Estimating tropospheric lifetimes and ozone-depletion potentials of

Environ. Sci. Technol. 1992, 26, 739-744

Estimating Tropospheric Lifetimes and Ozone-Depletion Potentials of Oneand Two-Carbon Hydrofluorocarbons and Hydrochlorofluorocarbons Jonathan S. Nimltz*st and Stephanie R. Skaggst Center for Global Environmental Technologies, New Mexico Engineering Research Institute, University of New Mexico, Albuquerque, New Mexico 87 13 1-1376, and Environmental Technology and Education Consultants, 3300 Mountain Road Northeast, Albuquerque, New Mexico 87106-1920

Tropospheric lifetimes and ozone-depletion potentials (ODPs) are estimated for all 53 possible one- and twocarbon hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs). The relationships among C-H bond strength, activation energy for removal of H by OH, tropospheric lifetime, and ODP are examined. Algorithms are developed that are easy to apply and accurate enough for initial screening purposes. On the basis of extant theory and our analysis, the controlling variables for determining HCFC tropospheric lifetimes include number of hydrogen atoms, molecular weight, number of carbons, number of chlorine atoms a and p to hydrogen, and number of fluorine atoms p to hydrogen. The formula presented predicts lifetimes for molecules with atmospheric lifetimes below 30 years with a root mean square (rms) error of a factor of 2.4. An algorithm is also presented to calculate ODP based on tropospheric lifetime; the overall rms error for calculating ODP from the structure is a factor of 2.5. In many cases, ODPs of chlorine-containing compounds are predicted to be below 0.001. These estimates also aid in malting tentative choices among alternative HFCs and HCFCs based on environmental considerations.

4

Introduction Hydrohaloalltanes are gaining importance as potential alternatives to fully halogenated compounds in many applications including refrigeration, foam blowing, firefighting, and aerosol propulsion. HCFCs 22,123, and 141b are already in commercial use, and other hydrofluoroalkanes such as HCFC-124, HFC-l34a, HCFC-l42b, HFC-l52a, and a blend of HCFC-225ca and HCFC-225cb may be approaching large-volume usage (1, 2). I t also appears likely that selected hydrogen-containing halocarbons will prove to be effective clean firefighting agents with acceptable environmental and toxicological properties ( 2 , 3 ) . However, reported data on many haloalkanes are scanty; a search of our literature database on over 650 oneto eight-carbon haloalkanes reveals that only half have even boiling points reported. Information on the environmental properties of most hydrohaloalkanes is limited or nonexistent at this time. Rigorously calculated twodimensional atmospheric lifetimes and ozone-depletion potentials (ODPs) require as input experimentally-determined photolytk cross sections and rates of reaction with hydroxyl radicals; they also require substantial computing time. Rapid and inexpensive algorithms are needed to screen potential candidate agents. As a molecule travels upward from the surface of the earth, it can be decomposed either in the troposphere (primarily by reaction with OH or, in some cases, photolysis) or in the stratosphere by photolysis from the shorter-wavelength light. The lifetime is defined as the time it takes for the quantity of a chemical released to drop to l / e or approximately 37% of its initial value; this lifetime corresponds to 1.41 half-lives. Major atmospheric t

University of New Mexico. Environmental Technology and Education Consultants.

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sinks for halocarbons include reaction with OH (if H is present) and photolysis. Tropospheric lifetimes for Hcontaining haloalkanes correlate with the interrelated factors C-H bond strength, activation energy, and rate constant for removal of H by OH (4). Photolysis becomes increasingly significant as molecules reach the stratosphere. Evidence is increasing that some additional sinks exist. For example, recent work has shown that halocarbons undergo degradation when exposed to certain soils (5). Atmospheric lifetime depends on the rates of all destructive processes. In order for a compound containing chlorine to have a low ODP it must also have a very short tropospheric lifetime, so that a large fraction is destroyed before reaching the ozone layer in the stratosphere. The primary atmospheric sink for many hydrogen-containing haloalkanes is reaction with hydroxyl radicals in the troposphere (6-8). Compounds containing hydrogen often have much lower tropospheric lifetimes than fully halogenated compounds because reaction with hydroxyl radicals ('OH) results in relatively rapid destruction (6). The process of hydrogen abstraction is illustrated in reaction A. The resulting haloalkyl radical (R') undergoes R-H + 'OH R' HQO (A)

