Efficient bulk mass accommodation of N 2 O 5 into neutral aqueous aerosol ” by

1) Most of the discussion centers on the uptake of N2O5 to nitrate aerosol. The conclusions drawn suggest large values for alpha and supports N2O5 ionization at the particle interface. What is less clear is if this is a general result for all aerosol at the same water activity. In the case of sulfate particles, labelled N2O5 likely evaporates from the interfacial region wo/the opportunity for exchange with unlabeled nitrate. The upper limit of 0.03 is achieved that is likely a combination of alpha, KH, and the reaction rates described. If KH and the hydrolysis rates are the same for sulfate and nitrate aerosol, is it correct to generalize the mass accommodation results derived from the nitrate aerosol experiments to all aqueous aerosol of comparable interfacial water activity? It would be helpful for the authors to provide some discussion on these points and the generality of the derived mass accommodation coefficient. I would find it very helpful if there was a second panel to Figure 3, which showed the processes for the sulfate particles.

2. I must be missing a very important point in the paper, and would like the authors to explain this to make the paper clearer.In particular, I understand that the kinetics experiments with nitrate particles indicate a large uptake coefficient that can be interpreted as a large mass accommodation coefficient.But, I am at a loss to understand why the results with sulfate particles, that show roughly an order of magnitude smaller uptake, cannot also be interpreted as a mass accommodation coefficient measurement.If the reaction proceeds half through the left channel in Figure 3, then the labelled nitrate so formed should stay in solution.If the mass accommodation coefficient is really larger than 0.1 on aqueous droplets then the uptake coefficient in these experiments should have been at least this large.But the observations show much smaller uptake kinetics.Does this not imply that the mass accommodation coefficient on sulfate must not be as large as on nitrate?
Response: This is indeed an important point of the manuscript, and obviously we need to clarify this better.In absence of aerosol phase nitrate, labelled nitronium not undergoing hydrolysis will react with non-labelled nitrate coming into the aqueous phase as well and reform N 2 O 5 and equilibrate with the gas phase again.Therefore, in absence of nitrate, uptake of labelled N 2 O 5 is exactly following the fate of non-labelled N 2 O 5 .The fast accommodation and dissociation of labelled and non-labelled N 2 O 5 into the aqueous phase is not becoming rate limiting.The amount of aqueous phase N 2 O 5 , nitronium and nitrate is in effective Response: we agree that the present results are strictly valid only for the compositions used in the present experiments.Since the observed gamma values for the pure sodium sulfate case follow that expected for non-labelled N 2 O 5 , labelled N 2 O 5 seems to follow the fate of nonlabelled N 2 O 5 , since not enough non-labelled nitrate is building up to allow exchange with that pool and larger uptake for labelled N 2 O 5 .Therefore, in fact, strictly speaking we are unable to prove that alpha and dissociation in aqueous aerosol devoid of nitrate is as fast as in presence of nitrate.Nevertheless, it is reasonable to assume (and all other laboratory studies support this) that water activity drives the reactivity with N 2 O 5 apart from the nitrate effect and the particle physical properties.Instead of a second panel to Figure 3, we will provide some results of box model simulations to demonstrate the different behavior of labelled and non-labelled N 2 O 5 for the two cases.Unfortunately, the dataset is not large enough in terms of nitrate concentration range to more precisely constrain the individual rate coefficients as a function of water activity.
Action in manuscript: Apart from providing more details by using the box model calculations of both nitrate and non-nitrate containing cases, the discussion is now clearly differentiating between conclusions for nitrate containing aerosol as derived from the present experiments, and possible implications for aqueous aerosol of different composition.
2) Most of the aerosol flow reactor community is familiar with the kinetic equations shown, for unlabeled reactants.Are there any special considerations that need to be accounted for regarding single, vs multiple collisions of the labelled N2O5 with aerosol and the walls?Or rather, in Fig. 3, how many times would you expect a labelled N2O5 to cycle through a particle or the wall of the flow tube over the time constant of the flow reactor?Is this important to the analysis or derivation of the equations presented?
Response: no it is not important, since we integrate over many labelled molecules arriving in the detection system, and we statistically evaluate in what chemical form they are at the moment of detection.Thus the first order loss rate coefficient is correctly derived from the observed net loss or appearance rates, independent of the number of molecules contributing to these, as long as counting statistics is not limiting the error.In fact, the condensed phase cycling of N 2 O 5 is very fast, and so is evaporation back to the gas phase, and the number of times an individual molecule (labelled or non-labelled) is entering the particle phase is limited by the collision rate with the particles, which is on the order of one per second for the aerosol conditions used.Since the number density of labelled molecules in the gas phase is of the same order of magnitude as that of the number density of particles, each particle receives at most one labelled N 2 O 5 molecule during the residence time in the flow tube.
Action in manuscript: due to the presentation of a more detailed scheme to showcase the different pathways of labelled and non-labelled N 2 O 5 in Figure 3a and e, as well as the aqueous phase turnover rates, this aspect is much more clear now.
3) What is the effect of labelled HNO3 that is generated in the source region?How would this be interpreted in the experiment.It is not uncommon for N2O5 sources to be 10:1 HNO3 to N2O5.What is the expected ratio in this experiment?
Response: The citric acid coating used to trap N 2 O 5 would not be able to differentiate from HNO3, in that sense the detection system is not able to resolve this.Though, the wall loss rate coefficient of labelled HNO3 is so large that for the present flow tube surface to volume ratio the dominant fraction of it would deposit at the entrance of the flow tube (Guimbaud et al., 2002), which was not observed; the uptake coefficient for labelled N 2 O 5 on the reactor walls was in the range of 10 -7 , which would also not lead to substantial HNO 3 production..We will add a note on this in the revised version.
Action in manuscript: more details about the impact of HNO3 is given at the beginning of the results and discussion section.2 were consistent in notation.It would also be helpful to denote between labelled and unlabeled here, as the unlabeled N2O5 uptake coefficient to nitrate aerosol could be pretty small even at high labeled N2O5 uptake coefficients, correct?

