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Inhibition and Promotion of Pyrolysis by Hydrogen Sulfide (HS) and Sulfanyl Radical (SH) 2
Zhe Zeng, Mohammednoor Altarawneh, Ibukun Oluwoye, Peter Glarborg, and Bogdan Z Dlugogorski J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b09357 • Publication Date (Web): 25 Oct 2016 Downloaded from http://pubs.acs.org on October 29, 2016
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The Journal of Physical Chemistry
Inhibition and Promotion of Pyrolysis by Hydrogen Sulfide (H2S) and Sulfanyl Radical (SH)
Zhe Zeng,1 Mohammednoor Altarawneh1*, Ibukun Oluwoye,1 Peter Glarborg,2 Bogdan Z. Dlugogorski1
1
School of Engineering and Information Technology, Murdoch University 90 South Street, Murdoch, WA 6150, Australia
2
Department of Chemical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
*
Corresponding author:
Phone: +61 89360 7507, Email:
[email protected] 1 ACS Paragon Plus Environment
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ABSTRACT
2 3
This study resolves the interaction of sulfanyl radical (SH) with aliphatic (C1-C4)
4
hydrocarbons, using CBS-QB3 based calculations.
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enthalpies and located the weakest link in each hydrocarbon. Subsequent computations
6
revealed that, H abstraction by SH from the weakest C‒H sites in alkenes and alkynes, except
7
for ethylene, appears noticeably exothermic. Furthermore, abstraction of H from propene, 1-
8
butene and iso-butene displays pronounced spontaneity (i.e., ∆rG° < -20 kJ mol-1 between 300
9
– 1200 K) due to the relatively weak allylic hydrogen bond. On the other hand, an alkyl
10
radical readily abstracts H atom from H2S, with H2S acts as a potent scavenger for alkyl
11
radicals in combustion processes. That is, these reactions proceed in the opposite direction
12
than those involving HS and alkene or alkyne species, exhibiting shallow barriers and strong
13
spontaneity. Our findings demonstrate that, the documented inhibition effect of hydrogen
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sulfide (H2S) on pyrolysis of alkanes does not apply to alkenes and alkynes.
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interaction with hydrocarbons, the inhibitive effect of H2S and promoting interaction of SH
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radical depend on the reversibility of the H abstraction processes. For the three groups of
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hydrocarbon, Evans-Polanyi plots display linear correlations between the bond dissociation
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enthalpies of the abstracted hydrogens and the relevant activation energies. In the case of
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methane, we demonstrated that, the reactivity of SH radicals towards abstracting H atoms
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exceeds that of HO2 but falls below those of OH and NH2 radicals.
We obtained the C-H dissociation
21
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INTRODUCTION
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Hydrogen sulfide (H2S) represents a major impurity in natural gas, and arises in gasification
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processing of fossil fuels. The pipeline-quality natural gas typically contains about 2000 ppm
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of sulfur species, in which H2S constitutes the predominant sulfur carrier.1 Although the
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oxidation mechanism of H2S has been studied under atmospheric2 and high pressure3
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conditions, its interactions with hydrocarbons remain poorly understood. An experimental
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investigation of Nguyen et al. have indicated that, H2S exhibits an inhibition effect on the
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pyrolysis of n-octane under pressure of 70 MPa.4,5
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oxidation competition between H2S and CH4, in systems involving the injection of H2S as an
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additive to CH4/air flames.6,7 Similarly, a recent study by Gerson et al.8 has linked the co-
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oxidation of H2S and CH4 with the H2/O2 chemistry showing that reaction of H2S with the
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molecular oxygen produces HO2. The latter promotes CH4 oxidation at low and intermediate
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temperatures.8
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(CH3SH) as a main product in the pyrolysis of alkyl sulfide, which partly origins from the
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direct combination of CH3 and SH radical through negligible activation barrier.9,10
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However, literature lacks detailed understanding of how H2S and hydrocarbons interact with
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each other, and the H2S inhibition mechanism remains open to speculations.
Likewise, Selim et al. reported the
Additionally, Vandeputte et al. reported the formation of methanethiol
40 41
A pioneering study of Gray et al. investigated the reaction between methyl radical (CH3,
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produced by photolysis of azomethane) and H2S. The investigators observed that, methyl
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radical promptly abstracts H atom from H2S, producing a SH radical and a methane molecule
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(see Reaction Ra below).11 Arican et al. further measured the rate constant of Ra as k(T) =
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1.67 × 10-13 exp(-1 054/T) cm3·molecule-1·s-1 within the temperature range of 334 – 432 K,12
46
while an analogous computational study revealed k(T) = 1.13 × 10-16 × T1.2 exp(- 722/T)
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cm3·molecule-1·s-1 for a wider temperature window of 200 – 3000 K.13 On the contrary,
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another experimental work of Perrin et al. discovered that, SH radical can extract one H from
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2-(Z)-C5H10 to form H2S in Reaction Rb, ensuing a reaction rate constant of k(T) = 1.00 × 10-
50
14
exp(-1 159/T) cm3·molecule-1·s-1 for a temperature range of 743 to 772 K.14
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CH3+ H2S → CH4 + SH
Ra
2-(Z)-C5H10 + ˙SH → CH2CH=CHCH2CH3 + H2S
Rb
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These two sets of reactions proceed in opposite directions, demonstrating that, SH radical
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may have different effect on alkanes and alkenes. Moreover, to the best of our knowledge,
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literature provides no experimental measurements and theoretical calculations of reactions of
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H2S and/or SH radical with other classes of hydrocarbons.
