Efficient bulk mass accommodation and dissociation of N2O5 in neutral aqueous aerosol

An isotope exchange experiment with the shortlived radioactive tracer 13N is used to trace N2O5 uptake into nitrate-containing aqueous aerosol particles. While uptake of 13N-labelled N2O5 to deliquesced Na2SO4 aerosol is consistent with previous studies, efficient exchange of labelled nitrate with the non-labelled nitrate pool was observed in the presence of aerosol-phase nitrate. The experiments provide direct evidence for efficient bulk mass accommodation of N2O5 into aqueous solution with αb > 0.4 at room temperature, as well as for the fast dissociation into nitronium and nitrate. While for experimental reasons this study is limited to non-acidic nitrate-containing aerosol, it is likely that bulk mass accommodation and dissociation are not limiting N2O5 uptake under wider ranges of conditions.


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 night-time 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 (Reaction R1).
Depending on location, N 2 O 5 may be removed primarily by heterogeneous hydrolysis to nitric acid or other products on aerosol surfaces, thus providing a night-time sink for atmospheric NO x (Reaction 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 2 decades. Laboratory investigations have encompassed measurement of uptake kinetics to a wide array of inorganic aerosols, like H 2 SO 4 /sulfates (Hallquist et al., 2003;Hanson and Lovejoy, 1994), NaCl/marine aerosol (Gaston and Thornton, 2016;George et al., 1994;Thornton and Abbatt, 2005), nitratecontaining inorganic aerosol (Hallquist et al., 2003;Mentel et al., 1999;Wahner et al., 1998) and mineral 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 Phillips et al., 2016). The uptake coefficient γ (defined 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, in contrast, 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 polycarboxylic 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 reactiv-G. Gržinić et al.: Efficient bulk mass accommodation and dissociation of N 2 O 5 ity and kinetic regime. Additionally, coating aqueous particles with insoluble organic films has been 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 (Reaction R3) is followed by dissociation into nitronium (NO + 2 , or its hydrated form H 2 ONO + 2 ) and nitrate (Reaction R4) with a rate coefficient, k 4 , estimated to fall between 10 5 and 10 7 s −1 (Mentel et al., 1999;Griffiths et al., 2009). The fate of nitronium is governed by a competition between the reaction with nitrate to yield molecular N 2 O 5 again (Reaction 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 (Reaction R7) (k 5 , between 10 7 and 10 9 M −1 s −1 ; Mentel et al., 1999;Behnke et al., 1997) and 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 behaviour as a function of a range of conditions, but they have not been unambiguously 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, Reaction R3 (also referred to as mass or bulk accommodation), the dissociation (Reaction R4) or Reaction R7 are rate limiting according to current understanding (Abbatt et al., 2012).
However, in the 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 , Reaction 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;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 gasphase 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 II 0 , of around 10 5 M −1 s −1 (Ammann et al., 2013;Griffiths et al., 2009), so that the uptake coefficient can be described via the resistor model as given by Eq. (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 (RH) was explained by a limiting α b of about 0.03 (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 II 0 . The effect of nitrate as mentioned above has been taken into account by using Eq.
(2) instead of a fixed rate coefficient k II 0 : This expression requires the knowledge of the concentrations of water and nitrate and the ratio of the two rate coefficients k 7 /k 5 , for which values between 0.02 and 0.06 lead to reasonable consistency with available data (Ammann et al., 2013;). 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 have remained elusive. In this study, we make specific use of the short-lived radioactive isotope 13 N (Ammann, 2001;Gržinić et al., 2015Gržinić et al., , 2014 to trace the exchange of 13 N-labelled nitrate resulting from uptake of labelled N 2 O 5 with the non-labelled nitrate pool in the aerosol phase. This allows us to obtain a direct estimate of α b and constraints for the N 2 O 5 dissociation (Reaction R4) and the recombination reaction (Reaction R5). The tracer method is very sensitive in detecting phase transfer of labelled N 2 O 5 at very low gasphase 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. (2015). However, this sensitivity comes at the expense of chemical selectivity in the sense that re-evaporating 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-labelled N 2 O 5 (Gržinić et al., 2014) and uptake of N 2 O 5 on citric acid aerosol (Gržinić et al., 2015). The short-lived radioactive tracer 13 N (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-labelled 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 set-up used in this study. 13 NO-containing gas from the accelerator facility (50 mL min −1 ) is mixed with ∼ 3 mL min −1 of 10 ppmv non-labelled NO in N 2 from a certified gas cylinder and nitrogen carrier gas (only a very small fraction of NO is labelled 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 −1 flow containing ∼ 8 ppmv O 3 produced by irradiating a 10 % O 2 in N 2 gas mixture with 185 nm 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 (Reaction R1). The resulting gas flow is mixed with a secondary gas flow containing aerosol (720 mL min −1 ) 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 consists of a glass tube 39.3 cm in length and 1.4 cm in inner diameter. The inside of the glass tube is coated with halocarbon wax to minimize N 2 O 5 losses to the wall by heterogeneous hydrolysis. A PTFE tube (6 mm diameter) is inserted coaxially into the flow tube to act as injector for the N 2 O 5 flow. The injector contains holes at the end, which allow the N 2 O 5 flow to be injected perpendicularly to the aerosol flow. Mixing is assumed to be rapid, and a laminar flow profile is assumed to have been established in the first few centimetres. A black shroud is used to cover the N 2 O 5 synthesis reactor and the aerosol flow tube in order to prevent NO 3 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 Milli-Q 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) and 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 of which is connected 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 aluminum plates: citric acid for trapping N 2 O 5 and NO 3 , a 1 : 1 mixture of NDA (N-(1-naphthyl)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. 13 N 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-labelled NO 2 and N 2 O 5 concentrations were around 10 11 molecule cm −3 . 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 Reactions 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 data points 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 was similar to the one reported by Gržinić et al. (2015Gržinić et al. ( , 2014, although in the present case the experiment was performed by measuring the change in signals under variation of the position of the injector (reaction time) and not the ratio of aerosol surface to volume. Appropriate corrections have been applied to the N 2 O 5 signal to account for NO 2 interference Table 1. Experimental parameters and results. The corrected uptake coefficients of 13 N-labelled N 2 O 5 are highlighted in bold.

