 1973, 34, 35-61. (19) Junker, A.; Berpmann, G. 2.Anal. Chem. 1974, 272, 267. (20) Franke, J. P.; de Zeeuw, R. A. Anal. Chem. 1978, 50, 1374-1380. (21) Ratziaff, K. L. Anal. Chem. 1979, 57, 232-235. (22) Kalivas, J.; Kowaiski, B. R., Laboratory for Chemometrics, Department of Chemistry, University of Washington, unpublished work, June 1982.
Present address: Laboratory for Chemometrics, Department of Chemistry, BElO, University of Washington, Seattle, WA 98195.
J. H.Kalivas' Department of Chemistry Montana State University Bozeman, Montana 59717 RECEIVED for review August 19, 1982. Accepted November 12, 1982. This work was supported by the Department of Chemistry, Montana State University, Bozeman, MT.
Temperature! Dependence of the Modified Pararosaniline Method for the Determination of Formaldehyde in Air Sir: There is currently considerable interest in methods for the measurement of formaldehyde in nonindustrial indoor environments, in particular, buildings insulated with urea formaldehyde foam insulation. The N.I.O.S.H. recommended method ( I , 2 ) employri chromotropic acid and sulfuric acid
for the analysis of the sampled air. The chromotropic ,acid method is relativelly insensitive and is potentially subject to interferences by both organic and inorganic compounds (3). Miksch et al. have recently published ( 3 ) a modified pararosaniline method. which has superior sensitivity for the
0003-2700/83/0355-0567$01.50/0 0 1983 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 55, NO. 3, MARCH 1983
Table I. Slopes and Intercepts from Calibration Lines Obtained from Pararosanaline Analysis of Standard Formaldehyde Solutionsa at 570 nm date 7120182 7/21/82 7/21/82 7/25/82 7/27/82 a
slope,b interAU.mL. cept,b fig-' AU 0.690 0.672 0.745 0.680 0.670
of best fit determined by method of least squares.
analysis of <50 ppb concentrations of formaldehyde in air and which is reputed to be more selective than chromotropic acid. We herein report our observations with the modified pararosaniline method and stress particularly the temperature dependence of the reaction and its consequences on the analytical results. The reaction mechanism proposed by Miksch et al. is reexamined and discussed in light of our observations.
EXPERIMENTAL SECTION Apparatus. Spectrophotometric determinations were made with a Perkin-Elmer Hitachi-Coleman 139 grating spectrophotometer and a Carey 17 spectrophotometer. Disposable 10-mm pathlength acrylic cuvettes or capped 20-mm pathlength optical glass cuvettes were used. Temperatures in the spectrophotometric cells were controlled with a Neslab RTE-8 thermostated circulating bath. Reagents. Pararosaniline (free base) (ClgHlgN30)and pararosaniline hydrochloride (ClgH18N3C1) were purchased from Sigma Chemical Co. Stock pararosaniline reagent (PRA) was purchased from CEA Instruments Inc. Formalin solution supplied by B.D.H. and methanol-free formaldehyde solutions prepared and standardized by the methods described by Miksch et al. (3) were employed. Their pararosanilineprocedure was employed except that 3.0-mL aliquots of the solutions to be analyzed were used with 300 pL of PRA reagent and 300 pL of 8 mM sodium sulfite solution. The stock PRA supplied by CEA Instruments Inc. was acidified by addition of sufficient concentrated hydrochloric acid to bring its [H+] to 1.68 M as determined by potentiometric titration with standard sodium hydroxide solution. Thus, for example, to 500 mL of stock PRA reagent whose [H+] was found to be 0.87 M was added 37.5 mL of 12.5 M concentrated HC1. Six standard formaldehydesolutions of concentrations corresponding to approximately 0.20,0.40,0.80, 1.2, 1.8, and 2.4 pgmL-l were
prepared daily in organic-free deionized water for calibration line determinations. Analytical blanks consist of 3.0 mL of the organic-free deionized water, 300 pL of PRA, and 300 pL of the 8 mM sodium sulfite solution and are also prepared daily for the calibration line determinations. Similar temperature-dependenceresulb were obtained by using pararosaniline reagent as prepared by Miksch's procedure, although calibration line slopes of lower sensitivity are obtained, even after [H+] adjustment.
