11115
J. Phys. Chem. 1995,99, 11115-11121
Observation of the Unimolecular Decomposition Pathways of Chemically Activated Acetic Acid by Fourier Transform Infrared Emission Spectrometry N. I. Butkovskaya? G. Manke 11, and D. W. Setser* Department of Chemistry, Kansas State University, Manhattan, Kansas 66506 Received: November 22, 1994; In Final Form: May 11, 1 9 9 9
The infrared chemiluminescence from vibrationally excited H20 and CO2 molecules in their respective ranges 3200-3900 and 2000-2400 cm-' was observed from the unimolecular decomposition of acetic acid in a fast flow reactor with 0.8 Torr of AI carrier gas. Activated CH3COOH molecules with an excitation energy of approximately 95 kcal mol-' were produced via the successive reactions H+CH2ICOOH HI+CH2COOH and H+CH2COOH CH3COOH*. The nascent vibrational distributions for H20 and C02 were determined by simulation of the experimental emission spectra. The H20 emission is mainly from the (0~21) (0~20) transitions with v2 I5, similar to the emission of H20 eliminated from activated ethanol, which has been observed earlier in this laboratory. The C02 emission is from Av3= -1 transitions with high excitation in v2 (v2 I25). The extremely high bending excitation is explained by the release of the energy in changing from the bent OCO geometry of the carboxyl group to the linear structure of the C02 molecule. The H20 and C02 relative emission intensities and RRKM calculations suggest that the unimolecular decomposition of CH3COOH proceeds through the two competing pathways, H20 4- CH2CO and C02 4- C&, with approximately 2 times higher probability of water formation; the threshold energies for the two unimolecular reactions must be less than 70 kcal mol-'.
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1. Introduction The thermal decomposition of acetic acid occurs via two competing first-order channels, leading to formation of water and ketene (la) or carbon dioxide and methane (lb):'-3
-
+ CH2C0 CH,COOH - C 0 2 + CH,
CH,COOH
H20
(14 (1b)
The respective Arrhenius equations were found to be k, = 10'2.45 exp(-64.9/RT) s-' and kb = 10'3.59exp(-69.8/RT) s-' between 530 and 762 "C in a flow reactor study.' RRKM calculations carried out in conjunction with a more recent shock-tube study2 at 1300- 1950 K showed that these values belong to the falloff region, and high-pressure Arrhenius parameters of loglo A = 13.1 f 0.3 and Ea = 72.7 f 3.5 kcal mol-' were recommended for both reactions. The small preexponential factors for both dehydration and decarboxylation are consistent with the structure of four-centered transition states. The branching ratio for (la) and (lb) was observed from the thermal decomposition of ethyl acetate in a shock-tube study3 by comparing IR emission intensities from the fundamental bands of H20 and C02 formed from the secondary decompositionreaction of acetic acid. The branching ratio for [C02]/[H20] was found to be about unity at a pressure of 170 Torr of AI bath gas, although the ratio was not very reliable (according to the authors) because of the very weak H20 emission intensity. The high-pressure Arrhenius parameters were evaluated to be logloA = 13.41 and E, = 65.5 kcal mol-'. However, at lower pressures ( e 5 Torr) the C02 yield decreased in comparison with that of the normal (thermally activated) acetic acid, while the H20 yield remained unchanged. Only channel (la) was reported4 as a secondary reaction from the unimolecular decomposition of ethyl acetate initiated by IR multiphoton absorption. Permanent address: Institute of Chemical Physics, Russian Academy of Sciences, 117334 Moscow, Russian Federation. @Abstractpublished in Advance ACS Abstracts, June 15, 1995. +
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The unimolecular dehydration and decarboxylationreactions of acetic acid have been investigated by ab initio methods5 The concerted dehydration process occurs via a four-centered transition state with threshold energy of 76.0 kcal mol-'. The decarboxylation also could be described by a four-centered transition state with threshold energy of 77.3 kcal mol-'. Subsequent c a l ~ u l a t i o n showed ~~ that the transition states identified in ref 5a actually were second-order saddle points on the potential surface. The structures corresponding to these second-order saddle points have qualitative, but not quantitative, significance as transition states (see Note Added in Proof). If the threshold energies for (1) were 75 kcal mol-', dissociation pathways with loose transition states producing radicals would be competitive with (la) and (lb) for high excitation energies; the experimental values of -65 kcal mol-' seem preferable for the threshold energies. In the present work we report observation of the C02 and H20 products by Fourier transform infrared (FTIR) detection following unimolecular decomposition of acetic acid activated by chemical reaction in a fast flow reactor. The experiments were done using sequential fast reactions of hydrogen atoms with iodoacetic acid and carboxymethyl radical: H 4- CH,ICOOH H
- + HI
+ CH2COOH
CH2COOH
CH3COOH*
(2) (3)
