1 Introduction

Ammonia (NH3), a principal alkaline gas in the atmosphere, not only plays a significant role in determining acidification and eutrophication of the ecosystems but it also neutralizes the acidic species (e.g., sulfuric acid (H2SO4), nitric acid (HNO3), hydrochloric acid (HCl)) (Aneja et al. 2001, 2008; Behera and Sharma 2010a). In this neutralization process, these acidic species are transformed into ammonium salts (ammonium sulfate ((NH4)2SO4), ammonium bisulfate (NH4HSO4), ammonium nitrate (NH4NO3), and ammonium chloride (NH4Cl)), which form the major components of PM2.5 (particulate matter of aerodynamic diameter <2.5 μm). This neutralization is also called as “gas-to-particle conversion processes.” The ionic species of these compounds (sulfate (SO 2−4 ), nitrate (NO −3 ), ammonium (NH +4 ), and chloride (Cl−)) constitute a major part of secondary inorganic aerosols (SIA; 20–40% of PM2.5) (Lin and Cheng 2007; Behera and Sharma 2010b). In the process of formation of SIA, gas-to-particle conversion occurs through condensation, which adds mass onto preexisting aerosols, and/or by direct nucleation of gaseous precursors (Finlayson-Pitts and Pitts 2006; Renard et al. 2004).

Before the gas-to-particle transformation process takes place, H2SO4 and HNO3 are formed from oxidation of sulfur dioxide (SO2) to H2SO4 and oxides of nitrogen (NO x ) to HNO3 (McMurry et al. 1983; Russell et al. 1983; Sharma et al. 2007). Hence, it is imperative to study the system comprising H2SO4, HNO3, HCl, and NH3, which is responsible for the formation of secondary PM2.5 (Baek et al. 2004; Makar et al. 2009).

The equilibrium chemistry describing the interactions of NH3 with other atmospheric constituents has been studied extensively in the past (e.g., Orel and Seinfeld 1977; Tang 1980; Russell et al. 1983; Bassett and Seinfeld 1984; Trebs et al. 2004; Baek and Aneja 2004; Sharma et al. 2007). However, there are only a few studies (i.e., Erisman et al. 1988; Harrison and Kitto 1992; Baek et al. 2004) that have described the chemical kinetics (for the estimation of rate constants) for the formation of ammonium salts.

Erisman et al. (1988) and Harrison and Kitto (1992) estimated the reaction rate constant for the conversion of NH3 to NH +4 with the pseudo-first-order chemical kinetic approach; the estimated rate constant would include conversion from all chemical reactions involving ammonia. A more in-depth study by Baek et al. (2004) estimated the reaction rate constants of individual reactions responsible for the formation of ammonium salts. The findings of this study were based on ambient air quality monitoring at two sites, one at upstream and the other at downstream of a commercial hog farm in eastern North Carolina, USA; the study concluded that local atmospheric and meteorology conditions (NH3 as 36.2 ± 27.4 μg m−3, SO2 <10 μg m−3, and solar radiation <600 W m−2) had a significant bearing on the rate constants.

The meteorological conditions in India or other places could be markedly different from the conditions reported in the North Carolina study. For example, in Kanpur City, India (latitude 26°26′ N and longitude 88°22′ E), prevailing atmospheric conditions are temperature of 37.9 ± 6.4°C (day) and 34.5 ± 4.7°C (night) and solar radiation of 808.2 ± 413.1 W m−2 (day) and 54.8 ± 16.9 W m−2 (night) (Behera and Sharma 2011) in summer. Particulate matter concentrations are also higher in Kanpur (PM10, 100–400 μg m−3; Sharma and Maloo 2005; Behera et al. 2011) than the levels reported in the North Carolina study.

Since the kinetics of formation of SIA depends on local atmospheric and meteorological conditions, this study has focused on SIA formation in conditions prevalent in the Indian subcontinent. Specifically, the study has examined the kinetics of formation of SIA components under varying concentrations of precursors gases (NO2, SO2, and NH3) with elevated levels (concentration >200 μg m−3) in an outdoor environmental chamber. An outdoor chamber is a better option for such a study, as it receives natural irradiation of sunlight and diurnal and seasonal variations of precursor gases and aerosol formation can be regulated (Jaoui et al. 2004; Martiän-Reviejo and Wirtz 2005).

