Ab Initio Chemical Kinetics of Methyl Formate Decomposition: The

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Ab Initio Chemical Kinetics of Methyl Formate Decomposition: The Simplest Model Biodiesel Wayne K. Metcalfe,* John M. Simmie, and Henry J. Curran Combustion Chemistry Centre, National UniVersity of Ireland, Galway, Ireland ReceiVed: December 21, 2009; ReVised Manuscript ReceiVed: March 19, 2010

The energetics and kinetics of methyl formate decomposition have been investigated by high-level ab initio calculations with rate constant predictions. The paucity of reliable experimental data for methyl formate has been circumvented by studying a very similar system, namely, the decarboxylation of acetic acid, in order to help validate the theoretical calculations. Our study shows that methyl formate decomposes to methanol and carbon monoxide, almost exclusively, with a high pressure limit rate constant of k∞1 ) 2.128 × 1012T0.735 exp(-34 535/T) s-1, and the decomposition of acetic acid to methane and carbon dioxide proceeds with a rate constant, k∞4 , of 1.668 × 1010T1.079 exp -35 541/T s-1. Experimental values for the formation enthalpy of methyl formate are discussed, and it is shown that these can be reconciled with our computed value for ∆Hf (298.15 K) of -360.1 ( 2.2 kJ mol-1. In turn, bond dissociation energies for all single bonds in the molecule are presented. Introduction The recent surge in interest in the production of new transport fuels from biomass has been triggered by (1) the realization that the existing dominant biofuel, ethanol, suffers from some serious shortcomings and (2) that biofuel production from crops or foodstuffs destined for human and animal consumption is far from ideal.1,2 Moreover, in comparison to hydrocarbons for which reliable chemical kinetic models and experimental data are available,3 the combustion chemistry of oxygenates is comparatively little known. As regards biodiesels, the ester linkage introduces new features into the reactivity of these compounds.4-6 Here, we present benchmark calculations for the simplest possible carboxylic ester, methyl formate (MF), and in particular a consideration of the initial steps in its pyrolysis. There are three probable channels for the molecular decomposition of methyl formate:

HC(O)OCH3 f TS1 f CH3OH + CO

(1)

HC(O)OCH3 f TS2 f 2H3CdO

(2)

HC(O)OCH3 f TS3 f CH4 + CO2

(3)

In a series of high-level calculations ranging from MP2, MP4, and CCSD(T) and the composite methods G2MP2, G2, and CBS-Q, Francisco7 computed mean barrier heights (the sum of electronic energy at 0 K and zero-point energy) of 314.2 ( 4.6, 325.5 ( 7.1, and 355.6 ( 9.6 kJ mol-1 for the three channels, respectively. A fourth channel leading to HCOH + H2CdO was judged not to be of significance given a computed activation barrier in excess of 435 kJ mol-1. All these values were relative to the cis-conformer (Z) of methyl formate, Figure 1, and were * To whom correspondence [email protected].

should

be

addressed.

E-mail:

Figure 1. Z-E conformers of methyl formate.

expressed as the geometric mean of the six theoretical methods employed. There are very few reliable experiments against which one could compare such theoretical calculations. Jain and Murwaha8 studied the kinetics of thermal decomposition at 760 K in the gas-phase at low pressures reporting the formation of formaldehyde, hydrogen, and carbon monoxide with an activation energy of 200 kJ mol-1. Lee9 has explored the vacuum-UV photodissociation dynamics of labeled methyl formate, and Pereira and Isolani10 studied the multiphoton gas-phase dissociation of both methyl and ethyl formates. Blom and Gunthard11 investigated the rotational isomerization in methyl formate (and methyl acetate) in a low-temperature matrix using thermal molecular beams. They determined that the anti-syn (Z) conformer is 19.9 ( 0.8 kJ mol-1 more stable. Davis studied the pyrolysis and ignition of methyl formate in shock waves,12 and Westbrook et al.13 developed a detailed chemical kinetic model for the oxidation of methyl formate that was validated against measured concentrations of intermediates in fuel-rich low-pressure premixed laminar flames. Dooley et al.14 also developed a kinetic model for methyl formate oxidation that was validated against shock tube ignition delays, and, separately against speciation data obtained by molecular-beam synchrotron photoionization mass spectrometry from lowpressure premixed laminar flames.15 Methyl formate is reported to be formed during the lowtemperature oxidation of dimethyl ether16 but at higher temperatures only in the presence of nitric oxide.17 It is a major component in the exhaust emissions from dimethyl ether fuelled engines.18

