Environ. Sci. Technol. 1990, 24, 1676-1679
perior to standard multiple linear regression for similar application (I@, also are being evaluated and are expected to improve the accuracy of the approach considerably.
Acknowledgments The access to software and assistance in software development provided by Dr. L. A. Carreira, as well as his and Dr. L. V. Azarraga's ideas on modeling concepts are greatly appreciated. The technical assistance of W. D. Payne is also gratefully acknowledged.
Literature Cited Shorter, J. Correlation Analysis i n Organic Chemistry; Clarendon Press: Oxford, U.K., 1973. Ariens, E. J., Ed. Drug Design; Academic Press: New York, 1976; Vol. VII. Bellamy, L. J. The Infra-red Spectra of Complex Molecules; Methuen and Co.: London, 1954. Katritzky, R.; Topsom, R. D. In Advances i n Linear Free Energy Relationships; Chapman, N. B., Shorter, J., Eds.; Plenum Press: London, 1972; Chapter 3. Wolfe, N. L.; Steen, W. C.; Burns, L. A. Chemosphere 1980, 9,403-408. Wolfe, N. L. Chemosphere 1980, 9, 571-579. Paris, D. F.; Wolfe, N. L.; Steen, W. C. Appl. Environ. Microbiol. 1982, 44, 153-158.
Drossman, H.; Johnson, H.; Mill, T. Chemosphere 1988, 17, 1509-1530. Paris, D. F.; Wolfe, N. L. Appl. Environ. Microbiol. 1987, 53,911-916. Steen, W. C.; Collette, T. W. Appl. Environ. Microbiol. 1989, 55, 2545-2549. Mabey, W.; Mill, T. J . Phys. Chem. Ref. Data 1978, 7, 383-415. Ellington, J. J.; S t a n d , F. E., Jr.; Payne, W. D.; Trusty, C. D. EPA/600/3-87/019, 1987. Zepp, R. G.; Wolfe, N. L.; Gordon, J. A,; Baughman, G. L. Environ. Sci. Technol. 1975, 9, 1144-1150. Collette, T. W. 19th International Symposium on Environmental Analytical Chemistry, Jekyll Island, GA, May 22-24, 1989. Hoy, R. M.; McClure, W. F. Appl. Spectrosc. 1989, 43, 1102-1 104. Carreira, L. A. Personal communication. Bloomfield, P. Fourier Analysis of Time Series: A n Introduction; John Wiley & Sons: New York, 1976. Seasholtz, M. B.; Archibald, D. D.; Lorber, A.; Kowalski, B. R. Appl. Spectrosc. 1989, 43, 1067-1072.
Received for review January 26, 1990. Revised manuscript received April 23, 1990. Accepted June 29, 1990. Note: Mention of trade names or commercial products does not constitute endorsement or recommendation for use by the U.S. Environmental Protection Agency.
Urban Aerosol Refractive Index Prediction by Partial Molar Refraction Approach Arthur W. Stelson
Department of Chemistry, Clark Atlanta University, Atlanta, Georgia 30314 The ambient aerosol of the polluted troposphere is a complex mixture of water, electrolytes, ionic solids, metal oxides and glasses, and carbonaceous material. Prediction of the refractive indexes of these inhomogeneous mixtures can be a formidable task. Contained within this paper is the necessary parameterization to estimate the mean real aerosol refractive index based on aerosol chemical composition and the partial molar refraction approach. This approach assumes all chemical constituents are homogeneously distributed throughout the aerosol phase. Consistency of the data is discussed, and this approach is verified by prediction of refractive indexes of NaOH-Si02-H20 mixtures. Finally, aerosol chemical composition data from the Los Angeles Basin are used to predict mean real aerosol refractive indexes. These values are compared to urban aerosol refractive indexes calculated via other techniques (light scattering).