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While the H abstraction reactions by O/H radical pool act as the initiation step for
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hydrocarbon oxidation,15 the presence of appreciable concentrations of SH in radical pool at
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elevated temperature could contribute to the overall oxidation mechanism. For this reason,
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this contribution investigates the reactivity of SH radical with a series of hydrocarbons (C1-
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C4), by deploying the density functional theory (DFT) at an adequately high level of theory.
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We cast the reaction sequence according to:
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RH + SH → R···H···SH → R + H2S 65 66
where RH signifies a gas-phase alkane, alkene or alkyne under the C4 chain limit.
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The objectives of this study are to: (i) present the potential energy surfaces for reactions 4 ACS Paragon Plus Environment
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between a SH radical and a series of hydrocarbons, (ii) compute the reaction rate parameters
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in Arrhenius equation over a temperature range from 300 K to 2000 K, (iii) relate the
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dependence of the calculated activation energies with the dissociation enthalpies of the
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relevant C‒H bonds, (iv) compare the reaction activity of a SH radical with other active
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combustion radicals, namely OH, HO2 and NH2 by examining the corresponding bimolecular
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reactions.
75 76 77
COMPUTATIONAL DETAILS
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Gaussian 09 suite of programs16 facilitated all structural optimisations, and served to
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calculate enthalpies as well as vibrational frequencies using the complete-basis-set CBS-QB3
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composite method.17 Several studies have already established that, the CBS-QB3 method
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offers accurate calculations of geometries and activation enthalpies of hydrogen abstraction
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reactions.18-20 For instance, a concise study of Pokon et al. applied this method to calculate a
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series of hydrocarbon deprotonation reactions in gas phase, with the results indicating a
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maximum deviation of 6.2 kJ·mol-1, relative to the corresponding experimental values.21 We
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further validated the accuracy of CBS-QB3 method and corroborate this result in the
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discussion part of the present article.
88 89
In the calculations, the absence of imaginary frequencies in all reactant and product species
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indicated true energy minima. In contrast, the computed transition structures retained one,
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and the only one imaginary frequency along the specific reaction coordinate. Since the effect
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of hindered rotors in reactants and transition structures cancels each other, we treated all
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hindered rotors as harmonic oscillators.
In addition, for selected reactions, we applied
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intrinsic reaction coordinate (IRC) calculation to confirm the reaction pathways.
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The ChemRate program22, based on the classical transition state theory (TST)23, afforded
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estimation of the reaction rate constants. As implemented in the KiSTheIP code, a one-
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dimensional asymmetrical Eckart barrier accounted for quantum tunneling effects on
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computed rate coefficients.24,25 The reaction rate parameters were fitted to the Arrhenius
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equation in the form of k(T) = A·Tn·exp(-Ea/RT), over a temperature range of 300 K to 2000
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K. Finally, Chemkin-Pro26 program served to obtain the equilibrium species concentrations
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for selected systems.
103 104 105
RESULTS AND DISCUSSION
106 107
Overview of Labile H Abstraction Sites in C1-C4 Hydrocarbons
108 109
In general, the titled reactions involve the following process:
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RH + SH → R···H···SH → R + H2S 111 112
in which SH radical abstracts single H from an hydrocarbon, and as a result, produces a
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radical R and H2S via the transition state [R···H···SH] structure. Most hydrocarbons display
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different sites for hydrogen abstraction by SH. For example, the SH radical can extract H
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from primary or secondary C‒H site in propane, resulting in a different radical R and a
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transition structure. The main interest lies in elucidating the most favorable routes during
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combustion processes. 6 ACS Paragon Plus Environment
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For this reason, we calculated the bond dissociation enthalpies (BDH) to locate the weakest
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C‒H bonds in all species studied in this paper. In subsequent computations, we assumed that,
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SH radical preferentially attacks the weakest C‒H bond in the hydrocarbons. Further
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calculation validates that H abstraction from weakest C-H site in hydrocarbon is featured
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with lower activation barrier in case of propane. Our computed BDH values have been
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compared with analogous experimental and the theoretical estimations summarised by Luo.27
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Table 1 demonstrates agreements between the recommended values of Luo27 and the present
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results, within the expected accuracy of the CBS-QB3 method.
127 128
Table 1.