10.1021/jp9120436  2010 American Chemical Society Published on Web 04/09/2010

Chemical Kinetics of Methyl Formate Decomposition The US EPA has recently reclassified MF so that it is no longer regarded as a volatile organic compound (VOC) and therefore is not subject to the usual restrictions regarding emissions to air. This is because it has the potential for use as a blowing agent (used in the manufacture of foamed plastic) replacing environmentally damaging CFCs and HCFCs.19 Lattelais et al.20 have studied the relative abundances in the interstellar and circumstellar medium of the isomers of methyl formate, namely, acetic acid and glycoaldehyde, HOCH2CHO. In an exception to the general rule they find that methyl formate is 10 times more abundant than its more stable isomer, acetic acid, and speculate that different formation routes and/or stronger absorption by acetic acid on dust grains is the cause. Computational Methods

TABLE 1: Comparison of Reaction Enthalpies Based on an Assumed ∆Hf (298.15K) for Methyl Formate with Those Computed Here (kJ mol-1) ∆Hf(298.15 K)

reaction 1

reaction 2

reaction 3

-336.9 -349.037 -362.338 -355.539 -359.4 (this work)

25.2 37.3 50.3 43.8 50.0 ( 1.4

119.5 131.6 144.6 138.1 140.7 ( 4.4

-131.1 -119.0 -106.0 -112.5 -109.7 ( 4.8

36

The k(T) values were than fitted to a modified Arrhenius expression to obtain the kinetic parameters A, n and Ea:

( )

k(T) ) ATn exp

We have used the multilevel methods G3,21-23 CBS-QB3,24 and CBS-APNO25 as embodied in the application G-03;26 these composite methods offer good accuracy at a reasonable computational cost. Since each employs different geometry optimization routines, obtaining similar energetic results implies geometrical independence. The computed geometries for MF are in very good agreement with that obtained by Curl27 in much earlier microwave studies. Intrinsic reaction coordinate calculations were used to connect reactants and products to the transition states; the latter were shown to have one imaginary frequency. Rate Constant Calculations. Thermochemical and kinetic parameters were calculated using the ChemRate program.28 The enthalpy of formation, ∆Hf(298.15 K), of Z methyl formate is taken from this work, see below. The enthalpy of formation of the three transition states involved in the decomposition of methyl formate were calculated from the enthalpy change when moving from methyl formate to the respective transition state. The enthalpy of methyl formate and the transitions states were taken as the average of the values from the three compound methods, CBS-QB3, CBS-APNO, and G3. The values for acetic acid and the considered transition state were calculated in an identical way, with the enthalpy of formation of acetic acid taken from the literature. Thermochemical properties were calculated as a function of temperature from statistical mechanical principles using ChemRate. Vibrational and translational frequencies were modeled using the rigid rotor harmonic oscillator (RRHO) approximation with the frequencies calculated at the B3LYP/6-311G(d,p) level and appropriately scaled.29 Low-frequency vibrations corresponding to the rotation of the methyl groups were omitted from the RRHO analysis and treated as hindered rotors. Potential energy scans about the rotors were also carried out at B3LYP/ 6-311G(d,p) to determine the barrier to rotation, the rotational symmetry, and the number of rotational minima. ChemRate determines moments of inertia for internal rotors based upon molecular structure and connectivity;30 these are subsequently employed in evaluating the contribution of the internal rotor to the partition function of the molecule.31 The thermochemistry of the species and transition states are used to calculate the high pressure limit rate constants as a function of temperature using canonical transition state theory:

kTST(T) )

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( ) (

σkBT ∆S‡ -∆H‡ exp exp h R RT

)

where σ is the reaction path degeneracy, kB is the Boltzmann constant, h is Planck’s constant, ∆S‡ is the entropy of activation, and ∆H‡ is the enthalpy of activation.