4) Like reviewer #1, I am also confused by the notation of [N2O5]p. It would be helpful if equation 3 and Figure
Response: as already mentioned in the response to Referee #1, we will adapt the notation and make clear that the quantities in equation refer to labelled molecules (which were the only direct observables of the experiment).Yes, the net uptake of non-labelled N 2 O 5 to nitrate containing aerosol is very low (Table 1, lowest row).Response: the ratio of NO 2 to N 2 O 5 is about 1 at 50% RH and about 0.45 at 70% RH.In the dry N 2 O 5 online production flow tube, NO 2 losses (due to heterogeneous disproportionation) are undetectable (<10 -8 ).Disproportionation of NO 2 in the aerosol phase is negligible.As mentioned by Referee #2, HNO 3 would rather be of concern as a product of hydrolysis of N 2 O 5 on the walls, for which we did not have evidence to impact on the measurements (see our response there).We have been more concerned by evaporation of non-labelled HNO3 from the walls that might lead to additional acidification and may thus contribute to the evaporation of labelled HNO 3 product from acidic aerosol discussed in our previous studies (Grzinic et al., 2014).But given the k w values reported, and if assuming that all N 2 O 5 lost to the walls would lead to HNO 3 in the gas phase and that HNO 3 would be taken up with unit uptake coefficient, particle phase nitrate and acidity remain dominated by that deriving from direct N 2 O 5 uptake.

Action in manuscript:
The effects of HNO3 are now discussed in more detail at the beginning of the results and discussion section.
3. I'm not sure that the net reaction probabilities and their interpretation is correct or at least well explained.I can see why the net uptake measured in this 13N system on nitrate containing particles would be higher than that for unlabeled N2O5 on nitrate containing particles, due to the added channel of "isotope exchange" (for short).But I do not see why there would be an order of magnitude larger net reactive uptake of 13N N2O5 on nitrate containing particles compared to 13N N2O5 reacting on sulfate particles.I think a simple box model using the ratio of k5/k7 and nitrate and water molalities might help.
Response: as mentioned above we will show some box model simulations in the revised version to show the different behaviors of labelled and non-labelled N 2 O 5 in presence and absence of nitrate.Essentially, in absence of nitrate, labelled N 2 O 5 behaves as non-labelled N 2 O 5 , because the amount of non-labelled nitrate in the particle phase is not enough for the 'isotope exchange' to become effective.In turn, it remains difficult to fully constrain rate coefficients for the different elementary reaction based on the limited dataset only.
Action in manuscript: Box model calculations are supplied and explained in the text in detail, along with the comparison between the cases of nitrate containing aerosol and pure sulfate.The isotope exchange becomes much more apparent, also from the more detailed reaction scheme provided in Figure 3, accompanying the box model results.

4.
Or the description of the results and their interpretation needs to be clearer.I don't see where the limitation in the sulfate system is to produce that much lower of a net reaction probability, if there is equal probability of 13N N2O5 becoming 13NO3-and 13NO2+.What would be the limitation to 13NO2+ in the sulfate particles that doesn't exist in the nitrate particles?
Response: as mentioned just above, 13 NO 2 + simply reacts with non-labelled nitrate back to N 2 O 5 if not reacted with H 2 O to form labelled nitrate.Therefore, on sulfate, the labelled N has the same fate as non-labelled N.
Action in manuscript: as mentioned above the comparison between the two cases is now explicitly explained in plots of the box model calculation results and the reaction scheme.

Lines 10 onward, page 2 -I don't think all previous estimates of bulk accommodation
were as low as implied here, only that net reactive uptake was lower.In other papers, a typical assumption was also that the accommodation coefficient was not limiting net uptake, see for e.g.Bertram and Thornton ACP 2009 and others.
Response: ok, we will detail this a bit more to mention the various limiting processes (dissociation, accommodation) and their ranges that have been applied to explain different datasets.

Action in manuscript:
An explicit discussion about the different limiting processes is now given.
6. Line 23, page 5 -sentence that starts here as a double negative at the end, making it difficult to interpret the meaning.Suggest: Thus, in this branch, all 13N labels remain in the aqueous phase given that HNO3 evaporation from neutral aerosol is unlikely.
Response: ok, thank you.
Action in manuscript: text changed accordingly.
7. Line 7, page 6 -this paragraph is interesting.In the Bertram and Thornton parameterization, there is a dependence of the equilibrium between N2O5(aq) = NO3-(aq) + NO2+(aq) on the water activity (molar concentration in that paper) that was inferred from the behavior of observed uptake coefficients.This dependence was in addition to that inferred for the fate of the NO2+.Seems this presents a possible physical explanation.
Response: Thank you for this hint; we are going into substantially more detail in the revised version to discuss the different kinetic assumptions in different suggested parameterisations and schemes, along with the box model calculations.This then also includes more details with respect to the dependence on water activity.
Action in manuscript: in addition to the extended discussion, we also reiterate the point of salting effects and the different kinetic regime towards the end of the results and discussion section.
8. Conclusions, last sentence: "The absence of accommodation limitation also helps rationalizing results from field experiments (Phillips et al., 2016;Wagner et al., 2013), where under some conditions uptake coefficients constrained by combined N2O5 and aerosol measurements are larger than those suggested by laboratory studies available to date."I'm not sure I completely agree with this conclusion.Do the measurements presented herein actually help explain field determinations of the reaction probability being larger than those measured in the laboratory?A few lines above, it was noted that the net reaction probability from this set of measurements was similar to previous values (at least for sulfate particles).The field observations are not deriving accommodation coefficients, but net reaction probabilities.I agree that if some previous laboratory studies concluded mass accommodation coefficients were <0.04, then field observations of net reaction probability greater than 0.04 would not be supported by such a conclusion (or vice versa).
Response: we agree, our point is maybe a bit too far going.We wanted to express the fact that most likely bulk accommodation would not limit uptake; and if strong sinks for NO 2 + would be present, accommodation would not limit reaction.We also agree that uptake coefficients inferred from field experiments larger than those in laboratory studies are not that frequent and often remain uncertain.We will adapt the tonality of our conclusions to reflect this discussion.