Introduction As ambient aerosol levels increase, visibility degradation becomes a problem due to scattering and absorption of light by fine particles. The key to determining light scattering and absorption of fine particles from aerosol chemical analysis and particle size distribution data is a methodology of predicting the refractive index (I). Tang et al. (2) showed that trends in ambient light scattering can be exemplified by NH4N03-(NH4)2S04-H20mixtures. Their calculations relied on the refractive index being measured as a function of aerosol composition. Stelson and Seinfeld (3) later demonstrated how the refractive index of any NH,N03-(NH4)2S04-H20mixture can be accurately predicted by the partial molar refraction ap1676
Environ. Sci. Technol., Vol. 24, No. 11, 1990
proach as outlined in Moelwyn-Hughes ( 4 ) . Due to promising results demonstrated for the NH,NO,-(NH4)2S04-H20system, this paper was written to parameterize the prediction of the refractive index for any common ambient urban aerosol chemical composition. Finally, this technique is tested on refractive index data for the NaOH-Si02-H20 system. Predictions for ambient urban aerosol mean real refractive indexes are also compared to values determined from light scattering.
Parameterization of Partial Molar Refractions The molar refraction, R, of a condensed phase can be defined as
R =V ( s ) where V is the molar volume in cm3 mol-' and n is the refractive index ( 4 ) . The molar volume is V = ExiMi/d (2) where x i is the mole fraction of species i, M iis the molecular weight of species i in g mol-', and d is the density of the condensed phase in g ~ m - ~ The . molar refraction of a mixture can be calculated from partial molar refractions, Ri,of constituents by using R = ExiRi (3) For example, calculation of the partial molar refraction of an aqueous electrolyte can be calculated from solution data noting
0013-936X/90/0924-1676$02.50/0
(4) 0 1990 American Chemical Society
Table I. Partial Molar Refraction Data Determined from Refractive Index Data for Aqueous Solutions and Ionic Solids species NaOH KOH NH40H Mg(OH)z Ca(OHh NaBr KBr NH,Br HCl NaCl KC1 NH4Cl MgC12 CaC1, PbC12 NaNO, KN03 NH4N03 PMNOJz NazS04 K2SOI (NH4)2SO, MgSO4 CaSO, PbS0,
Table 11. Other Ambient Aerosol Constituent Partial Molar Refractions
electrolyte partial molar ionic solid partial molar refractn? cm3 mol-' refractn, cm3 mol-' 5.37 f 0.05 7.60 f 0.10 9.22 f 0.02 8.75 f 0.32* 10.55 f 0.29* 12.77 f 0.05 14.86 f 0.07 16.91 f 0.18* 8.39 f 0.11 9.20 f 0.18 11.25 f 0.06 13.30 f 0.05 16.94 f 0.36 18.71 f 0.15 27.58 f 0.75* 11.16 *0.08 13.18 f 0.10 15.23 f 0.21* 31.44 f 0.43 15.34 f 0.09 19.55 f 0.21 23.27 f 0.20 13.35 f 0.13 15.38 f 0.45* 24.46 f 0.68*
species elemental carbon organic carbon SiOZ
4.12 8.00, 8.23 10.91, 10.45 11.59 13.98 15.79 8.53 10.90 12.58 15.41, 13.83 15.69 26.67, 26.91, 7.80, 12.59 9.83, 14.19, 11.57, 16.11, 30.73 15.16, 14.98,
partial molar molecular refractn, mass, cm3 mol-l g mol-'
A1203
Fe203 CaO MgO PbO KzO Pb HzO a
27.46 14.20 16.65 14.81
22.74, 22.82, 23.18 14.63 15.08, 15.21, 16.02 22.34, 22.43, 22.63
Asterisk denotes value based on additivity to minimize deviation.
