J . Phys. Chem. 1984, 88, 6675-6680 events involving H2 need be considered because the pressure of KI is only -1 mtorr or less. The rate equations describing the model kinetics are dn,/dt = -(A2 dnz/dt = -(A6
+ A4 + (k, + k4 + k3)[H2])nl
(k6 + k7)[H21)nz
(A, -k kz[H2l)ni
(Al)
As expected, this state decays with a characteristic rate equal to the sum of the rates of all of the processes leading from it. Initially, n2 = n3 = n4 = 0. Substitution of eq A5 into eq A1 yields the solution for the time dependence of the intermediate state (52S1j2 3,DJ) density
+
(A2)
dn3/dt = -(A5 + k~[H2l)n3+ ~ ~ [ H z+I ~ I+ k6[HZI)% (A31
6675
n,(t) = r/(q - P) exP(-Pt) - r/(q - P) exp(-qt)
(A@
where r = A , + k2[H2],q = A, + (k6 + k7)[H,], and p = ~~~~~~y~ kH2[H2].Further substitution of eq A5 and A6 into eq A3 yields dn4/dt = (4 + k4[Hzl)nl + (A5 + k~[Hzl)n,+ ~ ~ [ H z I ~ z the desired time dependence of the 4,PJ state which is presented in the text as eq 5 and the parameters for which are given in Table (-44) I. with the conservation of mass demanding n, + n2 + 11, + n4 = Values for the spontaneous emission rateslS are as follows: A , n, (t = 0), which for the sake of convenience is here set equal to = 6.1 X lo6, A4 = 1.24 X IO6, A , = 3.85 X lo7, and A , = 4..7 unity. The densities, n,, spontaneous emission coefficients, A,, and X lo7s-’. The value of k5 is taken to be 9.45 X lo-” cm3 s-l while rate coefficients, k,, are presented in Figure 1 . that Of k6 is 5 X lo-]’. Solution of eq A1 yields the time dependence of the 5,PJ state Registry No. KI, 7681-11-0; K, 7440-09-7;H2, 1333-74-0;deuterium, = exp(-(A2 + A4 + (k2 + k3 + k4HH~l)t) 645) 7782-39-0.
+
+
Kinetics and Equilibria in the System Br CH,OOH HBr for the Heat of Formation of the Methylperoxy Radical
+ CH,OO.
An Upper Limit
Osamu Kondo and Sidney W. Benson* Loker Hydrocarbon Research Institute, Department of Chemistry, University of Southern California, University Park MC-1661, Los Angeles, California 90089 (Received: May 16, 1984; In Final Form: August 1, 1984) Very low pressure reactor technique (VLPR) is used to study the reaction Br + C H 3 0 0 H * HBr + CH302.(1) at 298-333 K. The A factor for the reaction is estimated on the basis of the tight transition state model and is combined with the measured k l to give the Arrhenius equation: log (kl/(L/mol s)) = (9.2 f 0.3) - (3.2 f 0.4)/8, where f3 = 2.303RT kcal/mol. A lower limit of K I is measured at 333 K. Using an estimated &SIo = 3.6 f 1.1 eu, we then place the upper limits to DHo(CH300-H) < 89.6 kcal/mol, AHH,D(CH,OO) < 6.6 kcal/mol. Other pathways for reaction 1 are shown to be unimportant and the secondary reaction Bt + CH,OO HBr + C H 2 0 0 (the Criegee zwitterion) is shown to also be unimportant. From data on H202,t-Bu02Hand arguments about the probable upper limit for Kl we obtain DHo(CH30z-H) = 88.5 f 0.5 kcal/mol as a best value.
-
Introduction Methylperoxy radical ( C H 3 0 0 ) is known to play an important role in combustion and in the upper atmosphere.’ For instance, it is produced by the photochemical oxidation of methane and its subsequent reaction with ambient NO producing NOz is a key step in the formation of ozone in the troposphere.2,20 One of the important radical loss processes both in combustion and in atmospheric chemistry is the reation with HOz forming methyl hydroperoxide: CH300
+ HO,
-
CH300H
+ 0,
Recently, the possible fate of C H 3 0 0 H thus formed has been disc~ssed.~ Despite the important roles that C H 3 0 0 plays in all oxidation processe~,~ very few attempts have been made to fix its thermochemistry experimentally. In order to derive the heat of formation AHfo(CH300),Benzon5 had first assumed that the 0-H bond strength in the hydroperoxide is equal to that of hydrogen peroxide, (1) See for example: Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr., Kerr, J. A,; Troe, J.; Watson, R. T. J . Phys. Chem. ReJ Data 1982, 1 1 , 327. (2) Okabe, H. “Photochemistry of Small Molecules”; Wiley: New York, 1978. (3) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. J. Phys. Chem. 1983,87, 2190. Molina, M. J.; Arguello, G. Geophys. Res. Le??.1979, 6, 953. (4) Benson, S. W.; Nangia, P. S. Acc. Chem. Res. 1979, 12, 223. (5) Benson, S. W. J . Am. Chem. SOC.1965, 87, 972.