Action in manuscript:
Throughout the text, we have more clearly differentiated between nitrate containing aerosol to which our experiments relate, and non-(or less) nitrate containing aerosol, for which we can only suggest similar accommodation and dissociation rates.We have dropped the explicit comparison to the two field studies.
However, other laboratory studies and even parameterizations for similar aerosol systems as those used here, have concluded or assumed mass accommodation is not limiting (e.g.Bertram and Thornton, ACP 2009 and references therein), and thus that the limitations are in the chemistry and diffusion.
Response: We will mention the different limitations invoked in the different studies in more detail, and yes, we agree that physical effects (solubility and diffusion) might often be more important than considered so far.
Action in manuscript: as mentioned above, these physical effects are discussed in more detail now.
Thus, I would argue that for the reaction probabilities derived from field measurements that are larger than some laboratory measurements (pretty small fraction) are because of three possible reasons: (1) laboratory measurements have an additional limitation to net uptake not present (or reduced) in the atmosphere (could be salting out as suggested), (2) there are additional faster reaction pathways for N2O5 in ambient aerosol particles not yet probed in the laboratory, or (3) because the assumptions required in deriving the reaction probabilities from field observations are flawed.
It is hard to imagine there is something that reacts with NO2+ much faster than Chloride in solution (though it is possible), and in aqueous sea salt particles, the reaction probability is still only measured to be similar to that on aqueous sulfate particles.That to me suggest the limitation that seems to keep reaction probabilities < 0.05 at room temperature is less likely the NO2+ chemistry and instead the solubility, dissociation, and diffusion beforehand.Anyway, that is a long winded way of saying that I don't think there is support for that conclusion as written.
Response: we agree, we will summarize this discussion in the conclusion to reduce the potential impact of knowing that bulk accommodation is fast.The study remains certainly valuable enough because it provides direct evidence for the elementary reactions underlying aqueous phase N 2 O 5 chemistry and also allows constraining their rate coefficients at least for an aqueous aerosol with high nitrate content.We will adapt the tonality of our conclusions to reflect this discussion.
Action in manuscript: as mentioned above, we have now avoided a too detailed discussion of field experiments and their implication, but more explicitly constrain the conclusions to the aerosol compositions actually studied.

The aerosol is dried to 40% RH ('to prevent effloresence' line 39, page 2)
. This is quite far below the reported efflorescence RH of Na2SO4 of 58%, (e.g.quoted in J. Phys.Chem.A, 2007, 111 (42), pp 10660-10666), so partial or complete efflorescence may explain the low values of uptake observed for the 50% RH case of Na2SO4, as uptake onto solid sulfate is known to be slower.Could this be a possible reason?
Response: Indeed, partial or complete crystallization seems like the most likely explanation, as mentioned by the reviewer, and in light of what is reported by Gao et al. 2007 with regards to the efflorescence relative humidity for Na2SO4.We will update the paper to reflect this.

Action in manuscript:
As mentioned above, this has been added to the results and discussion section.

I think the discussion of salting effects requires more detail (do they have any evidence for the salting they propose?) and to be better linked to variation in RH.
Response: within the limited data set of this study, it is difficult to become more conclusive about the salting effects.As mentioned in the discussion, on page 6, from line 7, the fact that the water activity had a stronger effect on the uptake coefficient than different (though still high) nitrate to sulfate molar ratios.As indicated above in response to referee #3, we could only add that Bertram and Thornton (2009) have seen independent evidence for a water activity dependent equilibrium.Also the application of a more detailed kinetic scheme in box model calculations shown in the revised version does not allow constraining the solubility further.
Action in manuscript: This discussion has been added towards the end of the discussion section when reiterating the physical effects on the kinetic regime.

Introduction
The central role of NO x in the regulation of the oxidative capacity of the atmosphere is well established.N 2 O 5 , an important species of the nighttime chemistry of nitrogen oxides, has been identified as one of the major reservoir species and potential sinks of NO x (Abbatt et al., 2012;Chang et al., 2011).NO 2 reacts with O 3 to form NO 3 , which then react together to form N 2 O 5 (R1).
Depending on location N 2 O 5 may be removed primarily by heterogeneous hydrolysis to nitric acid or other products on aerosol surfaces, providing thus a nighttime sink for atmospheric NO x (R2) (Abbatt et al., 2012;Chang et al., 2011).
Removal of N 2 O 5 leads to a reduction of atmospheric NO x and consequent reduction of tropospheric ozone and thus the oxidative capacity of the atmosphere (Dentener and Crutzen, 1993;Evans and Jacob, 2005).The reactivity of N 2 O 5 with aerosols has been of ongoing interest for the past two decades.Laboratory investigations have encompassed measurement of uptake kinetics to a wide array of inorganic aerosols, like H 2 SO 4 /sulphates (Hallquist et al., 2003;Hanson and Lovejoy, 1994), NaCl/marine aerosol (Gaston and Thornton, 2016;George et al., 1994;Thornton and Abbatt, 2005), nitrate containing inorganic aerosols (Hallquist et al., 2003;Mentel et al., 1999;Wahner et al., 1998) andmineral dust (Karagulian et al., 2006;Wagner et al., 2008).Further constraints have also been derived from field observations of N 2 O 5 and aerosol abundance and composition (Bertram et al., 2009;Phillips et al., 2016).The uptake coefficient γ (defined as the as the probability that a gas kinetic collision of a molecule leads to its uptake at the interface) on deliquesced inorganic aerosol is in the 10 -1 -10 -2 range.Organic aerosol on the other hand presents a wider range of reactivities, with values approaching those of inorganic aerosols in certain cases such as for malonic acid (Griffiths et al., 2009;Thornton et al., 2003) at around 10 -2 , while in other cases the uptake coefficients go down to 10 -3 -10 -5 , such as for some polycarboxilic acids like citric acid (Gržinić et al., 2015), succinic acid or humic acid (Badger et al., 2006;Griffiths et al., 2009), long chained fatty acids and polyalcohols (Gross et al., 2009) that indicate varying effects of water content and viscosity on the reactivity and kinetic regime.Additionally, coating aqueous particles with insoluble organic films has shown to have an inhibiting effect on N 2 O 5 uptake (Anttila et al., 2006;Folkers et al., 2003) by restricting transport from the gas phase to the aerosol phase, reduced solubility in the organic phase or limited water availability.The hydrolysis of N 2 O 5 (g) is believed to proceed through a multistep process (Behnke et al., 1997;Mozurkewich and Calvert, 1988): molecular solvation (R3) is followed by dissociation into nitronium (NO 2 + , or its hydrated form H 2 ONO 2 + ) and nitrate (R4) with a rate coefficient, k 4 , estimated between 10 5 s -1 and 10 7 s -1 (Mentel et al., 1999;Bertram and Thornton, 2009;Griffiths et al., 2009).The fate of nitronium is governed by competition between the reaction with nitrate to yield molecular N 2 O 5 again (R5) with a nearly collision limited rate coefficient, k 5 , of 2.4×10 10 M -1 s -1 (Mentel et al., 1999), the reaction with H 2 O(l) to yield HNO 3 (R7) (k 5 , between 10 7 and 10 9 M -1 s -1 (Mentel et al., 1999;Behnke et al., 1997) ) or reactions with other nucleophiles (such as chloride ion) not considered further here.
The elementary reactions constituting this mechanism have been suggested based on the kinetic behavior as a function of a range of conditions, but have not been unambiguously been proven by detecting, e.g., NO 2 + directly.As long as nitrate is a minority species in the aerosol phase, the loss of N 2 O 5 is driven by reaction R7.Depending on the water content, either the transfer of N 2 O 5 into the aqueous phase, R3, also referred to as mass or bulk accommodation, the dissociation (R4) or R7 are rate limiting according to current understanding (Abbatt et al., 2012).
On the other hand, in presence of significant amounts of nitrate in the aqueous phase, the loss of nitronium ion by reaction with nitrate back to N 2 O 5 , R5, becomes significant, and the uptake of N 2 O 5 becomes lower with increasing nitrate content in the aerosol phase, typically by an order of magnitude.This effect is referred to as the 'nitrate effect' (Abbatt et al., 2012;Bertram and Thornton, 2009;Hallquist et al., 2003;Mentel et al., 1999;Wahner et al., 1998).
Most studies conducted related to N 2 O 5 reactivity with aqueous aerosol so far were based on measuring the net gas-phase loss of N 2 O 5 due to uptake on an aerosol.The kinetics were described with a simplified lumped mechanism by assigning an effective Henry's law constant, H, of N 2 O 5 of about 2 to 5 M atm -1 at room temperature and a net rate coefficient for the overall reaction of N 2 O 5 with H 2 O to HNO 3 , k 0 II , of around 2×10 5 M -1 s -1 (Ammann et al., 2013) (Ammann et al., 2013;Bertram and Thornton, 2009;Griffiths et al., 2009), so that the uptake coefficient can be described via the resistor model as given by equation (1).