+

a sequence of further reactions leading eventually to the formation of COz and hydrohalic acids, HX (6). This degradative sequence is initiated by the addition of O2to the haloalkyl radical to form a peroxy radical. The peroxy radical undergoes a net loss of one oxygen atom to form an alkoxyl radical; this process occurs either by loss of oxygen to NO (forming NOz) or by gaining a hydrogen atom to form a hydroperoxide followed by cleavage of the weak oxygen-to-oxygen bond (releasing OH). The alkoxyl radical then undergoes further degradative and oxidative reactions. Except in special cases, such as geminal dibromides that undergo rapid tropospheric photolysis, reaction A represents the initial step of the primary mechanism for removal of hydrogen-containing halocarbons from the troposphere. In order to estimate the tropospheric lifetimes of these compounds, it is therefore desirable to estimate the rates of reaction with hydroxyl radicals. The rate of reaction A is given by eq 1. rate = -d[RH]/dt = k['OH][RH] = k'[RH]

(1)

The hydroxyl concentration can be included in the rate constant because the relatively constant average concentration of 'OH in the troposphere is known to be approximately 6.5 (*2) X lo6 molecules/cm3, which corremol/L (6). Once the *OH sponds to 1.1 (*0.3) X concentration is included in k ', the reaction follows pseudo-first-order kinetics in [RH]. One caveat is that the tropospheric OH concentrations may vary in the future as other atmospheric trace gases change in concentration. Such fluctuations could affect HCFC lifetimes, though the effects would be expected to be small. Indirect evidence indicates that the average tropospheric OH concentration has changed within the historic past by approximately 25%. Tropospheric OH concentrations depend mainly on

0 1992 American Chemical Society

Environ. Sci. Technol., Vol. 26, No. 4, 1992 739

Table I. Predicted Tropospheric Lifetimes and ODPs for All One- and Two-Carbon HFCs, HCFCs, and HCCs

halocarbon no. 20 21 22

23 30 31 32 40 41 120 121

121a 122 122a 122b 123 123a 123b 124 124a 125 130 130a 131 131a 131b 132 132a 132b 132c 133 133a 133b 134 134a 140 140a 141 141a 141b 142 142a 142b 143 143a 150 150a 151 151a 152 152a 160 161

formula CHCl, CHClzF CHCIFz CHF, CHpClz CHzCIF CHPZ CH3Cl CH3F CHClZCC13 CHClzCClzF CHC1FCCl3 CHClZCClFz CHClFCC1,F CHFzCC13 CHClzCF3 CHCIFCCIFz CHFZCClzF CHC1FCF3 CHFzCCIFz CHFzCF3 CHClzCHClz CHZClCCl3 CHClFCHClz CH,ClCCl,F CH2FCCl3 CHClFCHClF CHFzCHClz CHpCICCIFz CHzFCClzF CHzClCF3 CHClFCHFp CHzFCCIFz CHF2CHFz CH2FCF3 CHzCICHClz CH3CC13 CHCIFCHzCl CHZFCHClz CH3CClZF CHzClCHFz CHCIFCHzF CHZCClFz CHzFCHFp CH3CF3 CHzCICHzCl CH,CHC12 CHzClCHzF CH3CHClF CHZFCHBF CH3CH F2 CH3CHzCl CH3CHzF

lifetime, years rig. calc estd

ODP per molecule rig. calc estd

0.17 1.9b 15.8c 411b,e

1.2

a

0.010' 0.005 0.048d 0.030 0.00

7.5 46 0.47 1.3b 2.83 O.OIOc 7.31 16 1.54f 1.3 3.7b 5.8 0.58 0.81 4.2 1.1

1.76

5.8 30 1.6 8.1 41

7.11

11.2

a

0.013 0.00 0.002 0.00 0.001 0.004 0.16 0.009 0.14 0.23 0.017d 0.013 0.09 0.13 O.O1gd 0.035 0.047 0.00 a 0.052

57 40.6 77 0.09 1.9 a 0.22 0.060 2.6 13 0.20 0.92 0.002 a 0.35 3.9b 3.6 0.047c 0.049 18 0.12 4.4b 4.8 0.070' 0.023 2.1 0.008 25 0.043 11.4b 8.4 0.00 0.00 15.6 33 a 0.05 7.8 0.14d 0.16 6.lf a 0.27 a 0.08 11.41 10.5 0.094d 0.10 a 0.76 a 0.49 22.6 13.9 0.0E~3~0.038 3.5b 0.020 2.4 0.00 64.2e3f 18 a 0.09 a 0.02 a 0.19 0.11 a 0.00 O.6Ob 0.70 0.00 1.86 0.60 a 0.04 0.00 0.19 0.28

Average of results reported on p a Nonzero but less than 0.001., 124 of ref 5. 'Personal communication, Dr. Peter Connell, Lawrence Livermore National Laboratory. dAverage of all one- and two-dimensional results reported on p 314 of ref 5. eLong-lived species not estimated accurately by algorithm. f Value from Report of the Ozone Scientific Effects Panel, UNEP, 1991.

processes other than reactions with HCFCs and are not significantly affected by HCFC emissions of a moderate scale. The tropospheric lifetime (7)is the inverse of the rate constant for reaction with OH (9): 7 = l/k' (2) where the pseudo-first-order rate constant k 'incorporates the average tropospheric OH concentration. 740