129 130
In the case of propane and n-butane, the secondary carbon displays the weakest C-H bond,
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while for iso-butane, the weakest C-H bond is that on associated with the tertiary carbon. For
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the alkenes and alkynes, the most vulnerable C‒H bond exists on the saturated carbon sites.
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In brief, the following sequence reflects the strength of the BDH of C‒H bonds:
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C‒H on unsaturated carbon > C‒H on saturated carbon (primary > secondary > tertiary)
136 137
Table 2 presents all hydrogen abstraction reaction considered in the present study. These
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reaction involve the weakest C-H bond of the target molecule.
139 140
Table 2.
141 142
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H Abstraction from Alkanes
144 145
In this section, we discuss the reactions of SH radical with alkanes, namely, methane, ethane,
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propane, n-butane and iso-butane, designated by R1 through R6 in Table 2. Figure 1 portrays
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all the relevant transition structures. For example, in the structure of transition state of R1,
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the distance between the C atom and the dissociated H atom increases to 1.64 Å (0.164 nm),
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whereas the separation between the abstracted H and S atoms corresponds to 1.44 Å.
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Examination of Fig. 1 reveals similar distances for other transition structures.
151
Figure 1.
152 153 154
Figure 2 depicts the potential energy surface for reactions between all C1-C4 alkanes and the
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SH radical. For methane (R1), the activation enthalpy corresponds to 65.9 kJ·mol-1. While in
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R2, reaction of SH radical with ethane molecule requires a relatively smaller barrier height of
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45.7 kJ·mol-1. This concurs with the trend of comparative BDH of methane (440.9 kJ·mol-1)
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and ethane (420.5 kJ·mol-1). In the case of propane, H abstraction from primary carbon site
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(BDH of 428.5 kJ·mol-1) in R3 requires a higher activation barrier of 46.6 kJ·mol-1 when
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compared to that of the weaker secondary links (BDH of 413.9 kJ·mol-1) in R4 (29.1 kJ·mol-
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1
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which is consistent with our previous assumption that SH radicals prefer to attack the weakest
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C‒H bond in the hydrocarbons with lower activation barriers. In the remainder of the paper,
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we focus on the most favourable channel for H abstraction from each molecule.
). Clearly, H abstraction from a weaker C‒H bond results in a lower activation enthalpy,
165 166
Figure 2.
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As demonstrated in Fig. 2 for alkanes, the enthalpy of the separated reaction products (R +
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H2S) exceeds that of separated reactants (RH + SH). The endothermic condition implies that,
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the reverse reactions, i.e., R1b, R2b, and R3b, prevail over forward Reactions R1, R2, and
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R3. This agrees well with the experimental and calculation results available in literature11-13,
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in which H2S reacts with methyl radical to form methane as the primary product. Table 3
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compares the calculated kinetic parameters of R1b with the analogous experimental
174
measurements. The reaction rate corresponds to 1.66 × 10-14 cm3·molecule-1·s-1 at 423 K, in
175
good agreement with the equivalent experimental value11 of 1.45 × 10-14 cm3·molecule-1·s-1.
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The agreement validates the present computational approach to estimate the kinetic
177
parameters of similar reactions that have no experimentally-measured values of rate
178
constants.
179 180
Table 3.
181 182
For propane, n-butane and iso-butane (Reaction R4, R5 and R6), the relative enthalpies of the
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TS structures lie between that of the reactants and products. In effect, this means that, the
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reverse reactions proceed without an enthalpy barrier. In Fig. 3, we present the results of the
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IRC calculation to confirm the transition state structures and the reaction pathways. All
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displayed points are calculated at a fixed C‒H‒S distance around the obtained TS, featuring
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one imaginary frequency. Although, the structures rest within the saddle point of each curve,
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the consecutive enthalpies increase as they approach the product. This behaviour necessitates
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the variational transition state theory (VTST) calculations to obtain the reaction rate
190
constants. For this purpose, we employed five points adjoining the product and minimised
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the reaction rate constant as a function of temperature and reaction coordinate. Due to the
192
absence of a transition structure, we are unable to evaluate the rate parameters for reverse
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reactions directly. Herein, we calculated an equilibrium constant with Chemkin26 at each
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temperature to derive backward reaction rate using of the rate of the forward reaction we
195
obtained with VTST (see supporting information for detail).
196 197
Figure 3.
198 199
As these reactions are considerably endothermic with a shallow or no reverse barrier, the
200
backward reaction dominates, with insignificant formation of H2S and CH3. That is, alkyl
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radicals (CH3, C2H5, C3H7 and C4H9) readily abstract H atoms from H2S to produce alkane
202
molecules and SH radicals. For C2H5 and prim-C3H7, the trivial activation barriers amount to
203
4.9 kJ·mol-1 and 2.9 kJ·mol-1, respectively at 298.15 K. For the remaining alkyl radicals, the
204
reactions proceed via barrier-less processes.
