Environ. Sci. Technol. 1999, 33, 2299-2301
Enantiomer Ratios for Apportioning Two Sources Of Chiral Compounds TERRY F. BIDLEMAN* RENEE L. FALCONER‡
,†
AND
Atmospheric Environment Service, 4905 Dufferin Street, Downsview, Ontario M3H 5T4, Canada, and Chemistry Department, Youngstown State University, Youngstown, Ohio 44555
A relationship is derived for estimating the contribution of chiral compounds from two sources A and B in an A-B mixture. The apportionment equation requires only the enantiomer ratios of the two sources and the resultant mixture (ERa, ERb, ERm) and corrects an erroneous relationship that was previously published. The use of ERs to apportion two sources was tested using synthetic mixtures of nonracemic (A) and racemic (B) heptachlor-exoepoxide (HEPX). ER values for the two source types and the mixture were determined by capillary gas chromatography on a chiral cyclodextrin column with detection by negative ion mass spectrometry. Results calculated for the fraction of the nonracemic component in the mixture (Fa) using the ERs agreed with the actual composition within +2.1 to -9.8%. The average error was -2.5%, and the propagated relative standard deviation in Fa was 4-6%. ER values can be determined with high precision and are not affected by analytical method recoveries nor by abiotic processes that take place during transport. These advantages make ERs especially attractive for source apportionment.
Introduction Degradation of chiral pesticides often takes place enantioselectively, yielding nonracemic residues. The distinct enantiomeric signatures of these residues can be used as markers to follow environmental transport and fate processes (1). Examples include using R-hexachlorocyclohexane (RHCH) enantiomers to trace snowmelt water in an arctic lake (2) and following volatilization of R-HCH and other chiral pesticides from water (3-5) and soils (4, 6). Nonracemic chlordane and heptachlor-exo-epoxide (HEPX) were recently reported in ambient air (4, 7, 8), and mecoprop residues from agricultural and nonagricultural sources were differentiated by their enantiomer compositions (9). Chiral analysis has also proved useful for investigating biodegradation of herbicides in groundwater (10) and soils (11). These studies provide an incentive to apportion pesticide sources on the basis of their enantiomeric signatures. In previous papers on enantiomers as tracers of emissions from soil and water (3-5), the following relationship was used to estimate the contribution of pesticides from two sources A and B having different enantiomer ratios ERa and ERb: * Corresponding author phone: (416)739-5730; fax: (416)739-5708; e-mail:
[email protected]. † Atmospheric Environment Service. ‡ Youngstown State University. 10.1021/es9901056 CCC: $18.00 Published on Web 05/22/1999
1999 American Chemical Society
Fa )
(ERm - ERb)
(1)
(ERa - ERb)
where Fa is the fraction of total pesticide originating from source A and ERm is the enantiomer ratio for the A and B mixture (2-4). Equation 1 was derived by assuming that ERm is the sum of Fa and Fb () 1 - Fa) multiplied by their respective ER values (3, 4). We have reconsidered eq 1 and found that this is algebraically incorrect. This paper presents a revised equation to calculate the contribution of chiral compounds from two sources and an experimental test of ERs for apportionment. The new equation is
Fa )
(ERm - ERb)(ERa + 1)
(2)
(ERa - ERb)(ERm + 1)
Equations 1 and 2 give similar answers when the difference between ERa and ERb is small. For nonracemic R-HCH volatilizing from lake water and mixing with racemic R-HCH in air, values of ERa ) 0.85, ERb ) 1.00, and ERm ) 0.91 have been reported (3). In this case, the estimated Fa is 0.60 using eq 1 and 0.58 using eq 2. If other workers have used eq 1 for a similar application in which the source ERs are fairly close, they have probably not gone too far astray. However, as shown below, the error incurred by using eq 1 increases substantially as ERa and ERb diverge.