 
Where α b denotes the bulk mass accommodation coefficient, c the mean thermal velocity of N 2 O 5 in the gas phase, D l the diffusion coefficient of N 2 O 5 in the aqueous phase, usually set to 10 -5 cm 2 s -1 for low viscosity aqueous aerosol, [H 2 O] the concentration of H 2 O in M, r the particle radius and l the reacto-diffusive length.The apparent levelling off of γ towards high relative humidity was explained by a limiting α b was set to aboutof about 0.03 at room temperature to explain the apparent levelling off of γ towards high relative humidity (Ammann et al., 2013) or by introducing a dependence of the dissociation rate, k 4 , on the water content, leading to an apparent water content dependence of k 0 II (Bertram and Thornton, 2009).The effect of nitrate as mentioned above has been taken into account by using equation ( 2) instead of a fixed rate coefficient k 0 This expression requires the knowledge of the concentrations of water and nitrate and the ratio of the two rate coefficients k 75 /k 57 , for which a values of between 0.02 and 0.06 leads to reasonable consistency with available data (Ammann et al., 2013;Bertram and Thornton, 2009).However, the actual size of the pool of dissolved N 2 O 5 (or its dissociated products NO 2 + and NO 3 -), the true value of the bulk mass accommodation coefficient, α b , and the rate coefficients for the individual reactions remained obscureelusived.In this study, we make specific use of the short-lived radioactive isotope 13 N (Ammann, 2001;Gržinić et al., 2015;Gržinić et al., 2014) to trace the exchange of 13 N-labelled nitrate resulting from uptake of labelled N 2 O 5 with the nonlabelled nitrate pool in the aerosol phase.This allows obtaining a direct estimate of α b and constraints for the N 2 O 5 disproportionation dissociation (R4) and the recombination reaction (R5).The tracer method is very sensitive in detecting phase transfer of labelled N 2 O 5 at very low gas phase concentrations and thus is able to escape any artefact nitrate effect due to build-up of nitrate during the course of a kinetic experiment for experiments with aerosol without any nitrate initially as discussed by Gržinić et al. (Gržinić et al., 2015).However, this sensitivity comes at the expense of chemical selectivity in the sense that reevaporating HNO 3 product from an acidic aerosol would interfere with the N 2 O 5 measurement as shown in our previous study (Gržinić et al., 2014).We therefore performed the experiments presented here with neutral sodium sulfate and sodium nitrate aerosol to avoid this interference.

Experimental section
A detailed description of the experimental method and setup can be found in our previous publications relating to the production of 13 N labeled N 2 O 5 (Gržinić et al., 2014) and uptake of N 2 O 5 on citric acid aerosol (Gržinić et al., 2015).Here we will present a very cursory description of the 13 N production method and the changes that have been implemented to the experimental setup for the present uptake measurements.
The 13 N short lived radioactive tracer (T 1/2 ≈ 10 min.) is produced via the 16 O(p,α) 13 N reaction in a gas target by irradiating a 20% O 2 in He flow with 11 MeV protons produced by the Injector II cyclotron at the Paul Scherrer Institute, Switzerland.The highly oxidized 13 N labeled species are reduced to 13 NO for transport via a 580 m long PVDF capillary tube to the laboratory.Figure 1 shows a schematic of the experimental setup used in this study. 13NO containing gas from the accelerator facility (50 ml/min) is mixed with ~3 ml/min of 10 ppmv non-labeled NO in N 2 from a certified gas cylinder and nitrogen carrier gas (only a very small fraction of NO is labeled with 13 N, about 10 -6 and lower).This gas flow is mixed in the N 2 O 5 synthesis reactor with a 50 ml/min flow containing ~8 ppmv O 3 produced by irradiating a 10% O 2 in N 2 gas mixture with 185nm UV light.The reactor is a glass tube of 34 cm length and 4 cm inner diameter, lined with PTFE foil and operated under dry conditions to minimize hydrolysis of N 2 O 5 on the walls.The gas phase chemistry of NO with O 3 results in the formation of NO 2 , NO 3 and finally N 2 O 5 (R1).The resulting gas flow is mixed with a secondary gas flow containing aerosol (720 ml/min) in an aerosol flow tube.This flow tube differs from the one that we used in our previous studies in that it is optimized for measurement of uptake coefficients in the 10 -1 -10 -2 range.It The signal on the particle filter is related to aerosol phase nitrate after removal of dissolved N 2 O 5 by stripping the gas phase N 2 O 5 in the denuder system.The equilibrium established by R4 and R5 is fast enough to ensure that.In turn, the amount of dissolved N 2 O 5 remains orders of magnitude smaller than the amount of nitrate built up in the particle phase along the flow tube, so that the net loss of N 2 O 5 in the gas phase corresponds to the net gain of nitrate in the particle phase.Unfortunately, due to experimental limitations, only a limited number of measurements could be performed.The 13 N tracer technique is dependent on smooth operation of the accelerator facilities and constant online 13 N production to be successful, which is not always the case.Individual experiments involved the acquisition of datapoints consisting of 15-20 activity measurements, each integrated over 60 s, for a given injector position.Overall, replicates from several different experiment series performed on several different operation days of the 13 N delivering facility were averaged to obtain values and standard deviations reported in Table 1.