RESULTS AND DISCUSSION The slopes and intercepts of the calibration lines obtained by using stock PRA as supplied by CEA Instruments Inc. are batch dependent. This is presumably due to the fact that both the [H+]and the concentration of pararosaniline in the stock solutions vary. I t has been found ( 4 ) , however, that if the acidity of the stock PRA reagent is adjusted by the addition of concentrated hydrochloric acid such that its [H+] is 1.7 M, consistent calibration line slopes can be obtained on an interlaboratory basis. The calibration line slopes thus obtained correspond t o sensitivities of 0.70 f 0.05 AU.mL.pg-' with correlation coefficients of the order of 0.999. In this way, a sensitivity 35% greater than that reported by Miksch can be achieved. It should be noted however, that slopes of even greater sensitivities can be obtained by using stock PRA reagent of lower [H+]. While the slopes of the calibration lines can consistently be obtained within lo%, in our laboratories, the intercepts, which approximate the absorbances of the analytical blank solutions, can show variations from 0.070 to 0.30 AU, a range of over 400% (see Table I). If the absorbances of the analytical blank were to be used as a measure of the formaldehyde content of the water being employed for the analyses, a formaldehyde concentration ranging from 0.10 to 0.43 pg-mL-l would have been indicated. This is, of course, an important consideration for inter- and intralaboratory quality control and quality assurance. It has been found that a 60-min period at room temperature (25-27 "C)is usually sufficient for the maximum color development of the chromogen which is measured spectrophotometrically a t 570 nm and gives calibration line slopes of 0.70 f 0.05 AUyg-rnL-l consistently. We noted, however, that the variations in the intercepts of the calibration lines are laboratory temperature related, even after the 60-min development period. See Table I. We therefore examined the temperature dependence of the absorbances of analytical blanks and standard solutions after the period of maximum chromogen development. The tem-
Table 11. Temperature Dependence of 57 0 nm Absorbances of Analytical Blanks and Standard Formaldehyde Solutions, Containing Pararosaniline Reagent and Sodium Sulfite
Standard solution containing 0.40 pg.mL-' formaldehyde prepared as described in the Experimental Section. Standard solution containing 1.20 fig.mL'' formaldehyde prepared as described in the Experimental Section. Net AU obtained by subtracting absorbance of reagent blank from absorbance of the formaldehyde solution at the same temperature. Line of best fit determined by method of least squares. a
ANALYTICAL CHIEMISTRY, VOL.
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Table HI. Temperature Dependence of 570-nm Absorbances of Analytical Blanks and Standard Formaldehyde Solutions, Containing Pararosaniline but No Sodium Sulfite T, "C
38.0 34.0 31.5 30.0 28.5 27.0 23.5 20.2
3.215 3.257 3.284 3.300 3.317 3.333 3.3 73 3.407
reagent blank -AU In AU -1.231 - 1.4B 7 -1.599 -1.726 -1.852 -1.938 -2.303 -2.501
0.292 0.233 0.20 2 0.178 0.157 0.144 0.100 0.082
slope,c In AUaK intercept,c In AU R
formaldehyde solutiona AU In AU 0.275 0.222 0.195 0.170 0.150 0.136 0.094 0.076
formaldehyde solution AU In AU -1.347 -1.561 -1.687 -1.833 -1.952 -2.056 -2.386 -2.617
0.260 0.210 0.185 0.160 0.142 0.128 0.092 0.073
-6933 21.07 0.9937
-6801 20.59 0.9951
Standard solution containing 0.40 pg.mL-' formaldehyde prepared as described in the Experimental Section. Standard solution containing 1.20 pg.mL-' formaldehyde prepared as described in the Experimental Section. Line of best fit determined b:y method of least squares. a