Derivation of Equation 2 Let Nt be the total moles of a chiral pesticide with contributions Nta and Ntb from sources A and B. Nta and Ntb are each the sum of (+) and (-) enantiomers, and the ERs are ratios of the (+)/(-) enantiomers. The following equations express the mass balance:
Nt ) Nta + Ntb
(3)
Nta ) N(+)a + N(-)a
(4)
Ntb ) N(+)b + N(-)b
(5)
ERa ) N(+)a/N(-)a
(6)
ERb ) N(+)b/N(-)b
(7)
Nta ) FaNt
(8)
Ntb ) FbNt ) (1 - Fa)Nt
(9)
Combine eqs 4-7:
N(+)a ) NtaERa/(ERa + 1)
(10)
N(-)a ) Nta/(ERa + 1)
(11)
N(+)b ) NtbERb/(ERb + 1)
(12)
N(-)b ) Ntb/(ERb + 1)
(13)
The enantiomer composition of the mixture (ERm) is determined by the (+) and (-) enantiomer contributions from each source:
ERm )
[N(+)a + N(+)b]
(14)
[N(-)a + N(-)b]
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Combine eqs 10-13 with eq 14:
ERm )
NtaERa/(ERa + 1) + NtbERb/(ERb + 1) Nta/(ERa + 1) + Ntb/(ERb + 1)
(15)
calculated Fa soila
ERm
eq 1
eq 2
eq 1
eq 2
0.187 0.257 0.305 0.396c
2 2 1 1
0.409 0.567c
2 1
)
0.580 0.675 0.724c
2 2 1
(17)
0.797
1
1.149 1.220 1.355 1.502 1.462 1.356 1.837 1.804 1.574 1.691 2.218 2.168 2.443
0.123 0.179 0.159 0.224 0.206 0.288 0.372 0.357 0.462 0.555 0.540 0.518 0.640
0.186 0.263 0.288 0.381 0.357 0.397 0.558 0.543 0.583 0.670 0.715 0.697 0.791
-34.3 -30.2 -47.8 -43.4 -47.9 -29.6 -34.4 -37.0 -20.4 -17.8 -25.4 -28.4 -19.7
-0.5 +2.3 -5.6 -3.8 -9.8 -2.9 -1.6 -4.2 +0.5 -0.7 -1.2 -3.7 -0.7
FaNtERa/(ERa + 1) + (1 - Fa)NtERb/(ERb + 1) FaNt/(ERa + 1) + (1 - Fa)Nt/(ERb + 1) (16)
Cancel Nt, rearrange, and solve for Fa:
Fa )
(ERm - ERb)/(ERb + 1) (ERa - ERm)/(ERa + 1) + (ERm - ERb)/(ERb + 1) (ERm - ERb)(ERa + 1) (ERa - ERm)(ERb + 1) + (ERm - ERb)(ERa + 1)
Expanding the denominator, canceling like terms, and refactoring yields eq 2.
Application to Synthetic Mixtures Experimental. Equation 2 was applied to estimating the fraction of a chiral compound arising from source A (Fa) in A-B mixtures, prepared from known proportions of nonracemic and racemic HEPX. Racemic HEPX was obtained as an analytical standard from the U.S. Environmental Protection Agency, Repository for Pesticides and Industrial Chemicals, Research Triangle Park, NC, The nonracemic HEPX was obtained by extracting soils from two farms in the midwestern United States where HEPX enriched in the (+) enantiomer had been found (12). Analyses were carried out by capillary gas chromatography on a BGB-172 column (20% tertbutyldimethylsilylated-β-cyclodextrin in OV-1701, 30 m × 0.25 mm i.d., 0.25 µm film, BGB Analytik AG, Switzerland) with detection by negative ion mass spectrometry, monitoring ions 316 and 318. Details of chromatographic conditions are given in ref 7. The two enantiomers of HEPX were baseline separated on the BGB-172 column, with the (+) enantiomer eluting first. Chromatograms of HEPX enantiomers in soil and ambient air have been published elsewhere (4, 6, 7, 12). Solutions containing nominally 0.1 ng µL-1 nonracemic (solution A) and racemic (solution B) HEPX were prepared in isooctane, and the concentration of solution B was assayed vs solution A by comparing peak areas (sum of both enantiomer peaks and average of results at ions 316 and 318). Solutions A and B were mixed to give the varying compositions (reported as Fa) in Table 1. The ER ) (+)HEPX/(-)HEPX of the binary mixtures (ERm), and solutions A (ERa) and B (ERb) were determined chromatographically and used to estimate Fa by eq 2. Fa was also calculated from the experimental data by using eq 1 to call attention to the errors that can potentially arise by using this incorrect relationship.
