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Ammonia Catalyzed Formation of Sulfuric Acid in Troposphere: The Curious Case of A Base Promoting Acid Rain Biman Bandyopadhyay, Pradeep Kumar, and Partha Biswas J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b01172 • Publication Date (Web): 03 Apr 2017 Downloaded from http://pubs.acs.org on April 5, 2017

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The Journal of Physical Chemistry

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Ammonia Catalyzed Formation of Sulfuric Acid in Troposphere: The Curious Case of A

2

Base Promoting Acid Rain

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Biman Bandyopadhyay,a,* Pradeep Kumara and Partha Biswasb

4

a

5

Jaipur – 302017, India.

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b

7

Corresponding Author’s e-mail address: [email protected]

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Abstract:

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Electronic structure calculations have been performed to investigate the role of ammonia in

10

catalyzing the formation of sulfuric acid through hydrolysis of SO3 in Earth’s atmosphere. The

11

uncatalyzed process involves a high activation barrier and, till date, is mainly known to occur in

12

Earth’s atmosphere only when catalyzed by water and acids. Here we show that hydrolysis of

13

SO3 can be very efficiently catalyzed by ammonia, the most abundant basic component in

14

Earth’s atmosphere. It was found, based on magnitude of relative potential energies as well as

15

rate coefficients, that ammonia is the best among all the catalysts studied until now (water and

16

acids) and could be a considerable factor in formation of sulfuric acid in troposphere. The

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calculated rate coefficient (at 298 K) of ammonia catalyzed reaction has been found to be ~105 –

18

107 times greater than that for water catalyzed ones. It was found, based on relative rates of

19

ammonia and water catalyzed processes that in troposphere ammonia, together with water, could

20

be the key factor in determining the rate of formation of sulfuric acid. In fact ammonia could

21

surpass water in catalyzing formation of sulfuric acid via hydrolysis of SO3 at various altitudes in

22

troposphere depending upon their relative concentrations.

Department of Chemistry, Malaviya National Institute of Technology Jaipur, J. L. N. Marg,

Department of Chemistry, Scottish Church College, 1 & 3 Urquhart Square, Kolkata - 700006, India.

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1. Introduction:

2

Sulfuric acid (SA) has caught the attention of the scientific community in the past few years

3

mainly owing to its importance in atmospheric chemistry. This importance is mainly due to its

4

contribution to acid rain1−4 and atmospheric nucleation processes,5−12 which have undeniable

5

consequences on environment, human health and climate change. The formation of SA,

6

particularly

7

experimental13−22 and theoretical research groups.23−34 The atmospheric formation of SA involves

8

two major steps. The first one is gas–phase oxidation of SO2 to SO3, while the second one is

9

hydrolysis of SO3 that results in formation of SA. Although a direct hydrolysis of SO2 is also

10

possible, but experimental1,20,21 and theoretical30,35 results available in the literature

11

indicates that the dominant path would be its oxidation to SO3 rather than hydrolysis.

12

The hydrolysis SO3 is known to occur via initial formation of a H–bonded complex between SO3

13

and water (WM) followed by its rearrangement to form SA.13,14 Subsequent studies, however,

14

showed that this process involving a single water molecule is highly unlikely to occur under

15

atmospheric conditions, largely owing to high activation barrier (~28 to 32 kcal mol−1)

16

associated with it.24−27

17

Morokuma and Muguruma26 were the first to show that addition of a second water molecule,

18

acting as a catalyst, reduces the activation barrier by an appreciable margin. A number of studies

19

estimated this barrier to be within the range of ~6.6 to 13 kcal mol−1.26,27,29,30,33 Over the last few

20

years, a number of studies have been carried out to investigate the catalytic efficiencies of

21

various species other than water and their contribution in atmospheric formation of SA.36−40

22

These studies include hydroperoxy radical,36 formic acid,37,38 SA (as autocatalyst)39 and nitric

23

acid.40 Except hydroperoxy radical, all the catalysts that have been tried thus far are acidic in

in

Earth’s

atmosphere,

has

received

widespread


attention

from

both

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nature. These catalysts were found to be as good as or better than water, based on the magnitude

2

of rate coefficients of the catalyzed hydrolysis of SO3, but the water catalyzed channel would

3

predominate in troposphere mainly due to its high concentration in this part of Earth’s

4

atmosphere.

5

Recently we showed that alkaline species (ammonia and amines) have similar efficiency as

6

carboxylic acids in catalyzing hydrogen atom transfer (HAT) reactions.41 Based on the idea we

7

investigated the possibility of ammonia (AM) catalyzing decomposition of carbonic acid and

8

found it to be effectively competing with already known catalysts (water, formic acid etc.) in

9

lower troposphere.42 Back in 2001, Larson and Tao showed that AM could facilitate the

10

hydrolysis of SO3 by reducing the barrier to a meager 2.25 kcal mol−1.43 Surprisingly, in

11

spite of such an encouraging result, to the best of our knowledge, there hasn’t been any

12

further investigation till date to estimate the impact of AM as catalyst in atmospheric

13

formation of SA.