The specific objectives of the present study were as follows: (1) ambient air sampling and characterization of gaseous species (O3, SO2, NO2, NH3, HNO2, HNO3, and HCl) and components of PM2.5 (i.e., ions (Na+, K+, Ca2+, Mg2+, NH +4 , NO −3 , SO 2−4 , and Cl−), including elemental carbon (EC) and organic carbon (OC); (2) estimation of reaction rate constants for the formation of (NH4)2SO4, NH4NO3, and NH4Cl; (3) role of meteorological parameters (i.e., temperature, relative humidity, and solar radiation) on the rate constants; and (iv) influence of ozone (O3) and existing particle surface on the rate constants.

2 Materials and methods

2.1 Experimental setup

An overview of the outdoor environmental chamber system along with other features of the experimental setup is shown in block diagram (Fig. 1). All features of this experimental setup can be broadly classified into two major components: (1) an environmental reaction chamber and (2) the inlet system for gas injection. The environmental reaction chamber facility comprised an outdoor 12.5-m3 Teflon film chamber (2 mil (54 μm) thick fluorinated ethylene propylene) with dimensions of 2.5 m (L) × 2.5 m (W) × 2.0 m (H) and is placed on the terrace of the Air Quality Laboratory, Indian Institute of Technology Kanpur, India.

Fig. 1
figure 1

Block diagram of the experimental setup for the environmental chamber

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The chamber is equipped with state-of-the-art analytical instruments to obtain concentration–time profiles of reactants and products during photooxidation of inorganic precursor compounds and other physical parameters such as solar light intensity, temperature, relative humidity, and pressure in the chamber. It was ensured that the chamber was leakproof by monitoring the pressure inside the chamber (which was slightly higher than the ambient pressure); the inside pressure remained unchanged for about 6–7 h. The details of this environmental chamber were described in Behera and Sharma (2011).

The gas-supplying system included reactant precursor gases (NO x (mixture of 80% NO2 and 20% NO), SO2, and NH3), which are responsible for the formation of SIA. These reactant gases (SIGMA Gases, New Delhi) were injected into the reaction chamber. Arrangement for proper flow of gases from cylinders was done with the help of gas regulator, mini gas regulator, and flow control panel box (Fig. 1). To obtain the desired initial gas concentration in the chamber, the required quantity of gas (in the chamber) was calculated on the basis of mass balance, considering the volume of the chamber. The rate of flow for injection of gas was maintained in the range of 25–40 ml min−1. Instruments were attached to the chamber through three Teflon ports: (1) two 8-mm diameter holes for monitoring of gases (NO x –NH3 and O3 analyzers), (2) one 14-mm diameter hole for sampling of SO2 gas, and (3) four 26-mm diameter holes for the particulate and gaseous sampling with denuder system. A data acquisition system for all instruments was housed in a thermally controlled laboratory room adjacent to the chamber.

2.2 Sampling methods

The study consisted of two sets of measurements: (1) ambient air sampling and (2) sampling in the environmental chamber, separately for day and night experiments. The purpose of the “ambient air sampling” was to check the correlation of ambient air with the initial background concentration maintained in the chamber air. To get the background characteristics of ambient air, sampling was done for 8 h (0000–0800 hours), prior to commencement of daytime chamber experiment at 0800 hours. Similarly, ambient air sampling was done for 8 h (1200–2000 hours), prior to commencement of nighttime chamber experiment at 2000 hours.

As part of the preparation for each run, the chamber door was kept open to ambient air and baked in sunlight for one full day (as per Odum et al. 1997). Then, the door was closed and specified quantities of gases were injected in the chamber continuously for 10–20 min. Residence time for the precursor gases after injection was 1.5 h and then sampling of the chamber air was undertaken for the next 4 h. In all experiments, the wall losses for gases and particles were accounted for to obtain the final concentrations. The experiments for this study were done during the summer season (May, June, and July 2009) when solar radiation was at its maximum.

Two Partisol® model 2300 four-channel speciation samplers (4-CSS) (Thermo Fisher Scientific Inc., USA) were used; one for ambient air quality and the other in the chamber to collect PM2.5 and gaseous species at a flow rate of 10 L min−1. Cartridges of the sampler, to be engaged in the chamber air sampling, were placed inside the chamber and were connected to the sampler kept outside the chamber. Three channels of the sampler (meant for chamber sampling) were utilized: two on Teflon filters (Whatman grade PTFE filters of 47 mm diameter) and one on quartz fiber filter (Whatman grade QM-A quartz filters of 47 mm diameter). The sequence of sampling through these three channels was as follows: (1) the first channel was meant for the PTFE filter with denuder systems to collect the gases and particulates for the first 1.5 h (during residence time) to get the initial concentrations in the chamber (to be used for estimating the kinetic rate constants), (2) the second channel with PTFE filter and denuder system was engaged to collect particulates and gases for the next 4 h (as the final concentration of experiments), and (3) the third channel with QM-A quartz filters was employed to collect particulates for 4 h (in parallel to the second channel). After sampling, the PTFE filters were analyzed for ions, denuders were utilized for analysis of gaseous species, and QM-A quartz filter was utilized for the analysis of EC and OC.