205 206
To gain further insights into the equilibrium condition of R1, we performed simple
207
equilibrium calculations with Chemkin-Pro26. The procedure required the thermochemical
208
data of the reactants (relatively to the forward path, i.e. CH4 and SH) and the products (CH3
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and H2S) as derived from their respective enthalpy of formation (NIST webbook), vibrational
210
frequencies and rotational constants (computed by CBS-QB3) with ChemRate22. In addition,
211
we also compared the results with using thermodynamic data from Burcat’s database.28
212
Figure 4 displays the equilibrium quantities of the reacting species for an initial concentration
213
of 25 % v/v CH4, and 25 % v/v SH in nitrogen balance, at different temperatures (300 – 2000
214
K), calculated with our derived thermodynamic data and that of Burcat (see supporting
215
information), respectively. The difference between two sets of data is within 6 %, which
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also validates the accuracy of the derived thermochemical data used in this work. The
217
equilibrium concentration of reactants significantly exceeds those of the products, implying
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that, the backward reaction plays a more significant role during H abstraction from alkanes.
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To this end, one can easily observe that the presence of H2S hinders the pyrolysis of CH4,
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concurring with the inhibition effect on n-octane.4,5 However, under oxidative conditions,
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the production of HO2 (i.e., a major oxidation carrier in the low – intermediate temperature
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windows) during the early stages of H2S oxidation (H2S + O2 → HS + HO2) may overshadow
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the overall inhibition activity of H2S during CH4/H2S co-oxidation scheme. This has been
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manifested by kinetic sensitivity analysis8 and a noticeable reduction in autoignition delay
225
time upon the addition of 1% H2S to methane at pressures ranging from 30-80 bar and
226
temperatures from 930-1050 K.
227
Figure. 4
228 229
Table 4 reports the Arrhenius parameters for the forward and the reverse reactions of H
230
abstractions from the weakest C‒H bond in C1-C4 alkanes. The rate parameters for Reactions
231
R4, R5 and R6 come from the VTST calculations, while those of R4b, R5b and R6b are
232
derived with equilibrium constant Kc and forward reaction rate kf at each temperature,
233
respectively. The classical TST formalism yielded the remaining rate parameters.
234 235
Table 4.
236 237 238
H Abstraction from Alkenes and Alkynes
239 240
In Fig. 5, we present the calculated potential energy surface for reactions involving ethylene,
241
propene, 1-butene, iso-butene, allene, propyne and 1-butyne.
242
comprise the abstraction of H atoms from the weakest C‒H bond in each hydrocarbon.
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Hydrogen abstraction from ethylene by SH differs significantly from other systems, with the
244
reaction endothermicity of 78.7 kJ·mol-1, and the transition state lying 3.4 kJ·mol-1 below the
245
separated products.
246
reaction pathway and it demonstrated a similar pattern with propane, n-butane and iso-butane,
247
as illustrated in Fig. 3. For the remaining species, the reactions are all exothermic and
248
proceed with plausible activation barriers. As opposed to alkanes, SH radical can extract one
249
H from the weak C‒H sites on alkenes/alkynes (except for ethylene) to produce H2S. This is
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consistent with the experimental work of Perrin et al.14, in which the authors observed the
251
formation of H2S as a result of H atom migration from 2-(Z)-C5H10 towards SH radical.
Consequently, an IRC calculation was conducted to elucidate the
252
Figure 5.
253 254 255
The H abstraction process in 1-butene incurs a trivial activation enthalpy of 1.8 kJ·mol-1 with
256
reaction exothermicity of 39.4 kJ·mol-1. Noticeably, the barrier heights rise to 16.7 kJ·mol-1
257
and 13.0 kJ·mol-1, for propene and 1-butyne, respectively. But for iso-butene, allene and
258
propyne, the reactions involve activation enthalpies of 39.8 kJ·mol-1, 35.5 kJ·mol-1 and 34.7
259
kJ·mol-1, in that order. All these values reside within the accuracy limit of the computational
260
methodology (CBS-QB3). Table 5 assembles the fitted Arrhenius parameters for Reaction R7
261
through R13. We obtained the rate parameters for Reaction R7 from VTST, and used TST for
262
the other reactions.
263 264
Table 5.
265 266
Validation of CBS-QB3 Calculations
267
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Although, the experimental data for H abstraction from hydrocarbons by SH radical are
269
scarce, we conducted three sets of comparison to confirm the accuracy of the calculated CBS-
270
QB3 results. Firstly, as shown in Table 1, we have computed the BDH values for different H-
271
abstraction site in aliphatic hydrocarbons, and compared them with analogous experimental
272
and theoretical estimations summarised by Luo27. The calculated results match the
273
recommended BDH values, but it appears that, the molecular complexity of higher
274
hydrocarbons leads to larger errors in BDHs. We computed the absolute mean error to be 5.9
275
kJ·mol-1, in good agreement with the results of another work of Pokon et al.21, who adopted
276
the same basis set to calculate a series of gas-phase deprotonation reactions with mean
277
absolute deviation of 6.2 kJ·mol-1 from experimental values.