14

It warrants a mention here that AM is known to participate in the atmospheric chemistry of both

15

SOx and SA in various capacities. AM reacts with SO3 to form sufamic acid44 which then reacts

16

with water to form ammonium bisulfate (NH4HSO4), which is also known to form via the

17

neutralization of SA by AM.44,45 Hydrolysis of SO2, which results in the formation of H2SO3, is

18

also known to be facilitated by AM.46 Here we would like to state without any ambiguity that the

19

main goal of this work is to investigate the role of AM as a catalyst in the formation SA through

20

hydrolysis of SO3. Therefore, we have restricted all the calculations and discussions centered

21

around that aspect only. Particularly owing to the facts that AM plays such an important role in

22

the atmospheric chemistry of sulfur oxides and no detailed work exists in literature regarding its



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catalyzing potential in atmospheric formation of SA, this work, we believe, is both timely and

2

important for understanding atmospheric chemistry of sulfur oxides and SA.

3

Hydrolysis of SO3 in presence of catalysts is known to proceed through two different channels,

4

and can be written in generalized forms in terms of the bimolecular encounters between either

5

SO3–WM and catalyst, say X (here, in this investigation, X = WM, and AM) or SO3 and WM–X

6

to give product molecule, SA + X (Scheme 1).

SO3-WM + X

SO3-WM-X

(Channel 1)

SA-X SA + X

SO3 + WM + X

(Channel 2)

SO3-WM-X

SA-X

7

(RC)

(PC)

8

Scheme 1 Formation of SA through hydrolysis of SO3 catalyzed by X (RC: Pre–reactive

9

complex and PC: Product complex)

10

Torrent–Sucarrat et al.39 investigated, the water catalyzed hydrolysis of SO3 by means of

11

electronic structure calculations. They constructed the potential energy surfaces (PESs) for the

12

reactions using CCSD(T)/cc–pV(T+d)Z level of theory with the geometries optimized at

13

B3LYP/cc–pV(T+d)Z level of theory and found that the calculated rate coefficients to be 1.84 ×

14

10−11 cm3 molecule−1 s−1 and 1.28 × 10−10cm3 molecule−1 s−1 for channels 1 and 2, respectively.

15

These values, they found, match closely with experimentally measured values of 2.1 × 10−10cm3

16

molecule−1 s−1.21 As the nature of interaction for ammonia and water are very similar when they

17

act as catalysts in HAT reactions, we have used the same level of theory in this work as well.

18

Here, we report formation of SA via AM catalyzed hydrolysis of SO3 and also check for its

19

potential contribution against other catalysts in Earth’s atmosphere, mostly in troposphere.

SO3 + WM-X


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Relative rates for AM catalyzed reaction have been calculated against WM catalyzed reaction to

2

quantitatively assess the impact of AM at various altitudes in troposphere.

3

2. Methodologies:

4

2.1. Computation:

5

Molecular geometries of all the species including isolated reactants and products, H–bonded pre–

6

reactive (RCs) and product complexes (PCs) and transition states (TSs) have been optimized at

7

B3LYP/cc–pV(T+d)Z level of theory. The normal mode frequencies of all these species have

8

also been calculated at the same level. The TSs were differentiated from the stationary points by

9

presence of a single imaginary frequency characteristic of first order saddle points. Intrinsic

10

reaction coordinate (IRC) calculations were carried out at B3LYP/cc–pV(T+d)Z level of theory

11

to ascertain that the TSs connected the intended RCs and PCs. In order to further improve the

12

energies, single point energy calculations at CCSD(T)/cc–pV(T+d)Z level of theory were carried

13

out with the geometries optimized at B3LYP/cc–pV(T+d)Z level of theory. All the relative

14

energies of various species reported here were obtained from calculations at CCSD(T)/cc–

15

pV(T+d)Z//B3LYP/cc–pV(T+d)Z level of theory, unless mentioned otherwise. The energetics of

16

the reactions have been computed by means of electronic structure calculations carried out using

17

G09 suites of programs.47

18

2.2. Rate Calculations:

kf1

kuni SA-X

(Channel 1)

SO3-WM-X

SA-X

(Channel 2)

(RC)

(PC)

SO3-WM-X

SO3-WM + X

kr1 kf2 SO3 + WM-X 19

kr2

kuni



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In the reaction sequences shown above, the RC (which, for both channel 1 and 2 as shown in

2

Scheme 1 and represented here as equation 1 and 2, respectively, is same, namely SO3–WM–X)

3

undergoes unimolecular decomposition (which, once again is identical for both channel 1 and 2)

4

via the corresponding TS to form the PC. If steady state approximation is applied to RC

5

assuming it to be in equilibrium with SO3–WM + X (for channel 1) or SO3 + WM–X (for

6

channel 2), the reaction rate (ν) can explicitly be written as:

7

For channel 1:

8

(1) = − = − = −

I

9

10

For channel 2:

(2) = − = − = −

II

where =

$

$ , = , = and =

%

%

11

Here, is the equilibrium constant for the formation of RCs and is the rate constant for

12

the unimolecular reaction of RCs leading to PCs. These parameters have been calculated by TST

13

as shown below:

14

=

*+,- ./0.1 *+,- ./0 .*1

3

.(4+, ./0.1 .4+, ./0 ) 56

789

=

*+,- ./0.1 *+,- .*/0.1

F(G6H FGSO −WM−X )

: ; =>? 3 I> = σΓ 3 ℎ =SO3−WM−X


3

.(4+, ./0.1 .4+, ) 56

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Here, Q denotes the product of translational, rotational, vibrational and electronic canonical

2

partition functions of the respective species referenced to their corresponding zero–point

3

energies (ZPE) and E denotes the ZPE corrected energies of the respective species. σ is the

4

reaction path number or reaction degeneracy and Γ is the tunnelling correction for the reaction,

5

which have been taken into account by assuming unsymmetrical Eckart barrier.48 T is the

6

temperature in Kelvin, kB and h are the Boltzmann and Planck constants, respectively and R is

7

the ideal gas constant. All rate coefficients reported in this work were calculated using

8

CCSD(T)/cc–pV(T+d)Z//B3LYP/cc–pV(T+d)Z level of theory. The rate coefficients were

9

calculated using transition state theory with TheRate program.49,50 2.3. Relative rate calculation:

10

11

According to equation I, the relative rate (JK ) between the WM and AM catalyzed reaction

12

following channel 1 can be written as:

JK (1) = 13

LM O

LM − O =

NM − NM

The same for channel 2 can be derived from equation II: JK (2) =

LM − O

LM − O =

NM − NM −

14

where P and P (X = WM and AM) are and for X catalyzed channel, respectively.

15

NMFNM NMFLM Now we know that, − = and − O = O

16

NMFP where (X = WM and AM) is the equilibrium constant for formation of − complex

17

from isolated and .

18

So,

O

LM −O 3Q JK (2) =

NM − 3Q 7 ACS Paragon Plus Environment


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Form the above equations, it is evident that the estimation of relative rates for both the reaction

2

channels is straightforward once the concentrations of WM and AM (for channel 1) and the

3

equilibrium constants for the formation of WM–WM and WM–AM (along with the concentrations of

4

WM and AM for channel 2) are known. It can easily be shown that the relative rate values for the

5

two reaction channels would essentially be same (see Supporting Information).

6

3. Result and Discussion:

7

3.1. Water catalyzed reactions: Energetic and rate constants

8

SO3–WM + WM ⇆ SO3–WM–WM → SA–WM → SA + WM

(Reaction 1)

9

SO3 + WM–WM ⇆ SO3–WM–WM → SA–WM → SA + WM

(Reaction 2)

10

It has already been discussed in the introduction section that uncatalyzed hydrolysis of SO3 is not

11

a feasible process under atmospheric condition. Therefore, we have not considered it in our

12

present work. The reaction catalyzed by water has been extensively studied by a number of

13

research groups19−22,24,27 and these available results provide us an opportunity to test the

14

competitiveness of our results. Here we have investigated two different channels for the water

15

catalyzed formation of SA, namely the reaction of SO3–WM complex with WM (reaction 1) and

16

the reaction of SO3 with WM–WM (reaction 2). Before studying these two reactions, the

17

stabilities of SO3–WM and WM–WM complexes compared to the corresponding isolated

18

monomers were calculated (Table 1) and compared with earlier investigation carried out by

19

Torrent–Sucarrat et al.39 The values were found to match qualitatively.

20

Subsequently equilibrium constants for these two complexes were computed at various

21

temperatures of our interest. The values are given in Table 2. Besides, concentration of WM–

22

WM was also calculated from the calculated equilibrium constants using WM concentration at

23

various temperatures and altitudes from the literature values.51 8 ACS Paragon Plus Environment

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The PESs for reaction 1 and 2 is shown in Figure 1 and the corresponding values are given in

2

Table 3. It is evident that both the reaction channels follow same path after formation of the RC

3

(SO3–WM–WM), which is 9.8 kcal mol−1 more stable compared to SO3–WM + WM and 13.7

4

kcal mol−1 with respect to SO3 + WM–WM. Both the channels are barrierless since the TS was

5

3.9 and 7.8 kcal mol−1 below the two reactants, respectively. The TS proceeds through a PC

6

(SA–WM) which is 23.6 and 27.4 kcal mol−1 more stable than the reactants and finally it

7

dissociates to give the final product SA and WM.