where subscript E refers to the electrolyte, and subscript w refers to water. NOTE: R , can be calculated from physical properties of pure water. RE calculated from eq 4 should be independent of ionic strength. Data exhibit no trend with molar ionic strength, indicating partial molar refractions are independent of ionic strength (5-7). Thus, this approach yields one parameter for each constituent for the prediction of the refractive index of a mixture if the solution density is known. Stelson and Seinfeld (8) discussed the important contributors to the aerosol mass loading in polluted urban atmospheres. The important cations are H+, Na+, K+, NH4+,Mg2+,ea2+,and Pb2+,and the important anions are OH-, Br-, C1-, NO3-, HSOc, and SO-:. Other important constituents are elemental carbon, organic carbon, water, Si02,A1203,and Fe20,. Constituents of possible improtance are CaO, MgO, PbO, K20, and Pb. The partial molar refractions for all cation-anion combinations and these other important constituents were calculated from data in Wolf et al. (9),Weast (IO), Stott and Bigg (3, Merwin ( I I ) , Cheneveau (6),and Larson et al. (1). Average values for electrolyte partial molar refractions and ionic solid partial molar refractions are listed in Table I. Table I1 contains values for partial molar refractions of other important ambient aerosol constituents. When ambient aerosol chemical composition measurements are performed, typically individual anion and cation concentrations are measured. A desirable feature of this approach would be to have the individual ionic partial molar refractions. A least-squares regression was performed to determine the values of the ionic partial molar refractions from the partial molar refractions for 18 cation-anion combinations of ambient aerosol significance (mass loading basis) calculated from the data in Wolf et al. (9,121. Only partial molar refractions based on solution refractive index and density data were used in the regression, and partial molar refractions based on additivity
3.11-1.25i 19.11 7.43 10.62 22.21 7.48 4.52 18.40 11.94 9.24 3.7124
12 84" 60.08 101.96 159.69 56.08 40.31 223.19 94.20 207.19 18.01534
0.259-0.104i 0.2275 0.1237 0.1042 0.1391 0.1334 0.1121 0.08244 0.1268 0.04459 0.2061
Assumed for comparative PurDoses.
Table 111. Partial Ionic Molar Refractions of Ions of Tropospheric Aerosol Importance partial ionic molar refraction, cm3 mol-' this study ref 4
ion
H+
0.00 f 0.00 0.93 f 0.01 3.03 f 0.04 4.89 f 0.02 0.03 f 0.08 1.93 f 0.07 11.06 f 0.30 4.43 f 0.03 11.84 f 0.03 8.39 f 0.11 10.19 f 0.06 13.45 f 0.10
Na+ K+ NH,+ Mgz+ CaZ+ PbZ+ OHBr-
c1-
N0f
so42-
0.46 2.12 0.24 1.19 12.12 9.30
RilMi? cm3 g-' 0.00 0.040 0.0775 0.271 0.001 0.0482 0.05338 0.260 0.1482 0.237 0.1643 0.1400
"This study.
were omitted. The results are listed in Table 111. Also, listed in Table I11 are partial ionic molar refractions calculated by Moelwyn-Hughes (4). Notice the data differ significantly though the trends are the same. This study's results are probably better suited for ambient aerosols because of the large amount of data analyzed and the inclusion in the regression of only data of ions present in ambient aerosols.
Calculation of Mean Real Refractive Index of Aerosols The mean real refractive index of a medium, n, can be calculated from
'=(
)
1 + 2 R / V 'I2 l-R/V
(5)
for an aerosol
where Ri is the partial molar refraction component i in cm3 mol-', Mi is the molecular mass component i in g mol-', [Si]is the concentration component i in pg m", and [AV] is the aerosol volume in pm3 ~ m - ~The . aerosol volume can be either measured or predicted by (7)
where 4i is the partial molar volume component i in cm3 Envlron. Scl. Technol., Vol. 24, No. 11, 1990
1077
:c ;
I
/
30 1 1 CORRESPONDENCE
/I
Table IV. Comparison of Partial Molar Refractions Calculated from Literature Datao'*
I
species NaCl KCL NaBr KBr a
r/. ov
I
10
1
20
1
30
I
Flgure 1. Cross plot of partial molar refraction of ionic solid versus partial molar refraction of electrolyte in water for 21 salts (9, 70).
mol-' and diis the density component i in g ~ m - Addi~. tionally, the mean aerosol density, d , can be calculated from
By use of the aerosol chemical composition data summarized in Stelson and Seinfeld (@, and density data from Weast ( I O ) , and from Larson et al. (I),a density range for ambient areosol between 1.4 and 1.7 g cm-3 is calculated. These data lie considerably below the value of 2.7 g cm-3 measured by Hanel in Mainz, West Germany.
