A Study on Three Factors Influencing Uptake Rates of Nitric Acid onto Dust Particles

Recent studies have indicated that the observed nitric acid (HNO₃) uptake rates (R HNO3 ) onto dust particles are much slower than R HNO3 used in the previous modeling studies. Three factors that possibly affect R HNO3 onto dust particles are discussed in this study: (1) the magnitude of reaction probability of HNO3 (γ HNO3 ), (2) aerosol surface areas, and (3) gas-phase HNO₃ mixing ratio. Through the discussion presented here, it is shown that the use of accurate γ HNO3 is of primary importance. We suggest that the use of γ HNO3 values between ~10?³ and ~10?? produces more realistic results than the use of γ HNO3 values between ~10?¹ and ~10?² does, more accurately modeling the nitrate formation characteristics on/in dust particles. We also discuss two different types of aerosol surface area, active and geometric, since the use of different aerosol surface areas often leads to an erroneous result in R HNO3 . In addition, the levels of the gas-phase HNO₃ are investigated with the example cases of TRACE-P DC-8 flights in East Asia. The HNO₃ levels were found to be relatively high, indicating that they can not limit nitrate formation in dust particles.


INTRODUCTION
Recently, several studies have reported that although East Asian dust particles have sufficient chemical aging (or contacting) times (say, 1-4 days) with atmospheric air pollutants, they were found to contain only small amounts of nitrate (and/or sulfate) (Song et al., 2007;Song et al., 2005;Maxwell-Meier et al., 2004).This fact possibly indicates that the gas-to-particle nitric acid (HNO 3 ) uptake rates (R HNO 3 ) onto dust particles are slower than previously estimated.This could also be an important correction to the results from pre-vious studies (Meskhidze et al., 2003;Song and Carmichael, 2001;Zhang and Carmichael, 1999;Dentener et al., 1996).For example, Meskhidze et al. (2003) inferred from the data of TRACE-P DC-8 Flight #13 that total nitrate (= =HNO 3 (g)+ +NO 3 -(p)) distribution between gas phase and East Asian dust particles reaches a near equilibrium (refer to Fig. 4 in Meskhidze et al. (2003)).Their work supported the opposite idea that dust particles could contain a quite large amount of nitrate that could completely neutralize dust-originated cationic components such as Ca 2+ + and Mg 2+ + .This study, therefore, intends to discuss possible causes of this discrepancy in order to offer a convincing explanation.
The ultimate purpose of estimating (or measuring) γ HNO 3 is to apply the result to the chemistry-transport modeling studies.However, because of the large differences in the magnitude of γ HNO 3 onto dust particles, atmospheric modelers have been confused about which value should be adopted in their modeling studies (Song et al., 2007;Bauer et al., 2004;Zhang and Carmichael, 1999;Dentener et al., 1996; and also the third group of γ HNO 3 as presented in Table 1).In addition, it appears that the parameterizations (or estimation method for γ HNO 3 ) for describing the heterogeneous interac-tion between HNO 3 and dust particles are questionable.Therefore, an impartial discussion is urgently required about both the magnitudes of γ HNO 3 onto dust particles and the parameterizations for the heterogeneous interactions between HNO 3 and dust particles.In this study, we discuss all the relevant and yet contentious issues regarding the heterogeneous processes between gasphase HNO 3 and dust particles.In addition, through this study we wish to provide a modeler's perspective regarding the chemical evolution of dust particles and the magnitude of γ HNO 3 onto dust particles.