8

Rate constant calculations were carried out for reaction 1 and 2 at various temperatures

9

corresponding to different altitudes in earth’s atmosphere. The values are listed in Table 4. At

10

298 K, the rate constant for reaction 1 (k1) was found to be 4.1 × 10−12 cm3 molecule−1 s−1

11

whereas that for reaction 2 (k2) was found to be 1.1 × 10−10 cm3 molecule−1 s−1. The calculated

12

values compare closely with 1.84 × 10−11 cm3 molecule−1 s−1 and 1.28 × 10−10cm3 molecule−1 s−1,

13

respectively, predicted by Torrent–Sucarrat et al.39 and 1.2 × 10−12 cm3 molecule−1 s−1 at 300 K

14

calculated by Jayne et al.21 In fact, the value we found for reaction 2 (k2), which happens to be

15

the faster between the two, matches quantitatively with experimentally determined upper limit of

16

the rate constant, 2.1 × 10−10 cm3 molecule−1 s−1.21

17

Both the reaction channels show monotonically negative temperature dependence, i.e. rate

18

constants decreases with increasing temperature, within the temperature range observed in

19

Earth’s troposphere and stratosphere (Figure 2). As a result the rate constant keeps increasing

20

with increasing altitude in troposphere, but shows opposite trend in the stratosphere due to

21

reversal in altitude dependence of temperature between these two regions in atmosphere.

22 23

3.2. Ammonia catalyzed reactions: Energetic and rate constants



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1

SO3–WM + AM ⇆ SO3–WM–AM → SA–AM → SA + AM

(Reaction 3)

2

SO3 + WM–AM ⇆ SO3–WM–AM → SA–AM → SA + AM

(Reaction 4)

3

AM catalyzed hydrolysis of SO3 proceeds in a very similar fashion as that of WM–catalyzed

4

process. Here, too, we found the reaction could proceed via two channels for the AM catalyzed

5

formation of SA, namely the reaction of SO3–WM complex with AM (reaction 3) and the

6

reaction of SO3 with WM–AM (reaction 4). Just like the WM–assisted reaction, the stability of

7

WM–AM complex compared to the corresponding isolated monomers (Table 1) and

8

subsequently, the equilibrium constant and concentration in troposphere were calculated (Table

9

2).

10

PES for AM catalyzed reactions 3 and 4 (Figure 3) looks similar to that for WM catalyzed

11

reactions 1 and 2 (Figure 1) except for the relative energies of various species involved therein

12

(Table 3). Here also both channels (reactions 3 and 4) follow same path after formation of the

13

RC (SO3–WM–AM). The RC is stabilized by 13.0 kcal mol−1 with respect to SO3–WM + AM

14

whereas the same is 15.8 kcal mol−1 compared to SO3 + WM–AM. The TS was found to be

15

energetically lying below both the reactants (by –13.0 and –15.8 kcal mol−1, respectively, in the

16

same order). Therefore, both the channels are barrierless with respect to the reactants. The TS

17

then proceeds through a PC (SA–WM), once again same for both channels, that is 27.1 and 29.9

18

kcal mol−1 more stable than the reactants, which dissociates to give the final product SA and

19

AM.

20

Rate constant calculations were carried out for reaction 3 and 4 at various temperatures

21

corresponding to different altitudes (Table 4). At 298 K, the rate constant for reaction 3 (k3) was

22

found to be 5.4 × 10−5 cm3 molecule−1 s−1 whereas that for reaction 4 (k4) was found to be 8.9 ×

23

10−5 cm3 molecule−1 s−1. It is evident from the above values that the AM catalyzed channels are ~ 10 ACS Paragon Plus Environment

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105–107 times faster than the water catalyzed channels. In fact, the rate constants for AM

2

catalyzed channels are greater than all the values predicted till date in presence of various

3

catalysts.36−40 It is ~ 103–104 times than SA catalyzed rate constant (Torrent–Sucarrat et al.39

4

showed SA catalyzed rate constant to be two orders of magnitude greater than WM catalyzed

5

rate constant), ~102–103 times than FA catalyzed rate constant (Hazra and Sinha37 showed FA

6

catalyzed rate constant to be three orders of magnitude greater than WM catalyzed rate constant,

7

Long et al.38 calculated the rate constant for FA catalyzed reaction to be 5.58 × 10−7and 1.62 ×

8

10−8 cm3 molecule−1 s−1), ~ 107–108 times than HNO3 catalyzed rate constant (Long et al.40

9

calculated HNO3 catalyzed rate constant to be 5.26 × 10−12 and 3.00 × 10−13 cm3 molecule−1 s−1)

10

and ~ 103–104 times than OH2 radical catalyzed rate constant (4.37 × 10−9 cm3 molecule−1 s−1

11

calculated by Gonzalez et al.)36

12

Both the reaction channels, i.e. reactions 3 and 4, show negative temperature dependence just as

13

observed for the WM catalyzed channels within similar temperature range (Figure 2). The slopes

14

for AM catalyzed channels are, though, steeper than their WM catalyzed counterparts. As a

15

result the increments in rate constants for AM catalyzed channels with increasing altitude in

16

troposphere (where temperature decreases steadily with increasing altitude) is significantly

17

higher than that for WM catalyzed channels. A more detailed discussion on this aspect is given

18

in the next section.