Results and Discussion
The measurements were performed at 50% and 70% RH for all three of the solutions in question.The operating procedure is similar to the one reported by Gržinić et al. (Gržinić et al., 2015;Gržinić et al., 2014), although in this case the experiment was performed by measuring the change in signals under variation of the position of the injector (reaction time) and not aerosol surface to volume ratio.Appropriate corrections have been applied to the N 2 O 5 signal to account for NO 2 interference on the denuder coating used for N 2 O 5 (citric acid) as well as for the small amounts of NO 3 present in the gas phase, as described in our previous studies.Before each experimental run a wall loss measurement was performed without aerosol by moving the injector in 5-10 cm steps along the length of the aerosol flow tube and measuring the gas phase N 2 O 5 signal, in order to obtain the pseudo-first order wall loss rate constants (k w ) for each experiment.These values varied between ~3x10 -2 and ~7x10 -2 s -1 , depending on humidity.
Because of the short residence time in the aerosol flow tube and its reduced surface to volume ratio, losses to the wall were less pronounced than in our previous studies.The citric acid coating used to trap N 2 O 5 in the denuder system is not able to differentiate N 2 O 5 from HNO 3 .Though, any significant presence of HNO 3 formed along the walls upstream of the aerosol flow tube would have been noticed due to its very large wall loss rate coefficient (Guimbaud et al., 2002), which was not observed; the uptake coefficient for labelled N 2 O 5 on the reactor walls calculated from k w was in the range of 10 -7 , which would not lead to substantial HNO 3 production.NO 2 concentrations in the system were measured by switching a NO x analyzer in place of the SMPS system at the beginning of the experiment.By comparing this result to the 13 N 2 O 5 and 13 NO 2 signals from 13 N labelled N 2 O 5 and NO 2 , the concentration of non-labelled N 2 O 5 in the system was also calculated, as described in our previous studies (Gržinić et al., 2015;Gržinić et al., 2014).The uptake measurements were performed in a similar fashion to the wall loss measurements, although in this case aerosol was introduced at each step.By using Eq. 3, which describes gas-aerosol phase interaction kinetics, we can estimate the uptake coefficient.where C g *(t=0) (t=0) is the gas-phase labelled N 2 O 5 concentration in molecules cm -3 at time zero, C p *(t) (t) is the N 2 O 5 labelled particle phase nitrate concentration in the particle phaseexpressed as number of particle phase labelled nitrate ions per volume of gas phase, in ions cm -3 , k w is the wall loss constant, measured as described above, and k p denotes the apparent first order rate constant for gas-phase loss of labelled N 2 O 5 to the aerosol phase, which can be related to the effective uptake coefficient (γ * eff ) of labelled N 2 O 5 by Equation 4, where S p is the total aerosol surface area to gas volume ratio of the aerosol and ω is the mean thermal velocity of N 2 O 5 .Figure 2 shows the appearance of 13 N in the aerosol phase as a function of time performed together with leastsquares fits using Eq. ( 3) with γ * eff as the only variable.The true uptake coefficients were then obtained by correction for gas phase diffusion of N 2 O 5 , as described by Pöschl et al. (2007), which leads to considerable corrections for uptake coefficients above 0.1 and particle diameters around 400 nm.The diffusion coefficient was taken as 0.085 cm -2 s -1 at room ambient temperature and ambient pressure (Tang et al., 2014).Table 1 shows the results obtained for the various aerosols, with corresponding experimental parameters, including γ * eff as returned from the fits to the data and γ * after the diffusion correction.In absence of aerosol phase nitrate, the obtained γ * results for Na 2 SO 4 at 70% RH are is comparable to those that reported by Mentel et al. (Mentel et al., 1999).