Prior to PTFE filter (meant for ions), two glass honeycomb denuders were kept in series to absorb gaseous components of air; the first denuder was coated with sodium carbonate (Na2CO3) to absorb HCl, nitrous acid (HNO2), HNO3, and SO2 and the second denuder was coated with citric acid to absorb NH3. The filter pack contained both a 47-mm diameter Teflon filter and a nylon filter. The nylon filter above the Teflon filter was installed to capture NH +4 and NO −3 from the NH4NO3, which might have dissociated on the Teflon filter (Yu et al. 2006). Denuders were cleaned and coated before the start of the experiment. The first denuder (known as Na2CO3 denuder) was coated with 1% glycerine and 1% Na2CO3 in a 50% mixture of methanol and ultrapure Milli-Q water (Yu et al. 2006). The citric acid denuders were coated with 2% citric acid in a 50% mixture of methanol and ultrapure Milli-Q water (Baek and Aneja 2004). Coated denuders were dried following coating using a zero air system in the laboratory before being subjected to sampling. Sampled denuders were extracted using 10 ml ultrapure Milli-Q water immediately after sampling and the aliquots were refrigerated till ion chromatography (IC) analysis was undertaken (as per the method by the US Environmental Protection Agency (USEPA) 1999b).

Concentrations of NO x and NH3 (chemiluminescence principle) and O3 (UV absorption spectrophotometer) were monitored by online analyzers with a time resolution of 5 min. During the sampling period, meteorological parameters (temperature, relative humidity, and solar radiation) were recorded using a wind monitor (WM251 EnviroTech, New Delhi).

2.3 Gravimetric and chemical analysis

PM2.5 mass concentration was determined gravimetrically by weighing the PTFE filters before and after the sampling using a digital microbalance (Mettler-Toledo MX-5, USA; sensitivity of 0.001 mg). Prior to weighing, filters were equilibrated in a controlled desiccator (temperature of 20 ± 5°C and relative humidity of 40 ± 2%) for at least 24 h before and after the sampling. Prior to sample collection, quartz filters were baked at 600°C for a minimum of 3 h to remove residual carbon from untreated filters. Field blanks (one in five filters) were collected and analyzed in parallel to the exposed filter papers as a part of QA/QC as per the USEPA (1998).

Water-soluble ions (NH +4 , Ca2+, Mg2+, Na+, K+, NO −3 , SO 2−4 , and Cl−) were extracted from the PTFE filters using ultrapure Milli-Q water following the USEPA reference method (Compendium Method IO-4.2, EPA/625/R-96/010a; USEPA 1999a). The nylon filter was extracted using 5 ml 1.8 mM Na2CO3/1.7 mM NaHCO3 solution (anion IC eluent) to recover collected nitric acid volatilized from the PTFE filter. The samples extracted from PTFE and nylon filters were ultrasonicated at a temperature of about 60°C for 1 h and were filtered through a 0.22-μm filter paper to remove insoluble matter. Chemical analyses of the extracted samples from denuders, Teflon filters, and nylon filters were carried out using IC (Metrohm 761 compact IC, Switzerland). Ion recovery efficiencies were determined by spiking known quantity of ion mass and reproducibility tests were performed by replicate analysis, one out of every 10 samples. Recovery efficiencies varied between 95% and 105%, and reproducibility tests had acceptable results within ±10% for all species analyzed.

A 0.512-cm2 punch from the QM-A quartz filter was analyzed for eight fractions of carbon following the Interagency Monitoring of Protected Visual Environments thermal/optical reflectance protocol on a DRI Model 2001 carbon analyzer (Chow et al. 2004). The eight fractions of carbon analyzed were (1) four OC fractions (OC1, OC2, OC3, and OC4 evolved at 140°C, 280°C, 480°C, and 580°C, respectively, in a helium atmosphere), (2) an OP fraction (pyrolyzed carbon fraction), and (3) three EC fractions (EC1, EC2, and EC3 at 580°C, 740°C, and 840°C, respectively, in an atmosphere of 2% O2 and 98% He). OC was measured as OC1 + OC2 + OC3 + OC4 + OP, and EC was measured as EC1 + EC2 + EC3 − OP (Chow et al. 2004). The concentrations were blank subtracted using the average filter blank concentration.