-Ea RT

As all the reactions considered in the decomposition of methyl formate involve the transfer of a hydrogen atom, we have corrected our rate constants for tunneling via the Wigner approximation:32

κ)1+

( )(

1 hcν˜ 24 kBT

2

1+

RT ∆EB,0

)

This method only requires the imaginary “frequency” associated with the transition state, ν˜ , and electronic barrier height, ∆EB, 0. We have shown previously33 that this method produces similar results to the Eckart formula and to the approach proposed by Skodje and Truhlar34 over the conditions of this study. Rate constants were also calculated as a function of pressure using RRKM theory with a time-dependent solution of the master equation. Collisional energy transfer is treated using an exponential down model with 〈∆Edown〉 ) 400 cm-1. Argon was used as the bath gas. Results and Discussion Enthalpy of Formation. Methyl formate can exist in two conformational forms; in agreement with Uchimaru et al.,35 we find that the cis (Z) rotamer, with an OdC-O-C dihedral angle of 0°, is more stable by ∆H(298.15 K) ) 21.2 ( 0.4 kJ mol-1 than the trans or rotamer, Figure 1, with an interconversion, Z h E barrier of ∆H‡(298.15 K) of 52.5 ( 0.5 kJ mol-1. There are at least four experimental values36-39 for the formation enthalpy of methyl formate that range from -336.9 to -362.3 kJ mol-1; if we compare the reaction enthalpies for channels 1-3 based on each of the four experimental values with our ab initio computed heats of reaction, Table 1, then the Gladii et al.36 and Guthrie37 results can be ruled out. An average of the Hine and Klueppet38 and the Baldt and Hall39 values is in good agreement with our computed value of -359.4 ( 4.1 kJ mol-1 for the Z-rotamer of methyl formate. In turn this agrees with computations by Sumathi and Green.40 As an independent check, the reaction enthalpy for the isodesmic and nearly, but not quite, isogeitonic5 reaction:

Z HC(O)OCH3 + CH3C(O)CH3 f Z CH3C(O)OCH3 + CH3C(O)H has been calculated at -1.5 ( 0.6 kJ mol-1; in conjunction with formation enthalpies of -217.9 ( 0.7 for acetone,41 -413.5

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TABLE 2: Bond Dissociation Energies (kJ mol-1) bond D(H-C(O)OCH3) D(HC(O)-OCH3) D(HC(O)O-CH3) D(HC(O)OCH2-H)

this work 418.1 423.0 389.0 420.9

( ( ( (

1.4 3.1 5.0 0.4

literature 399.2 ( 8.444 425.9 ( 4.245 383.7 ( 12.645

( 1.2 for methyl acetate,42 and -166.1 ( 0.5 for acetaldehyde;43 this yields ∆Hf(298.15 K) of -360.2 ( 1.6 kJ mol-1 for the Z-conformer of methyl formate. There is therefore good agreement between these values. The bond dissociation energies were also computed directly; for example:

˙ H2) + H(H ˙) D(HCOOCH2-H) ) H(HCOOC H(Z HCOOCH3) where H is the enthalpy at 298.15 K computed by each of the three composite methods CBS-QB3, CBS-APNO and G3; the results are shown in Table 2. All single bond scission reactions in methyl formate therefore have substantially higher barriers, >40 kJ mol-1, than the molecular processes. A similar situation exists in the acetic acid system.46 Thermochemistry. Thermochemical properties of methyl formate, acetic acid, and the transition states considered in their decompositions were calculated from statistical mechanics, Table 3. Barrier Heights. Methyl Formate. We have carried out G3, CBS-QB3, and CBS-APNO computations for all three channelssexcept that the CBS-APNO procedure does not converge for channel 3sand find, in agreement with Francisco, that the zero-point corrected electronic energy barrier heights, ∆E‡(0 K), increase from (1) 285.5 ( 4.1 (error corresponds to the standard deviation, σ) kJ mol-1 to (2) 321.2 ( 1.8 kJ mol-1 to (3) 348.3 ( 3.5 kJ mol-1; as before, these barrier heights are expressed relative to the Z conformer of methyl formate, Figure 2. Numerical agreement for the individual barrier heights is reasonable except for reaction 1, the formation of methanol and carbon monoxide, where a difference of 27 kJ mol-1 is somewhat larger than expected (and which cannot be accounted for by confusion over the starting geometry of methyl formate), but otherwise the theoretical picture is fairly clear-cut; all of the recent computations that use advanced methods are substantially in agreement on the relative importance of the three channels. The reason for the numerical discrepancy in the barrier height for reaction 1 between Francisco and this work is due to a difference in the energies of the transition state TS1, Figure 3; we find a transition state for the reaction:

Z HC(O)OCH3 f TS1 f CH3OH + CO which is lower in energy by 28.5 kJ mol-1 using the identical multilevel method G2 as used by Francisco. The other transition states, TS2 and TS3, and the reactant itself are in complete agreement with the G2(0 K) numbers given in the Supporting Information document that accompanies the Francisco paper; the reason for this discrepancy is unknown. Comparison with Experiment. Direct experimental evidence for reactions 1-3 is quite sparse and probably not very reliable given the well-known tendency for wall-catalyzed reactions to