Environ. Sci. Technol., Vol. 26, No. 4, 1992

Table 11. Ranges of Strength for Various Types of Covalent Bonds to sp3 Carbon bond type

bond strength, kcal/mol

bond type

bond strength, kcal/mol

C-H C-F

92-106 105-117 70-86

C-Br c-I

64-72 48-57 64-108

c-c1

c-c

The most accurately known atmospheric lifetimes for one- and two-carbon HFCs and HCFCs have been calculated by three independent methods (and groups of researchers) using two-dimensional atmospheric models (6). Although the methods of calculation differ slightly and the reported uncertainties are 40-50%, the lifetimes obtained by these three methods generally agree within 15%. The averages of the three calculated lifetimes reported for 21 HFCs and HCFCs are given in Table I. Rates of reaction with OH depend on the related factors of activation energy and C-H bond strength. Bond strength, also known as bond dissociation enthalpy or energy (BDE) is the minimum energy required to break a particular bond. Bonds can break either homolytically or heterolytically. Homolytic bond cleavage, shown in reaction B, is of greater relevance to atmospheric degradation of haloalkanes: R-X R' + X' (B) -+

where, in the case of haloalkanes, R is an alkyl or haloalkyl group and X can be a hydrogen or halogen atom or another alkyl or haloalkyl group. The energy consumed in this bond-breakingprocess equals the energy released when the same two radicals combine to form a new bond. Normal ranges for strengths of various types of covalent bonds to sp3 hybridized carbon are shown in Table I1 (9). A general relationship exists between bond strength and the activation energy needed for a bond-breaking process. The stronger the bond, the more difficult it is to break and, in general, the higher the activation energy and the lower the rate constant for the reaction. Within a related series of compounds, the activation energy is approximately proportional to bond strength (10). Activation energy determines the rate of reaction (i.e., rate of destruction) and therefore the tropospheric lifetime.

Methods We have examined relationships among C-H bond strength, activation energy for reaction with hydroxyl radical, and tropospheric lifetime, and have reviewed previous methods of estimating these quantities. Presented herein is a new, parameterized algorithm for predicting tropospheric lifetimes of one- and two-carbon HFCs and HCFCs within a rms error factor of 2.4 and ODPs with a rms error factor of 1.4 if the lifetime is known or a factor of 2.5 if based on the structure alone ( 4 ) . This simple, theoretically-supportable algorithm is easy and inexpensive to apply and accurate enough for initial screening purposes. This algorithm, shown in equation 3, generates estimated 7 = 0.787(M/nH) X e~p(-2.060n,-~~ - 4.282,~+ 1.359np.~ + 0.926na.c1) (3) tropospheric lifetimes for compounds with atmospheric lifetimes under 30 years. The constants have been fitted to the rigorously calculated data available, and n with the subscripts a or /3 and F or C1 represents the number of a: or @ fluorine or chlorine atoms present, respectively. a: means a substituent is attached to the same carbon atom as the hydrogen atom being considered; /3 means the substituent is attached to the carbon atom adjacent to the

Table 111. Parameters for Fitting of Lifetime Algorithm ( e s 4) constant

parameter value

t-value

C1

-0.2391 00 -2.060 -4.282 1.359 0.9262

-0.60

c2

c3 c4

c5 c6

-6.45 -3.29 3.00 2.04

Eliminated from the model. Table IV. Parameters for Fitting of ODP Algorithm (eq 7) constant

parameter value

t-value

c1

-2.993 -3.858 1.510

-15.7 -5.05 4.76

C2

c3

carbon atom bonded to the hydrogen. The subscript 2C indicates a term to be added only if the compound contains two carbon atoms. The constants in eq 3 were determined by fitting the model shown in eq 4 to the rigorously calculated data using multiple regression (11). In (Tn,/M) = c1 + C2nu-F + C3na-Cl+ C4,ZC + c5ng-F + C6nB-Cl (4) Two long-lived outliers were eliminated (HFCs 23 and 143a), leaving lifetime data on a total of 20 compounds. The effect of the a-fluorine was found to be not statistically significant. The reduced model (omitting the a-fluorine term in eq 4) has the estimated parameters shown in Table 111. The adjusted rz for this reduced model was 0.69, and the F-ratio was 10.94 with 11degrees of freedom (p < 0.001). Equation 4 is derived in the derivations section. Tropospheric lifetimes can also be calculated for molecules containing two different types of hydrogen atoms. For the two-carbon HFCs and HCFCs that each contain two types of reactive hydrogens (HFCs l43,152a, and 161), lifetimes were computed by calculating a lifetime based on each type of hydrogen separately, then combining the two into an overall lifetime according to eq 5, where T~ and 1/7 = 1/71 + 1 / 7 2 (5) T~ are tropospheric lifetimes based on the abstraction of each of the two types of hydrogen separately. ODP can be related to a lifetime via eq 6, where ncl is