2.4 Reaction rate constants

The important reactions of NH3 with H2SO4, HNO3, and HCl in the gas-to-particle conversion process to produce ammonium salts of PM2.5 are summarized in reactions R1 to R3 (adopted from Finlayson-Pitts and Pitts 2006; Baek et al. 2004; Behera and Sharma 2011):

$$ \begin{array}{*{20}{c}} {{\text{2N}}{{\text{H}}_{{3}}}{\text{(g) + }}{{\text{H}}_{{2}}}{\text{S}}{{\text{O}}_{{4}}}{\text{(aq) }}\xrightarrow{{{k_{\text{S}}}}}{\text{ (N}}{{\text{H}}_{{4}}}{{)}_{{2}}}{\text{S}}{{\text{O}}_{{4}}}{\text{(aq)}}} \hfill & {{\text{(R1)}}} \hfill \\ {{\text{N}}{{\text{H}}_{{3}}}{\text{(g) + HN}}{{\text{O}}_{{3}}}{\text{(g) }}\xrightarrow{{{k_{\text{N}}}}}{\text{ N}}{{\text{H}}_{{4}}}{\text{N}}{{\text{O}}_{{3}}}{\text{(s) or (aq)}}} \hfill & {{\text{(R2)}}} \hfill \\ {{\text{N}}{{\text{H}}_{{3}}}{\text{(g) + HCl(g)}}\xrightarrow{{{k_{\text{Cl}}}}}{\text{ N}}{{\text{H}}_{{4}}}{\text{Cl(s) or (aq)}}} \hfill & {{\text{(R3)}}} \hfill \\ \end{array} $$

Reaction R1 can be assumed as a pseudo-second-order reaction for the degradation of NH3, and the rate of degradation of NH3 can be expressed as (Baek et al. 2004):

$$ \frac{{{\text{d}}\left[ {{\text{N}}{{\text{H}}_3}} \right]}}{{{\text{d}}t}} = - 2{k_{\text{S}}}\,{\left[ {{\text{N}}{{\text{H}}_3}} \right]^2} $$
(1)

where k S is the reaction rate constant for (NH4)2SO4 formation. The initial condition at time t = 0, [NH3] = [NH3]0, and at boundary condition of time t = τ, [NH3] = [NH3] τ . Hence, NH3 concentration after any reaction time τ can be obtained from Eq. 1 as:

$$ {\left[ {{\text{N}}{{\text{H}}_3}} \right]_{\tau }} = \frac{{{{\left[ {{\text{N}}{{\text{H}}_3}} \right]}_0}}}{{2{k_{\text{S}}}\,\tau {{\left[ {{\text{N}}{{\text{H}}_3}} \right]}_0} + 1}}. $$
(2)

Rearranging Eq. 2, the k S can be expressed as:

$$ {k_s} = \frac{1}{2} \times \frac{{{{\left[ {{\text{N}}{{\text{H}}_3}} \right]}_0} - {{\left[ {{\text{N}}{{\text{H}}_3}} \right]}_{\tau }}}}{{{{\left[ {{\text{N}}{{\text{H}}_3}} \right]}_0} \times {{\left[ {{\text{N}}{{\text{H}}_3}} \right]}_{\tau }}}} \times \frac{1}{\tau } $$
(3)

The degradation rate of HNO3 in the formation of NH4NO3 (reaction R2) can be expressed in terms of the kinetic equation as:

$$ \frac{{{\text{d}}\left[ {{\text{HN}}{{\text{O}}_3}} \right]}}{{{\text{d}}\tau }} = - {{\text{k}}_{\text{N}}} \times {\left[ {{\text{N}}{{\text{H}}_3}} \right]_{\tau }}\left[ {{\text{HN}}{{\text{O}}_3}} \right] $$
(4)

where k N is the reaction rate constant for te formation of NH4NO3 (reaction R2). Considering the initial and boundary conditions of HNO3 as HNO3 = [HNO3]0 at time t = 0 and HNO3 = [HNO3] τ at time t = τ. Now substituting the value of [NH3] τ from Eq. 2 in Eq. 4 and solving with the initial and boundary conditions, the final expression of k N is:

$$ {k_N} = - 2{k_s} \times \ln \left[ {\frac{{{{\left[ {{\text{HN}}{{\text{O}}_3}} \right]}_{\tau }}}}{{{{\left[ {{\text{HN}}{{\text{O}}_3}} \right]}_0}}}} \right] \times \frac{1}{{\ln \left( {2{k_s}.\tau .{{\left[ {{\text{N}}{{\text{H}}_3}} \right]}_0} + 1} \right)}} $$
(5)