The rate constant of reaction 2 may be estimated as k2 > 2 x lo-'' cm3 molecule-' s-I by analogy to other iodide compounds.6 Abstraction reactions of iodine atoms bound to sp3 hybridized carbon atom are generally fast and proceed with little or no activation barrier, whereas OH or H abstraction requires considerable activation energy. For instance, activation barriers for the H C2H50H H20 C2H5 and H C2H5OH H2 CHFHOH reactions are 3.5 and 4.6 kcal mol-', respectively, with corresponding room-temperature rate constants of 2.9 x and 3.2 x cm3 molecule-' s-I, respectively.' The rate constant for the H CH30H CH30 H2 reaction is of
+
+
-. + +
+
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0022-3654/95/2099-11115$09.00/0 0 1995 American Chemical Society
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11116 J. Phys. Chem., Vol. 99, No. 28, 1995 the same order, k = 2.3 x cm3 molecule-' s-' at 298 K.8 Iodine abstraction dominates the hydrogen atom reaction mechanism with iodoacetic acid at room temperature. The direct OH or H abstraction is improbable for reaction 3, and it should proceed mainly through the recombination mechanism at 300 K. At 1 Torr of Ar, the acetic acid molecule formed with average energy of E"=95.3 kcal mol-' will undergo unimolecular decomposition rather than collisional deactivation. The infrared chemiluminescence from this reaction system consisted of carbon dioxide and water emission in the ranges 2000-2400 and 3200-3900 cm-I, respectively. At relatively high concentrations of reactants, methane was also detected, but this weak emission around 3000 cm-' will not be discussed in this paper. On the basis of the relative emission intensities, reaction 1a seems to be approximately 2 times more probable than reaction lb for acetic acid with an excitation of -95 kcal mol-'. In making this estimate, the nonemitting fractions of molecules assigned from the analysis of the vibrational distributions were taken into account. The nascent vibrational distributions of C02 and H20 were fitted by computer modeling of the infrared emission spectra. Reaction lb generates CO2 with a high level of excitation in the bending mode, whereas the vibrational excitation of H20 is relatively low for both the stretching and bending modes. These vibrational distributions are used to discuss the reaction dynamics of l a and lb.
2. Experimental Section A detailed description of the experimental method has been given elsewhere? The infrared emission spectra were recorded at 2 cm-' resolution using a BIO-RAD FTIR spectrometer (FTS60). The spectrometer chamber and the tube connecting the observation window with the spectrometer were continuously flushed with dry air in order to remove water and carbon dioxide. Absorption of the chemiluminescent radiation from the reactor by atmospheric water and C02 was avoided. The response of the detection system, an InSb detector cooled by liquid nitrogen, was calibrated with a standard blackbody source. Chemical reactions took place in a 4 cm diameter Pyrex flow reactor with Ar carrier gas. The flow velocity was about 130 m s-' at 0.5 Torr, corresponding to a reaction time of -0.25 ms before observation. The total pressure could be varied from 0.5 to 2 Torr with a throttling valve. The H atoms were generated by a microwave discharge in a flowing HdAr mixture. The degree of dissociation of H2 in this apparatus has been measured to be 50% in previous work? The hydrogen flow was simultaneously changed with variation of reactor pressure, so that the hydrogen atom concentration was constant in all of the experiments, [HI = 3.3 x lot3 molecules ~ m - ~The . iodoacetic acid was introduced into the reactor through a ring injector located 20 cm downstream of the H2 inlet and 3.5 cm upstream of a NaCl observation window. The emission through the NaCl window was collected with a short focal length CaF2 lens and directed into the FTIR spectrometer. The iodoacetic acid was carried into the reactor with an argon flow, which passed over the solid sample heated to 60-65 "C. The CH2ICOOH concentration varied with the pumping speed used for the reactor and the flow of Ar over the sample. The typical concentration was 2.7 x 10l2molecules ~ m - as ~ measured , by condensing the iodoacetic acid from the flow into a cold trap and weighing the sample. The flow lines and the reactor were heated to 60 "C to prevent condensation of the iodoacetic on the walls. Commercial tank grade Ar was passed in succession through three molecular sieve filled traps cooled by acetone/dry ice
Butkovskaya et al. C n i m o l e c u l a r decomposition of Acetic Acid (E*=95.3 kcal/mol)
1j I 'i / I
420
CH4
I
2000
2200
2400
2600
2800
3000
3200
"
'
"
3400
'
3600
3800
Wavenumbers (cm-1)
Figure 1. Global infrared emission spectrum of the products from the
+
-
unimolecular decomposition of activated acetic acid from the H CHzCOOH CH3COOH' reaction for a reaction time of 0.8 ms and 2 Torr pressure with [HI = 3.3 x 1013molecules cm-3 and [ICHzC(O)OH] = 2.7 x 1OI2 molecules ~ m - ~ .
mixture and liquid nitrogen. Tank grade H2 and iodoacetic acid (Aldrich) were used without purification.