0022-3654/84/2088-6675$01.50/0
Le., DHo(CH300-H) = DHO(H0,-H) = 89.6 f 2 kcal/mol based on AHC(H0,) = 5.0 f 2 kcal/mol measured by Foner and Hudson., The validity of this assumption was given further support by Nangia and Benson7 in their analyses of the decomposition kinetics of R 2 0 3and Rz04 both in the gas phase (R = SFS)and in solution (R = t-Bu). Recent renewal of interest in H 0 , chemistry, however, has prompted the remeasurement of AHfo(HO,) and a value of AHfo(H02) = 3.5;; kcal/mol is currently recommended by Shum and Benson in their review article.8 With A ~ f o 2 g 8 ( C H 3 0 0 H=) -30.9 f 1.0 and DH0298(H02-H) = 88.2 f 0.4 kcal/mol = DH0298(CH302-H), this gives AHfo298(CH30z)= 5 . 2 f 1.1 kcal/mol. Since AHfo(CH300)will provide an important data base for the group additivity scheme of the various polyoxide ~ e r i e s independent ,~ measurements of this value are highly desirable. Recently, Khachatryan et al.1° have studied the equilibrium reaction CH, + 0, C H 3 0 0 in the low-temperature oxidation of methane by the ESR detection of C H 3 0 0 radical and obtained a value of AHfo(CH,OO) = 2.8 ( 6 ) Foner, S. N.; Hudson, R. L. J . Chem. Phys. 1962, 36, 2681. (7) Nangia, P. S.; Benson, S . W. J . Phys. Chem. 1979, 83, 1138. (8) Shum, L. G. S.; Benson, S. W. J . Phys. Chem. 1983, 87, 3479. (9) Benson, S. W.; Shaw, R. “Organic Peroxides”; Wiley: New York, 1970; Vol. 1, 105. (10) Khachatryan, L. A.; Niazyan, 0.M.; Mantashyan, A. A,; Vedeneev, V. I.; Teitel’Boim, M. S . Int. J . Chem. Kinet. 1982, 14, 1231.
0 1984 American Chemical Society
Kondo and Benson
6676 The Journal of Physical Chemistry, Vol. 88, No. 26, 1984 kcal/moEwith the nominal error limit of f 1.6 kcal/mol. While this is in reasonable agreement with the most recent estimate, we feel that, due to the rather complex nature of their system, the error involved is more likely to be f2.5 kcal/mol and so not sufficiently accurate. In order to obtain a more accurate value of AHf"(CH,OO), we have employed the very low pressure reactor (VLPR) to study the system C H 3 0 0 H Br F= C H 3 0 0 + HBr (1)
+
The rate constant of the forward reaction is also of interest since this reaction could provide a temporary sink of active Br in the form of HBr in the atmospheric BrO, catalytic system.