ODP = kln& exp(k,/r) (6) the number of chlorine atoms in the molecule. The reasoning behind the development of eq 6 is given in the derivations section. The statistical model for eq 6 is shown in eq 7. In (ODP) = c1 + czncl c3/7 (7)

+

Equation 7 was fitted to the rigorously calculated data using multiple regression (11),giving the parameters shown in Table IV. The adjusted rz for the model in eq 7 was 0.87, and the F-ratio was 17.1.0for 7 deg of freedom. Substituting the parameters from Table IV into eq 7 gives eq 8, which was ODP = 0.05013nc11.510 exp(-3.858/~) (8) used to estimate the ODPs shown in Table I. Equation 8, taken together with eq 3, allows the estimation of ODPs for all one- and two-carbon HFCs and HCFCs. The estimated 95% confidence interval for the calculated ODP

based on the structure in this two-stage estimation is ODP/2.5 to 2.5 X ODP. Results and Discussion A new parameterization scheme for estimating tropospheric lifetimes of one- and two-carbon HCFCs and HFCs has been developed; the algorithm is simple, yet chemically reasonable. Estimated tropospheric lifetimes (calculated using eq 3) and ODPs (from eq 7) for all 53 possible oneand two-carbon HFCs, HCFCs, and HCCs (hydrochlorocarbons) are given in Table I. The rigorously calculated values available are given for comparison. The only two compounds for which the estimated lifetime was not within a factor of 2.6 of the rigorously calculated lifetime were the two longest-lived species: HFCs 23 and 143a. Several factors may enter into this discrepancy. Calculated lifetimes of over 30 years are considered less reliable than shorter lifetimes (6). For long-lived compounds, a larger fraction will reach the stratosphere (passing above most OH radicals), and photolysis in the stratosphere will be the main destruction mechanism (12). The algorithm was therefore fitted using only compounds with lifetimes below 30 years (omitting HFCs 23 and 143a) (11). The fact that the estimated overall lifetimes for the short-lived compounds containing two types of hydrogen atoms (HFCs 152 and 161) are within a factor of 3 of the rigorously calculated lifetimes based on experimental data supports the validity of the algorithm. The presence of fluorine on the a-carbon did not significantly affect the lifetime; this was shown by the low absolute value of t (((2) obtained in the linear multiple regression (11).Consequently,a factor for a-fluorine atoms was left out of the algorithm. The presence of a-chlorine(s) and a second carbon atom contributes to lower activation energy and decreased tropospheric lifetime. The presence of fluorine or, to a lesser extent, chlorine in the p position increases both activation energy and lifetime. These parameters allow predictions to be made as to which isomer among several will have the shorter tropospheric lifetime and the lower ODP. For example, it is predicted that HCFC-123 will have a significantly shorter tropospheric lifetime and lower ODP than its isomer HCFC-123a. Theoretical Background Activation Energies. The relationship between bond strength and activation energy for the bond-breaking reaction is described by the semiempirical Polanyi-Evans theory (13). However, in using this method, an error of 1 kcal/mol in activation energy leads to an error in rate constant (and lifetime) of a factor of 5, and the scatter of the data is too great to provide useful predictions for halocarbons. A more sophisticated method of calculating activation energies is required: one such method is the bond energy-bond order (BEBO) approach (14,15). The Morse potential parameters are needed to compute the repulsion energy between the end groups. Activation energies can be calculated, though they are quite sensitive to input parameters, which must therefore be known accurately. In the best cases, computed values match observed values within 1kcal/mol, about the same accuracy as that obtained from the Evans-Polanyi plots, Rate of Reaction with Hydroxyl. Several efforb have been made to predict rate coefficients for H-atom abstraction reactions more accurately than is possible using either Evans-Polanyi plots or BEBO calculations. One method is to plot the logarithm of the rate constant for the 'OH abstraction reaction versus bond dissociation energies (16). However, the compounds used in this plot did not include haloalkanes. More extensive studies have Envlron. Sci. Technol., Vol. 26, No. 4, 1992