Similarly, the reaction rate constant for the formation of NH4Cl (k Cl) can be derived from reaction R3 as:

$$ {k_{\text{Cl}}} = - {2}{k_{\text{S}}} \times \ln \left[ {\frac{{{{\left[ {\text{HCl}} \right]}_{\tau }}}}{{{{\left[ {\text{HCl}} \right]}_{{0}}}}}} \right] \times \frac{1}{{\ln (2{k_{\text{S}}} \times \tau \times {{[{\text{N}}{{\text{H}}_{{3}}}]}_0} + 1)}}. $$
(6)

3 Results and discussion

3.1 Performance evaluation of the chamber experiments

The validity of the chamber experiments was established by comparing the photolysis rate of NO2 (i.e., k 1: the index of the light intensity) measured through chamber experiments with the theoretical estimates of k 1 using actinic flux and absorption cross-section in the wavelength ranging from 290 to 430 nm (as per the procedures given in Finlayson-Pitts and Pitts 2006) for the same days of chamber experiments. Specifically, NO x (mixture of 80% NO2 and 20% NO) was injected into the chamber and irradiated with sunlight, followed by measurements of NO, NO2, and O3. Based on the actinometry of steady state, k 1 was estimated from the experimental outcomes using Eq. 7:

$$ {k_1} = \frac{{{k_2}\left[ {{{\text{O}}_3}} \right]\left[ {\text{NO}} \right]}}{{\left[ {{\text{N}}{{\text{O}}_2}} \right]}} $$
(7)

where k 2 is the rate constant of the NO and O3 reaction to produce NO2 and O2 in cubic centimeters per molecule per minute; O3, NO, and NO2 are the concentrations in molecules per cubic centimeter. The value of k 1 from the experiments was found to be 0.315 ± 0.073 min−1 and, from the theoretical estimation in ambient air, it was 0.461 ± 0.091 min−1; these two estimates of k 1 were statistically not different (at 5% level of significance) with the paired t test done with Minitab 15 English software (number of data points = 75). The chamber validity was also examined in terms of (1) chamber temperature versus outside ambient air temperature, (2) chamber relative humidity versus outside ambient relative humidity, and (3) behavior of injected ambient PM2.5 into the chamber versus outside ambient PM2.5 (for details, Behera and Sharma 2011 can be referred). The designed chamber was found adequate for simulating atmospheric conditions including photochemical reactions.

Aerosol and gaseous wall deposition rates were estimated by measuring the rate at which the pollutant concentrations decreased with time (following first-order decay) when the chamber was closed (Behera and Sharma 2011). These wall losses of pollutants were accounted while estimating gas-to-particle conversion in subsequent experiments.

3.2 Ambient air characterization

Table 1 summarizes the ambient air levels of measured gaseous pollutants (O3, SO2, NO2, NH3, HNO2, HNO3, and HCl) and PM2.5 with its chemical characteristics ions (Na+, Ca2+, Mg2+, NH +4 , NO −3 , SO 2−4 , and Cl−) and carbons (OC and EC). The purpose of this section is to present the overall idea of levels of the pollutants in the ambient air during chamber experiments and to check the correlation of background concentration with initial concentration in the chamber. The average 24-h concentration of PM2.5 was 115.9 μg m−3, which exceeded the Indian National Ambient Air Quality Standard of 60 μg m−3 (24-h average). The presence of large levels of NH +4 , SO 2−4 , NO −3 , and Cl− suggests the formation of secondary particles in significant amounts (38.3%) in the study area.

Table 1 Summary of characterization of ambient air during the chamber experiment period (unit: micrograms per cubic meter)
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The mean molar ratio of NH +4 to SO 2−4 was observed to be 3.5 ± 0.8 (mostly >2), indicating full neutralization of H2SO4 by NH3. The excess of NH +4 was inferred to be associated with NO −3 and Cl−. The ionic composition of PM2.5 was evaluated with regard to overall charge balance between the major anions (Cl−, NO −3 , and SO 2−4 ) and NH +4 . The equivalent molar ratio of the following combinations were found to be (1) NH +4 /SO 2−4  = 3.55, (2) NH +4 /NO −3  = 2.65, and (3) (NH +4 )/(2 × SO 2−4  + NO −3  + Cl−) = 1.01. From these results, it was confirmed that sufficient NH +4 was present to neutralize the acidic components of ambient air (H2SO4, HNO3, and HCl) to possibly form (NH4)2SO4, NH4NO3, and NH4Cl in the study area.