Metcalfe et al. play a role in the combustion chemistry of oxygenates in static and flow reactors in particular; see, for example, a flow reactor study on dimethoxymethane.47 Indeed, in a very early study Steacie48 showed that increasing the surface area of his reactor accelerated the rate of decomposition of methyl formate. The G3 transition states for the three decomposition channels for methyl formate are shown in Figures 3-5. Intrinsic reaction coordinate calculations at MP2(full)/6-31G(d) show that TS1 connects to the Z-rotamer of methyl formate, whereas TS2 and TS3 connect to the trans, or E, rotamer, Figure 1. Computed dimensionless reaction coordinates, WTS, vary from 0.378, 0.450, to 0.365 for the three transition states TS1-TS3 respectively; that for TS4 is 0.389, so these are all early transition states.49 Acetic Acid. There are, however, a number of direct experimental studies for the decarboxylation of acetic acid:

CH3C(O)OH f TS4 f CH4 + CO2

(4)

with activation energies ranging from 259 to 304 kJ mol-1; the most credible are the batch and flow reactor experiments of Blake and Jackson,50,51 and the shock tube studies of Mackie and Doolan,52 which hover around 297 kJ mol-1 in quite good agreement with a theoretical value of 300 kJ mol-1 from ab initio multiconfigurational SCF and G2 calculations by Duan and Page53 and with the ∆H‡(0 K) ) 301 kJ mol-1 from a QCISD(TC)/6-311++G(d,p)//MP2/6-31G(d,p) contemporaneous study by Nguyen et al.;46 both of these studies took as their zero of energy the Z-conformer of acetic acid, Figure 6. It is also in agreement with a later value of 299.2 kJ mol-1 from a simplified G2 model study by Moreira.54 Earlier, less sophisticated, theoretical calculations had been predicting much higher barriers, for example, a reaction barrier of 374 kJ mol-1 at MP4/6-31G//HF/6-31G.55 Infrared multiphoton experiments by Longfellow and Lee56 have shown that decarboxylation occurs under collisionless conditions and proceeds through a four-centered transition state. Since the transition state for reaction 4 closely resembles that for channel 3ssee Figure 7sit serves as a useful check of the results obtained for methyl formate. We have computed a barrier, ∆E‡(0 K), of 277.3 ( 3.8 kJ mol-1 from CBS-QB3, G3, and CBS-APNO calculations for channel 4; this is based on the trans or E rotamer of the reactant with a H-O-CdO dihedral of zero. The Z-rotamer is more stable by 21.2 ( 1.0 kJ mol-1 and the Z-E interconversion barrier is 48.2 ( 0.3 kJ mol-1; in both cases the H-C-CdO dihedral angle is 0°. These relative energies are in very good agreement with the work of Duan and Page53 and Nguyen et al.46 The computed geometries of the Z-rotamer are in reasonable agreement with electron diffraction57 and microwave58,59 studies. Note that our barrier implies an activation energy of ca. 290 kJ mol-1 at 1500 K, which is approximately the mean temperature of the shock tube experiments of Mackie and Doolan. Rate Constants. High pressure limit rate constants have been calculated from the thermochemistry in Table 3 using canonical transition state theory between 500 and 2500 K with tunneling accounted for using the Wigner formula.32 Apparent rate constants for the decomposition of methyl formate and acetic acid have been calculated from RRKM theory with master equation analysis for pressure falloff between 0.01 and 100 atm and between 500 and 2500 K. Methyl Formate. Table 4 contains derived high pressure rate expressions for the three decomposition channels of methyl formate. Not surprisingly, from our earlier barrier height discussion, the channel producing methanol and CO, through

Chemical Kinetics of Methyl Formate Decomposition

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Figure 4. G3 geometry of methyl formate transition state TS2; OCOC dihedral angle is 102.1°.

Figure 2. Potential energy diagram for methyl formate, G3(0 K) kJ mol-1.

Figure 5. G3 geometry of methyl formate transition state TS3; OCOC dihedral angle is 136.5°.

Figure 3. G3 geometry of methyl formate transition state TS1; OCOC dihedral 36.6°.