Discussion In developing this parameterization, several points were not mentioned that may be important. First, the dissociations of sulfate and nitrate may have to be evaluated in developing a parameterization. Second, this parameterization relies on electrolytes and ionic solids having the same partial molar refractions. Third, is the data set on which this parameterization is based representative of all existing data? Fourth, how does partial molar refractions based on actual data compare to ones calculated by using additivity or partial ionic molar refractions for species not included in the initial parameterization? Fifth, how does this approach perform in predicting the refractive indexes of exemplinary systems like NH4N03-(NH4)2S04-H20 or NaOH-Si02-H20? Finally, how does this parameterization, used in conjunction with ambient aerosol chemical composition data, perform in predicting the mean real refractive indexes of ambient aerosols, and how do these data compare to values based on light scattering? The effect of dissociations of sulfate and nitrate can be evaluated with refractive index and density data for sulfuric acid and nitric acid from Wolf et al. (9) and dissociation data from Chen and Irish (13) and Krawetz (14). The value for RH,HS04 is 13.89 f 0.35 versus 13.45 f 0.52 for RH,H,SO~ and for RHNO~ iS 10.5 f 0.5 VerSUS 10.32 f 0.27 for RH,NOp Within accuracy of measurement and predictions, these values indicate the dissociations of sulfate and nitrate need not be evaluated, and RH,H,so4.andRHSNoB can be used for all sulfuric acid and nitric acid species. The question whether electrolytes versus ionic solids have the same partial molar refractions can be answered Environ. Sci. Technol., Vol.
9.20 f 0.18 11.25 f 0.06 12.77 f 0.05 14.86 f 0.07
9.19 f 0.17 11.29 f 0.10 12.74 f 0.15 14.93 i 0.17
av % diff 0.10 f 1.9
0.35 f 0.71 0.24 f 0.78 0.47 f 0.81
Reference 9. *Reference 6.
Table V. Comparison of Partial Molar Refraction of Electrolytes Based on Additivity, Calculation from Literature Data," and Least-Squares Calculated Partial Ionic Molar Refractions
PARTIAL MOLAR REFRACTION OF ELECTROLYTE IN WATER (cm3gmols'i
1678
REi,cm3 mol-' ref 9 ref 6
24,
No. 11, 1990
species HBr Hf,N03NH,N03 Mg(N03):, Ca(N03):,
Dartial molar refraction. cm3 mol-' ionic molar additivity refs 6-8, 15 refractns 12.00 f 0.24 10.32 f 0.27 15.23 f 0.21 20.33 f 0.38 22.57 f 0.47
12.32 f 0.2918 10.55 f 0.0620 15.13 f 0.0320 14.94 f 0.5718 24.44 & 0.0520
11.84 & 0.03 10.19 f 0.06 15.08 f 0.08 20.41 f 0.20 22.31 f 0.19
References 6-8 and 15.
