The central role of NOx in the regulation of the oxidative capacity of the atmosphere is well established. N2O5, 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 NOx (Abbatt et al., 2012; Chang et al., 2011). NO2 reacts with O3 to form NO3, which then react together to form N2O5 (Reaction R1). NO2+NO3⇄N2O5 Depending on location, N2O5 may be removed primarily by heterogeneous hydrolysis to nitric acid or other products on aerosol surfaces, thus providing a night-time sink for atmospheric NOx (Reaction R2) (Abbatt et al., 2012; Chang et al., 2011). N2O5+H2O(l)→2HNO3(aq) Removal of N2O5 leads to a reduction of atmospheric NOx 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 N2O5 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 H2SO4/sulfates (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 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 N2O5 and aerosol abundance and composition (Bertram et al., 2009; 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 reactivity and kinetic regime. Additionally, coating aqueous particles with insoluble organic films has been shown to have an inhibiting effect on N2O5 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 N2O5(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 (NO2+, or its hydrated form H2ONO2+) and nitrate (Reaction R4) with a rate coefficient, k4, estimated to fall between 105 and 107 s-1 (Mentel et al., 1999; Bertram and Thornton, 2009; Griffiths et al., 2009). The fate of nitronium is governed by a competition between the reaction with nitrate to yield molecular N2O5 again (Reaction R5) with a nearly collision-limited rate coefficient, k5, of 2.4×1010 M-1 s-1 (Mentel et al., 1999), the reaction with H2O(l) to yield HNO3 (Reaction R7) (k5, between 107 and 109 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. N2O5(g)⇄N2O5(aq)N2O5(aq)→NO2(aq)++NO3(aq)-NO2(aq)++NO3(aq)-→N2O5(aq)NO3(aq)-+H(aq)+⇄HNO3(aq)NO2(aq)++H2O(liq)→NO3(aq)-+2H(aq)+ 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. NO2+ directly. As long as nitrate is a minority species in the aerosol phase, the loss of N2O5 is driven by Reaction R7. Depending on the water content, either the transfer of N2O5 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 N2O5, Reaction R5, becomes significant, and the uptake of N2O5 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 N2O5 reactivity with aqueous aerosol so far were based on measuring the net gas-phase loss of N2O5 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 N2O5 of about 2 to 5 M atm-1 at room temperature and a net rate coefficient for the overall reaction of N2O5 with H2O to HNO3, k0II, of around 105 M-1 s-1 (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 Eq. (1). 1γ=1αb+c4HRTDlkIIH2Ocoth⁡r/l-l/rl=DlkIIH2O, where αb denotes the bulk mass accommodation coefficient, c the mean thermal velocity of N2O5 in the gas phase, Dl the diffusion coefficient of N2O5 in the aqueous phase, usually set to 10-5 cm2 s-1 for low-viscosity aqueous aerosol, [H2O] the concentration of H2O 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 αb of about 0.03 (Ammann et al., 2013) or by introducing a dependence of the dissociation rate, k4, on the water content, leading to an apparent water content dependence of k0II (Bertram and Thornton, 2009). The effect of nitrate as mentioned above has been taken into account by using Eq. (2) instead of a fixed rate coefficient k0II: kII=k0II1-11+k7H2Ok5NO3-. This expression requires the knowledge of the concentrations of water and nitrate and the ratio of the two rate coefficients k7/k5, for which values between 0.02 and 0.06 lead to reasonable consistency with available data (Ammann et al., 2013; Bertram and Thornton, 2009). However, the actual size of the pool of dissolved N2O5 (or its dissociated products NO2+ and NO3-), the true value of the bulk mass accommodation coefficient, αb, and the rate coefficients for the individual reactions have remained elusive. In this study, we make specific use of the short-lived radioactive isotope 13N (Ammann, 2001; Gržinić et al., 2015, 2014) to trace the exchange of 13N-labelled nitrate resulting from uptake of labelled N2O5 with the non-labelled nitrate pool in the aerosol phase. This allows us to obtain a direct estimate of αb and constraints for the N2O5 dissociation (Reaction R4) and the recombination reaction (Reaction R5). The tracer method is very sensitive in detecting phase transfer of labelled N2O5 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. (2015). However, this sensitivity comes at the expense of chemical selectivity in the sense that re-evaporating HNO3 product from an acidic aerosol would interfere with the N2O5 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.