Experimental Section Materials. Methyl hydroperoxide was synthesized by the methylation of hydrogen peroxide (H202)with dimethyl sulfate [(CH3),S04] in alkaline solution at 25 "C according to the method described by Criegee." The reaction products were directly extracted with diethyl ether after the solution was acidified by sulfuric acid. The ether solution was dried with anhydrous Na2S04 and then ether was evaporated by fractional distillation. Special care was taken to remove ether completely since it was found that diethyl ether reacts with Br ca. 10 times faster than C H 3 0 0 H ( k = 1.6 X cm3/(molecule s) at 298 K).12 For this purpose, the solution was further purified by several trapto-trap distillations at -55 "C until on ether peaks could be seen in the mass spectra ( m / e 74 and 59 were utilized for this purpose). The resultant solution was passed through a column containing molecular sieve (4 A) to further remove water. The purity of the sample was determined by mass spectrometry and N M R and found to contain 93% methyl hydroperoxide and 7% water. The concentration of ether was found to be less than 0.1%. The sample was kept at dry-ice temperature when not in use and no appreciable decomposition was observed during a period of several months. In order to eliminate traces of hydrocarbon, helium (Air Products) was further purified by passing through molecular sieve (4 A) at 77 K. Bromine (Mallinckrodt) was mixed (3% or 10%) with high-purity helium for the microwave discharge. HBr (Matheson) was used for the equilibrium constant measurements after degassing several times. Apparatus and Procedures. The VLPR system used for the present study has already been describedi3 and no significant changes have been made. Br atoms were generated in the quartz tube (phosphoric acid treated) enclosed by the 2.45-GHz microwave cavity and introduced into the Knudsen reactor through a tapered capillary having approximate diameters of 300 jtm and 1 mm at the two ends. It was ca. 2 cm long. The conductance was estimated at ca. 0.2% of that of the exit aperture of the reactor which was enough to prevent back-diffusion of molecules into the microwave cavity. (Back-diffusion of molecules, especially hydroperoxide, was found to cause severe fluctuation of the Br signal.) All the surface of the capillary exposed to the gas was coated with halocarbon wax to prevent any surface-catalyzed recombination of Br. The Knudsen reactor used had a volume of 227 cm3 and was characterized by the escape rate constant, keM= 1.09(T/M)i/2 s-', where T and M are the absolute temperature and the mass in amu, respectively. The inside of the reactor was halocarbon wax coated to prevent any wall destruction of the atoms and radicals. The temperature of the reactor was controlled (fO.l "C) by passing a heating liquid through the outer jacket of the reactor and was continuously monitored by two copper-constantan thermocouples. The various flow rates of C H 3 0 0 H were established by changing the pressure in the calibrated buffer volume (ca. 500 cm3) connected to the reactor via a 100-cm-long capillary (0.051 (1 1) Criegee, R. In "Methodender Organischen Chemie" (Houben-Weyl); Sauerstoff verbindungen 111; Georg Thieme Verlag: 1952; Vol. 8. Benson, S. W. Int. J . Chem. Kinet. 1984, 16, 949. (12) Kondo, 0.; (13) Heneghan, S.P.; Knoot, P. A.; Benson, S.W. Inr. J . Chem. Kinet. 1981, 13, 671.
cm in diameter). The stability of C H 3 0 0 H throughout the Pyrex capillary was checked by comparing the spectra between the capillary sampling and direct injection. We have especially looked at m / e 30 (CH20) and m / e 18 (H,O) carefully for the possible occurrence of the wall-catalyzed decomposition process: CH300H
wall
CHzO + H 2 0 (or CH3OH
+ '/202)
We could not, however, observe any difference between these two sampling methods, indicating that C H 3 0 0 H is stable during the process of gas handling. Hence, the concentration of C H 3 0 0 H could be calculated from the known flow rate by making a correction for its purity (93%). The molecules which exit the aperture of the reactor diffused consequently through the two differentially pumped chambers, thus creating a molecular beam. The beam was chopped at 200 Hz before entering the ionzer of the quadrpuole mass spectrometer (UTI 100 C) and its ac component was detected with a lock-in analyzer (Dynatrac 3). The mass spectrometer was controlled by a microcomputer data processing unit (UTI programmable peak selector) enabling us to observe up to nine peaks simultaneously. The choice of the electron energy of the ionizer is the most critical factor for the experiments. We would have liked to operate the ionizer at an energy less than the appearance potential of Br+ from HBr (- 17 eV) so that we could prevent any contribution to the Br ( m / e 79) peak from the presence of HBr. The present instrument, however, would not operate below 18 eV. Its severe loss of sensitivity and poor resolution did not allow us to operate it below 30 eV. We have chosen 35 eV as a compromise and a correction has been made to subtract the contribution from HBr to (Br peak) in all the experiments. In separate experiments, this correction factor (c = 179/180) has been determined by flowing HBr both alone and with added Br/He flow, and was found to be 0.254 f 0.002 at this electron energy. Although this correction was not important for the kl determinations (where [Br] N [HBr]), it placed a severe limit on the precision of the equilibrium constant measurements in which [Br] > k2[Br]) to 2 (when k2[Br] >> keR).