   
At 50% RH, it is likely that the Na 2 SO 4 particles remained effloresced (Gao et al., 2007) (the lowest RH in the aerosol conditioning system was 40%), explaining the low γ of 0.0053, which is comparable to that previously reported for dry ammonium sulfate (Hallquist et al., 2003).In presence of aerosol phase nitrate, uptake of 13 N-labelled N 2 O 5 is drastically higher than the net uptake of non-labelled N 2 O 5 observed in earlier studies by (Bertram and Thornton, 2009;Griffiths et al., 2009;Hallquist et al., 2003;Mentel et al., 1999;Wahner et al., 1998) or that predicted by the IUPAC recommended expression also included in the table.A strong dependence of γ * on humidity is observed, with an increase by a factor about three from 50% to 70% relative humidity.On mixed Na 2 SO 4 / NaNO 3 aerosol, the uptake is very close to that of pure NaNO 3 aerosol, at both humidities.Since the measured uptake coefficient for 13 N labelled 13 N N 2 O 5 into the nitrate containing aerosol is about an order of magnitude larger than any uptake coefficient measured into not strongly acidic aqueous aerosol in previous studies, room temperature estimates of the bulk mass accommodation coefficient, α b , our results provide a direct indicationdemonstrate that gas -aqueous phase exchange of N 2 O 5 at room temperature and its dissociation is are considerably more very efficient than previously thought under comparable conditions, as also suggested by Mentel et al. (Mentel et al., 1999), based on experiments with NaNO 3 , Na 2 SO 4 and NaHSO 4 .aerosol.
More insight into the interpretation of the present experiments with 13 N labeled N 2 O 5 can be obtained by deconvoluting the chemical mechanism of N 2 O 5 hydrolysis (R3-7) to take into account the fate of the labelled and non-labelled species separately.
Assuming that the labeled N 2 O 5 molecules contain only one 13 N atom (due to the very low labeled to non-labeled NO ratio of around 10 -6 ) and under the assumption that no isotopic effects are in play, the chemical mechanism can be assumed to proceed as shown in Figure 3a.We first assume that upon dissociation of 13 NNO 5 , there is an equal possibility that the 13 N label will end up either in the nitronium ion (NO 2 + ) or in the nitrate ion (NO 3 -), with rate coefficients k 4 /2.In the first scenario (left right branch of the pathway for 'N * NO 5 ' in Fig. 3amechanism) the 13 N label ends up on the nitrate ion (R4'''').The corresponding non-labelled nitronium ion, if not reacting with H 2 O, R7'', may reacts with the excess non-labelled nitrate to reform form non-labelled N 2 O 5 .(R5),while only This N 2 O 5 is predominantly non-labeled, since a negligible fraction reacts with the labeled 13 NO 3 -ion (R5'') and thus most of the labeled 13 NO 3 -is lost in the excess nitrate pool present in the aerosol and the likelihood of recombination of the non-labelled nitronium with the labeled nitrate is very small.N 2 O 5 re-evaporating to the gas phase is therefore non-labeled.Thus, in this branch, all 13 N labels remain in the aqueous phase given that if evaporation as HNO 3 does not occur, which is unlikely for our neutral aerosol.As evident from the experiments, the net rate of transfer of labelled N 2 O 5 into the aerosol nitrate pool, and thus the combination of bulk accommodation and dissociation, is very highfast.
In the other scenario (right left branch of 'N * NO 5 ' pathway in Fig. 3a) of the mechanism, 13 N ends up on the nitronium ion (R4''), and there are two possibilities for its further fate.The 13 NO 2 + can react with water (R7''), bringing the label into the particulate nitrate pool.Alternatively 13 NO 2 + can react with NO 3 -from the nitrate pool (R5') to reform 13 NNO 5 which can eventually reevaporate.Obviously which of these two sub-channels are prevalent depends on water and nitrate concentrations as well as the rate coefficients of the two competing reactions.The water and nitrate concentrations for the conditions of the present experiments were derived from the AIM model (Clegg et al., 1998) and are also listed in Table 1.In presence of nitrate, (R5') is the dominant pathway, as shown by Mentel et al. (Mentel et al., 1999) and Wahner et al. (Wahner et al., 1998), where values for the ratio k 5 /k 7 of 35 around 900 and 10260, respectively, have had been used as fitting parameters to explain the entirety of the nitrate effect.This is consistent with the fact that the net uptake of 13 N labelled N 2 O 5 is more than an order of magnitude larger than that of non-labelled N 2 O 5 , indicating that the R5' sub-channel is dominant.
In Figure 3b, we report the results of box model calculations (described in the supporting information) for the scheme shown in Figure 3a to substantiate these effects for NaNO 3 aerosol at 70% RH.We have used the rate coefficients for k 4 = 5 × 10 6 s -1 , k 5 = 2.4 × 10 10 M -1 s -1 and k 7 = 2.6 × 10 7 M -1 s -1 as suggested by Mentel et al. (1999) for NaNO 3 aerosol at various humidities; the bulk accommodation coefficient α b was set to one.Figure 3b (left y-axis) directly demonstrates the rapid removal of labelled nitrogen from aqueous phase N 2 O 5 and its appearance as labelled nitrate.Parallel to that, labelled N 2 O 5 disappears much more quickly from the gas phase and appears as aerosol phase nitrate than non labelled N 2 O 5 , as shown in Figure 3d.It is also instructive to look at the rates of individual reactions contributing to the aqueous phase budget of labelled species plotted in Figure 3b and those of the nonlabelled species in Figure 3c: Even though R5' brings back half of the labelled N 2 O 5 (rate of R5' is half of the dissociation rate, Figure 3b), the fraction of labelled N 2 O 5 drops below half of its initial value, since the exchange reactions R4 and R5 are fast, so that it may cycle through the aqueous phase part of the scheme many times.The rate of R5'' (labelled nitrate with non-labelled nitronium) is not getting competitive, so that labelled nitrate remains in the nitrate pool.The γ * values calculated from the net N 2 O 5 loss rates are about 0.26 for labelled N 2 O 5 , in good agreement with the value observed in the experiment, 0.29, and 0.0033 for nonlabelled N 2 O 5 .The latter is consistent with the observation by Mentel et al. but lower than that suggested by the parameterization given in equation ( 1) based on the IUPAC recommendation and listed in Table 1 or that suggested by Bertram and Thornton (2009) or Griffiths et al. (2009) developed based on a wider data set with other aerosol compositions.Box model simulation of the mixed salt case (not shown), also at 70% RH, returns essentially the same results, 0.25 and 0.009, for the uptake coefficient of labelled and non-labelled N 2 O 5 , respectively, also in line with our measured γ * of 0.26 for labelled N 2 O 5 .The right column of Figure 3, plots e,f,g,h, present the box model results for Na 2 SO 4 aerosol at 70% RH.The main difference is that in this case, R5 represents only a negligible pathway for non-labelled nitronium resulting from R4'', so that the majority of labelled nitrate recycles back to labelled N 2 O 5 via R5''.As a result, both labelled and non-labelled species behave exactly parallel, both in terms of rates and concentration.When solubility and rate coefficient are taken the same as those for the nitrate aerosol, the magnitude of the calculated uptake coefficient is an order of magnitude too high.The difference between the kinetics described by Mentel et al. (1999) and Bertram and Thornton (2009) is that overall uptake is limited by the dissociation, k 4 , in the latter, while Mentel et al.