Aerosol
NaNO 3 NaNO 3 NaNO 3 /Na 2 SO 4 NaNO 3 /Na 2 SO 4 Na 2 SO 4 Na 2 SO 4 Molar mixing ratio -  (3) to the data as shown in Fig. 2. b Corrected for diffusion in the gas phase. c Including 30 % uncertainty related to the ratio of aerosol surface to volume. d From AIM model (Clegg et al., 1998). e k 7 /k 5 = 0.02. f Calculated using Eqs. (1) and (2)  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 gasphase 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 ∼ 3 × 10 −2 and ∼ 7 × 10 −2 s −1 , depending on humidity. 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 . However, 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 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) is the gas-phase labelled N 2 O 5 concentration in molecules cm −3 at time zero, C * p (t) is the labelled particle-phase nitrate concentration expressed as number of particle-phase labelled nitrate ions per volume of gas phase, in ions cm −3 , k w is the wall loss rate coefficient, measured as described above, and k p denotes the apparent first-order rate coefficient 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 Eq. (4), where S p is the total ratio of the total particle surface area to gas volume 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 least-squares 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 ambient temperature and pressure (Tang et al., 2014). Table 1 summarizes the results obtained for the various aerosols, experimental conditions, γ * eff as returned from the fits to the data and γ * after the diffusion correction. In the absence of aerosol-phase nitrate, γ * for Na 2 SO 4 at 70 % RH  NaNO 3 NaNO 3 (fit) Na 2 SO 4 Na 2 SO 4 (fit) NaNO 3 +Na 2 SO 4 NaNO 3 +Na 2 SO 4 (fit)

% RH
NaNO 3 NaNO 3 (fit) Na 2 SO 4 Na 2 SO 4 (fit) NaNO 3 +Na 2 SO 4 NaNO 3 +Na 2 SO 4 (fit) is comparable to that reported by 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 the presence of aerosol-phase nitrate, uptake of 13 Nlabelled N 2 O 5 is drastically higher than the net uptake of non-labelled N 2 O 5 observed in earlier studies Griffiths et al., 2009;Hallquist et al., 2003;Mentel et al., 1999;Wahner et al., 1998) or that predicted by the IUPAC-recommended expression (Ammann et al., 2013) also included in the table. A strong dependence of γ * on humidity is observed, with an increase by a factor of about 3 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 N 2 O 5 into the nitratecontaining aerosol is about an order of magnitude larger than any uptake coefficient measured into not strongly acidic aqueous aerosol in previous studies, our results demonstrate that at room temperature gas-aqueous-phase exchange of N 2 O 5 and its dissociation are very efficient, as also suggested by 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-labelled N 2 O 5 can be obtained by deconvoluting the chemical mechanism of N 2 O 5 hydrolysis (Reactions R3-R7) to take into account the fate of the labelled and non-labelled species separately. Assuming that the labelled N 2 O 5 molecules contain only one 13 N atom (due to the very low labelled to non-labelled ratio of around 10 −6 for the initial NO) and under the assumption that no isotopic effects are in play, the chemical mechanism can be assumed to proceed as shown in Fig. 3a.
We 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 (right branch of the pathway for N * NO 5 in Fig. 3a) the 13 N label ends up on the nitrate ion (Reaction R4 ). The corresponding non-labelled nitronium ion, if not reacting with H 2 O (Reaction R7), reacts with the excess non-labelled nitrate to form non-labelled N 2 O 5 (Reaction R5), while only a negligible fraction reacts with the labelled 13 NO − 3 (Reaction R5 ). Thus, most of the labelled 13 NO − 3 is lost in the excess nitrate pool present in the aerosol. N 2 O 5 re-evaporating to the gas phase is therefore non-labelled. Therefore, in this branch, all 13 N labels remain in the aqueous phase given that evaporation as HNO 3 is unlikely for our neutral aerosol. As evident from the experiments, the net transfer of labelled N 2 O 5 into the aerosol nitrate pool, and thus the combination of bulk accommodation and dissociation, is very fast.