3. Experimental Results
+
3.1. IR Chemiluminescence from the H CH2IC(O)OH Reaction System. The global emission spectrum of the products from reactions 2 and 3 is shown in Figure 1. This spectrum was measured at a total pressure of 2.0 Torr with a reaction time of 0.8 ms and a resolution of 2 cm-I. The strong chemiluminescence in the 2000-2400 cm-' range belongs to highly vibrationally excited COZ. Emission in the 3200-3900 cm-' range consists of H20 stretching vibrations. The weak emission around 3000 cm-' may be attributed to the C-H stretching vibrations of methane (Av3 = -1 of some combination band with v2 or v4 bending mode excitation). This CHq emission, which could only be observed from experiments with high concentrations of reagents and At > 0.5 ms, will not be considered further. The C02 and H20 spectra are analyzed to obtain vibrational distributions in the sections below. However, the ratio of the intensities can be utilized to estimate the branching ratio for reaction 1. The average ratio of the integrated intensities determined from six spectra, corrected for the response function of the detector, is Z(C02):Z(H20) = (2.9 f 0.3):l.O. Combining this ratio with the ratio for the emission band strengths,which is 3.2:l.O as calculated from the known values of the v3 fundamental band strengths in absorption, S,", gives an approximate [C02]/[H20] ratio of unity. The Av3 = - 1 emission band strengths were obtained from S", = 9.53 x lo-'' cm-'/ molecule cm-2 for C02 and S", = 0.72 x cm-'/molecule cm-* for HzO'O by multiplying by the cube of the band center frequency. This [C02]/[H20] ratio has an uncertainty because of the possible dependence of the band strength on the v1 and v2 vibrational excitation, because of the collisional mixing of the populations in the V I and v3 states of H20 and because of the unknown fraction of molecules in the ground vibrational state. Analysis of C02 and H20 spectra to obtain vibrational distributions, vide infra, suggests that this fraction is likely to be significant. The total C02 emission intensity from reactions 2 and 3 was compared to the HF intensity from the H f cF3I reaction systemgcfor the same concentration of H atoms in the reactor. The experiment was done by sequentially adding known CFJ and ICH2COOH concentrations to the reactor and recording the spectra. The intensities were corrected for response and then divided by the Einstein coefficients to obtain relative concentra-
Unimolecular Decomposition Pathways
J. Phys. Chem., Vol. 99, No. 28, I995 11117
Q
E*-95.3 26
24 1
,
20
22 l
l
,
I
18 J
,
16
14
I
1
,
(0,~2,1)-(0,~2,0)
12 1
/
8
10 I
,
,
6
J
1
P
F3"
CO,
I
,
,
,
)
,
R(vl,O,l)-(vl,O,O)
r---I4=vl
Emission
-3
'
t
I
~
0 = v2
2
4
,
-300
- 2
1250 -250
n
$I,,, $
\
n-
U U-
;200
-102
Figure 2. Schematic diagram of the energetics for the decomposition of acetic acid. The numbers in parentheses for the barrier heights are from ab initio c a l c ~ l a t i o n s .These ~ ~ calculated energies are for secondorder saddle points,5band these values probably are too large (see Note Added in Proof).