19 20

3.3. Relative impact of ammonia in troposphere

21

We would like to mention here that rate coefficients alone provides an incomplete picture

22

regarding the impact of catalysts in atmosphere as overall contribution of every catalyst also

23

depends on its concentration. The impact of catalysts on a certain reaction become more realistic



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Page 12 of 33

1

once atmospheric concentrations of catalysts are also considered in computing the kinetic

2

parameters.37,39,42,52 Therefore, we have computed the relative rates (JK ) for AM with respect to

3

WM to obtain a more realistic picture of relative impact of the former in troposphere.

4

Beside concentration, temperature dependence of rate constants is also crucial in determining the

5

relative impact of two different catalysts on the same reaction,52 as the temperature changes

6

appreciably in Earth’s atmosphere with time, region and altitude. The Arrhenius plot (Figure 2)

7

indicates that the reactions exhibit negative activation energy. The slope (which gives the overall

8

activation energy) is negative for all four reaction channels investigated. We calculated the

9

overall activation energies for the four channels to have quantitative comparison between the

10

WM and AM catalyzed channels. It was found that the values for the two WM catalyzed

11

channels are –2.5 kcal mol−1 (Reaction 1) and –4.2 kcal mol−1 (Reaction 2). The same for the

12

AM catalyzed channels were found to be –5.9 kcal mol−1 (Reaction 3) and –7.2 kcal mol−1

13

(Reaction 4). It can be inferred from the above values that the increment in rate constants with

14

altitude in troposphere (i.e. decreasing temperature) will be more pronounced for the AM

15

catalyzed pathways as compared to WM catalyzed channels.

16

Relative rates of the AM catalyzed reactions with respect to the WM catalyzed ones were

17

calculated at various altitudes in troposphere to obtain a realistic picture of the impact of AM in

18

formation of SA in troposphere, particularly against that of WM. The average concentration of

19

AM at 0 km altitude is known to be ~ 100 pptv to 10 ppbv.53−55 The known maximum limits for

20

mixing ratios of AM at 5, 10 and 15 km altitude are 500,56 10057 and 30 pptv,58 respectively. Not

21

many studies exist in literature investigating the concentration of AM at various non–zero

22

altitude levels in troposphere. Therefore, we have considered an appreciably wide range of

23

concentrations (up to 0.1 % i.e. 1/1000th of the abovementioned limits) for AM at 5, 10 and 15


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1

km altitude while calculating relative rates. The relative impacts of AM at various altitude levels

2

are discussed below:

3

3.3.1. 0 km Altitude:

4

Depending upon Earth’s surface temperature and relative humidity, the concentration of WM at

5

0 km altitude can vary from 5.16 × 1016 to 2.35 × 1018 molecules cm−3, when the temperature

6

range is taken from 280 K to 320 K and relative humidity range is considered between 20% to

7

100%.51 On the other hand, AM concentration can vary from 2.29 × 109 to 2.62 × 1011 molecules

8

cm−3 if the same temperature range (i.e. 280 – 320 K) is considered along with 100 pptv to 10

9

ppbv as the range for AM mixing ratio. The relative rates for both channels within the above

10

mentioned temperature range are given in Table 5. We have considered the two extreme

11

concentration limits for the two catalysts, i.e. 20% and 100% relative humidity for WM and 100

12

pptv and 10 ppbv mixing ratios for AM.

13

We found that at 100% relative humidity for WM and 100 pptv mixing ratio for AM, i.e. under

14

the condition disfavouring the AM catalyzed reaction most compared to the WM catalyzed one,

15

the relative rate varies from 0.319 (at 280 K) to 0.005 (at 320 K). So, when the mixing ratio of

16

AM is at its minimum and relative humidity is highest, then too, the AM catalyzed pathway

17

could contribute over 30% of SA formation compared to the same via WM catalyzed reaction. If

18

the other extreme of the spectrum is considered, i.e. at 20% relative humidity for WM and 10

19

ppbv mixing ratio for AM, relative rate could vary from 2.61 (at 320 K) to as high as 160 (at 280

20

K). It warrants a mention here that, mixing ratio of AM has been found to be as high as 2 ppmv

21

near open air cattle farms.59

22

3.3.2. 5 km altitude:



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Page 14 of 33

1

The average concentration of WM at 5 km altitude51 is known to be 2.41 × 1016 molecules cm−3

2

and the highest mixing ratio for AM at that altitude is known to be ~500 pptv,56 which turns out

3

to be 7.57 × 109 molecules cm−3. The relative rate (JK ) calculated using the above two

4

concentrations came out to be 31.2 (Table 6). The value would be 1, i.e. the rate of the WM and

5

AM catalyzed reactions would be same if AM concentration is 2.43 × 108 molecules cm−3 or 16

6

pptv, which is just ~3% of the highest limit value. This result implies that at 5 km altitude, for

7

any mixing ratio value of 16 pptv or higher AM catalyzed hydrolysis of SO3 would be favourable

8

than WM catalyzed hydrolysis process.