Figure 6. Z-E conformers of acetic acid.

rapidly diminishes with increasing temperature, with the largest contribution, a factor of 1.86, encountered for reaction 1 at 500 K. The effect reduces to 1.2 at 1000 K and 1.1 at 1500 K. Tunneling is most important for reaction 1 (when compared to the other pathways) as it has the lowest energy barrier and the largest imaginary frequency (-1568 cm-1 at B3LYP/6311G(d,p)) corresponding to the hydrogen transfer. The apparent rate constants for the decomposition of methyl formate have been calculated from RRKM theory with master equation analysis to account for pressure falloff between 0.01-100 atm and 500-2500 K. The rate constants for reaction 1 as a function of temperature and pressure between 1000 and

TS1, is the dominant decomposition route for methyl formate over all temperatures and pressures considered, Figure 8. The channel producing two molecules of formaldehyde has a much smaller pre-exponential factor compared to the other two paths as the transition state (TS2) involves the loss of the methyl rotor. The methyl rotor actually becomes less hindered when moving from methyl formate to TS1 and TS3, with rotational barriers of 2.97 kJ mol-1 for MF, 2.26 kJ mol-1 for TS1, and 1.46 kJ mol-1 for TS3. The contribution from tunneling is quite small due to the temperatures examined in this study. The effect of tunneling

TABLE 3: Thermochemical Properties of Species and Transitions States species MF TS1 TS2 TS3 AA TS4

∆H°f (kJ mol-1)

S (J mol-1)

Cp (J K-1 mol-1)

298 K

298 K

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

-359.41 -71.46 -39.12 -9.96 -432.25 -133.68

286.78 301.83 277.93 299.03 286.00 286.08

63.50 70.01 66.02 69.53 65.50 73.84

76.80 81.33 80.37 82.52 80.37 87.46

89.72 92.08 93.42 94.09 93.36 98.66

101.08 101.66 104.61 103.93 104.22 107.96

119.06 117.31 121.93 119.29 120.92 122.45

132.22 129.06 134.19 130.46 133.06 133.04

152.10 146.91 151.98 147.38 151.85 149.06

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Metcalfe et al.

Figure 10. Computed rate constant for reaction 1 at 1 atm; effect of 〈∆Edown〉. (green) 800 cm-1, (red) 400 cm-1, (blue) 200 cm-1, s limit pf∞. Figure 7. G3 transition state for acetic acid decarboxylation, TS4; OCOH dihedral angle is 180.0°.

Figure 8. Calculated high pressure limit rate constants of methyl formate decomposition as a function of inverse temperature. Products: (black) CH3OH + CO2, (red) 2CH2O, (green) CH4 + CO2.

Figure 9. Apparent rate constants as a function of pressure for MF f CH3OH + CO. s p f ∞, (red) 100 atm, (green) 10 atm, (blue) 1 atm, (light blue) 0.1 atm, (purple) 0.01 atm.

TABLE 4: High Pressure Limit Rate Constants, k1∞/s-1 reaction

A (s-1)

MF f CH3OH + CO MF f CH2O + CH2O MF f CH4 + CO2

2.128 × 10 2.158 × 109 4.536 × 1011 12

n

Ea/R (K)

0.735 1.280 0.832

34 535 38 234 42 075

2000 K are shown in Figure 9. The Arrhenius parameters at different pressures are also included, Table 5. The Arrhenius parameters for the other channels as a function of pressure are included in the Supporting Information. Our calculations estimate that the rate of decomposition of methyl formate to methanol and carbon monoxide at 1 atm is

TABLE 5: k1 as a Function of Pressure for HC(O)OCH3 f CH3OH + CO, k/s-1. *k cm3/mol-1 s-1 p (atm)

A (s-1)

pf0* 10-2 10-1 10° 101 102 pf∞

1.914 × 10 1.516 × 1060 4.539 × 1057 1.951 × 1050 8.839 × 1033 1.441 × 1020 2.128 × 1012 59

n

Ea/R (K)