The mean OC concentration was 20.2 ± 7.6 μg m−3 (17.4% of PM2.5 mass) and the mean EC concentration was 6.0 ± 2.8 μg m−3, comprising 5.2% of PM2.5 mass. The higher value of ambient air OC/EC ratio (i.e., 3.4) than at sources (i.e., 2.1 (Behera and Sharma 2010b) and 1.2 (Yu et al. 2004)) indicates the presence of secondary organic aerosols. To get the mass closure of PM2.5 components, particulate organic mass (OM) was estimated by multiplying the OC levels by a factor of 1.4 to account for hydrogen, oxygen, and nitrogen present in OM (Turpin and Lim 2001; Ho et al. 2003). Based on the PM2.5 mass closure exercise, it was estimated that Na+, Ca2+, Mg2+, NH +4 , SO 2−4 , NO −3 , Cl−, OM, and EC accounted for 72.7% of the PM2.5 mass. The major PM2.5 components were OM (>24.4%) and sulfate (>14.8%). The sequence for the percentage of contribution of these components to PM2.5 mass was organic matter > sulfate > nitrate > ammonium > EC > calcium > sodium > magnesium > chloride. It is to be noted that the purpose of the sampling was to check the correlation of ambient air characteristics with the chamber air. The statistical comparison is discussed in the subsequent section.

From diurnal variations of the gaseous species, particulate species, and meteorology (Table 1), it could be inferred that (1) levels of O3, SO2, NO2, NH3, and HNO3 were higher during daytime, (2) HNO2 and HCl were higher during nighttime, (3) PM2.5 was higher during daytime, (4) particulate Na+, Ca2+, Mg2+, SO 2−4 , OC, and EC were higher during daytime, and (5) particulate NO −3 and Cl− were higher during nighttime.

3.3 Details of chamber experimental runs

A total of 32 chamber experimental runs (16 during the day and 16 during the night) were performed. In each run, NO2, SO2, and NH3 were injected in the chamber in desired concentrations. The chamber facilitated reactions of gases with each other and with constituents of ambient air along with measurements of gaseous and particulate concentration as a function of time. The objective of these experiments was to generate the experimental outcomes meant for the estimation of reaction rate constants for the formation of SIA components in PM2.5. The particulate and gaseous sampling in the chamber during the experiments were done by Partisol® model 2300 4-CSS along with glass denuder systems. For details of the sampling, the “Sampling methods” section can be referred.

As described in the “Sampling methods” section, the sequence of sampling through the three channels of the 4-CSS was as follows: (1) the first channel was meant for the PTFE filter with denuder systems to collect the gases and particulates for the first 1.5 h (residence time) to get the initial concentrations in the chamber (to be used for estimating the kinetic rate constants), (2) the second channel with PTFE filter and denuder system was engaged to collect particulates and gases for next 4 h, and (3) the third channel with QM-A quartz filters was employed to collect particulates for 4 h (in parallel to the second channel).

The overall observed average meteorological parameters in the chamber during the chamber experiments were (1) temperature, 43.2 ± 8.3°C (day) and 35.2 ± 5.8°C (night); (2) relative humidity, 58.1 ± 25.2% (day) and 67.6 ± 26.7% (night); and (3) solar radiation, 716.6 ± 403.8 W m−2 (day) and 45.4 ± 12.2 W m−2 (night).

Figure 2 shows the correlation between the ambient air concentration and the initial background concentration maintained in the chamber (sampling done from channel II of the 4-CSS sampler in the chamber). We have considered four parameters for the correlation analysis, i.e., mass concentrations of PM2.5 and particulate NH +4 , SO 2−4 , and NO −3 . From the correlation coefficient values (Fig. 2), it was observed that the initial particulate chamber characteristics were well matched with the ambient air characteristics. In all four cases, the slopes of the regression lines were not statistically different from 1 (at 5% level of significance), suggesting that the mass concentration of PM2.5 and particulate NH +4 , SO 2−4 , and NO −3 are nearly the same inside and outside of the chamber.