2100
2000
2200
2300
00 2400
Wavenumbers (cm- 1)
Figure 3. C02 emission spectra (corrected for the response function) tions. The [ C O ~ ( V I V ~ V ~ ) ] / [ratio HF(V was ) ~ constant for three from the unimolecular decomposition of acetic acid. (1) P = 0.8 Torr sets of data after adjustment to the same [CF3I] and [ICH2and Ar = 0.35 ms; (2) P = 2 Torr and At = 0.8 ms. Model calculation COOH]. This ratio was 1.1 f 0.2 with consideration of the for spectrum 1 corresponds to the COZvibrational distribution in Figure HF(v=O) population, but without consideration of the CO~(VIV~~O)4. The C02 distribution for spectrum 2 is described in the text. Ticks population. The HF or C02 intensities from the secondary on the top bar indicate band centers for the (0,vz.l) - (O,v2,0) bands; reactions is proportional to the product of the primary and side ticks on the bars below indicate P and R lines with the highest secondary rate constants. Since formation of H20 was not intensity for the (v,,O,l) - (v,,O,O) bands. included in the analysis, these data strongly suggest that the appearance of several spectra from experiments with At = product of k2 and k3 is slightly larger than the product of the 0.25-0.5 ms closely matched the spectrum 1 of Figure 3. primary and secondary rate constants for the H CF3I system.9c However, relaxation of C02 could be observed for longer times The energy available to the products may be obtained from or higher Ar pressures, as displayed by spectrum 2, which was the enthalpy changes for reactions 3 and 1. The energy diagram acquired at a pressure of 2 Torr and At = 0.8 ms. The spectra for decomposition via (la) and (lb) is shown in Figure 2. The consist of a broad emission in the 2000-2400 cm-I range, energy levels of the products were calculated from the heats of which spreads far to the red side from the C02 fundamental formation for the corresponding molecules (kcal mol-') Ak?f0298 band (YO = 2349.3 cm-I), with a maximum around 2200 cm-I. = -103.5 (CH3COOH), -57.8 (H20), -1 1.4 (CH2CO), -94.05 A computer modeling approach was used to obtain the (C02), -17.8 (CHq).'I The average excitation energy for acetic vibrational distributions corresponding to the observed spectra. acid, E* = 95.3 kcal mol-', was calculated according to eq 4 The three normal modes of COz have frequencies of v 1 O = 1388.3, v 2 O = 667.3, v3O = 2349.3 cm-I, corresponding to E* = -W, 3RT+ E, (4) symmetric stretching, bending, and antisymmetric stretching vibrations, respectively. The observed emission may be deThe enthalpy of reaction 3, - M o o , is the bond energy Do(Hscribed by the overlap of the transitions with Av3 = -1 with CH2COH)I2 = 92.8 zk 2.2 kcal mol-'. For this atom-radical combination and hot bands: (v[,vk,v3) - (v1,vk,v3-1). The band reaction, an activation energy of zero was assumed. Since the centers were calculated using the conventional formula for the thermal vibrational energy of CH2C(O)OH has been ignored, vibrational energy levels: l 4 95.3 kcal mol-' is a lower limit to p. The energies available
+
+
to the product channels are (&(a)) = 61.0 kcal mol-' and (Eav(b))= 103.6 kcal mol-'. Barrier heights of 64 kcal mol-] were assigned to both transition states from the experimental Arrhenius activation energie~.~ It has been suggestedI3that the excess energy at the transition state, E, = E* - Eo, will be shared statistically among the products of unimolecular decomposition. The remaining energy, Ep, is released according to the potential surface gradients in the exit channel. For the decomposition under study, channels 1a and 1b both have Ex = 3 1.3 kcal mol-', because of the nearly equal threshold energies. The potential energy release in (la) is Ep = 29.7 kcal mol-', while that for (lb) is very much larger, Ep= 72.3 kcal mol-'. Thus, a nonstatistical vibrational energy distribution may be expected for the eliminated C02 molecule. 3.2. Analysis of the Carbon Dioxide Emission Spectrum. Figure 3 shows two C02 spectra that have been corrected for the response function of the detection system. Spectrum 1 was measured at 0.8 Torr and for a reaction time of 0.35 ms. The
+
G(v,,v,',v3) = c w i ( v i di/2) ccx;k(vi
+ + d ; w v k + dJ2) + g,2Z2 ( 5 )
where di is the degeneracy of the vibration vi (dl = d3 = 1; d2 = 2), and 1 is the vibrational angular momentum due to the degeneracy of the bending vibration, v2. The frequencies, mi, anharmonicity coefficients, Xik, and g22 coefficient were taken from the 1iterat~re.I~ The two branches for E - E transitions ( I = 0 both in the upper and lower state) were represented by the formula v = vo (B' B")m f (B' - B")m2, where m = J 1 for the R branch and m = -J for the P branch.I4 In these transitions all the lines with odd J are missing, because of the identical nuclei with zero spin. In the parallel bands with 18 0 (l7 - l7,A - A, ...), the Q branch was added for which v = vo (B' - B")J f (B' - B")J These bands have no missing lines due to nuclear spin statistics. In the formula for line positions B' and B" are the rotational constants in the upper
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+
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11118 J. Phys. Chem., Vol. 99, No. 28, 1995
Butkovskaya et al.
Figure 4. C 0 2 ( v l r v ~ , 1 )vibrational distribution used to simulate the spectrum from the unimolecular decomposition of CH3COOH for a reaction time of 0.35 ms and pressure of 0.8 Torr.