9


10

At this altitude the average concentration of WM49 is 4.92 × 1015 molecules cm−3 and the highest

11

mixing ratio for AM is ~100 pptv,57 i.e. 8.48 × 108 molecules cm−3. The JK value for these

12

concentrations of WM and AM comes out to be 118 (Table 6). For AM concentration of 7.19 ×

13

106 molecules cm−3 (0.85 pptv) JK becomes 1. Therefore, at 10 km altitude, for any mixing

14

ratio value of 0.85 pptv or higher, the AM catalyzed formation of SA would predominate over

15

WM catalyzed one.

16


17

Concentration of WM51 and AM58 at 15 km altitude are 1.96 × 1013 molecules cm−3 and 1.24 ×

18

108 molecules cm−3, respectively. The concentration of AM corresponds to its highest mixing

19

ratio value of ~30 pptv at this altitude. When relative rate was calculated for the above two

20

concentrations, it came out to be 16900 (Table 6). This implies that the AM catalyzed reaction

21

rate would be equal to the WM catalyzed reaction rate (i.e. JK = 1), when AM concentration

22

becomes 7.34 × 103 molecules cm−3 or 1.78 × 10−3 pptv, which is only 0.006 % of the highest


Page 15 of 33

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1

mixing ratio value. As a result, it can safely be assumed that at 15 km altitude the AM catalyzed

2

formation of SA would almost always be preferable over the WM catalyzed reaction.

3 4

4. Conclusion:

5

Effect of ammonia as a catalyst on the formation of sulphuric acid (produced due to the

6

hydrolysis of SO3) in the tropospheric part of Earth’s atmosphere has been studied by means of

7

quantum chemical calculations. It is shown, by means of relative rates, that ammonia catalyzed

8

pathway would routinely predominate over the water catalyzed pathway for this reaction. This

9

predominance would increase with altitude which was verified by calculating the relative rates of

10

the reaction by two catalysts in the range of 0–15 km altitude of the atmosphere.

11

It was found that, in terms of the absolute rate constant values, ammonia is the most efficient

12

amongst all the catalysts studied till date, including water, formic acid, sulphuric acid, nitric acid

13

and hydroperoxy radical. At 298 K, the rate constant for ammonia catalyzed reaction was found

14

to be greater than 10−5 molecules cm−3 s−1, which is at least 102-103 times higher than that by any

15

other catalysts studied till date.

16

The temperature dependence of the rate constants for both water and ammonia catalyzed

17

processes were studied through Arrhenius plots of the rate constants at various temperatures

18

encountered in Earth’s troposphere. It was found that both water and ammonia catalyzed

19

pathways showed negative temperature dependence; the dependence being stronger for the later.

20

As a result the rate constant of ammonia catalyzed reaction becomes even larger than that for the

21

water catalyzed reaction at lower temperatures, i.e. at higher altitudes in troposphere, where

22

temperature decreases with increasing altitude.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

Nonetheless, the rate constant alone cannot be employed as a reliable marker for the efficiency of

2

a particular catalyst in Earth’s atmosphere. In terms of relative rate, too, which provides a more

3

complete picture regarding the impact of two different catalysts, we found ammonia to outweigh

4

water under almost all conditions at various altitude levels in troposphere.

Page 16 of 33

5 6

ASSOCIATED CONTENT

7

Supporting Information

8

Free energy profiles, Equilibrium constants and unimolecular rate constants, Concentration of

9

catalysts, Cartesian coordinate of optimized molecular structures and normal mode frequencies,

10

Absolute electronic energies, ZPE correction and thermal correction to Gibbs free energies of all

11

species. This material is available free of charge via the Internet at http://pubs.acs.org.”

12

Acknowledgements:

13

The authors acknowledge Dr. Arijit K. De, IISER, Mohali for Gaussian 09 calculations. BB and

14

PK acknowledge DST, Govt. of India for the financial support through sanctioned project [No.

15

ECR/2016/000280 and No. ECR/2016/000279, respectively]. BB and PK acknowledge

16

Computer Centre, MNIT Jaipur and PB acknowledge Scottish Church College, Kolkata for

17

computational facilities.

18 19 20 21 22 23 16 ACS Paragon Plus Environment

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1

2 3


References:

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4

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5

A. Chemical Mechanisms of Acid Generation in the Troposphere. Nature 1985, 317, 27-

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35.

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3. Finlayson–Pitts, B. J.; Pitts, J. N., Jr. Atmospheric Chemistry: Fundamentals and Experimental Techniques; John Wiley and Sons: New York, 1986. 4. Wayne, R. P. Chemistry of Atmospheres, 3rd ed.; Oxford University Press: Oxford, U.K., 2000.

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5. Weber, R. J.; McMurry, P. H.; Eisele, F. L.; Tanner, D. J. Measurement of Expected

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Atmospheric Spectra and Corresponding Synthetic Spectra Calculated Line by Line

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Around 825 cm−1. Appl. Opt., 1983, 22, 647-649.