+
Kondo and Benson
6678 The Journal of Physical Chemistry, Vol. 88, No. 26, 1984
3c
TABLE I: Estimation of the A Factor for Reaction 1 Using CH300H as a Reference Transition State
T=333K
degree of freedom reference reaction (TS = CH300H) spin R In 2 symmetry amu 128) translation (amu 48 external rotation 1*3/13= 133 reaction coordinate (Br-Ha0 asymmetric stretch) new H-Br stretch (1850 cm-I) 1300-cm-' H-0-0 bend (in-plane) 700-cm-' Br.H.0 bend (in-plane) H - 0 - 0 restricted free rotor (f, =I 1) 700-cm-' Br.H.0 bend (out-of-plane) new 300-cm-' (Br.H).O-O bend (in-plane) new (Br.H).O-O restricted free rotor ( I , = 13.8) standard state (atm L/mol) R In (R'T)
M*300,
-
I
1
I
I
1
0
I 2
I i
I 3 [Her]
I 4
I 5
I 6
7
rnolecules/cc
x
Figure 3. Plot of F v s . [HBr] at 333 K.
A300
The rate constants kl can be obtained by multiplying the slopes of the lines by the known escape rate constants for Br at each temperature since the term in braces can be taken as unity under all our experimental conditions as discussed above: X
cm3/(molecule s)
k1(333 K) = (2.05 f 0.21) X
cm3/(molecule s)
kl(298 K) = (1.34 f 0.13)
The listed error limits were estimated from the observation that measurements of IBr'/zBrwere reproducible to *4% at zBr'/zBr = 1.5. The precision of the rate constant measurements was about *lo% ( 2 4 . Equilibrium Constant Measurements. Reaction 1 could be reversed by adding HBr to the constant flow of Br/He and C H 3 0 0 H , thus by making the rate of reaction -1 comparable C H 3 0 0 HBr C H 3 0 0 H Br (-1)
+
-
+
to that of the forward reaction 1. Solving the steady-state concentrations of Br and C H 3 0 0 , we can express the effects of the addition of HBr on [Br] (increase) by the following equation: l 3 F=
[Brl [Br], - [Br]
--
-
-
keBr kl[CH300H]
eu
-41.8 1.4 0 2.9 4.9 0
0 0.3 (2.8)a
-2.9 1.4 5.8 6.4 total -21.6 (-19.1)
(L/(mol s)) = e Z ( k T / h )exp(AS*/R) = l o g 9(log5)
in parentheses correspond to bent complex with Br.H.0 angle of 135' and assumed free rotation about the axis. N.b. In our estimates of the uncertainty of AS* we have generally assigned an estimate of i l eu, which is less than a factor of 2 in k . Most of the uncertainty arises not from uncertainties in frequencies but rather in geometry. Thus, the bent and linear TS are extremes in the calculation. By choosing the geometric mean we feel our maximum error is reduced to a factor of 2 or 1.4 eu in AS*. a Values
using these equations and assuming that each peak height (Z79 and Zg0)was measured to *l% and the error involved in the determination of c was f0.8%. Due to the relatively large value of c (0.254), the second and third terms in eq VI contribute almost the same magnitude as the first term, resulting in about f30% error in ZBr and hence f54% error in F a t the highest [HBr]. The solid line in Figure 3 is the least-squares fit to five data points assuming that the observed increase in F with the increase in [HBr] is meaningful. Unfortunately, however, the large uncertainty in F did not permit us to place an upper limit on K I ;hence, only the lower limit was determined by connecting the upper sides of the error bar (2u) (dashed line). From its slope and the value of keBr/keR= 0.771, we find K , > 0.46 at 333 K For the solid line
where we have neglected the self-reaction of C H 3 0 0 (reaction 3). Inclusion of reaction 3 results in about 5% decrease in [CH 3 0 0 ] and in turn less than 1% decrease in F, a completely negligible effect. Figure 3 shows a plot of F against [HBr] at 333 K. In these runs, the concentration of C H 3 0 0 H was set at 7.75 X lOI3 molecues/cm3, which corresponds to the initial F value of 1.38 & 0.12. Each experimental point inevitably involves a large error due entirely to the presence of the large amount of HBr which was required to reverse the reaction appreciably. The relative errors in F and ZBr are given by eq V and VI, respectively
where
- c180
(VW where c is the correction factor for due to HBr (see Experimental Section). The error bars in Figure 3 were evaluated by zBr
= z79
K,
0.8 f 0.3 at 333 K
Discussion The Arrhenius parameters for reaction 1 obtained by casting the measured rate constants into an Arrhenius form involve large errors due to the relatively narrow temperature range (35 K) and the small increment of k , (ca. 50%). Thus, we have adopted a different approach. A suitable transition-state (TS) model calculation will allow us to estimate the A factor for the reaction with good accuracy (usually better than a factor of 2).15 The estimated A factor will then be combined with the experimentally determined rate constants to obtain the activation energy for the reaction. The details of calculation are given in Table I. We have assumed that the reaction proceeds via a tight transition state where 0.H and H-Br distances are elongaed by 0.3 A compared with the normal covalent lengths. The calculations have been made for two extreme cases corresponding to the linear (0-H-Br) and the bent (assumed LO-HeBr angle of 135') transition state. The adopted geometry of the transition state (for the linear case) is shown in Figure 4. The molecular parameters with the exception of the dihedral angle 4 have been assigned by analogy with those known for Hz02 and CH30CH3.22 In their ab initio MO study of the internal (22) "CRC Handbook of Chemistry and Physics", 62nd ed.; CRC Press: Boca Raton, FL., 1981.