Fig. 2
figure 2

Correlation between ambient air and initial chamber characteristics: a PM2.5 concentration; b NH +4 concentration; c SO 2−4 concentration; d NO −3 concentration

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3.4 Rate constants for the formation of SIA components

Table 2 presents the estimated rate constants (k S, k N, and k Cl) for reactions of NH3 with H2SO4, HNO3, and HCl to form (NH4)2SO4, NH4NO3, and NH4Cl; k S = 2.68 × 10−4 m3/μmol/s, k N = 1.59 × 10−4 m3/μmol/s, and k Cl = 5.16 × 10−5 m3/μmol/s. It is to be noted that experiments were performed as per the procedures in the “Sampling methods” section. It was observed that the rate of formation of (NH4)2SO4 was 2.7 times faster than the rate of formation of NH4NO3.

Table 2 Experimental outcomes for rate constants of formation of (NH4)2SO4, NH4NO3, and NH4Cl
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The rate constants k S and k N showed statistically significant difference (at 5% level of significance) in day and night values; k Cl did not show such a difference. The D/N (i.e., daytime/nighttime values) ratio was 1.3 for k S, 0.33 for k N, and 1.01 for k Cl. The rate of formation of NH4NO3 was observed to be faster in nighttime than daytime. During daytime, the higher temperature volatilizes particulate NH4NO3 and it can also lead to the dissociation of NH4NO3 back to HNO3 and NH3, and during nighttime, in addition to lower temperatures, higher relative humidity diminishes the volatility of NH4NO3 (Lin et al. 2006; Wu et al. 2009).

The faster rate of formation of (NH4)2SO4 during daytime could be explained by enhanced conversion of NH3 and H2SO4 into (NH4)2SO4 in the presence of higher solar radiation. Ren et al. (2002) have reported that the OH radical during daytime was approximately 8 × 106 molecules cm−3, which was about 10 times higher than the levels observed during nighttime. Unlike semivolatile NH4NO3, (NH4)2SO4 does not evaporate from aerosol with increasing ambient temperatures (Wu et al. 2009) and the reaction forming (NH4)2SO4 is not reversible.

To determine uncertainties in the estimation of reaction rate constants, we computed the measurement errors of NH3, HNO3, and HCl as 6.3%, 9.2%, and 8.9% respectively. By following the procedures of Yu et al. (2005), the overall uncertainties in estimating reaction rate constants were 15.3%, 11.5%, and 11.2%, respectively, for k S, k N, and k Cl.

To the best of our knowledge, a chamber-based kinetic study involving multiple reactions (under realistic background air) for SIA formation has not been reported. Therefore, direct comparison of reaction rate constants estimated in this study with the literature-reported rate constants may be difficult, but arguably, our study closely simulated atmospheric reactions responsible for the formation of SIA. However, an attempt was made to compare our results with the study done by Baek et al. (2004) where they estimated rate constants from the ambient air sampling at two sites in North Carolina, USA (Table 3). In comparison to the rate constants reported by Baek et al. (2004), the mean value of k S was about 2.3 times higher, k N was about 2.2 times higher, and k Cl was 0.603 times the value reported by Baek et al. (2004). The reasons for higher k S in this study could be due to the following reasons: (1) meteorological parameters, e.g., higher temperature and solar radiation in Indian conditions and (2) existing particulate surface (due to higher levels of background particulate matter), which could play a significant role in enhancing the condensation process that leads to the formation of these compounds.

Table 3 Comparison of results with previous studies
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Similarly, the higher values of k N in this study might be due to the presence of a larger particle surface area. Anttila et al. (2004) have also reported that the reversibility of a chemical reaction diminishes if reactants are adsorbed and the reaction takes place on the aerosol surface. With the same argument, backward reaction of NH4NO3 (formed on the aerosol surface) is not likely to take place and thus enhances the rate of formation of NH4NO3 in the presence of existing aerosols. In addition, solar radiation could play an important role during daytime for enhanced HNO3 formation resulting in the increased rate of formation of NH4NO3.

The lower value of k Cl in this study (compared to Baek et al. 2004) could be due to noninfluence of sea salt on the PM2.5 for the study area (Behera and Sharma 2010b). It is to be noted that Kanpur is situated about more than 1,200 km from the nearest sea coast.