+
and lower vibrational state, equal to B, = Be - &(vi dJ2). Rotational constants Be = 0.3906 cm-I; al = 12.32, a2 = -7.37 and a3 = 30.58 (in cm-I) were taken from ref 15. To calculate the relative intensities of individual rotational lines, we used the expression
I = v3(2J
+ 1) exp(-B’J(J + l)/kT)S,$,
(6)
where Su is the rotational line intensity or Honl-London factor (ref 14, p 422), and S, is the square of the rotationless transition moment, which is equal to 0.328, 0.459, and 0.556 D for the transitions from the upper levels with v3 = 1, 2 and 3, respectively.I6 Each (vI,vz’,v~)- ( v I , v ~ [ , v ~ -band ~ ) was calculated assuming a Boltzmann distribution of rotational states and taking into account that the vibrational angular momentum quantum number 1 may have values 1 = v2, v2 - 2, ..., 0. The population of the states with different 1 for every ( v I , v ~ , set v~) was assumed to be Boltzmann. A serious ambiguity in modeling CO2 spectra arises from the very close values of anharmonicity coefficients ~ 2 = 3 -12.37 and x33 = -12.47, which gives similar positions of the PQR peaks for (VI,V?,V~) and (vl,v2-2’,~3+1) bands. We first will assign the C02 spectrum assuming a v3 population with v3 = 1 only. This distribution gives a lower limit to the vibrational energy released to CO2, since the energy of one quantum of antisymmetric v3 mode is 1015 cm-’ larger than the energy of 2 quanta of bending vibration. The pronounced peaks in the COz emission spectrum correspond to the positions of the Q branches of the (O,v2’,1) (O,v2‘,0)transitions. The less distinct Q branches of the (1,v2‘,1) - (1,v2[,0) transitions are also noticeable on the red side of the maximum of the spectrum. According to these observations, the simulation was made in a following manner: the spectrum was first approximated by (O,v~l,l)- (O,v2’,0) transitions; then, one after another, (v1,v2~1)- (v1,v2~,0) transitions with V I = 1, 2, etc., were added to obtain the best fit. For bands with 1 > 5, the resulting Q “line” is stronger than the maximums of R and P branches, while in bands with 4 > 1 > 0 the inverse situation exists. Consequently, we can state that the blue side of the spectrum consists mainly of P and R branches from low-v2 states. Figure 4 displays the vibrational distribution used to calculate the model spectrum 1 presented in Figure 3. The distribution is peaked on (O,ll,l) and (O,O,l). The high population of the (0,0,1) level, which is evident from the band centered at 2350 cm-’ in Figure 3, is explained by the collisional
energy transfer to the C02 impurity in the Ar gas. In fact, the intensity of this CO2 (001) band varied from one experiment to another and it was virtually absent if greater care was taken to purify the Ar. Hereafter, the C02 (001) population will be ignored. The calculated mean vibrational energy of the C02 molecules for the distribution in Figure 4 is equal to (E,) = 33.7 kcal mol-’. This may be compared with the total energy released in the reaction of 103.6 kcal mol-’, which gives (h(CO2)) = 0.32. From the modeling of the spectrum, we can not make a definite conclusion about the relative populations of v 3 = 1 and 2. However, the majority of the energy is in the V I and v2 modes and a narrow distribution in v3 will not seriously affect the assignment of the average energy. We also made simulations of the COz spectrum for two other distributions, one with v3 = 2 and one with v3 = 3. The former distribution, which provided a reasonably good match to the experimental spectrum, is peaked on vz = 9 and involves V I levels up to V I = 5 and v2 levels up to v2 = 21. The shape of this distribution closely resembles that in Figure 3, and the calculated mean vibrational energy for the distribution with v3 = 2 is equal to (EY)= 34.6 kcal mol-’. The distribution for v3 = 3, which gave a less satisfactory fit to the spectrum, involved V I levels up to V I = 3 and v2 levels up to v2 = 17 with a maximum at v2 = 5 and had a mean vibrational energy of (E,) = 36.0 kcal mol-’. Distributions with higher v3 values were not considered because their combination bands could not reproduce the peaked bell shape of the spectrum due to the reduction of the intensity of the Q heads. From the point of view of reaction dynamics, which is discussed in section 4, we expect a distribution declining in v3 with (v3) GZ 1. We must note the very similar energies of the V I and 2v2 levels (Fermi dyad), which results in a collisional energy exchange between the series of states (VI ,vz,v3), (VI+ l,v2-2,~3), ( V I+2,~2-4,~3), etc.” This could complicate the determination of the nascent distribution because of the rapid collisional transfer within each (v1+i,v~-2i,l), i = 0, 1, ..., group. However, the distribution in Figure 4, which matches spectrum 1 of Figure 3, shows that such relaxation does not occur at pressures lower than 1 Torr for At = 0.35 ms. The population in a set of related states appears as a decaying “wave” from the (0,11,1) to (5,1,1) state. The higher pressure spectrum in Figure 3, which does show relaxation, was fit using equal probabilities of all the states within each (vl+i,v2-2i,l) group (complete equilibration). The P(v2) distributions for (O,v*,1) states for spectrum 2 is peaked on v2 = 7 and 8 with v2 = 23 as the highest populated level. Although the Q lines of (O,v2,1) states are likely underestimated in this case, the general fit is rather satisfactory, showing that equilibration between V I and 2v2 levels does take place at higher Ar pressures and longer reaction times. 3.3. Analysis of the Water Emission Spectrum. A typical H20 emission spectrum in the 3400-3900 cm-I range is shown in Figure 5. The raw spectrum measured at 0.8 Torr of Ar and a resolution of 2 cm-’ was corrected for the instrumental response function. Although the available resolution gives a partly resolved rotational structure for the spectrum, the direct assignment of individual lines is complicated by the centrifugal distortion and resonance effects characteristic of the water molecule. The basic (001)-(OOO) emission band was calculated from the absorption band taken from the HITRAN database.I0 The line positions of the combination and hot ( v ~ z v ~ ) ( V I V Z v3-1) bands were calculated by red-shifting the band centers of the basic v3 band by Av = YO‘ - YO, where yo’= G ( v I v ~ v ~ ) - G(VI’V~/V~’), vo = G(001) - G(000) and G(vlv2v3) is given by expression 5 with di = 1 and 1 = 0. The frequencies and anharmonicity coefficients were taken from ref 14. It was
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Unimolecular Decomposition Pathways
11
h
,
$1
'
I
(b)
I
I
I
J. Phys. Chem., Vol. 99, No. 28, 1995 11119
H,,0 Emission
I
!