by cross-plotting values for each. Figure 1 is a cross plot for 21 cation-anion combinations and indicates the data scatter around the line of 1:l correspondence. A leastsquares fit yields
Y = (0.995 f 0.038)X - (0.664 f 0.473) r = 0.992 (9) Thus, the assumption that the partial molar refraction for an electrolyte is the same as the one for an ionic solid is fairly justified. The representative nature of the data set on which this parameterization is based can be evaluated by comparing partial molar refractions based on data in ref 9 versus ref 5. Table IV contains values for both for 4 electrolytes. Notice that excellent agreement exists. Table V contains a comparison of partial molar refractions based on additivity data and partial ionic molar refractions for five electrolytes that were not included in the original least-squares regression. Notice that all values are in good agreement with the exception of the values for Mg(N03)2. Apparently, something is wrong with the refractive index or density data for Mg(N03)2in ref 5. The exact source of this discrepancy will have to be resolved by future study. The applicability of this approach has been shown for the NH4N03-(NH4)2S04-H20 system by Stelson and Seinfeld (3). An additional application was performed on the NaOH-Si02-H20 system in this work and is displayed in Figure 2. Notice that this approach and parameterization demonstrates the trends of the data but has poorer absolute agreement. In this prediction, actual density values were used. The refractive index data used in this comparison are of questionable quality (very old), and the solution temperature is unknown. Finally, this approach was used to predict the mean real refractive index of ambient urban aerosol. Table VI compares values calculated by this approach and aerosol chemical composition data from Stelson and Seinfeld (8), values based on light scattering (I6-I9), and one actual measurement (20). The values for this study have a minimum and maximum value based on chemical speciation assumptions. The average value for this study lies about 4 % below the light-scattering values. This deviation
chemical composition are compared to values based on light-scattering measurements. Good agreement (within 4 % ) exists, indicating the applicability of the partial molar refraction approach to complex ambient aerosol systems. Registry No. KOH, 1310-583; NH40H, 1336-21-6; Mg(OH)2,
/ 0.850
1309-42-8; Ca(OHIz, 1305-62-0; NaBr, 7647-15-6; KBr, 7758-02-3; NH4Br, 12124-97-9; HCl, 7647-01-0; NaC1, 7647-14-5; KC1, 7447-40-7;NH4Cl, 1212502-9; MgCl,, 7786-30-3; CaClZ,10043-52-4; PbClZ,7758-95-4; NaN03, 7631-99-4; KN03, 7757-79-1; NH4N03, 6484-52-2; Pb(N03)z, 10099-74-8; NaZSO4, 7757-82-6; KzS04, 7778-80-5; (NH4)zS04,7783-20-2; MgS04, 7487-88-9; CaS04, 7778189; PbS04, 7446-14-2;C, 7440-44-0; Alz03, 1344-28-1;Fe203, 1309-37-1;CaO, 1305-78-8;MgO, 1309-48-4;PbO, 1317-36-8; KzO, 12136-45-7;Pb, 7439-92-1; H+, 12408-02-5; Na+, 17341-25-2; K+, 24203-36-9; NH,+, 14798-03-9; Mg2+,22537-22-0;Ca2+,14127-61-8; Pb2+,14280-50-3;OH-, 14280-30-9; Br-, 24959-67-9;Cl-, 16887-00-6; NO3-, 14797-55-8; S042-, 14808-79-8; NaOH, 1310-73-2; S O z , 7631-86-9; HzO, 7732-18-5.
Literature Cited
0.05
0.00
0.10
5
MOLE FRACTION OF SILICON DIOXIDE
Figure 2. Predlcation of the refractive indexes of NaOH-Si0,-H,O solutions. Data from ref 6.
Table VI. Comparison of Mean Refractive Index Predictions for Ambient Tropospheric Aerosol study
location
refractive index
this study
Los Angeles Basin
Mathai and Harrison (16) Ensor et al. (17) Hanel (20) Grams et al. (18) Bhardwaia et al. (19)
Calgary, AB, Canada
1.43 f 0.02 min 1.47 i 0.03 max 1.53 f 0.05
Los Angeles Basin Mainz, West Germany Boulder, CO Tvson, MO
1.50 1.57 f 0.04 1.55-O.044i 1.55 f 0.03
can be possibly explained by partial volatilization of material from the filter samples used to determine the aerosol composition in this study or the method of predicting the aerosol density.