Results and Discussion The values of ERa for the two farm soils were as follows: soil 1 ) 3.258 ( 0.070 (n ) 12) and soil 2 ) 2.249 ( 0.055 (n ) 4); ERb for the racemic HEPX was 0.995 ( 0.009 (n ) 16), determined by multiple injections and calculation of the ERs using responses at each ion. Standard deviations for ERm values ranged from 0.004 to 0.043 with an average of 0.018 (n ) 4-6). Fa values calculated from eqs 1 and 2 were compared to the prepared compositions over a range of Fa from ∼0.2 to 0.8. Errors obtained using eq 2 were small, ranging from +2.1% to -9.8% and averaging -2.5%. Using the standard deviations of ERa and ERb values above and an 2300
9
% error
actual Fa
Substitute from eqs 8 and 9:
ERm )
TABLE 1. Fractional Contribution of Nonracemic HEPX (Fa) in a Mixture Derived from Nonracemic (Soil)a and Racemic (Standard)b Sources, Estimated from Eqs 1 and 2
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Source A, ERa ) 3.258 (soil 1) and 2.249 (soil 2). b Source B, ERb ) 0.995 (HEPX standard). c Duplicate experiments using freshly prepared solutions. a
average ERm of 1.800 ( 0.018, the propagated percent relative standard deviations in Fa are 4-6%. The experimental uncertainties obtained using eq 2 are thus quite realistic. Equation 1 is mathematically incorrect and, for the mixtures in Table 1, underestimates Fa by ∼20-50%. The errors are larger for mixtures prepared from extracts of soil 1 than those prepared from soil 2, corresponding to greater differences between the ERs of the end members for the former mixtures. The direction of eq 1 error depends on the values of ERa and ERb. For mixtures in Table 1, where ERa > ERb, the errors are negative. However, for a situation where ERa ) 1.00, ERb ) 0.2, and ERm ) 0.6, eqs 1 and 2 predict values of Fa ) 0.50 and 0.38, respectively. Taking the eq 2 result as correct, the error incurred in using eq 1 is +32%. We feel that it is important to point out the large errors that can potentially arise from using eq 1, since it has been published in several papers (3-5). This paper has provided the framework for employing ERs to apportion contributions in mixtures derived from two sources. The utility of such methods is obviously restricted to situations where the ERs of the two source types and the resultant mixture are sufficiently different to be distinguished analytically. Knowing the precisions of these ERs, the minimum error in Fa can be estimated as above. However, there are likely to be other contributions to the uncertainty, such as variation in the ERs of the sources. For example, relative standard deviations in the ERs of chlordane compounds in soils of the midwestern United States are on the order of 1-3% for replicate analyses of a single soil (12), but they are 12-17% for the 24 soils sampled (4). Such variability would need to be considered if enantiomeric data were used to estimate the relative contribution of chlordane volatilization from soil to ambient air on a regional basis. The approach described in this paper is based on enantiomer data for a single compound and cannot be extended to more than two source types. This is because the ER of a third source could be derived simply from a combination of sources A and B. Multiple enantiomeric tracers may be of aid in apportioning more than two sources. The variability in ERs is far lower than for concentrations, which spanned 3 orders of magnitude in the midwestern soils (12). Moreover, ERs are not affected by analytical recovery factors nor by abiotic process that take place during transport (e.g., photolysis, hydrolysis, atmospheric deposition). Such advantages make enantiomers especially attractive as tracers (1).
Acknowledgments We thank Andrea Leone for supplying the soil extracts and Colleen Bodner for assistance with the analysis. Thanks also to several co-workers and an anonymous reviewer for checking the algebra.
Literature Cited (1) Bidleman, T. F.; Falconer, R. L. Environ. Sci. Technol. 1999, 33, 206A-209A. (2) Falconer, R. L.; Bidleman, T. F.; Gregor, D. J.; Semkin, R.; Teixeira, C. Environ. Sci. Technol. 1995, 29, 1297-1302. (3) Ridal, J. J.; Bidleman, T. F.; Kerman, B.; Fox, M. E.; Strachan, W. M. J. Environ. Sci. Technol. 1997, 31, 1940-1945. (4) Bidleman, T. F.; Jantunen, L. M. M.; Harner, T.; Wiberg, K.; Wideman, J. L.; Brice, K.; Su, K.; Falconer, R. L.; Aigner, E. J.; Leone, A. D.; Ridal, J. J.; Kerman, B.; Finizio, A.; Alegria, H.; Parkhurst, W. J.; Szeto, S. Y. Environ. Pollut. 1998, 102, 43-49. (5) Jantunen, L. M. M.; Bidleman, T. F. J. Geophys. Res. 1996, 101, 28837-28846; (corrections) 1997, 102, 19279-19282.
(6) Finizio, A.; Bidleman, T. F.; Szeto, S. Y. Chemosphere 1998, 36, 345-355. (7) Bidleman, T. F.; Jantunen, L. M. M.; Wiberg, K.; Harner, T.; Brice, K. A.; Su, K.; Falconer, R. L.; Leone, A. D.; Aigner, E. J.; Parkhurst, W. J. Environ. Sci. Technol. 1998, 32, 1546-1548. (8) Ulrich, E. M.; Hites, R. A. Environ. Sci. Technol. 1998, 32, 18701874. (9) Buser, H.-R.; Mu ¨ ller, M. D. Environ. Sci. Technol. 1998, 32, 626633. (10) Zipper, C.; Suter, M. J.-F.; Haderlein, S. B.; Gruhl, M.; Kohler, H.-P. E. Environ. Sci. Technol. 1998, 32, 2449-2455. (11) Garrison, A. W.; Schmitt, P.; Mertens, D.; Kettrup, A. Environ. Sci. Technol. 1996, 30, 2070-2076. (12) Aigner, E. J.; Leone, A. D.; Falconer, R. L. Environ. Sci. Technol. 1998, 32, 1162-1168.
Received for review January 29, 1999. Revised manuscript received April 15, 1999. Accepted April 19, 1999. ES9901056
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