I .
4 because of the overlap of the latter with the ~ 1 , = 3 2 emission bands. Generally, the decrease in the v2 population followed a geometric progression with a specific factor for every v2 vibrational number; various simulations converged (to within 25%) of a common factor for the geometric progression. A vibrational distribution with a decreasing stretching mode population is similar to the H20 ( v I , ~ , vdistribution ~) from the H20 elimination reaction of e t h a n ~ land ' ~ the HF(v) distribution from elimination reaction of CH3CH2F or CF3CH3.20 By extrapolating the P1.3 distribution to ~ 1 , = 3 0 using the similarity to the HF(v) distributions, we obtain P1.3 = 54, 35, 9 and 2 for V1,3 = 0, 1, 2, and 3, respectively. If the distribution in v2 for Vl.3 = 0 is taken to be the same as for V1.3 = 1, the calculated mean vibrational energy of the eliminated H20 molecules is equal to (Ev) = 14.7 kcal mol-'. Comparison with (Eay)= 61 kcal mol-' gives (f"(H20)) = 0.24. 4. Discussion
3400
3500
3600
3700
3800
3900
Figure 5. (a) H20 emission spectrum (corrected for the response function) from the unimolecular decomposition of acetic acid at 0.8 Torr and At = 0.35 ms. (b) Computer simulation of the spectrum corresponding to the vibrational distribution indicated in the text.
assumed that the rotational energy does not depend on the vibrational state, Le., the rotational energies of the levels were assumed to be the same for each ( V I V ~vibrational V~) level. To improve this approximation, some line positions were determined as a difference of corresponding rovibrational levels. This was possible for transitions from the (01 l), (021), (031), (101), (1 1l), (002), and (012) states, because these and corresponding v3-1 energy levels were presented in the HITRAN database. The harmonic approximation plus the frequency ratio to the third power was used to obtain Einstein coefficients for higher levels by scaling the Einstein coefficient of the (001) - (000) transition.Is The collisional equilibration between the nearly resonant V I and v3 stretching levels of H20 was taken into account, and the Boltzmann population of vibrational levels within each group of (v1,3v2)states was adopted in making the calculation for the spectra. The selection of the populations were made to obtain the best visual resemblance with the experimental spectrum. Additional details of the procedure used in our laboratory for computer simulation of the water spectrum are described e1se~here.I~ The calculated spectrum, also shown in Figure 5 , corresponds to the superposition of the emission bands with vibrational distribution P1,3 = 77, 19, and 4 for VI,^ = 1, 2, and 3, respectively, and P2(1) = 23, 20, 18, 16, 14, 9; P2(2) =36, 29, 21, 14, 0, 0; and P2(3) = 59, 29, 12, 0, 0, 0. Here P1.3 is the total weight of the states with a given vibrational number v1.3 and Pz(v1.3) is the weight of the states with a particular bending vibrational number, v2 = 0, 1, ..., 5 for ~ 1 . 3quanta of excitation in ~ 1 . 3 . The distribution is normalized to give 100% in the sum of VI,^. The necessity of including bending vibrations in the simulated spectrum of H20 followed directly from the bands on the blue side of the spectrum around 3800 cm-I, since only combination bands with v2 f 0 can contribute to that range due to the small anharmonicity coefficient ~ 2 = 3 20.3 cm-' (for comparison, x13 = 165.8 cm-' and 2x33 = 95.2 cm-I). Just as for fitting the H ~ ~ ( v I spectrum v ~ v ~ )from the decomposition of C2H50H,I9 the assignment of the v2 = 0-3 populations for v1,3 = 1 required to fit the spectrum is more precise than for v2 1
RRKM calculations of the rate constants for unimolecular dissociation (la) and (lb) were performed using the molecular and transition state frequencies? which gave preexponential factors of 1013.57 and 10'3.43s-l at 1000 K, respectively. For a critical energy3of EO = 64 kcal mol-', the RRKh4 rate constants are 9.0 x lo7 s-' and 7.1 x lo7 s-' for (la) and (lb), respectively, at an energy of 95 kcal mol-'. These values are consistent with our observations of IR emission from H20 and C02 formed by the reactions of vibrationally excited CH3COOH molecules that are in an Ar bath gas with a collision rate with Ar of about 1.4 x lo7 collisions/s. The hard-sphere collision rate was obtained using molecular diameters of u = 5.6 A for CH3COOH and u = 3.4 8, for Ar with a pressure of 2 Torr. Similar calculations with critical energies of EO = 72.8 kcal mol-' for (la) and EO = 72.6 kcal mol-' for (lb) that were favored by the semiempirical estimations2 give an order of magnitude smaller rate constants, 6 x lo6 s-' and 5 x lo6 s-I. In this case, the collisional deactivation rate would exceed the unimolecular decomposition rates and product emission would not have been observed. This proves that the threshold energies for both channels (la) and (lb) must be less than 70 kcal mol-', and values of about 65 kcal mol-' seem very rea~onable.