peratures of the developed solutions were raised to 38 "C in the spectrophotometric cell holder which is capable of holding up to four cuvettes simultaneously and the absorbances of the solutions noted as the temperature was decreased to below room temperature. In this way we ensured that we were not merely observing the temperature effect on maximum chromogen development noted by Miksch in his paper. The absorbances were read against a zero blank of organic-free deionized water. The temperature of the zero blank was measured directly with an immersion thermometer and the recorded temperatures were assumed to be the same as those of the PRA-containing analytical solutions, as these were kept capped throughout the determinations. Cooling was effected over a BO-90-min period. Table 11, summarizes our observations. Analysis of tlhe data indicates that a plot of In AU vs. I/ T is linear (From the van't Hoff equation, AH" values of 3.4 kJ.mol-l and 3.3 kJ-mol-l for the equilibrium process IIa * IIb IIc can be obtained by using the reagent blank temperature-absorbance values in Tables I1 and 111. We thank the reviewers for pointing this out to us.) with correlation coefficients of the order of 0.990. We repeated these
experiments with cdmilar solutions but this time omitting the final addition of the 300-pL aliquot of 8 mM sodium sulfite solution. Table 111, summarizes our findings. Again, a sirnilar linear dependence of In AU vs. 115"as was observed previously is evident for the analytical blank and the standard solutions. However, it can also be seen that the formaldehyde present in the standard solutions has correspondingly decreased the absorbance of the resultant solutions at 570 nm. A saturated solution of pararosaniline (free base) in water was then prepared, and after 60 min equilibration, its absorbance-lemperature properties were similarly examined. No similar temperature-dependence properties were observed this time. These findings suggest that instead of the mechanism proposed by Miksch, equilibria of the type depicted in Scheme I are occurring, involving the canonical forms of the dye cation, IIa, and its protoriated forms IIb-IIc ( 5 ) . Consistent with this mechanism, we offer the following spectroscopic evidence: The absorbance of an approximately 0.004% solution of pararosaniline (free base) in water has,,A at 538 nm in agreement with that noted by Nauman et al. (6). An equilibration period of approximately 60 min at 25 "C after
ANALYTICAL CHEMISTRY, VOL.
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dilution of the saturated solution of the free base is required for the absorbance to reach a maximum value. After equilibrium has been achieved, there is no temperature dependence on the absorbance a t this ,A,, suggesting that dissociation of I has been achieved. The absorbance at 570 nm increases only slightly as the temperature is increased. The absorbance and A,, properties of a diluted solution of pararosaniline hydrochloride differ in that no such equilibration period is required. The ,A, is at approximately 542 nm at 25 "C, and its absorbance is temperature dependent. It is shifted relative to that of the solution of the pararosaniline free base presumably since the solution derived from the hydrochloride has a lower pH than that from the free base. Addition of hydrochloric acid to aqueous solutions prepared either directly from pararosaniline (free base) or pararosaniline hydrochloride reveals that (a) the respective absorbances a t 538 nm, or 542 nm, decrease and (b) the respective A,, positions shift progressively up to 570 nm with increasing [H+]. These observations are in agreement with those of Dasgupta (5) and Nauman (6). Our findings however, suggest that the ions IIa-c (and their respective canonical forms) exist in equilibrium. The absorbances of these aqueous solutions which are due to the absorbance of the dye cation IIa (5) are temperature and [H+] dependent. This could account for the reagent blank absorbance-temperature dependences reported in Tables I1 and 111. As seen in Table 111, the addition of the pararosaniline reagent prepared either from the free base or from the stock PRA to dilute formaldehyde solutions in the absence of sodium sulfite results in a decrease in the 570-nm absorbances of the solutions at each particular temperature. This absorbance decrease is consistent with the removal of some of IIa from the equilibrium mixture to form the aminocarbinol IIIa or the Schiff base IIIb (5). Addition of sodium sulfite to the resultant solution (followed by