278 279
Secondly, we compared the reaction rate of Ra (CH3 + H2S → CH4 + SH) with the
280
experimental data. As mentioned earlier, this reaction had previously been studied both
281
experimentally and theoretically11-13. Figure 6 contrasts our calculated rate constants with the
282
literature values. Our results compare well with the experimental data that were obtained for
283
a relative narrow temperature range (334 – 432 K). On the other hand, the Arrhenius
284
expression of Mousavipour et al.13, computed at a lower level of theory (MP2/6-311+G(d,p)),
285
overestimates the rate coefficient at lower temperatures.
286
constants of R1 derived from the thermochemical data calculated in this work deviate by only
287
6% of analogous values calculated based on Burcat’s database.28 This serves as a validation
288
for the accuracy of calculated vibrational frequencies and rotational constant within the
289
adapted CBS-QB3 methodology.
290
temperature dependency of Gibbs free energy (∆rG°) for all reactions (from 300 K – 1200 K).
291
The decreasing trend of Gibbs free energy indicates that all considered H abstraction
292
reactions become more spontaneous as the temperature increases.
Additionally, the equilibrium
Figure S1 in supporting information demonstrates the
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Figure 6.
294 295 296
Thirdly, we examined Reaction Rb (2-(Z)-C5H10 + SH → CH2CH=CHCH2CH3 + H2S, see
297
Fig. S2 in supporting information) to confirm the accuracy of our calculation when compared
298
with the experimental data of Perrin et al.14
299
Arrhenius equation within the temperature range of 300 – 2000 K to obtain k(T) = 6.51 × 10-
300
14
301
results fitted between 743 – 772 K to k(T) = 1.0 × 10-14 exp(-1 159/T) cm3·molecule-1·s-1, with
302
a relatively larger pre-exponential factor.
303
aforementioned reaction, and the supporting information provides the relevant potential
304
energy surface.
305
Bearing in mind plausible source of errors in the experimental work as well the accuracy
306
benchmark of the adopted theoretical methodology, the difference depicted in Fig. 7 remains
307
within an order of magnitude. A plausible source for the discrepancy in Figure 7 might stem
308
from treating all hindered rotors in the (2-(Z)-C5H10) as harmonic oscillators. It is a very
309
daunting task to accurately account for all coupled internal rotations in the rather complex
310
molecular structure of (2-(Z)-C5H10).
Our calculated results were fitted to the
exp(-1 219/T) cm3·molecule-1·s-1. This equation somewhat overestimates the experimental
Figure 7 assesses the Arrhenius plot of the
Our calculated data seem to somewhat overestimate the reaction rate.
311 312
Figure 7.
313 314
Relationship between BDH of Abstracted C‒H Bond and Activation
315
Enthalpy of SH + Hydrocarbon Reaction
316 317
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318
radical, we introduced the Evans-Polanyi plots as illustrated in Fig. 8. The abstraction rate
319
(represented by activation enthalpy) generally depends on the strengths of the dissociated C‒
320
H bond (as reflected by the corresponding BDH) and the activity of the attacking radical
321
(SH). The figure compares the linear correlations between activation enthalpy ∆E and BDH
322
for each group of hydrocarbons.
323
Figure 8.
324 325 326
The orbital hybridisation in double and triple-bonded carbon leads to strong C‒H bonds on
327
the unsaturated carbon atoms. For example, all H atoms of ethylene connect to unsaturated
328
carbon atoms (=CH2), which results in significantly higher BDH (462.8 kJ·mol-1) if compared
329
with allylic C-H bonds in propene (359.3 kJ·mol-1). This explains the outlier position of
330
ethylene among the studied alkene molecules (see Fig. 8), and elucidates the reason for the
331
C2H3 radical abstract H from H2S, via a barrierless pathway.
332 333
As illustrated in Fig. 8, the weakest C-H bond in alkanes is much stronger than that in
334
alkenes/alkynes. Generally, the extra orbital overlap on unsaturated C weakens the C‒H
335
bond on the vicinal saturated carbons, resulting in lower BDH for alkenes and alkynes (i.e.,
336
on saturated C site) compared to alkanes. Based on our kinetic analysis, we report that, the
337
forward reaction predominates for alkenes and alkynes, whereas the backward process
338
governs the reactions involving alkanes.
339 340
Furthermore, since the reaction rate relies on the strength of the dissociated C‒H bond and
341
the reaction activity of the SH radical, we calculated the BDH of S-H in H2S molecule as
342
380.4 kJ·mol-1. This value forms a distinct boundary between the set of reactions that
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343
proceed in a forward direction and those that advance in the reverse direction. On the left
344
side (Fig. 8), BDHs of alkenes and alkynes are smaller than that of S-H. This means that, SH
345
can abstract H from these species. On the contrary, the C‒H bond in alkanes remain much
346
stronger than the S‒H bond in H2S, resulting in species to the right of 380.4 kJ·mol-1
347
abstracting H from H2S, to form alkane molecules.