741

been conducted on rates of reaction of *OHwith alkanes (17-22) than with haloalkanes ( 4 , 8, 23). An additivity scheme has been developed to calculate room temperature rate coefficients for reaction A based on the number of equivalent hydrogen atoms and the substitution pattern (12). This approach can successfully predict rate coefficients within a factor of “2, but is somewhat cumbersome computationally and only valid at room temperature. A more general expression has been developed that accounts for molecular weight and allows calculations at other temperatures (24). The line-of-centers collision approach permits computation of the reaction rate coefficient from the knowledge of only the bond dissociation enthalpies. Conversely, if the rate constant is known, the bond strength can be calculated. Unfortunately, in many cases bond dissociation enthalpies (BDEs, bond strengths) are not known and must be estimated. Several generalizations have been made about trends in bond strength with substitution pattern (25). For example, chlorine, bromine, or iodine atoms a to a C-H bond generally reduce both the homopolar and heteropolar BDEs. Fluorine substituents a to C-H bonds appear to have little or no effect on the homopolar or heteropolar C-H BDE. These observations have been refined into an additivity scheme for estimating C-H BDEs (7). This additivity scheme can be used to predict experimental bond strengths to within approximately 2-3 kcal/mol, comparable to experimental errors. BDEs may also be obtained from infrared spectra (26). Although estimates of reaction rates and corresponding lifetimes based on correlations with thermochemistry are highly uncertain at this time, progress is being made in quantum mechanical calculations to obtain accurate reaction rates using variational reaction-path methods (27). Rate constants for reaction with *OHand tropospheric lifetimes for haloalkanes have been estimated by the following steps: finding the bond dissociation enthalpy for each nonequivalent C-H bond either from the literature or by estimation, calculating the activation energy and rate constant according to simple formulas, and then using these quantities to calculate a lifetime (2). This method is useful if the BDE is known with a high degree of accuracy. However, since BDEs are generally only known to within 1-2 kcal/mol, this method suffers some drawbacks. It is highly sensitive to errors in BDEs; propagation of an error of 2 kcal/mol in BDE leads to an error of greater than a factor of 5 in an estimated lifetime. Such propagation of errors can be circumvented by estimating activation energies and rate constants directly from structural features without the use of BDEs. The great majority of chemical reaction rate constants can be expressed readily in the Arrhenius form given in eq 9 (28) iz = A exp(-E,/RT) (9) where A is the Arrhenius preexponential or frequency factor, E, is the activation energy, R is the gas law constant, and T is the absolute temperature. Equation 9 can be modified to the explicitly temperature-dependent form shown in eq 10, where A’, E:, and n are the new parameters. k = A T exp(-E,‘/RT) (10)

A parameterized correlation of chemical structure with the rate of hydrogen abstraction by hydroxyl for haloalkanes has been reported previously (IO). For a set of 10 halomethanes and 18 haloethanes a “universal” rate coefficient was developed that depends only on the mo742

Environ. Sci. Technol., Vol. 26, No. 4, 1992

lecular weight and the number of abstractable hydrogen atoms in the haloalkane. This rate coefficient is given in eq 11, where nH is the number of extractable hydrogen k ( T ) = 106%HM-1F,5exp[-(E/R - 450)/Tl

(11)

atoms of a given type, M is the molecular weight, T is the absolute temperature, and R is the gas constant. The activation energy E at 298 K is given by a group additivity scheme. Although it provides reasonable overall rate constants near room temperature and is attractive for its ease of use, this approach generates functions that differ markedly from current experimental data both in the preexponential and activation energy terms. For this reason it was decided to modify the approach taken in ref 10. Derivations For global averaging, it is helpful to estimate an average global temperature for the reaction occurring; such a temperature is related to the average height at which the reaction occurs. This average temperature for reaction of haloalkanes with tropospheric ‘OH is believed to be approximately 277 K (6). If the temperature is taken as 277 K, [‘OH] is taken as 1.1 X M (or 6.5 X lo5 molecules/cm3), and units are converted to year-,, then k ’ = k[’OH] = 498(nH/M) exp(-[(E,/R)- 4501/277} year-’ (12)

Tropospheric Lifetime. Combining eqs 2 and 12 yields the relationship of activation energy to tropospheric lifetime: T = 0.00201(M/nH) exp([(E,/R) - 450]/277) (13) Assuming that E,/R can be estimated parametrically by eq 14 and substituting eq 14 into eq 13 and combining E, = c1 + cZna.F+ c3nt,.c1+ C4,ZC + c5np.F+ c6np.c1 (14) constants gives eq 15. Fitting this equation to the rigT =

cl(M/nH) exp(c2na.F + C3na-CI + C4,ZC

+ C5np-F + c6np-Cl) (15)

orously calculated atmospheric lifetime data, as described in the Methods section, yields eq 3. This scheme considers that, as a first approximation, the contributions of the first, second, and third substituent of each type are equal. It has the advantage of only requiring six parameters. This equation applies only to one- and two-carbon haloalkanes containing at least one hydrogen atom and no bromine or iodine (only the halogens fluorine and/or chlorine). If a molecule contains more than one type of reactive hydrogen, the equations for tropospheric lifetime must account for two reaction pathways for hydrogen abstraction; each process has its own rate constant (kl’ and h i ) . Since the rate constants k,’ and k,’ include the (constant) ‘OH concentration, and these reactions are pseudo-firstorder in the hydrogen-containing haloalkane -d[A]/dt = k,’[A] + kZ’[A] = ( k l ’ + k,’)[A] = k’btal[A] (16) The overall rate constant (kiOtd)for destruction is the sum of the individual rate constants for the processes occurring. It follows that 7 = l / k & d = l/(ki’ + k,’) (17) Replacing k,’ with 1 / ~and , k,’ with 1/r2gives 7