-11.87 -14.24 -13.21 -10.80 -5.81 -1.64 0.74

39 168 43 286 43 597 42 601 39 188 36 217 34 535

approximately equal to the high pressure limit at the lowest temperatures, but becomes significantly smaller as the temperature increases, with more than 2 orders of magnitude difference at 2500 K. This is dependent on our assumed value for 〈∆Edown〉 of 400 cm-1. The effect of changing the 〈∆Edown〉 by a factor of 2 on the rate constant at 1 atm was calculated. Increasing the collisional efficiency causes an increase in the decomposition rate at 1 atm, while decreasing the efficiency causes a subsequent decrease in the rate at 1 atm, Figure 10. It is clear that the average energy transferred during collisions is an important parameter in estimating pressure dependent systems, but also a parameter which is difficult to decipher without experimental evidence. Comparison with PreWious Estimates. In the absence of reliable experiments, only a comparison with previously estimated high-pressure rate constants is possible and that only for reaction 1. The unimolecular decomposition reaction forming methanol and carbon monoxide was included as a pressureindependent reaction in the methyl formate oxidation mechanism recently published by Westbrook et al.13 The rate constant was estimated as k1 ) 1.00 × 1014T0.0 exp(-31 454/T) s-1. At low temperatures (500 K) this estimate disagrees strongly with the calculation presented in this work, with a rate constant of 4.78 × 10-14 s-1 compared to a value of 2.07 × 10-16 s-1, more than 230 times larger than our calculated value. However, under more combustion-relevant temperatures, the Westbrook estimate compares more favorably with our current value. For example at 1000 K the Westbrook estimate is 2.19 s-1 compared to our value of 0.343 s-1 (approximately a factor of 6), and at 2000 K the Westbrook estimate and our current calculations are much closer at 1.48 × 107 and 1.80 × 107 respectively. Acetic Acid. The rate constant for the decarboxylation of acetic acid was calculated using the same methods described for methyl formate. Comparing Figures 5 and 7 it is clear that this reaction proceeds via a similar transition state as the decarboxylation channel in methyl formate. As there are some experimental measurements of this reaction,50-52,60 it enables

Chemical Kinetics of Methyl Formate Decomposition

J. Phys. Chem. A, Vol. 114, No. 17, 2010 5483 minimize errors. Rate constants have been calculated for three decomposition channels of methyl formate as a function of temperature and pressure. The decomposition is dominated by a single channel producing methanol and carbon monoxide over all temperatures and pressures. The other two channelssproducing two molecules of formaldehyde, and methane and carbon dioxide, respectivelyscan be confidently removed from a detailed kinetic mechanism describing methyl formate pyrolysis/ oxidation between 500 and 2500 K and for all pressures.

Figure 11. Comparison of calculated high pressure limit rate constant for acetic acid decomposition to methane and carbon dioxide versus experimental values. 9 Mackie et al.,52 Blake et al. •,50 ∆ Blake et al.,51 ∇ Bamford et al.,60 s this study.

us to validate our rate estimation methods and provide confidence in our predictions of the unknown methyl formate decomposition system. A comparison of our rate constant calculation versus the available data is shown in Figure 11. Bamford and Dewar60 studied the kinetics of acetic acid vapor by a flow method in quartz tubes between 773 and 1173 K and pressures of 12-166 Torr. The major products found were ketene, ethylene, methane, carbon dioxide, and carbon monoxide. The product distribution was explained by two unimolecular decomposition reactions producing ketene and water, and methane and carbon dioxide, respectively, with ethane and carbon monoxide being formed by subsequent reactions of ketene. A rate constant of 8.0 × 1011 exp(-31 200/T) s-1 for the reaction CH3C(O)OH f CH4 + CO2 was determined. Blake and Jackson,51 building on their previous work,50 also studied acetic acid decomposition in a flow system between 804 and 1035 K at pressures of 7-160 Torr. Major products found were ketene and water, and methane and carbon dioxide in equal amounts. Traces of carbon monoxide, ethylene, and ethane were also detected, and like Bamford and Dewar, they attributed these products to further reactions of ketene. They also performed “radical trapping” experiments using equal or excess amounts of toluene and concluded that neither the dehydration or the decarboxylation reactions involve radical chain mechanisms. They suggested 4-centered transition states for both reactions and determined a rate constant of 3.89 × 1013 exp(-35 130/T) s-1 for the decarboxylation of acetic acid. Mackie and Doolan52 undertook a single-pulse shock tube speciation study of acetic acid vapor over the temperature range of 1300-1950 K. They detected the same products as the previous studies but also measured trace amounts of propene, propyne, and butenes at the higher temperatures of their study. They modeled their experimental speciation data using a kinetic mechanism, taking the rate constants for the dehydration and decarboxylation reactions from the work of Blake and Jackson. These rate constants were subsequently optimized to fit the experimental concentration profiles. Mackie and Doolan also performed a master equation analysis and determined a high pressure rate expression for the decarboxylation reaction of 1.26 × 1013 exp(-36 560/T) s-1. Overall, the agreement between our calculated rate expression, k∞4 ) 1.668 × 1010T1.079 exp(-35 541/T)s-1 s-1, and the available data is good, which gives us greater confidence in our calculations of the methyl formate system. Conclusion The heat of formation of methyl formate has been calculated from ab initio calculations, utilizing an isodesmic reaction to

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