3.5 Factors affecting rate constants

3.5.1 Meteorology

Figure 3 illustrates the association between meteorological parameters (temperature, relative humidity, and solar radiation) and rate constants for the formation of (NH4)2SO4, NH4NO3, and NH4Cl (both for daytime and nighttime). There was a good correlation between temperature and rate constants (Fig. 3a). A significant positive correlation (r = 0.56) between k S and temperature suggests that temperature is a key factor that influences the rate constant. For k N and k Cl, a significant negative correlation was observed (r = −0.46 for k N and r = −0.42 for k Cl), suggesting that a higher temperature triggers the backward reactions of R2 and R3 responsible for the formation of NH4NO3 and NH4Cl. It can be argued here that NH4NO3 and NH4Cl are volatile in nature and, with the increase in temperature, they volatize and backward reaction is triggered (Lin et al. 2006; Wu et al. 2009).

Fig. 3
figure 3

Relationship between reaction rate constants (k S, k N, and k Cl) and a temperature, b relative humidity, c solar radiation during experiments. Correlation coefficients are indicated in parentheses

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The rate constants k N and k Cl illustrate a significant correlation with relative humidity (r = 0.75 for k N and r = 0.51 for k Cl; Fig. 3b). The hygroscopic nature of PM2.5 is enhanced with the increase in relative humidity of the ambient air. As a result, the volatility of the compounds (present in PM2.5) reduces and reversibility of NH4NO3 and NH4Cl is expected to cease under higher relative humidity (Mozurkewich 1993). In the case of reaction rate constant k S, relative humidity did not show any significant influence. The influence of solar radiation on the rate constants was observed to be significant only in the case of k S (r = 0.62; Fig. 3c).

3.5.2 Ambient background levels of pollutants

It needs to be recognized that there might be other issues of variability in the estimated rate constants. The observed coefficients of variation (CV) of reaction rate were 0.51 (k S), 0.56 (k N), and 0.68 (k Cl). The high values of CV suggest that reaction rates could be a function of the initial concentrations of PM2.5 and O3. From Table 4 (correlation matrix), the following observations were made: (1) OC and O3 correlated well with PM2.5, indicating that the ambient levels of OC are dependent on PM2.5 and O3 levels; (2) rate constants k S, k N, and k Cl correlated well with PM2.5, establishing the positive role of existing PM2.5 on SIA formation; (3) background level of OC did not show significant correlation with rate constants k S, k N, and k Cl; (4) O3 correlated well with k S and k N, indicating the role of the OH radical in the formation of (NH4)2SO4 and NH4NO3; (5) k N and k Cl correlated well with k S; it may be noted that in the model formulation (see the “Reaction rate constants” section) for the estimation of rate constants, k N and k Cl depend on the values of k S .

Table 4 Pearson correlation coefficients between background levels and rate constants
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The order of the correlation coefficients (Table 4) between initial PM2.5 concentration and rate constants was 0.71 for k S, 0.59 for k N, and 0.42 for k Cl. The positive correlations suggest that the surface provided by initial aerosols enhances condensation and adsorption of precursor gases (e.g., Holmes 2007) that could facilitate enhanced formation of (NH4)2SO4, NH4NO3, and NH4Cl.

4 Conclusions

The present study investigates the kinetics for the formation of SIA components in PM2.5 from the possible interactions of acid gases, ammonia, primary aerosols, and meteorological parameters through experiments in an outdoor environmental chamber. The reaction rate constants for the formation of (NH4)2SO4, NH4NO3, and NH4Cl through the chemical reactions of NH3 with H2SO4, HNO3, and HCl (i.e., k S, k N, and k Cl) were estimated as (1) k S = 3.04 × 10−4 m3/μmol/s, k N = 7.91 × 10−5 m3/μmol/s, and k Cl = 5.14 × 10−5 m3/μmol/s during daytime and (2) k S = 2.32 × 10−4 m3/μmol/s, k N = 2.40 × 10−4 m3/μmol/s, and k Cl = 5.19 × 10−5 m3/μmol/s during nighttime.

The positive correlation of k S with temperature suggests that the formation of (NH4)2SO4 is triggered by the rise in temperature. The rate constants k N and k Cl illustrate a significant positive correlation with relative humidity, indicating that the volatility of NH4NO3 and NH4Cl reduces under higher relative humidity, which results in an increase in their rate of formation. The influence of solar radiation on k S was observed to be significant, which resulted in higher formation rate of (NH4)2SO4 during daytime. The positive correlations between rate constants and background PM2.5 concentration suggested that the surface provided by initial aerosols could enhance condensation and adsorption of precursor gases, resulting in the higher rate of formation of SIA components in PM2.5 in polluted areas. The finding of this study suggests the use of thermodynamic equilibrium models for better evaluation of the results as future scope of work.