=

l/(l/TI

+ 1/72)

(18)

or 1/7 =

1/71

+ 1/72

(19)

Therefore, if two types of hydrogen are present, the total lifetime can be computed using eq 19. If the variables are redefined, eq 19 also represents the relationships among tropospheric, stratospheric, and atmospheric lifetimes. For this relationship, T is taken to be the overall atmospheric lifetime, T~ is the tropospheric lifetime, and T~ is the stratospheric lifetime. However, it should be noted that stratospheric lifetime (r2)is not on ) of a parallel basis with tropospheric lifetime ( T ~ because the increased importance of halocarbon removal by 0[‘D] and by photodissociation. Pseudo-first-order kinetics may therefore not be appropriate for stratospheric halocarbon reactions. To convert a reported tropospheric lifetime to an “average”activation energy, eq 13 can be rearranged and solved for E,/R to give E,/R = 277 1n (498n,T/M) 4- 450 (20) Combining the constants yields E,/R = 2170 277 [In (nHT/M)]

+

(21)

Equation 21 enables the estimation of activation energies from lifetimes for those compounds that have only one type of reactive hydrogen. Ozone-Depletion Potential. ODP depends on the fraction of molecules surviving to reach the stratosphere and the number of chlorine or bromine atoms delivered per molecule. The algorithm we have developed for ODP has the form ODP = A F T s (22) where A is a normalizing constant, F, is a reactivity factor depending on the number of chlorine atoms in the molecule, and F, is a survival factor (the fraction of molecules surviving transport to the stratosphere). The reactivity factor can be approximated as n@, the number of chlorine atoms in the molecule raised to a power determined by fitting. If 7 is the tropospheric lifetime of a compound, the fraction surviving to reach the stratosphere is exp(-c3/7), where c3 is a constant representing transit time through the troposphere to the tropopause. This transit time is approximately the same for all the molecules considered because the main transport mechanism is eddy diffusion (physical mixing). Substituting these expressions into eq 22 gives eq 23. ODP = clncf* exp(-c,/~) (23) Fitting the constants using the rigorously calculated ODPs and estimated tropospheric lifetimes for 11 HFCs and HCFCs gives c1 = 0.05013, c2 = 1.510, and c3 = 3.858. Making these substitutions in eq 23 gives eq 24, which was used for estimating ODP values. ODP = 0.05013nc11.510 exp(-3.858/7) (24) Equation 24, taken with eq 3, allows an estimation of ODPs for all one- and two-carbon HFCs and HCFCs. These estimates are shown in Table I, with the rigorously calculated values for comparison (8). Summary and Conclusions The relationships among C-H bond strength, activation energy for removal of H by OH, tropospheric lifetime, and ODP have been examined. Equations have been presented that allow the calculation of all of these four quantities from any one, or calculation of all four, based on chemical structure alone. Tropospheric lifetimes and ODPs have

been estimated for all 53 possible one- and two-carbon HFCs and HCFCs. The estimated tropospheric lifetimes of these compounds range between 1week and 46 years; estimated ODPs range from 0.00 to 0.20. Many compounds are predicted to have short tropospheric lifetimes (below 10 years) and ODPs below 0.05. In many cases ODPs of chlorine-containing compounds are predicted to be below 0.001. Although the estimates are very rough, on the basis of these results it is anticipated that the following species may be long-lived (possibly having tropospheric lifetimes greater than 10 years): 122b, 123b, 124a, 131b, 132c, and 133b. The following species (for which the rigorously calculated ODPs are not available) may have ODPs above 0.05: 121a, 122a, 122b, 123a, 123b, 124a, 130a, 131a, 131b, and 132c. All of the estimated values are of course subject to verification by laboratory investigations and comprehensive atmospheric model calculations. The approach taken here will be tested for extension to three-carbon and bromine-containing compounds when the rigorously calculated lifetimes and ODPs for these compounds become available. Registry No. CHCl,, 67-66-3; CHC12F, 75-43-4; CHC1F2,7545-6; CHF3,75-46-7; CHZC12,75-09-2;CHZClF, 593-70-4; CHZFZ, 75-10-5; CH3C1, 74-87-3; CHSF, 593-53-3; CHClZCC13, 76-01-7; CHC12CClZF, 354-14-3;CHClFCC13,354-11-0;CHClZCClF,, 35421-2; CHClFCCl,F, 354-15-4; CHFZCCl3, 354-12-1; CHClZCF3, 306-83-2;CHClFCClF2,354-23-4; CHF2CCl,F, 812-04-4; CHClFCF3, 2837-89-0; CHF2CClF2, 354-25-6; CHFZCF3, 354-33-6; CHClzCHClz, 79-34-5; CH&lCC13,630-20-6; CHClFCHClZ, 35928-4; CH2ClCCl,F, 811-95-0; CH,FCC13,2366-36-1; CHClFCHClF, 431-06-1; CHF&HC12,471-43-2; CH2ClCClF2, 1649-08-7;CHZFCClZF, 1842-05-3; CHzClCF3, 75-88-7; CHClFCHF2, 431-07-2; CH2FCClF2,421-04-5;CHFZCHFZ, 359-35-3;CHZFCF,, 811-97-2; CH&lCHC12,79-00-5; CH&C13,71-55-6; CHClFCH,Cl,430-57-9; CH2FCHC12,430-53-5; CH,CClzF, 1717-00-6; CH&lCHFz,33865-8; CHClFCHZF, 338-64-7; CH3CClF2, 75-68-3; CHZFCHFZ, 430-66-0; CH3CF3, 420-46-2; CHZClCHzCl, 107-06-2;CH3CHC12, 75-34-3; CH&lCHZF, 762-50-5; CHSCHClF, 1615-75-4;CHZFCHZF, 624-72-6; CH3CHF2, 75-37-6; CH3CH2C1, 75-00-3; CHSCHZF, 353-36-6; 03,10028-15-6.