suggest faster dissociation and limitation by the interplay of the reactions of NO 2 + with H 2 O and NO 3 -.Replacing k 4 by the parameterization suggested by Bertram and Thornton, keeping k 5 as before, but replacing k 7 such that k 7 /k 5 =0.06 as suggested by Bertram and Thornton, yields γ = 0.06, in reasonable agreement with the uptake coefficient measured here (0.027).However, this can as well be achieved by the Mentel et al. kinetics scheme via lowering k 7 by one order of magnitude to achieve lower net uptake, which is what has been used in the calculations shown in Figure 3f,g,h.In view of the limited dataset it has been beyond the scope of this study to Since the uptake coefficient of 13 N-labelled N 2 O 5 was similar for the aerosol composed of a 1:1 nitrate to sulfate molar ratio mixture and for the pure nitrate aerosol at both humidities, the present results do not allow retrieveing more precise rate coefficients for R4, R5 and R7,.The present results clearly indicate that accommodation and dissociation of N 2 O 5 are not limiting net uptake for aerosol containing substantial amounts of nitrate.but indicate that R4 and R5 are fast enough to not become rate limiting, and that R7 is at least an order of magnitude slower than R5, consistent with k 5 /k 7 ratios reported earlier.
Furthermore, these experiments provide direct evidence that these elementary steps actually exist, because otherwise exchange with the non-labelled nitrate pool would not occur.
The measured uptake coefficient increases with RH (water content) as the increase in water concentration promotes the reaction of 13 NO 2 + with water (R7'') while at the same time a decrease in nitrate concentration suppresses the 13 NNO 5 reformation sub-channel (R5'').However, as argued above, in presence of nitrate at several M, the dominant fate of the label in the right left branch of the mechanism in Fig. 3a is the reformation of labeled N 2 O 5 .If bulk accommodation would limit uptake, In such a situation the measured uptake coefficient would be only slightly larger than α b /2, with α b /2 contributed by the left right branch of the mechanism shown in Fig. 3, and a minor contribution from the right left branch.Our results therefore strongly indicate that α b must be at least about twice as high as the uptake coefficient of 13 N-labelled N 2 O 5 measured for NaNO 3 and NaNO 3 /Na 2 SO 4 aerosols and thus α b >0.4 when including the uncertainties related to aerosol surface to volume ratio and correction for gas phase diffusion.In the box model simulations discussed above, α b has been set to one.The only systematic uncertainty not considered in this is the assumption that isotope effects do not influence the symmetry of the disproportionation reaction (R4).
Interestingly, the measured uptake coefficient is more sensitive to the water activity, irrespective of whether it is pure nitrate or mixed nitrate / sulfate particles, than to the fractional nitrate content.In spite of the fact that the expected ratio k 7 (see Table 1) increases substantially from pure nitrate to mixed nitrate / sulfate, still bulk accommodation and dissociation are not limiting, and the efficient exchange of the label with the non-labelled nitrate pool dominates the behavior.Thus, indicating thatan increase of α b , solubility in terms of salting effects, or of the dissociation could explain the might increase of the uptake coefficient of labelled N 2 O 5 by a factor of three four from 50 to 70 % RH.In combination with the insensitivity to composition (water molarity increases much less), this suggests that salting effects should be considered for N 2 O 5 to effectively reduce its solubility (and maybe also α b ) for high ionic strength.As discussed first by Mentel et al. (1999), and later by Griffiths et al. (2009) and Bertram and Thornton (2009), the kinetic regime may shift between limitation by R7, R4 or R3 low and high water activity, and it remains difficult to unambiguously assign the kinetic regime.Also from the present study, the evidence for the fast dissociation is very strong for the high nitrate mole fractions used, and we can only suggest that the dissociation is similarly fast for the salt aerosol in absence of nitrate.
On a side note, in principle, we cannot exclude a surface contribution.Since also the suggested bulk accommodation is followed via obviously very fast dissociation into nitronium and nitrate, this process will occur close to the surface anyhow, with a short reacto-diffusive length (in contrast to the much slower hydrolysis reaction of nitronium with H 2 O).Therefore, for instance, varying the surface to volume ratio of the aerosol would not allow differentiating bulk from surface accommodation.Though, we would prefer not invoking a surface process if bulk phase processing explains the observations.
Obviously, for this techniquethe fast isotope exchange that allows tracking the dissociation of dissolved N 2 O 5 to work adepends on the presence of a nitrate pool has to be available and, which it has to be substantial enough to 'trap' the 13 N tracer and prevent its release.In other words, this method traces uptake of N 2 O 5 into the non-limiting pool of aqueous nitrate.In absence of nitrate, R7'' and R7'' dominate in both branches (Fig. 3e), and the measured uptake coefficient for the 13 N labelled N 2 O 5 is comparable to that reported with other techniques for the same aerosol, in the range of a few 10 -2 for Na 2 SO 4 at 70% RH in this study or for (NH 4 ) 2 SO 4 reported by Gržinić et al. (Gržinić et al., 2014), both consistent with available literature.For comparison, calculated uptake coefficients based on the parameterization and values from the IUPAC evaluation (Ammann et al., 2013), implemented in equation ( 1) and ( 2), are also listed in Table 1.