~ Values of 73 kcal mol-' from the shock-tube study of 19842or the ab initio values5 of 77 kcal mol-' are too high (see Note Added in Proof). The branching between (la) and (1b) is an important property of the decomposition reaction of acetic acid, and we present an estimate from the IR emission data. The Einstein coefficients should be reliable, since existing data indicate that neither of the C02 and H20 transition moments for the ( v I , v ~ , v ~ ) ( v I , v ~ , v ~bands - ~ ) are seriously affected by excitation in V I and v2. It was directly shown16 that the Av3 = -1 parallel C02 bands with equal v3, but different V I and v2, have essentially equal transition moments up to V I I 3 and v2 I 6. Data for water,'O though more limited (by v2 = 2), also give equal transition moments for (0191) (0~20)bands. The more important question is the fraction of molecules in the nonemitting v3 = 0 states. Due t o the similarity of the dynamics, we may draw an analogy between formation of H20 and several examples of four-centered HF elimination reactions for which HF(v=O) populations were determined from laser gain experiments or from linear surprisal Owing to this analogy, we made the extrapolation in the above section to obtain P,(O): P3(l) = 1.5:1.0, as in the distribution of HF(v) from CH3CH2F. According to this assignment, up to 54% of water molecules could be formed without excitation in the stretching vibrations. Moreover, for Boltzmann equilibration between V I and v3
-
-
Butkovskaya et al.
11120 J. Phys. Chem., Vol. 99, No. 28, 1995 modes, 57% of the molecules of the ~ 1 , manifold 3 are in the v3 = 0 state, from which emission is negligible. Thus, about 80% of the water molecules do not contribute to the observed emission and this explains why the intensity from H20 in Figure 1 seems so weak. The dynamics for C02 elimination differ from H2O elimination, but some analogy to the water elimination process can be found by inspection of the geometry of the four-centered transition states for decarboxylation and dehydration. For this inspection we used the geometries corresponding to the secondorder saddle point^,^ which should be close to the transition state geometries for the atoms in the four-membered ring (see Note Added in Proof). The eometry for decarboxylation has C-0 distances of r1 = 1.16 and r2 = 1.27 A. The former is nearly the equilibrium C02 distance, while the distance in the ring is stretched by 0.11 A. The vibrational excitation in the product may be expected to correspond to the statistical distribution of the excess energy among the symmetric and antisymmetric normal stretching vibrations plus the local mode excitation according to the extension of 1-2. If we look at the potential surface of C02 as a function of two C-0 distances (ref 14, p 203), the local-mode coordinate, r2 = 1.27 8, is characterized by an energy of -28 kcal mol-' over the zero vibrational level. When transformed into the antisymmetric normal mode, this energy is sufficient for excitation of v3 5 4. The geometry for dehydration has one 0-H distance, which is nearly the equilibrium value, rl = 0.95 A, with the other OH stretched, 1 2 = 1.26 A. The Sorbie-Murre11 potential energy surface2' for H20 gives about 41 kcal mol-' for the energy in a OH local mode for this distance, corresponding to four v3 quanta. Both geometries have one coordinate at nearly the equilibrium internuclear distance, while the other one is stretched to an extent corresponding to v3 = 4. Since reorganization in CO2 and H20 during traversal of the exit channel leads to a decrease of r2, excitation above v3 = 4 is doubtful. The observed decreasing vibrational distribution in ~ 1 , for 3 H20 agrees with this analysis. This analogy permits us to assume a decreasing vibrational distribution for the stretching vibrations of C02, similar to the one obtained for H20. If we assume the same fraction for PdO) for C02 and P1,3(0)for H20, which correspond to 50% of the molecules with no stretching excitation, the [CO2]/ [H20] ratio becomes approximately 0.4: 1.0, showing that water formation is roughly 2 times more probable. If the v3 distribution for C02 is sharply peaked on v3 = 1 or even on v3 = 2 (which we believe to be unlikely), the P3(0) fraction of C02 molecules would be less than our estimate and the water formation channel would be even more important. The reliability of our analysis for the branching ratio is difficult to assess, but formation of H2O seems slightly more important than C02. The larger probability of channel (la) is consistent with the higher RRKM rate constant for this channel, but these calculations are very sensitive to the EO values that are not accurately established. According to the sum rule,22 the mean vibrational energy available for the products of a unimolecular reaction may be expressed as