348 349 350
Activity of SH Radical Compared with Those of OH, NH2 and HO2
351 352
In order to gain further insights into the role of SH radical in combustion processes, we
353
explored the reactivity of SH radical, by comparing it with that of NH2, OH and HO2 from
354
literature. Figure 9 contrasts the rate constants for H abstraction from methane by the four
355
radicals.
356
overlapping rate constants. Theoretical calculations of Mebel and Lin yielded 60.2 kJ·mol-1
357
as the activation energy for the reaction CH4 + NH2 → CH3 + NH3,29 i.e., very close to the
358
value of 61.2 kJ·mol-1 calculated herein for analogous reaction involving SH radical.
359
Abstraction by OH30 and HO231 radicals incurs the fastest and the slowest reaction rate,
360
respectively. The reaction of CH4 + NH2 → NH3 + CH3 proceeds predominantly in the
361
forward direction, in contrast to similar abstraction by the SH radical. Comparably, HO2
362
radical seems relatively inactive with a reported activation barrier of 87.9 kJ·mol-1. Thus, we
363
conclude that, the radical activities follow the order of OH > NH2 > HS > HO2.
Interestingly, H abstraction from methane by SH and NH2 radicals display
364 365
Figure 9.
366 367
This ordering follows the strengths of the freshly formed O‒H, N‒H and S‒H bonds. For 16 ACS Paragon Plus Environment
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368
example, the S‒H bond is weaker than O‒H and N‒H bonds and hence OH and NH2 remain
369
more effective in abstracting H atom from the hydrocarbon chain. Along the same line of
370
enquiry, the O‒H bond in H2O2 constitutes a weaker bond justifying its lower reactivity.
371 372 373
CONCLUSIONS
374 375
This contribution has reported the thermokinetic parameters for reactions of SH radicals with
376
a series of C1-C4 hydrocarbons. The inhibition effect of H2S on pyrolysis of alkanes stems
377
from the facile abstraction of H atom from H2S by alkyl radicals, exposing H2S as an
378
effective scavenger of alkyl radicals. The presence of weaker allylic C‒H bonds in alkenes
379
and alkynes forces the overall reaction to proceed in the forward direction, i.e., in the
380
direction of forming the H2S and alkenyl and alkynyl radicals. A linear relationship exists
381
between activation barriers and bond dissociation enthalpies of the attacked C‒H sites. BDH
382
of H2S of 380.4 kJ·mol-1 separates the species whose radicals abstract H from H2S, from
383
those whose hydrogen atoms are abstracted by HS.
384
compared to that of OH, HO2 and NH2 radicals follows the order of OH > NH2 > HS > HO2.
The reactivity of the HS radical
385 386 387
ASSOCIATED CONTENT
388 389
Supporting Information
390 391
The Supporting Information is available free of charge on the ACS Publications website at
392
DOI:
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393 394
Coordinates and calculated enthalpy values for all structures, thermodynamic data
395
calculated for R1, Gibbs free energy for all reactions at high temperature calculated in
396
this work
397 398 399
AUTHOR INFORMATION
400 401
Corresponding Author
402 403
* Email:
[email protected], Phone: +61 8 9360 7507
404 405
Notes
406 407
The authors declare no competing financial interest.
408 409 410
ACKNOWLEDGEMENT
411 412
This study has been supported by grants of computing time from the National Computational
413
Infrastructure (NCI) Australia and from the Pawsey Computing Centre in Perth as well as
414
funds from the Australian Research Council (ARC).
415
University for postgraduate research scholarships.
Z. Z. and I. O. thank Murdoch
416 417
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The Journal of Physical Chemistry
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13. Mousavipour, S. H.; Namdar-Ghanbari, M. A.; Sadeghian, L. A theoretical study on the
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15. El Marrouni, K.; Abou-Rachid, H.; Kaliaguine, S. Density functional theory kinetic
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16. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J.
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18. Casasnovas, R.; Frau, J.; Ortega-Castro, J.; Salvà, A.; Donoso, J.; Muñoz, F.
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Simplification of the CBS-QB3 method for predicting gas-phase deprotonation free energies.
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19. Vandeputte, A. G.; Sabbe, M. K.; Reyniers, M. F.; van Speybroeck, V.; Waroquier, M.;
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Marin, G. B. Theoretical study of the thermodynamics and kinetics of hydrogen abstractions
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20. Vandeputte, A. G.; Reyniers, M. F. A theoretical study of the thermodynamics and kinetics
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21. Emma K. Poken; Matthew D. L.; Steven F.; George C. S. Comparison of CBS-QB3,
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22. Mokrushin V.; Bednov V.; Tsang, W.; Zachariah M.; Knyazev V. ChemRate, NIST:
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23. Truhlar, D. G.; Garrett, B. C.; Klippenstein, S. J. Current status of transition-state theory.
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J. Phys. Chem. A 1996, 100, 12771-12800.