A detailed description of the experimental method and set-up can be found in our previous publications relating to the production of 13N-labelled N2O5 (Gržinić et al., 2014) and uptake of N2O5 on citric acid aerosol (Gržinić et al., 2015). The short-lived radioactive tracer 13N (T1/2≈10 min) is produced via the 16O(p,α)13N reaction in a gas target by irradiating a 20 % O2 in He flow with 11 MeV protons produced by the Injector II cyclotron at the Paul Scherrer Institute, Switzerland. The highly oxidized 13N-labelled species are reduced to 13NO 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. 13NO-containing gas from the accelerator facility (50 mL min-1) is mixed with ∼ 3 mL min-1 of 10 ppmv non-labelled NO in N2 from a certified gas cylinder and nitrogen carrier gas (only a very small fraction of NO is labelled with 13N, about 10-6 and lower). This gas flow is mixed in the N2O5 synthesis reactor with a 50 mL min-1 flow containing ∼ 8 ppmv O3 produced by irradiating a 10 % O2 in N2 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 N2O5 on the walls. The gas-phase chemistry of NO with O3 results in the formation of NO2, NO3 and finally N2O5 (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 N2O5 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 N2O5 flow. The injector contains holes at the end, which allow the N2O5 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 N2O5 synthesis reactor and the aerosol flow tube in order to prevent NO3 photolysis and thus N2O5 loss. Aerosol is produced by nebulizing 0.1 %wt. NaNO3, Na2SO4 and 1 : 1 NaNO3/ Na2SO4 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 85Kr 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 85Kr 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 13N-containing gaseous species (N2O5, NO3 and NO2) are trapped by lateral diffusion and chemical reaction on a series of parallel, selectively coated aluminum plates: citric acid for trapping N2O5 and NO3, a 1 : 1 mixture of NDA (N-(1-naphthyl)ethylene diamine dihydrochloride) and KOH for trapping NO2. 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 13N 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 NO2 concentration measured with a NOx analyzer to the 13NO2 and 13N2O5 signals on the denuder plates and particle filter, respectively. The gas-phase non-labelled NO2 and N2O5 concentrations were around 1011 molecule cm-3. The signal on the particle filter is related to aerosol-phase nitrate after removal of dissolved N2O5 by stripping the gas-phase N2O5 in the denuder system. The equilibrium established by Reactions R4 and R5 is fast enough to ensure that. In turn, the amount of dissolved N2O5 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 N2O5 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 13N tracer technique is dependent on smooth operation of the accelerator facilities and constant online 13N 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 13N delivering facility were averaged to obtain values and standard deviations reported in Table 1.

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. (2015, 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 N2O5 signal to account for NO2 interference on the denuder coating used for N2O5 (citric acid) as well as for the small amounts of NO3 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 N2O5 signal in order to obtain the pseudo-first-order wall loss rate constants (kw) 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 N2O5 in the denuder system is not able to differentiate N2O5 from HNO3. However, any significant presence of HNO3 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 N2O5 on the reactor walls calculated from kw was in the range of 10-7, which would not lead to substantial HNO3 production. NO2 concentrations in the system were measured by switching a NOx analyzer in place of the SMPS system at the beginning of the experiment. By comparing this result to the signals from 13N-labelled N2O5 and NO2, the concentration of non-labelled N2O5 in the system was also calculated, as described in our previous studies (Gržinić et al., 2015, 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. Cp∗tCg∗t=0=1-e-(kw+kp)t1+kwkp,kp=Spωγeff∗4, where Cg∗(t=0) is the gas-phase labelled N2O5 concentration in molecules cm-3 at time zero, Cp∗(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, kw is the wall loss rate coefficient, measured as described above, and kp denotes the apparent first-order rate coefficient for gas-phase loss of labelled N2O5 to the aerosol phase, which can be related to the effective uptake coefficient (γeff∗) of labelled N2O5 by Eq. (4), where Sp is the total ratio of the total particle surface area to gas volume of the aerosol and ω is the mean thermal velocity of N2O5. Figure 2 shows the appearance of 13N in the aerosol phase as a function of time performed together with least-squares fits using Eq. (3) with γeff∗ as the only variable. The true uptake coefficients were then obtained by correction for gas-phase diffusion of N2O5, 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, γeff∗ as returned from the fits to the data and γ∗ after the diffusion correction. In the absence of aerosol-phase nitrate, γ∗ for Na2SO4 at 70 % RH is comparable to that reported by Mentel et al. (1999). At 50 % RH, it is likely that the Na2SO4 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 13N-labelled N2O5 is drastically higher than the net uptake of non-labelled N2O5 observed in earlier studies (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 (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 Na2SO4/NaNO3 aerosol, the uptake is very close to that of pure NaNO3 aerosol, at both humidities. Since the measured uptake coefficient for 13N-labelled N2O5 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, our results demonstrate that at room temperature gas–aqueous-phase exchange of N2O5 and its dissociation are very efficient, as also suggested by Mentel et al. (1999), based on experiments with NaNO3, Na2SO4 and NaHSO4 aerosol.