Literature Cited (1) Impact of a CFC Ban on the Cost and Performance of

Household Refrigerators, Centrifugal Chillers, and Commercialllndustrial Refrigeration Systems; A. D. Little, Inc.: Cambridge, MA, Aug 1989; (ref 53674-10). (2) Nimitz, J. S.; Tapscott, R. E.; Skaggs, S. R.; Beeson, H. D. Alternative Training Agents Phase I-Survey of Near-Term Candidate Fire-Extinguishing Agents and Predicting Properties of Halocarbon Mixtures. ESL-TR-90-39; Engineering and Services Laboratory, Air Force Engineering and Services Center: Tyndall AFB, FL, Apr 1990; Vol. 1. (3) Tapscott, R. E.; Lee, M. E.; Watson, J. D.; Nimitz, J. S.; Rodriguez, M. L.; Morehouse, E. T.; Walker, J. L. NextGeneration Fire Extinguishing Agent Phase IVFoundation for New Training Agent Development. ESLTR-87-03; Engineering and Services Laboratory, Air Force Engineering and Services Center: Tyndall AFB, FL, Aug 1989; Vol. 4. (4) Howard, C. J.; Evenson, K. M. J. Chem. Phys. 1976, 64, 197-202. ( 5 ) Khalil, M. A. K.; Rasmussen, R. A. Geophys. Res. Lett. 1989, 16, 679-682. (6) Scientific Assessment of Stratospheric Ozone: 1989. World Meteorological Organization, Global Ozone Research and Monitoring Project No. 20, Vol. 11, Appendix; AFEAS Report; United Nations Environment Program; United Nations: New York, 1989. (7) Wuebbles, D. J.; Connell, P. S. A Screening Methodology

for Assessing the Potential Impact of Surface Releases of Chlorinated Halocarbons on Stratospheric Ozone. UCID-19233; Lawrence Livermore National Laboratory: Berkeley, CA, Nov 1981. Environ. Sci. Technol., Vol. 26, No. 4, 1992

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Jeong, K.-M.; Kaufman, F. J . Phys. Chem. 1983, 86, 1816-1821. The CRC Handbook of Chemistry and Physics, 69th ed.; Weast, R. C., Ed.; Chemical Rubber Company: Boca Raton, FL, 1989. Cohen, N. StructureReactivity Relationships for Predicting Environmentally Hazardous Chemicals. EPA-600/3-86/ 672; U.S.Government Printing Office: Washington, DC, 1986; p 41. Hinze, J. L. Number Cruncher Statistical System (NCSS), Version 5.0, Kaysville, UT, 1987. Hendry, D. G.; Kenley, R. A. Atmospheric Reaction Products of Organic Compounds. EPA-560/ 12-79-001;U.S. Government Printing Office: Washington, DC, 1979. Evans, M. G.; Polanyi, M. Trans. Faraday Sac. 1938,34, 11. Johnston, H. S,; Parr, C. J. Am. Chem. Sac. 1963,85,2544. Johnston, H. S. Gas Phase Reaction Rate Theory; Ronald Press: New York, 1966; p 339. Gaffney, J. S.;Levine, S. Z. Int. J. Chem. Kinet. 1979,11, 1197-1209.