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24. Eckart C. The penetration of a potential barrier by electrons. Phys. Rev. 1930, 35 (11),
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25. Canneaux, S.; Bohr, F.; Henon, E. KiSThelP: a program to predict thermodynamic
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26. Reaction Design, San Diego, CHEMKIN-PRO, 15131; 2013.
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27. Luo, Y.-R. Handbook of bond dissociation energies in organic compounds. Taylor and
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28. Burcat, A. Ideal gas thermodynamic data in polynomial form for combustion and air
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pollution use (http://garfield.chem.elte.hu/Burcat/burcat.html).
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29. Mebel, A. M.; Lin, M. C. Prediction of absolute rate constants for the reactions of NH2
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30. Atkinson, R. Kinetics of the gas-phase reactions of OH radicals with alkanes and
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cycloalkanes. Atmos. Chem. Phys. 2003, 3, 2233-2307.
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31. Aguilera-Iparraguirre, J.; Curran, H. J.; Klopper, W.; Simmie, J. M. Accurate benchmark
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calculation of the reaction barrier height for hydrogen abstraction by the hydroperoxyl radical
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from methane: implications for CnH2n+2 where n = 2 → 4. J. Phys. Chem. A 2008, 112, 7047-
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Table 1. Comparison of the calculated BDH with the literature values for all hydrocarbons studied in this work.27 Hydrocarbon
The broken bonds
BDH calculated
Recommended BDH
Absolute
species
(in bold)
in this work
[27]
error
(kJ·mol-1)
(kJ·mol-1)
(kJ·mol-1)
Methane
CH4
440.9
439.3±0.4
1.6
Ethane
CH3CH3
425.5
420.5±1.3
5.0
CH3CH2CH3
428.5
422.2±2.1
6.3
CH3CH2CH3
413.9
410.5±2.9
3.4
CH3CH2CH2CH3
426.4
421.3
5.1
CH3CH2CH2CH3
414.8
411.1±2.2
3.7
(CH3)2CHCH3
428.1
419.2±4.2
8.9
(CH3)3CH
406.6
400.4±2.9
6.2
CH2=CH2
462.8
465.3±3.3
2.5
CH3CH=CH2
466.7
464.8
1.9
CH3CH=CH2
446.6
N/A
N/A
CH3CH=CH2
359.3
368.6±2.9
9.3
CH2=CHCH2CH3
418.9
410.5
8.4
CH2=CHCH2CH3
346.1
350.6
4.5
CH2=CHCH2CH3
447.6
N/A
N/A
CH2=CHCH2CH3
465.9
N/A
N/A
CH2C(CH3)CH3
371.3
362.8±2.5
8.5
CH2C(CH3)2
469.6
N/A
N/A
CH2=C=CH2
379.3
371.1±12.6
8.2
Propane
n-Butane
iso-Butane
Ethylene
Propene
1-Butene
iso-Butene
Allene
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Propyne
CH≡CCH3
382.6
372.0±4.2
10.6
1-Butyne
CH≡CCH2CH3
362.3
355.6
6.7
Mean Absolute Error
5.9
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Table 2. Reactions studied in this work, C in bold indicates the H abstraction site(s) for each hydrocarbon. R1b, R2b and R3b denote the reverse reactions of R1, R2 and R3. Reactant
Reaction CH4 + SH → CH3 + H2S
R1
CH3 + H2S →CH4 + SH
R1b
C2H6 + SH → CH2CH3 + H2S
R2
CH2CH3 + H2S → C2H6 + SH
R2b
C3H8 + SH → CH2CH2CH3 + H2S
R3
CH2CH2CH3 + H2S →C3H8 + SH
R3b
C3H8 + SH → CH(CH3)2 + H2S
R4
CH(CH3)2 + H2S → C3H8 + SH
R4b
C4H10 + SH → CH3CHCH2CH3 + H2S
R5
CH3CHCH2CH3 + H2S → C4H10 + SH
R5b
C4H10 + SH → C(CH3)3 + H2S
R6
C(CH3)3 + H2S → C4H10 + SH
R6b
Ethylene
C2H4 + SH → CH=CH2 + H2S
R7
Propene
C3H6 + SH → CH2=CHCH2 + H2S
R8
1-Butene
C4H8 + SH → CH2=CHCHCH3 + H2S
R9
iso-Butene
C4H8 + SH → CH2=C(CH2CH3) + H2S
R10
Allene
C3H4 + SH → CH2=C=CH + H2S
R11
Propyne
C3H4 + SH → C≡CCH2 + H2S
R12
1-butyne
C4H6 + SH → CH≡CCHCH3
R13
Methane
Ethane
Propane
n-Butane
iso-Butane
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Table 3. Arrhenius parameters fitted between 334 K and 432 K for Reaction R1b; k(T) = A·exp(-Ea/RT) for both experimental measurements12 and theoretical calculations. A
Ea
(cm3·molecule-1·s-1)
(kJ·mol-1)
Experiment
1.67 × 10-13
8.8
[12]
TST with Eckart
6.76 × 10-13
13.3
This work
Source
Method
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Table 4. Arrhenius parameters fitted between 300 and 2000 K for alkane + SH radical; k(T) = A·Tn· exp(-Ea/RT). A