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58. Höpfner, M.; Volkamer, R.; Grabowski, U.; Orphal, M. G. J.; Stiller, G.; von Clarmann,

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Assoc., 2010, 60, 210-218.

12 13 14 15 16 17 18 19 20 21 22 23


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1

Figure 1 ZPE corrected PES for reaction 1 and 2 along with structures of related species

2

optimized at B3LYP/cc-pV(T+d)Z level of theory

3 4 5 6 7 8 9 10 11 25 ACS Paragon Plus Environment


1

Figure 2 Arrhenius plots for reactions 1, 2, 3 and 4

0.0

-2.5 SO3-WM + AM SO3 + WM-AM

-5.0

SO3-WM + WM

log10k

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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SO3 + WM-WM -7.5

-10.0

-12.5 3.2

3.6

4.0 -1

2

1000/T (K )

3 4 5 6 7 26 ACS Paragon Plus Environment

4.4

4.8

Page 27 of 33

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1

Figure 3 ZPE corrected PES for reaction 3 and 4 along with structures of related species

2

optimized at B3LYP/cc-pV(T+d)Z level of theory

3 4 5 6 7 8 9 10 27 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 2 3 4

Page 28 of 33

Table 1 Relative energies (with and without ZPE corrections) and relative free energies of the dimeric species calculated at CCSD(T)/cc–pV(T+d)Z//B3LYP/cc–pV(T+d)Z level. The values calculated at B3LYP/cc–pV(T+d)Z level are given in parentheses. All the values are in kcal mol−1 ∆T ∆TUVG ∆W ∆WUVG SO3–WM

WM–WM

WM–AM

–9.9

–7.7

–0.2

2.0

(–10.4)

(–8.1)

(–0.7)

(1.5)

–5.9

–3.8

1.7

3.8

(–6.1)

(–4.0)

(1.5)

(3.6)

–7.0

–4.9

0.1

2.2

(–7.2)

(–5.1)

(–0.1)

(2.0)

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29


Page 29 of 33

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1 2 3 4


Table 2 Equilibrium constants (cm3 molecule-1) for SO3–WM, WM–WM and WM–AM. Concentration (molecules cm−3) of WM–WM and WM–AM has been calculated using 100 % relative humidity for WM, and 10 ppbv mixing ratio for ammonia at at 0 km altitude (Table S1). For other altitudes concentrations ([WM]and [AM]hi) given in Table S2 are used. Temp Alt. SO3–WM WM–WM Concentration WM–AM Concentration (K) 280

1.33 × 10−19

3.39 × 10−21

2.26 × 1014

5.97 × 10−20

4.03 × 109

290

8.32 × 10−20

2.69 × 10−21

6.16 × 1014

4.44 × 10−20

5.37 × 109

298

5.85 × 10−20

2.27 × 10−21

1.36 × 1015

3.56 × 10−20

6.77 × 109

300

5.37 × 10−20

2.18 × 10−21

1.61 × 1015

3.38 × 10−20

7.08 × 109

310

3.57 × 10−20

1.79 × 10−21

3.82 × 1015

2.62 × 10−20

9.05 × 109

320

2.44 × 10−20

1.49 × 10−21

8.25 × 1015

2.07 × 10−20

1.11 × 1010

5 km

259

4.07 × 10−19

5.87 × 10−21

3.41 × 1012

1.20 × 10−19

2.20 × 107

10 km

230

2.72 × 10−18

1.51 × 10−20

3.66 × 1011

4.01 × 10−19

1.67 × 106

15 km

213

1.07 × 10−17

3.00 × 10−20

1.15 × 107

9.55 × 10−19

2.32 × 103

20 km

216

9.00 × 10−18

2.75 × 10−20

2.51 × 106

8.56 × 10−19

–

25 km

219

6.43 × 10−18

2.32 × 10−20

6.31 × 105

6.91 × 10−19

–

30 km

224

4.31 × 10−18

1.90 × 10−20

1.30 × 105

5.36 × 10−19

–

35 km

235

1.90 × 10−18

1.26 × 10−20

2.16 × 104

3.18 × 10−19

–

40 km

250

6.99 × 10−19

7.67 × 10−21

3.18 × 105

1.69 × 10−19

–

0 km

5 6 7 8 9 10 11 12 13 14 15 16 17 18



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 2 3 4

Page 30 of 33

Table 3 Energies (with and without ZPE corrections) and free energies of the RCs, TSs and PCs with respect to isolated SO3 and WM–X (X = WM and AM) calculated at CCSD(T)/cc– pV(T+d)Z//B3LYP/cc–pV(T+d)Z level. The values calculated at B3LYP/cc–pV(T+d)Z level are given in parentheses. All the values are in kcal mol−1 Species ∆T ∆TUVG ∆W ∆WUVG SO3–WM–WM

TSWM

SA–WM

SA + WM

SO3–WM–AM

TSAM

SA–AM

SA + AM

–16.9

–13.7

–2.5

0.8

(–17.3)