More insight into the interpretation of the present experiments with 13N-labelled N2O5 can be obtained by deconvoluting the chemical mechanism of N2O5 hydrolysis (Reactions R3–R7) to take into account the fate of the labelled and non-labelled species separately. Assuming that the labelled N2O5 molecules contain only one 13N 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 13NNO5, there is an equal possibility that the 13N label will end up either in the nitronium ion (NO2+) or in the nitrate ion (NO3-), with rate coefficients k4/2. In the first scenario (right branch of the pathway for N∗NO5 in Fig. 3a) the 13N label ends up on the nitrate ion (Reaction R4′′). The corresponding non-labelled nitronium ion, if not reacting with H2O (Reaction R7), reacts with the excess non-labelled nitrate to form non-labelled N2O5 (Reaction R5), while only a negligible fraction reacts with the labelled 13NO3- (Reaction R5′′). Thus, most of the labelled 13NO3- is lost in the excess nitrate pool present in the aerosol. N2O5 re-evaporating to the gas phase is therefore non-labelled. Therefore, in this branch, all 13N labels remain in the aqueous phase given that evaporation as HNO3 is unlikely for our neutral aerosol. As evident from the experiments, the net transfer of labelled N2O5 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∗NO5 pathway in Fig. 3a) of the mechanism, 13N ends up on the nitronium ion (Reaction R4′), and there are two possibilities for its further fate. The 13NO2+ can react with water (Reaction R7′), bringing the label into the particulate nitrate pool. Alternatively 13NO2+ can react with NO3- from the nitrate pool (Reaction R5′) to reform 13NNO5, which can eventually re-evaporate. 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 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 k5/k7 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 NaNO3 aerosol at 70 % RH. We have used the rate coefficients for k4=5×106 s-1, k5=2.4×1010 M-1 s-1and k7=2.6×107 M-1 s-1 as suggested by Mentel et al. (1999) for NaNO3 aerosol at various humidities; the bulk accommodation coefficient αb was set to 1. Figure 3b (left y axis) directly demonstrates the rapid removal of labelled nitrogen from aqueous-phase N2O5 and its appearance as labelled nitrate. Parallel to that, labelled N2O5 disappears much more quickly from the gas phase and appears as aerosol-phase nitrate than non-labelled N2O5, 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 N2O5 (rate of Reaction R5′ is half of the dissociation rate; Fig. 3b), the fraction of labelled N2O5 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 N2O5 loss rates are about 0.26 for labelled N2O5, in good agreement with the value observed in the experiment, 0.29, and 0.0033 for non-labelled N2O5. 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 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 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 non-labelled N2O5, respectively, also in line with our measured γ∗ of 0.26 for labelled N2O5.

The right column of Fig. 3 (e, f, g, h) presents the box model results for Na2SO4 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 N2O5 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 Bertram and Thornton (2009) is that overall uptake is limited by the dissociation, k4, in the latter, while Mentel et al. (1999) suggest faster dissociation and limitation by the interplay of the reactions of NO2+ with H2O and NO3-. Replacing k4 by the parameterization suggested by Bertram and Thornton, keeping k5 as before but replacing k7 such that k7/k5=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 k7 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 N2O5 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 13NO2+ with water (Reaction R7′) while at the same time a decrease in nitrate concentration suppresses the 13NNO5 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 N2O5.

If bulk accommodation would limit uptake, the measured uptake coefficient would be only slightly larger than αb/2, with αb/2 contributed by the right branch of the mechanism, and a minor contribution from the left branch. Our results therefore strongly indicate that αb must be at least about twice as high as the uptake coefficient of 13N-labelled N2O5 measured for NaNO3 and NaNO3/Na2SO4 aerosols and thus αb > 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, αb 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 k7[H2O] /k5[NO3-] (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 behaviour. Thus an increase of αb, solubility in terms of salting effects, or of the rate of dissociation could explain the increase of the uptake coefficient of labelled N2O5 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 Bertram and Thornton (2009), 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 H2O). 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 N2O5 depends on the presence of a nitrate pool, which has to be substantial enough to “trap” the 13N tracer and prevent its release. In other words, this method traces uptake of N2O5 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 13N-labelled N2O5 is comparable to that reported with other techniques for the same aerosol, in the range of a few 10-2 for Na2SO4 at 70 % RH in this study or for (NH4)2SO4 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.

Highly efficient uptake of 13N-labelled N2O5 into nitrate-containing aqueous aerosol was observed and attributed to the exchange of 13N-labelled nitrate as dissociation product of N2O5 with the nitrate pool in the aqueous phase. This allow us to suggest a very large value for the bulk mass accommodation coefficient for N2O5 into an aqueous aerosol at room temperature of αb > 0.4 at high relative humidity and fast dissociation at > 106 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 13N-labelled N2O5 is similar to that observed by Wachsmuth et al. (2002), where 83–86Br isotopes have been used to determine the bulk accommodation coefficient of HOBr on aqueous bromide-containing aerosol. The large value of αb obtained for N2O5 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 N2O5 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 13N-labelled N2O5. At least this study would exclude any accommodation limitation and supports previous indications that reaction and diffusion limit uptake of N2O5 to low-viscosity aqueous aerosol (Gržinić et al., 2015; Gaston and Thornton, 2016).