Atkinson, R. Int. J . Chem. Kinet. 1980,12,761-765. Cohen, N. Int. J . Chem. Kinet. 1982,14,1339-1362. Darnall, K.R.; Atkinson, R.; Pitts, J. N., Jr. J. Phys. Chem. 1978,82,1581-1584. Greiner, N. R. J. Chem. Phys. 1970,53,1070-1076. Baldwin, R. R.; Walker, R. W. J. Chem. SOC.,Faraday Trans. 1 1978,75,140-155. Shaw, R. J . Phys. Chem. Ref. Data 1978, 7, 1179-1190. Perry, R. A,; Atkinson, R.; Pitts, J. N., Jr. J. Chem. Phys. 1976,64, 1618-1620. Heicklen, J. Int. J . Chem. Kinet. 1981,13,651-665. Egger, K.W.; Cocks, A. T. Helv. Chim. Acta 1973,56, 1537-1553. Zavitsas, A. A. J . Phys. Chem. 1987,91,5573-5577. Truhlar, D. G.; Schwenke, D. W.; Kouri, D. J. J. Phys. Chem. 1990,94,7346-7352. Benson, S. W. Thermochemical Kinetics, 2nd ed.; John Wiley and Sons: New York, 1976; pp 10-13.

Received for review April 3,1991.Revised manuscript received September 4, 1991. Accepted December 2, 1991.

Passive Ozone/Oxidant Sampler with Coulometric Determination Using I,/Nylon-6 Charge-Transfer Complex Seiichiro Kannot and Yukio Yanagisawa" Harvard School of Public Health, 665 Huntington Avenue, Boston. Massachusetts 02 115

rn A new passive sampler for ozone/oxidants and its simple analytical system have been developed. The sampler consists of a carbon paper collector coated with nylon-6 polymer and potassium iodide, several layers of membrane filters to remove interferences, and a spacer and Teflon meshes to control sampling rate. Iodine liberated by an oxidation reaction of KI with ozone is stabilized by forming a charge-transfer complex with nylon-6 and is accumulated in the nylon-6 layer. The amount of I2 is determined by constant-current coulometry using the collector as a positive electrode and a zinc plate as a counter electrode. This procedure is simple, requiring no pretreatment. The sampler was applicable for measurement of 6-8-h average personal exposures to ozone/oxidants. The effects of surface wind velocity, temperature, and humidity were small. However, with relative humidities below 20%, it would underestimate the ozone/oxidant concentration.

Introduction Atmospheric ozone has been a serious environmental problem in industrialized countries because of its adverse health effects. Peak ambient ozone concentrations are still high enough to cause transient changes in lung function, respiratory symptoms, and airway inflammation in healthy people (I). These transient effects were more closely related to cumulative daily exposure than the l - h peak concentration of ozone. The effect of long-term chronic exposures to ozone is not defined yet, but current levels are sufficient to cause premature aging of the lung. Even in a rural area of western Massachusetts, for example, hourly ozone concentration exceeded 100 ppb for more than 6 h a day, while nitric oxide and nitrogen dioxide concentrations were below 20 ppb (1). Personal exposure +Presentaddress: National Institute of Industrial Health, Ministry of Labor, 6-21-1 Nagao, Tama-ku, Kawasaki, Kanagawa 214 Japan. 744

Environ. Sci. Technol., Vol. 26, No. 4, 1992

levels to ozone, however, have not been clarified yet due to lack of a suitable personal sampler. Several types of analyzers for ozone in air are commercially available (2). One is the photometer, which measures ultraviolet absorption of ozone a t 250-260 nm. Another is the chemiluminescence detector, which measures light produced by a reaction between ozone and ethylene. The chemiluminescence method is specific to ozone and suitable for ambient air monitoring. An analyzer based on amperometry is also available. The neutral buffered potassium iodide (NBKI) method is a wet chemical method to measure ozone/oxidants in ambient air (3). In the NBKI method, ozone/oxidants in the air are introduced into the neutral buffered KI solution and liberate I,. The amount of I2 is determined by measuring the UV absorbance of the solution at 365 nm. A passive sampler for ozone using the reaction of ozone and 1,2-dipyridylethylene, and spectrophotometric determination, was reported ( 4 ) . The sampler is simple and specific to ozone, but is not applicable to personal monitoring, because it requires shielding from UV radiation and wind. An attempt to apply the NBKI method to the passive sampler using a filter paper impregnated with the NBKI solution was reported by Suzuki et al. (5) After the filter paper was exposed to air, I, on the filter paper was extracted and titrated with sodium thiosulfate. This passive sampler suffered a loss of I2 due to sublimation of I2 during and after the sampling, with resultant low sensitivity. To apply the NBKI method to personal exposure measurements, the vapor pressure of I, must be lowered to prevent loss. The sublimation of I, observed with the NBKI filter paper method could be avoided by absorbing the I, on nylon-6, which is known to form a charge-transfer complex (CTC) with I2 (6). This interaction could lower the vapor pressure of 12. The liberation of I2followed by formation of the CTC can be regarded as a charge process of a pos-

0013-936X/92/0926-0744$03.00/0

0 1992 American Chemical Society