Ea n
Reaction (cm3·molecule-1·s-1)
(kJ·mol-1)
R1: CH4 + SH → CH3 + H2S
7.78 × 10-22
3.02
66.3
R2: C2H6 + SH → CH2CH3 + H2S
4.37 × 10-22
3.41
42.2
R3: C3H8 + SH → CH2CH2CH3 + H2S
8.51 × 10-22
3.39
43.2
R4: C3H8 + SH → CH(CH3)2 + H2S
5.25 × 10-18
1.79
34.6
R5: C4H10 + SH → CH3CHCH2CH3 + H2S
3.26 × 10-20
2.53
31.3
R6: C4H10 + SH → C(CH3)3 + H2S
1.56 × 10-17
1.94
24.3
R1b: CH3 + H2S →CH4 + SH
2.15 × 10-22
3.15
3.4
R2b: CH2CH3 + H2S → C2H6 + SH
5.89 × 10-23
3.06
1.1
R3b: CH2CH2CH3 + H2S →C3H8 + SH
5.25 × 10-22
2.74
0.4
R4b: CH(CH3)2 + H2S → C3H8 + SH
7.64 × 10-21
3.61
8.7
R5b: CH3CHCH2CH3 + H2S → C4H10 + SH
6.86 × 10-13
0.03
12.1
R6b: C(CH3)3 + H2S → C4H10 + SH
1.03 × 10-12
0.03
9.6
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Table 5. Arrhenius parameters fitted between 300 and 2000 K for alkene + SH radical and alkyne + SH radical; k(T) =A·Tn·exp(-Ea/RT). A
Ea n
Reaction (cm3·molecule-1·s-1)
(kJ·mol-1)
R7: C2H4 + SH → CH=CH2 + H2S
2.96 × 10-25
3.31
81. 3
R8: C3H6 + SH → CH2=CHCH2 + H2S
2.00 × 10-24
3.79
9.9
R9: C4H8 + SH → CH2=CHCHCH3 + H2S
2.19 × 10-23
3.40
0.4
R10: C4H8 + SH → CH2=C(CH2CH3) + H2S
2.69 × 10-22
3.32
36.5
R11: C3H4 + SH → CH2=C=CH + H2S
2.51 × 10-22
3.37
30.2
R12: C3H4 + SH → C≡CCH2 + H2S
2.24 × 10-21
3.36
29.1
R13: C4H6 + SH → CH≡CCHCH3
1.10 × 10-22
3.32
8.01
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Figure 1. Transition state structures for H abstraction from the weakest C‒H bond of the studied hydrocarbons. Distances are in Å.
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Figure 2. Potential energy surface of C1-C4 alkanes + SH radical, computed at CBS-QB3 level of theory. H atom is abstracted from weakest C-H, as illustrated by the product radicals. Values of relative enthalpy and Gibbs free energy (in italic and brackets) at 298.15 K, are in kJ·mol-1.
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Figure 3. IRC calculation for reaction pathway of SH + propane/n-butane/iso-butane. Red dots indicate the transition structure identified at saddle point. Green dots denote the structures adopted in VTST calculations.
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Figure 4. The equilibrium amounts of reactants (CH4, SH) and products (CH3, H2S) for an initial mixture of 25 % v/v CH4, 25 % v/v of SH and 50 % v/v of dilution N2 at different temperatures. Calculations are conducted at constant pressure (1 atm) and temperature for each point.
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Figure 5. Potential energy surface for selected alkene/alkyne + SH radical, computed at CBSQB3 level of theory. H atom is abstracted from weakest C-H, as illustrated by the product radicals. Values of relative enthalpy and Gibbs free energy (in italic and brackets) at 298.15 K
are
in
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Figure 6. Comparison of rate coefficients obtained in this work (CBS-QB3 basis set) with experimental and theoretical (MP2/6-311++G(d,p)) values for Reaction Ra: CH3+ H2S → CH4 + SH.
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The Journal of Physical Chemistry
Figure 7. Comparison of rate coefficients obtained in this work (CBS-QB3 basis set) with experimental values for Reaction Rb: 2-(Z)-C5H10 + SH → CH2CH=CHCH2CH3 + H2S.
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Figure 8. Evans-Polanyi plots (activation enthalpy of SH + hydrocarbons versus BDHs of the weakest C-H bonds in hydrocarbon molecules). The black border denotes the BDH of H2S at 380.4 kJ·mol-1. All numbers are in kJ·mol-1 at 298.15 K.
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Figure 9. Rate constants for H abstraction from CH4 by SH, NH2, HO2 and OH radicals, units of k are in cm3·molecule-1·s-1. Results are taken from this work (SH + CH4) and the literature (NH2/HO2/OH + CH4).
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TOC/ABSTRACT ART
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The Journal of Physical Chemistry
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