In the other scenario (left branch of N * NO 5 pathway in Fig. 3a) of the mechanism, 13 N ends up on the nitronium ion (Reaction R4 ), and there are two possibilities for its further fate. The 13 NO + 2 can react with water (Reaction R7 ), bringing the label into the particulate nitrate pool. Alternatively 13 NO + 2 can react with NO − 3 from the nitrate pool (Reaction 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. 13 N*NO 5 (g) N*NO 5 (aq) 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 the presence of nitrate, Reaction R5 is the dominant pathway, as shown by Mentel et al. (1999) and Wahner et al. (1998), where values for the ratio k 5 /k 7 of around 900 and 260, respectively, had been used as fitting parameters to explain the entirety of the nitrate effect. In Fig. 3b, we report the results of box model calculations (described in the Supplement) for the scheme shown in Fig. 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 1. 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 Fig. 3d. It is also instructive to look at the rates of individual reactions contributing to the aqueous-phase budget of labelled species plotted in Fig. 3b and those of the non-labelled species in Fig. 3c: even though Reaction (R5 ) brings back half of the labelled N 2 O 5 (rate of Reaction R5 is half of the dissociation rate; Fig. 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 Reaction 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 non-labelled N 2 O 5 . The latter is consistent with the observation by Mentel et al. (1999) but lower than that suggested by the parameterization given in Eq. (1) based on the IU-PAC recommendation and listed in Table 1 or that suggested by  or Griffiths et al. (2009) developed based on a wider dataset 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 nonlabelled 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 Fig. 3 (e, f, g, h) presents the box model results for Na 2 SO 4 aerosol at 70 % RH. The main difference is that in this case, Reaction (R5) represents only a negligible pathway for non-labelled nitronium resulting from Reaction (R4 ), so that the majority of labelled nitrate recycles back to labelled N 2 O 5 via Reaction (R5 ). As a result, both labelled and non-labelled species behave exactly parallel, in terms of both 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  is that overall uptake is limited by the dissociation, k 4 , in the latter, while Mentel et al. (1999) 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 also be achieved by the Mentel et al. (1999) kinetics scheme via lowering k 7 by 1 order of magnitude to achieve lower net uptake, which is what has been used in the calculations shown in Fig. 3f, g, h. In view of the limited dataset it is beyond the scope of this study to retrieve more precise rate coefficients for Reactions (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. 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 (Reaction R7 ) while at the same time a decrease in nitrate concentration suppresses the 13 NNO 5 reformation sub-channel (Reaction R5 ). However, as argued above, in the presence of nitrate at several M, the dominant fate of the label in the left branch of the mechanism in Fig. 3a is the reformation of labelled N 2 O 5 .
If bulk accommodation would limit uptake, the measured uptake coefficient would be only slightly larger than α b /2, with α b /2 contributed by the right branch of the mechanism, and a minor contribution from the 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 the ratio of aerosol surface to volume and correction for gas-phase diffusion. In the box model simulations discussed above, α b has been set to 1. The only systematic uncertainty not considered in this is the assumption that isotope effects do not influence the symmetry of the disproportionation reaction (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 [H 2 O] /k 5 [NO − plain the increase of the uptake coefficient of labelled N 2 O 5 by a factor of 4 from 50 to 70 % RH. As discussed first by Mentel et al. (1999), and later by Griffiths et al. (2009) and , the kinetic regime may shift between limitations by Reactions (R7), (R4) or (R3) between 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 salt aerosol in the absence of nitrate.
On a side note, in principle, we cannot exclude a surface contribution. Since also the suggested bulk accommodation is followed by 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. However, we would prefer not invoking a surface process if bulk phase processing explains the observations.
Obviously, the fast isotope exchange that allows tracking the dissociation of dissolved N 2 O 5 depends on the presence of a nitrate pool, which 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 the absence of nitrate, Reactions (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. (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 Eqs. (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 nitratecontaining aqueous aerosol was observed and attributed to the exchange of 13 N-labelled nitrate as dissociation product of N 2 O 5 with the nitrate pool in the aqueous phase. This allow us to suggest 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 dissociation into nitrate and nitronium actually occurs and thus also supports the arguments behind the nitrate effect. The observed behaviour of 13 N-labelled N 2 O 5 is similar to that observed by 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). 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 (Gržinić et al., 2015;Gaston and Thornton, 2016).
Data availability. The data underlying Fig. 2 are provided in Table S1 of the Supplement. The complete set of differential equations is provided in Table S2. MATLAB code to solve this set of differential equations for the two cases shown in Fig. 3 is attached to the Supplement.
The Supplement related to this article is available online at doi:10.5194/acp-17-6493-2017-supplement.