(–14.0)

(–2.8)

(0.5)

–9.5

–7.8

5.0

6.7

(–9.2)

(–7.5)

(5.2)

(7.0)

–31.1

–27.4

–15.6

–11.9

(–28.5)

(24.9)

(–13.0)

(–9.3)

–17.1

–15.7

–12.4

–11.0

(–15.0)

(–13.6)

(–10.3)

(–8.9)

–18.6

–15.8

–4.5

–1.7

(–18.9)

(–16.1)

(–4.8)

(–2.0)

–17.4

–15.8

–3.6

–2.0

(–17.2)

(–15.6)

(–3.3)

(–1.7)

–33.0

–29.9

–17.8

–14.7

(–30.5)

(–27.4)

(–15.3)

(–12.2)

–16.0

–14.6

–10.7

–9.4

(–13.9)

(–12.5)

(–8.6)

(–7.3)

5 6 7 8 9 10 11 12


Page 31 of 33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Table 4 Rate constants (cm3 molecule-1 s-1) for reactions 1, 2, 3 and 4. Individual values of Keq

2

and kuni are given in Table S1 in Supporting Information

Altitude

Temperature

WM catalyzed

AM catalyzed

Reaction 1

Reaction 2

Reaction 3

Reaction 4

(k1)

(k2)

(k3)

(k4)

280

7.58 × 10−12

2.98 × 10−10

2.38 × 10−4

5.33 × 10−4

290

5.32 × 10−12

1.64 × 10−10

1.03 × 10−4

1.92 × 10−4

298

4.08 × 10−12

1.05 × 10−10

5.44 × 10−5

8.94 × 10−5

300

3.82 × 10−12

9.41 × 10−11

4.67 × 10−5

7.43 × 10−5

310

2.81 × 10−12

5.60 × 10−11

2.24 × 10−5

3.05 × 10−5

320

2.10 × 10−12

3.44 × 10−11

1.12 × 10−5

1.33 × 10−5

5 km

259

1.74 × 10−11

1.21 × 10−9

1.73 × 10−3

5.86 × 10−3

10 km

230

7.11 × 10−11

1.28 × 10−8

4.85 × 10−2

3.30 × 10−1

15 km

213

1.95 × 10−10

6.93 × 10−8

5.21 × 10−1

5.84

20 km

216

1.71 × 10−10

5.61 × 10−8

3.87 × 10−1

4.07

25 km

219

1.34 × 10−10

3.71 × 10−8

2.16 × 10−1

2.01

30 km

224

9.96 × 10−11

2.26 × 10−8

1.08 × 10−1

8.66 × 10−1

35 km

235

5.44 × 10−11

8.19 × 10−9

2.58 × 10−2

1.54 × 10−1

40 km

250

2.60 × 10−11

2.38 × 10−9

4.48 × 10−3

1.85 × 10−2

0 km

(K)

3 4 5 6 7 8 9 10 11 12 13 14 15 31 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 2

3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18 19 20 21 22 23 24

Page 32 of 33

Table 5 Relative rates of AM catalyzed reaction with respect to WM catalyzed process at 0 km altitude Temperature (K) [WM]hi[AM]hi# [WM]hi[AM]lo [WM]lo[AM]hi [WM]lo[AM]lo 280

31.9

0.319

160

1.6

290

10.2

0.102

51.0

0.51

298

4.25

0.0425

21.2

0.212

300

3.48

0.0348

17.4

0.174

310

1.29

0.0129

6.46

0.0646

320

0.522

0.00522

2.61

0.0261

#

[WM]hi and [WM]lo represents concentrations corresponding to 100% and 20% relative humidity. [AM]hi and [AM]lo represents concentrations corresponding to 10 ppbv and 100 pptv mixing ratios, respectively. Concentrations (molecule cm−3) are given in Table S1.

Table 6 Relative rates of AM catalyzed reaction with respect to WM catalyzed process at various altitudes in troposphere Temperature 10 % of 1% of 0.1% of Altitude [AM]hi* (K) [AM]hi [AM]hi [AM]hi 0 km

298

6.34

0.634

0.0634

0.00634

5 km

259

31.2

3.12

0.312

0.0312

10 km

230

118

11.8

1.18

0.118

15 km

213

16900

1690

169

16.9

*

[AM]hi here represents maximum mixing ratio at 0, 5, 10 and 15 km altitudes. The values are 10 ppbv, 500 pptv, 100 pptv and 30 pptv, respectively. Concentrations (molecule cm−3) are given in Table S2.


Page 33 of 33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic

1 2

3

SO3-H2O + X

SO3-H2O-X

H2SO4-X

SO3 + H2O-X

SO3-H2O-X

H2SO4-X

X = H 2O

k (298 K) = 1.05 × 10−10 cm3 molecule-1 s-1

X = NH3

k (298 K) = 8.94 × 10−5 cm3 molecule-1 s-1


Ammonia Catalyzed Formation of Sulfuric Acid in ... - ACS Publications

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