1 Research and Theoretical Background
The HNO 3 uptake into dust particles causes the replacement of carbonate (CO 3 2-) originally associated with crustal Ca 2+ + (and/or Mg 2+ + ) in dust particles via the following reaction: Similar carbonate replacement reactions occur with the uptake of other acidic substances such as H 2 SO 4 and SO 2 .Based on this mechanism, Table 2 presents the "dust chemical aging index", defined as the ratio of estimated CO 3 2-equivalence ([CO 3 2-] in μeq/m 3 ) to crustal cation equivalence ([Ca 2+ + ] + + [Mg 2+ + ]) at several different locations in East Asia (Song et al., 2007;2005).As presented in Table 2, the ratios range from 0.39 to 0.87, indicating that the remaining carbonate fractions in the dust particles range from 39-87%, respectively, even after the chemical aging times of 24-84 hrs.Several single particle chemical analysis studies with East Asian dust particles reached the same conclusions (Ro et al., 2005;Zhang et al., 2003;Zhang and Iwasaka, 1999).The replaced CO 3 2-fractions of 13-61% are believed to be released from dust particles by nitrate (and/or sulfate) formation.The small percentages of the replaced carbonate, even with the long chemical aging times, are obvious evidences of slow R HNO 3 onto dust particles.
where k denotes the mass transfer coefficient (1/s), v HNO 3 the molecular mean velocity of HNO 3 (cm/s), and S a the aerosol surface density (μm 2 /cm 3 ).In this study, we discuss these three possibly influential factors to determine which factor (or factors) is really responsible for the observed discrepancy in R HNO 3 onto dust particles.

2 Reaction Probability of HNO 3 (γ γ HNO 3 )
First of all, the slow R HNO 3 could result from low γ HNO 3 onto dust particles.As mentioned in the Introduction, large differences have been reported in the magnitude of γ HNO 3 onto dust particles (Song et al., 2007;Johnson et al., 2005;Umann et al., 2005;Harnisch and Crowley, 2001a, b;Underwood et al., 2001a, b;Fenter et al., 1995).Fig. 1 presents how fast HNO 3 can be transferred from the gas phase into dust particles with different γ HNO 3 values, using eqns.( 1) and (2).For example, when γ HNO 3 = =0.1, the 10 e-folding lifetime (τ 10 , defined as the time at which C HNO 3 /C HNO 3,0 = = 1/10e= =0.037; τ 10 = =(1+ +ln10)/k, where k represent the mass transfer coefficient in eqn.( 2)) is only 1.41 hrs.When γ HNO 3 = =0.01,τ 10 becomes 8.03 hrs.In other words, 96.3% of HNO 3 is partitioned into the particulate phase within 8.03 hrs, when γ HNO 3 = =0.01.The partitioned HNO 3 is then rapidly converted into nitrate, being associated with Ca 2+ + and Mg 2+ + ions inside the dust particles.For example, if the HNO 3 levels of 1-3 ppb are converted into nitrate at STP at a yield of 96.3%, nitrate concentrations of 2.6-7.7 μg/m 3 should be found in the dust particles after relatively short chemical aging times (within few hours).Once these amounts of nitrate are formed in the dust particles, the particles (particularly Ca 2+ + ) can be completely neutralized only by nitrate in most typical dusty situations.HNO 3 levels of 1-3 ppb were frequently observed with high dust concentrations over the downwind areas from the polluted regions in East Asia (this will be discussed in more detail in section 2.4; also refer to Bauer et al. (2004)).However, such large amounts of nitrate have never been found in dust particles, particularly in East Asia (Song et al., 2007;Ro et al., 2005;Song et al., 2005;Zhang et al., 2003).In contrast, when γ HNO 3 = = 10 -3 -10 -5 , R HNO 3 become much slower (τ 10 =3.1-91.8days).With the initial C HNO 3 of 1-3 ppb and γ HNO 3 of 10 -4 , the converted amount of nitrate after the interacting times of 8 hours is 0.095-0.29 μg/m 3 , which is 1) Ratio averaged over the flight paths (ACE-ASIA Flights) and over the measured periods (Seoul). 2) 3) The average production rate of 4) Estimated elapsed times between pollution plume injections and measurements 2) [NO 3 -] max (μg/m 3 ) 3) (μg/m 3 •hr) We selected the data from the dust storm periods of the campaigns.In this calculation, while we cannot estimate the individual amounts of nitrate and sulfate, we can estimate the combined amounts of "nitrate+ +sulfate" concentration in the dust particles by equating the replaced carbonate equivalences to the "nitrate+ +sulfate" equivalences.In an extreme case, carbonate in dust particles could be replaced only by NO 3 -.These amounts ([NO 3 2-] mmmmmmmm ). are then divided by chemical aging times to obtain the maximum possible nitrate uptake rates.As shown in Table 2, the rates range from 0.01 to 0.26 μg/m 3 •hr.These values are in general comparable to the estimated rates above (0.01-0.04 μg/m 3 •hr), particularly for the cases of ACE-ASIA C-130 Flights #6, #7, and #8 which recorded results in the range 0.05-0.07μg/m 3 •hr (again, it is important to remember that the average uptake rates actually represent the production rates of NO 3 Although in this study we do not intend to estimate γ HNO 3 onto dust particles, one of the objectives of this study is to decide which values of "already-measured" γ HNO 3 in Table 1 can be adopted in the dust chemistry modeling studies.Based on the calculations above, the modeling studies with γ HNO 3 of ~10 -3 -~10 -5 could produce more consistent results with the field measurement data.