Conclusion and atmospheric implications
Highly efficient uptake of 13 N-labelled N 2 O 5 into nitrate containing aqueous aerosol was observed and attributed to the exchange of 13 N labeled nitrate as disproportionation dissociation product of N 2 O 5 with the nitrate pool in the aqueous phase.This allows deriving suggesting a very large value for the bulk mass accommodation coefficient for N 2 O 5 into an aqueous aerosol at room temperature of α b > 0.4 at high relative humidity and fast dissociation at > 10 6 s -1 .This also provides direct evidence that the fast disproportionation dissociation into nitrate and nitronium at > 10 6 s -1 actually occurs, and thus also supports the arguments behind the nitrate effect.The observed behavior of 13 N-labelled N 2 O 5 is similar to that observed by Wachsmuth et al. (Wachsmuth et al., 2002), where 83-86 Br isotopes have been used to determine the bulk accommodation coefficient of HOBr on aqueous bromide containing aerosol.The large value of α b obtained for N 2 O 5 at room temperature implies that other limiting processes must be at work to explain the insensitivity of the uptake coefficient to water content at high relative humidity (Abbatt et al., 2012;Griffiths et al., 2009;Thornton et al., 2003), which was partly interpreted as accommodation limitation.Possible other aspects may be the temperature dependence of the solubility of N 2 O 5 or salting effects as discussed in these previous studies, for which also strong indications come from this study to explain the strong water activity dependence of the observed uptake coefficient of 13 N labelled N 2 O 5 .At least this study would exclude any accommodation limitation and supports previous indications that reaction and diffusion limit uptake of N 2 O 5 to low viscosity aqueous aerosol (Gaston and Thornton, 2016).The absence of accommodation limitation also helps rationalizing results from field experiments (Phillips et al., 2016;Wagner et al., 2013), where under some conditions uptake coefficients constrained by combined N 2 O 5 and aerosol measurements are larger than those suggested by laboratory studies available to date.Average S/V ratio (m 2 /m 3 ) 5.66×10 -3 5.00×10 -3 3.36×10 -3 4.76×10 -3 3.42×10 -3 3.00×10  3) to the data as shown in Fig. 2 b corrected for diffusion in the gas phase c including 30% uncertainty related to the aerosol surface to volume ratio d from AIM model (Clegg et al., 1998) e k 7 /k 5 = 0.02 f calculated using equations ( 1) and (2), with k 0 II = 10 5 M -1 s -1 and H = 2 M atm -1 the fraction of labelled N 2 O 5 in the aqueous phase (red, left axis) and ratio of labelled nitrate to the total number of labeled N 2 O 5 initially available (green, left axis); rates of reactions relevant for the budget of aqueous phase 13 N (light to dark blue, right axis); (c) rates of reactions relevant for the budget of non-labelled species in the aqueous phase; (d) eEvolution of normalized gas phase N 2 O 5 (labelled, red; non-labelled, brown) and aqueous phase nitrate (labelled, green; non-labelled, olive) as a function of time.(e, f, g, h) scheme and plots of the same quantities, but for Na 2 SO 4 aerosol at 70% RH in absence of pre-existing nitrate.
The following chemical reactions have been used to describe the aqueous phase chemistry of non-labelled N 2 O 5 : The chemical scheme for labelled N 2 O 5 is analogous and assumes that the position of the labelled N * atom within the N 2 O 5 is not relevant, such that upon dissociation, labelled nitronium and labelled nitrate are formed at equal rates, but that otherwise the rate coefficients are the same as for the non-labelled species: Due to the small fraction of labelled N, reactions among labelled species are not included in the scheme.The set of differential equations listed in Table S1 were used to solve for the evolution of all gas and aqueous phase species with time using Matlab.
The exchange rate coefficients to describe gas-aqueous and aqueous-gas transfer of N 2 O 5 were obtained from the steady state condition given by Henry's law equilibrium, thus gasaerosol equilibrium in absence of chemical reaction (assuming that the gas phase chemical reactions of N 2 O 5 are in steady state on the time scale of gas -aerosol equilibration).The steady state of the gas phase N 2 O 5 concentration in equilibrium with aqueous phase N 2 O 5 is described by: k bg is the first order rate coefficient for the release to the gas phase in units of s -1 , V p is the total aqueous phase aerosol volume per volume of gas phase in liter cm -3 , S p the total aerosol surface area per volume of gas phase in cm 2 cm -3 , p N2O5 is the partial pressure of N 2 O 5 in atm, R is the gas constant (8.314J mole -1 K -1 ), T is the temperature, H is the Henry's law constant in M atm -1 , H' is the ratio of the aqueous phase molarity of N 2 O 5 to the gas phase concentration in molecule cm -3 and N av is Avogadro's number (note that [N 2 O 5 ] aq is in units of M, while [N 2 O 5 ] g is in units of molecule cm -3 ).The same result can also be obtained from The apparent net uptake coefficient, γ and γ * , can be derived from the effective loss rates of the gas phase N 2 O 5 and N * NO 5 , respectively, obtained from the solutions to the differential equations, via: We note that due the fact that we neglect aqueous phase diffusion in the kinetics, these uptake coefficients are only representing estimates and should be compared with caution to the measured data.In principle they represent the uptake coefficients expected for small enough particles (smaller than those in the experiments) such that liquid phase diffusion would not play a role.While the apparent reacto-diffusive length based on the net hydrolysis kinetics is rather large, the true dissociation as suggested here is rather fast.Inclusion of diffusion would require an explicit depth resolving model, which was beyond the scope of this analysis.The : notation in equation (3) and Figure 2 changed 2. Lines 25 on -what are the relative amounts of NO2 and N2O5.NO2 is known to undergo slow disproportionation to HNO3.Is this a concern here?What about wall production of 13HNO3 and its incorporation into the particles due to revolatilization?
photolysis and thus N 2 O 5 loss.Aerosol is produced by nebulizing 0.1% wt.NaNO 3 , Na 2 SO 4 and 1:1 NaNO 3 /Na 2 SO 4 solutions in MilliQ water.The resulting aerosol flow is dried over a Nafion membrane diffusion drier (RH of the drying gas outside is adjusted to 40% RH to prevent efflorescence), passed through an 85 Kr bipolar ion source and an electrostatic precipitator to equilibrate the charge distribution and subsequently remove the charged particles, respectively.A humidifier is placed after the ion source to adjust the humidity of the gas flow to the required experimental levels.The overall gas flow exiting from the aerosol fast-flow reactor is split into two flows via a T-connector, one to an SMPS (Scanning Mobility Particle Sizer) system used to characterize the aerosol, consisting of a 85 Kr bipolar ion source to re-establish charge equilibrium, a differential mobility analyzer (DMA, TSI 3071) and a condensation particle counter (CPC, TSI 3022).The other part of the gas flow is directed into a parallel plate diffusion denuder system, where the various 13 N containing gaseous species (N 2 O 5 , NO 3 and NO 2 ) are trapped by lateral diffusion and chemical reaction on a series of parallel, selectively coated aluminium plates: citric acid for trapping N 2 O 5 and NO 3 , a 1:1 mixture of NDA (N-(1-naphtyl) ethylene diamine dihydrochloride) and KOH for trapping NO 2 .The aerosol particles, which have small diffusivity, pass without loss through the denuder system and are trapped on a glass fiber filter placed at the exit.The radioactive decay of 13 N is measured by placing a CsI scintillator crystal with PIN diode detectors (Caroll and Ramsey, USA) on each of the denuder traps and the particle filter. 13N decays by β + decay and the resulting positron annihilates with an electron with emission of two coincident γ-rays in opposite directions.The resulting signal can be related to the concentration of the species in the gas and particle phase by comparing the NO 2 concentration measured with a NO x analyzer to the 13 NO 2 and 13 N 2 O 5 signals on the denuder plates and particle filter, respectively.The gas-phase non-labeled NO 2 and N 2 O 5 concentrations were around 10 11 molecule cm -3 .

Fig. 1 .Fig. 2 .Fig. 3 .
Fig. 1.Schematic of the modified experimental setup used in this study considering steady state for the aqueous phase N 2 O 5 concentration in an individual aerosol particle:Where v p is the volume of an individual aerosol particle in liter, and s p its surface area in cm 2 .Thus, the rate coefficients describing the gas -aqueous phase exchange are:

Table 1 .
Experimental parameters and results

Table S1 :
Differential equations.[N 2 O 5 ] aq is in units of M, while [N 2 O 5 ] g is in units of molecule cm -3 .The rate coefficients are explained in more detail below.