1
(E,) = aE,
+ bEP
(7)
where a and b are coefficients less than unity (see Figure 2 for E, and .Ep). The coefficient a may be estimated as the ratio of the number of vibrational modes in the eliminated molecule relative to the total in the transition state, giving a * 0.17 for H20 and a % 0.22 for C02. This sets b = 0.31 for reaction l a and b = 0.30 for reaction Ib. (In the calculation of the latter value, the C02 mean vibrational energy, (E.,) = 28.6 kcal mol-',
was adjusted for a v3 distribution that included a %50% fraction with v3 = 0.) These values are somewhat higher than the typical b = 0.24 established for four-centered HF-elimination react i o n ~ , which ~ . ~ ~ may be explained by the larger number of degrees of freedom in H20 and C02. In the case of C02, the specificity of the release to high bending excitation arises from relaxation of the critical configuration corresponding to the electronic structure of a carbon atom with sp2 hybridization in the carboxyl group (bent OCO) to sp hybridization in CO2 (linear OCO). The high excitation of the bending vibration in C02 may be qualitatively understood from the examination of the geometry of the transition state for (Ib). In the transition state the OCO angle is 146.6". Considering the potential surface of C02 as a function of OCO angle (ref 23, p 435) at the C-0 transition state distances rI = re = 1.16 and r2 = 1.27 A, the OCO angle of 147" corresponds to a potential energy of about 69 kcal mol-', which is close to the .Ep for decarboxylation. This energy is sufficient for the excitation of up to 36 bending quanta. Of course, some reorganization of C02 takes place during the separation from CHq leading to an increase of the OCO angle and producing preferentially v2 FZ 11. It should be mentioned, that in the transition state for dehydration, the HOH angle of 142.8' corresponds to an amplitude of vibrational bending of the free water molecule with v2 = 2.21 Hence, the observed decreasing v2 vibrational distribution for H20, with an average excitation of (v2) = 2, is in agreement with the geometry of the transition state. The ketene molecules produced in (la) also undergo a transformation from bent to linear structure. But, in this case the change in angle is not so large as for the case of C02 (in the transition state geometry LCCO I 166" ) and the vibration which may be assigned to CO stretching (2151.8 cm-I) would not receive much excitation because the potential energy of the stretched C-C bond (in the transition state r = 1.417 A, compared to equilibrium re = 1.315 A) can be shared between many stretching modes. Hence, it is not surprising that we do not observe any obvious ketene emission. In any case, weak ketene emission in the region of C-0 stretching frequency around 2152 cm-' would be obscured by the strong C02 emission. We wish to emphasize that the global appearance of the H20 and C02 spectra were unchanged with varying Ar pressure between 0.5 and 1.5 Torr of Ar for a reaction time of 0.5 ms and [HI 3.3 x l O I 3 molecules ~ m - ~A. similar result was found for the H ~ ~ ( v I distribution v ~ v ~ ) from the decomposition of ethanol. Except for the collisional coupling between V I and v3 of H20, we believe that the infrared chemiluminescence gives nascent vibrational distributions. This claim agrees with the vibrational relaxation rate constants for the asymmetric stretching and bending modes of C02, which are 1.5 f 0.1 x and 7 f 1 x cm3 s-' for C02(001) and C02(010), re~pectively.~~ The collisional probabilities for relaxation of V I 3 and v2 of H20 are 12.7 x and '6 x re~pectively.~~ 5. Conclusions
The observed infrared emission spectra from the products of the unimolecular decomposition of chemically activated acetic acid molecules with 95.3 kcal mol-' of energy show that the decomposition proceeds via two channels giving water and carbon dioxide with the branching fraction for H20 being approximately 2 times larger than for C02. With the help of an RRKM calculation, it was determined that both channels must
J. Phys. Chem., Vol. 99, No. 28, 1995 11121
Unimolecular Decomposition Pathways have a threshold energy