3 Surface Area
There is another possible mechanism that could slow down R HNO 3 into dust particles: the application of a smaller surface area to eqn.(2).For example, in an estimating procedure of γ HNO 3 , Umann et al. (2005) introduced an "active surface area (S A )" (for greater detail, refer to both Umann et al. (2005) and Matter Engineering, Appendix IV of Operating Instructions LQ1-DC, SKM990318-7b).A similar type of active surface area, so-called "Fuchs surface", was also introduced by Pandis et al. (1991) and Shi et al. (2001).Whichever active surface area is used, S A has a tendency to become smaller than the "geometric surface area") (S G ), when the coarse-mode fraction is large, such as in dust and sea-salt aerosol cases.Therefore, if we use S A instead of S G for the gas-to-particle mass transfer process, R HNO 3 could become slow.Table 3 presents the typical ratios of S A to S G for dust and seasalt particle distributions (Sander and Crutzen, 1996;Zhang et al., 1994;Jaenicke, 1993).The ratios range between 0.11 and 0.41.In particular the ratio is 0.11 for the two typical dust cases, indicating that R HNO 3 become slower by a factor of 0.11, even if the same γ HNO 3 is used.Here, the relevant question is whether S A can be applied to eqn.(2).Umann et al. (2005) used S A with the concept of the "actual surface area" that is accessible for impinging gas molecules that can typically be measured by a BET (Brunauer, Emmett and Teller) type of instrument.However, both the active (μm 2 /cm 3 ) and Fuchs (1/cm 3 ) surface areas are not the "actual/accessible surface area", but an imaginary aerosol-surface area conveniently adjusted to consider the changing mechanism in the gas-to-particle mass transfer in accordance with the aerosol size changes (Pandis et al., 1991).For the fine particles, the gas-to-particle mass transfer (uptake) rates are proportional to the second moment (i.e., surface area), whereas for the coarse particles, R HNO 3 are proportional to the first moment (i.e., radius).Therefore, the S A -to-S G ratios are small when the coarse aerosol fraction is large, whereas the ratios are close to unity when the fine fraction is dominant.The variation in uptake mechanism with the aerosol size can be taken into account by the use of Fuchs and Sutugin kinetics (1971)    137.07 15.72 0.11 4.02×10 -5 3.50×10 -4 3.12×10 -4
As shown in Table 3, the values of k G are consistent with k F , whereas the values of k A are smaller than k F by a factor of ~0.1.Meanwhile, the use of S A in eqn.
(2) also leads to an erroneous estimation of γ HNO 3 .One example of the erroneous results is shown in Fig.These values are also closer to the second group of γ HNO 3 in Table 1 that we recommended to be used in the future dust chemistry modeling studies.