Br
+ C H 3 0 0 H + HBr + C H 3 0 0
The Journal of Physical Chemistry, Vol. 88, No. 26, 1984 6679 TABLE 111: Frequency Assignments of frequency, frequency, cm-' type cm 1325 3100 (3) C-H stretch 586 1450 (3) H-C-Hbend 834 1150 (2) CH, rock 880 0-6 stretch CH,aO 3450
/
TABLE I1 Kinetic Parameters for the Br Reactions
+ ROOH
-
AHf', kcal/mol HBr
+ ROO
log (Ai/ El, ki(298 K), R T , K (L/(mol s)) kcal/mol 106L/(mol s) ref H 300-350 10.1 i 1.3 4.4 i 1.9 7.4 h 2.6 16 CH, 298-333 9.2 i 0.3 3.2 i 0.4 8.1 f 0.8 this work t-Bu 300-350 9.4 i 0.4 3.3 0.6 9.9 f 1.0 17 rotations, Radom et aL2, have shown that the most stable conformation of CH,OOH is found at the dihedral angle of 140' or at 220'. The barrier height at the cis position was calculated to be 8 kcal/mol. At the trans position a barrier close to zero (-0.1 kcal/mol) was calculated so that the 0-H group can rotate essentially freely between the angles of 90' and 270'. Such a "restricted free rotor" model has been adopted for the present study since no other experimental information is currently available on this point. As a reference transition state, we have chosen CH,OOH itselP4 since (1) we can avoid any uncertainties associated with the estimations of the entropies of C H 3 0 0 H and the model compound and (2) the effects of the internal rotation could be more properly taken into account by adopting the parent molecule as a model TS. The entropies of the restricted free rotor were calculated via the equation SO,,,
= 4.6
+ (R/2)
In I,
+ R In (A0/2.n)
(VIII)
where I, is the moment of inertia of the rotor in amu A2 and A0 represents the range of angle in which the 0-H group rotates freely (A0 N T in this case). In the bent transition state, one of the degenerate O-H-Br bending motions is replaced by the free rotation of H about the axis passing through 0 and Br. The calculated values are A = 108.9L/(mol s) and A = 109.5L/(mol s) for the linear and bent transition states, respectively. Since the accuracy of our experiments does not allow us to distinguish between these two extremes, a best choice will be provided by taking the geometric mean of both values: log (A/(L/mol s)) = 9.2 f 0.3 The uncertainty of a factor of 2 should be adequate to encompass the whole possible range. By using the measured k l , we obtain the following Arrhenius equation: log (kl/(L/mol s)) = (9.2 f 0.3) - (3.2 f 0.4)/8
(IX)
where 8 = 2.303RT kcal/mol. In Table 11, we summarize the Arrhenius parameters together with the values of k , at 298 K for the reactions Br
+ ROOH
-
HBr
+ ROO (R = H, CH,,
and t-Bu)
studied by the VLPR technique in this laboratory. It should be noted that due to the difficulty associated with the gas handling, (23) Radom, L.; Hehre, W. J.; Pople, J. A. J . Am. Chem. SOC.1972, 94, 2371. (24) Similar result was obtained when CHBOOBr (So = 76.4 eu) was
chosen as a reference TS.
H030
type H-0-0 bend C-0-0 bend C-0 stretch int rotation ( V , = 1 kcalimol) restricted free rotation
TABLE IV: Thermochemical Data for the Species Involved in Reaction 1 at 298 K Br CH,OOH HBr CH,OO
/
Figure 4. Assumed geometry of the transition state.
0-H stretch
CH,OOH
So, cal/(mol K)
26.7 41.8
-30.9 f 1" 66.8 i l C
-8.7 47.5