Conclusions This paper outlines and parameterizes a promising technique for appraising mean real aerosol refractive indexes. In parameterizing this approach, it has been shown that ionizations need not be calculated for the nitrate and sulfate systems, the existing different data sets are in substantial agreement, and a good approximation for refractive index prediction of ionic solid-aqueous electrolyte mixtures is to assume the ionic solid and electrolyte partial molar refractions are the same. This partial molar refraction approach performs well at predicting refractive indexes of NH4N0,-(NH4)zS04-H20 and N a O H - S O z H20mixtures. In comparison to ambient urban aerosol, these test systems are quite simple and more rigorous solution properties need to be measured and predicted. In Table VI, predictions of refractive indexes based on aerosol
(1) Larson, S. M.; Cass, G. R.; Hussey, K. J.; Luce, F. Enuiron. Sci. Technol. 1988, 22, 629-637. (2) Tang, I. N.; Wong, W. T.; Munkelwitz, H. R. Atmos. Enuiron. 1981, 15, 2463-2471. (3) Stelson, A. W.; Seinfeld, J. H. Atmos. Enuiron. 1982, 16, 2507-2514. (4) Moelwyn-Hughes, E. A. Physical Chemistry, 2nd rev. ed.; Pergamon Press: New York, 1961; p 397. (5) Pickard, R. H.; Houssa, A. H. J.; Hunter, H. In International Critical Tables of Numerical Data; Physics, Chemistry and Technology; McGraw-Hill: New York, 1930; Vol. VII, pp 63-108. (6) Cheneveau, C. In International Critical Tables of Numerical Data; Physics, Chemistry and Technology; McGraw-Hill: New York, 1930; Vol. VII, pp 12-16. (7) Stott, V.; Bigg, P. H. In International Critical Tables of Numerical Data; Physics, Chemistry and Technology; McGraw-Hill: New York, 1928; Vol. 111, pp 24-26. (8) Stelson, A. W.; Seinfeld, J. H. Enuiron. Sci. Technol. 1981, 15,671-679. (9) Wolf, A. V.; Brown, M. G.; Prentiss, P. G. In CRC Handbook of Chemistry and Physics, 54th ed.; Weast, R. C., Ed.; CRC Press: Cleveland, OH, 1973; pp D192-D234. (10) Weast, R. C., Ed. CRC Handbook of Chemistry and Physics, 54th ed.; Cleveland, OH, 1973; pp B63-B156. (11) Merwin, H. E. In International Critical Tables of Numerical Data; Physics, Chemistry and Technology; McGraw-Hill: New York, 1930; Vol. VII, pp 16-33. (12) Franklin, J. N. Matrix Theory; Prentice-Hall: Englewood Cliffs, NJ, 1968; Section 2.7. (13) Chen, H.; Irish, D. E. J. Phys. Chem. 1971, 75,2672-2681. (14) Krawetz, A. A. Ph.D. Dissertation, University of Chicago, 1955. (15) Beattie, J. A.; Brooks, B. T.; Gillespie, L. J.; Scatchard, G.; Schumb, W. C.; Tefft, R. F. In International Critical Tables of Numerical Data; Physics, Chemistry and Technology; McGraw-Hill: New York, 1928; Vol. 111, pp 51-111. (16) Mathai, C. V.; Harrison, A. W. Atmos. Enuiron. 1980, 14, 1131-1135. (17) Ensor, D. S.;Charlson, R. J.; Ahlquist, N. C.; Whitby, K. T.; Husar, R. B.; Liu, B. Y., H. J. Colloid Interface Sci. 1972, 39, 242-251. (18) Grams, G. W.; Blifford, I. H., Jr.; Schuster, B. G.; DeLiusi, J. J. J . Atmos. Sci. 1972, 29, 900-905. (19) Bhardwaja, P. S.; Herbert, J.; Charlson, R. J. Appl. Opt. 1974,13, 731-734. (20) Hanel, G. Tellus 1968, 20, 371-379.
Received for review December 5, 1989. Revised manuscript received June 4,1990. Accepted July 5, 1990.
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