4 HNO 3 Concentration in the Gas Phase (C HNO 3 )
The third factor that could affect R HNO 3 into dust particles is C HNO 3 (from eqn.1).If C HNO 3 is low, R HNO 3 becomes slow.Or, if the amounts of HNO 3 are not sufficient, the amounts of nitrate formed in dust particles can be limited by the insufficient the amounts of HNO 3 , even with fast R HNO 3 .Particularly, extremely low C HNO 3 could occur over the areas where NH 3 concentrations are high.Over such areas, HNO 3 can be depleted by the reaction of HNO 3 (g)+ +NH 3 (g) → NH 4 NO 3 (aerosol).For example, East Asia has large NH 3 emissions (Kim et al., 2006).Fig. 3 presents C HNO 3 and the Ca 2+ + concentrations measured by TRACE-P DC-8 Flights #9 and #13 over the Yellow Sea and East China Sea (see panels (c) and (g)).As presented in pan-els (d) and (h), the air masses originated from the Gobi desert and the arid areas in Inner Mongolia, and then passed through the highly polluted, high NO x and NH 3 emission areas in China such as Beijing, Tianjin, Qingdao, Dalian, Nanjing, and Shanghai, as well as various Chinese agricultural areas (Kim et al., 2006).The high levels of Ca 2+ + indicate that the air masses intercepted by DC-8 Flights #9 and #13 contained high levels of dust particles.In the two flights, the observed levels of HNO 3 were increased up to as high as 7 ppb (see panel (g)).The typical HNO 3 levels reported from other TRACE-P DC-8 and P3-B flights in the boundary layer under the continental outflow situations ranged between ~1 ppb and ~3 ppb.Despite the coexistence of the high levels of dust particles and HNO 3 , Song et al. (2007;2005) reported very low nitrate (and/or sulfate) concentrations inside dust particles over the areas close to the flight paths of TRACE-P DC-8 Flights #9 and #13.This is an important correction to the results from Meskhidze et al. (2003).They insisted that the coexistence of high levels of Ca 2+ + and HNO 3 in the TRACE-P DC-8 Flight #13 was firm evidence that HNO 3 had already filled up the dust particles (i.e., complete neutralization of Ca 2+ + or 100% carbonate replacement had occurred).
Again, the presence of high HNO 3 levels indicates that the low nitrate concentrations in the dust particles were not a result of the low C HNO 3 levels, but were rather due to the small γ HNO 3 that was reduced even smaller than 10 -3 .

CONCLUSIONS
The observed R HNO 3 onto dust particles were much slower than previously estimated.In addition, R HNO 3 have been overestimated in several previous dust   (2005).With respect to the third factor, we showed that the observed C HNO 3 was relatively high, sometimes increasing up to as high as ~7 ppb in the marine boundary layer in East Asia, for example.C HNO 3 can not limit nitrate formation in dust particles.

Fig. 1 .
Fig. 1.Ten e-folding lifetimes (τ 10 ) with different reaction probability of HNO 3 .The parameters for log-normal aerosol distribution used in this figure are presented in the box (Zhanget al., 1994).
2. Umann et al. (2005) estimated γ HNO 3 from the field measurements in Sahara desert, using equations (1) and (2) with S A .We selected three dust episodes (E3, E4, and E5) from Umann et al.'s work (2005), and then re-estimated γ HNO 3 with S A and S G .As shown in Fig. 2, when S G is used instead of S A , the values of γ HNO 3 are decreased down to 0.004-0.02,which are smaller than Umann et al.'s values (γ HNO 3 = =0.03-0.18).

Fig. 2 .
Fig. 2. Estimation of γ HNO 3 with two different types of surface areas (S A and S G ).
for which three possibilities were discussed here: (1) the magnitude of γ HNO 3 , (2) aerosol surface area, and (3) C HNO 3 .Regarding the second factor, we suggested that S G should be used in eqn.(2) instead of S A , which had been used, for example, in Umann et al.'s study

Table 1 .
Reaction Probability of HNO 3 onto dust particles.

Table 2 .
Average dust chemical aging indices and maximum HNO 3 uptake rates in East Asia.
or other