acidification, in the case of pararosaniline (free base)), results in a rapid formation of a purple chromogen with a strong absorbance a t A, 570 nm. This is the chromogen that is being measured in the calibration curve determinations. The structure is most likely IV, the alkyl sulfonic acid, or its protonated forms (5). Analysis of the data in Table I1 suggests that the absorbances of the solutions containing this chromogen are temperature dependent. However, their net absorbances at each temperature which are obtained by subtracting the absorbance due to the analytical reagent blank at those temperatures are constant to within the limits of experimental error. CONCLUSION The temperature-absorbance dependences observed are consistent with a mechanism involving changes in the relative equilibrium concentrations of the dye cation IIa. The intercepts of the calibration curves which are due to the absorbances of the analytical blanks and which contain only IIa-c are therefore temperature dependent. The reproducibility of the intercepts can therefore only be achieved by strict temperature control of the solutions during the spectrophotometric analysis. On the other hand, the net absorbance of the alkylsulfonic acid chromogen IV which is also measured at 570 nm is independent of temperature under the conditions of the analytical procedure. Thus, the slopes of the calibration
curves are independent of temperature. Since the PRA is in a large excess, relative to the amounts of IV under these conditions, the contribution of IIa to the total absorbance is a constant additive amount to the absorbance of the resultant solutions at each particular temperature. Finally, and most importantly, we wish to emphasize that since the absorbances of the final solutions are temperature sensitive, accurate determinations o f formaldehyde concentrations by using this method can only be achieved if all the solutions are spectrophotometrically analyzed a t the same temperature. Alternatively, the calibration lines for a typical daily analytical determination can be obtained by using absorbance values from which the absorbance value of the analytical blank has been subtracted. In this case, the analytical blank should be used as the zero blank for all of the solutions being measured since it will presumably be at the same temperature as these solutions during the analytical determinations. Failure to recognize this temperature sensitivity will result in the introduction of large errors. ACKNOWLEDGMENT We acknowledge the contribution of Concord Scientific Corp., Downsview, Ontario, Canada, in developing the methodology for the control of the pH values of the analytical solutions. The reviewers are thanked for their constructive criticisms. Registry No. Pararosaniline, 569-61-9;formaldehyde, 50-00-0. LITERATURE C I T E D "Manual of Analytlcai Methods", 2nd ed.;Natlonal Institute of Occupational Safety and Health: Washlngton, DC, 1977; Vol 1, pp 125-1, 125-9. American Publlc Health Association Intersociety Committee "Methods of Air Sampllng and Analysis", 2nd ed.; Katz, M., Ed.; American Public Health Assoclatlon: Washlngton, DC, 1977; pp 300-307. Mlksch, R. R.; Anthon, D. W.; Fanning, L. 2.; Hollowell, C. D.; Revzan, K.; Glanville, J. Anal. Chem. 1981,53, 2118-2123. Eaman, M., Concord Sclentlfic Corp., Downsview, Ontario, Canada, personal communication. Dasgupta, P. K.; DeCesare, K.; Ullrey, J. F. Anal. Chem. 1980, 52, 1912-1922. Nauman, R. V.; West, P. W.; Tron, F.; Gaeke, G. C. Anal. Chem. 1960, 32, 1307-1311.
Also at Geortec Ltd., 5 Atlantlc Avenue, St. John's, Newfoundland, Canada A1E 1K9.
Paris E. Georghiou*l Leo Harlick Department of Chemistry Memorial University of Newfoundland St. John's, Newfoundland A1B 3x7, Canada Linda Winsor David Snow Geortec Ltd. 5 Atlantic Avenue St. John's, Newfoundland A1E 1K9, Canada
RECEIVED for review August 23, 1982. Accepted November 10,1982. The National Research Council of Canada, and the U.F.F.I. Centre, Department of Consumer and Corporate Affairs, Canada, are thanked for financial support. The Department of Chemistry, Memorial University of Newfoundland is also thanked.