Kinetics of the Reaction of OH Radicals with a Series of Branched Alkanes at 297 k 2 K

ROGER ATKINSON," WILLIAM P. L. CARTER, SARA M. ASCHMANN, ARTHUR M. WINER,

and JAMES N. PITTS, JR. Statewide Air Pollution Research Center, University of California, Riverside,

California 92521

Abstract

Relative rate constants for the reaction of OH radicals with a series of branched alkanes have been determined a t 297 ? 2 K, using methyl nitrite photolysis in air as a source of OH radicals. Using a rate constant for the reaction of OH radicals with n-butane of 2.58 x lo-'' cm3/molecule . s, the rate constants obtained are ( x 10" cm'/molecule . s): isobutane, 2.29 ? 0.06; 2-methylbutane, 3.97 ? 0.11; 2,2- dimethylbutane, 2.66 ? 0.08; 2-methylpentane, 5.68 ? 0.24; 3-methylpentane, 5.78 2 0.11; 2,2,3-trimethylbutane, 4.21 3- 0.08; 2,4-dimethylpentane, 5.26 ? 0.11; methyl- cyclohexane, 10.6 ? 0.3; 2,2,3,3-tetramethylbutane, 1.06 ? 0.08; and 2,2,4-trimethyl- pentane, 3.66 0.16. Rate constants for 2,2-dimethylbutane, 2,4-dimethylpentane, and methylclohexane have been determined for the first time, while those for the other branched alkanes are in generally good agreement with the literature data. Primary, secondary, and tertiary group rate constants a t room temperature have been derived from these and previous data for alkanes and unstrained cycloalkanes, with the secondary and tertiary group rate constants depending in a systematic manner on the identity of the neighboring groups. The use of these group rate constants, together with a previous determination of the effect of ring strain energy on the OH radical rate constants for a series of cycloalkanes, allows the a priori estimation of OH radical rate constants for alkanes and cycloalkanes at room temperature.

Introduction

It is well recognized that photolysis and reaction with hydroxyl (OH) and nitrate (NO3) radicals and with ozone are the major gas- phase reactions responsible for the homogeneous degradation of organics emitted into the atmosphere [l-41. For the majority of organic com- pounds studied to date the reaction with OH radicals is the most important of these loss processes 11-41. Hence OH radical reaction rate constants are necessary in order to assess the atmospheric lifetimes of most organics. In view of the large number of organics emitted into

* Author to whom correspondence should be addressed.

International Journal of Chemical Kinetics, Vol. 16, 469-481 (1984) 0 1984 John Wiley & Sons, Inc. CCC 0538-8066/84~040469-13$04.00

470 ATKINSON ET AL.

the atmosphere by natural and anthropogenic sources, the use of pre- dictive relationships C3,5-81 is an attractive and cost-effective means of estimating these rate data. However, in order to develop such schemes for the reliable a priori prediction of rate constants, a large and accurate data base is necessary.

Recently, using a relative rate technique, we have determined the rate constants for the reaction of OH radicals with a series of n-alkanes (propane through n-decane) [81 and showed that, contrary to earlier structure-reactivity relationships [7,9-111, the rate constant per sec- ondary C-H bond is not constant. Rather, these recent data showed [8] that the rate constant per -CH2- group depends significantly on the neighboring groups, and rate constants for -CH,- groups bonded to two -CH2- groups, to one -CH2- and one -CH3 group, and to two -CH3 groups were derived [81. In the present work, this previous study [8] has been extended to investigate a series of branched alkanes in order to derive rate constants for >CH- and other -CH2- groups.

Experimental

The experimental technique has been described previously [8,121 and hence only the relevant details are given here. Hydroxyl radicals were generated by the photolysis, at wavelengths A b 290 nm, of methyl nitrite (CH30NO) in air at part-per-million (1 ppm = 2.39 x 1013 molecule/cm3 at 297 K and 735-torr total pressure) concentrations:

CH30N0 + hu + CH,O + NO

CH30 + 0, -+ HCHO + H02

HOz + NO -+ OH + NO,

In order to minimize the formation of 0, during these irradiations, NO was added to the reaction mixtures, which had initial concentrations of: CH30N0, 8-27 ppm; NO, -5 ppm; and 0.5-1.0 ppm each of the reference and reactant alkanes. Ultrazero air (Liquid Carbonic, ~ 0 . 1 ppm hydrocarbons) was used as the diluent gas.

Irradiations were carried out in a -60-L FEP Teflon cylindrical reaction bag surrounded by 24 GE F15T8-BL 15-W blacklights. In this work, the maximum light intensity was used, corresponding to a photolytic half-life for CH30N0 of -10 min. Prior to irradiation, the reaction bag-lamp assembly was covered with an opaque cover to avoid any photolysis of the reactants.

The reactants were quantitatively monitored by gas chromatography with flame ionization detection. n-Butane, CH30N0, and the branched alkanes, apart from 2-methylbutane, were analyzed using a 20-ft x 1/8-in stainless-steel column with 5% DC703/C20M on 100/120 mesh

OH RADICALS AND BRANCHED ALKANES 47 1

AW, DMCS Chromosorb G, operated at 333 K. For the irradiations involving n-butane and 2-methylbutane, these alkanes were analyzed using a 36-ft x 1/8-in stainless-steel column of 10% 2,4-dimethyl- sulfolane (DMS) on C-22 firebrick (60/80 mesh), operated at 273 K. NO, NO,, and O3 were monitored by chemiluminescence instruments. Methyl nitrite was prepared and stored as described previously [la].

Results

Irradiations of a series of CH,ONO-NO-alkane-air mixtures were carried out at 297 k 2 K and -735-torr total pressure. In order to optimize the gas chromatographic analyses and to obtain, insofar as possible, similar alkane conversion rates during the experiments, the following alkane mixtures were used: n-butane + isobutane; n-butane + 2-methylbutane; n-butane + 2-methylpentane + 2,2,3,3-tetramethylbutane + 2,2,4-trimethylpentane; n-butane + 2,2-dimethylbutane + 2,4-dimethylpentane + methylcyclohexane; and n-butane + 3-methylpentane + 2,2,3-trimethylbutane, with n-butane being used as the reference alkane [8,121. For these mixtures, duplicate irradiations were carried out with differing initial concentrations of CH30N0.

The OH radicals generated from the photolysis of CH30N0 in air can, besides reacting with CH,ONO, NO, NO,, and the alkane reaction products, react with the alkanes and n-butane (the reference alkane):

(1) OH + alkane -+ products

(2) OH + n-butane -+ products

Since the alkanes are consumed essentially solely (>99% [8,12l) by reaction with OH radicals, and since dilution due to sampling is avoided by use of a collapsible Teflon reaction bag, then [8,12]

d ln[alkanel - - k l d ln[n-butane1 dt k2 dt

-

and

(11)

where k , and K 2 are the rate constants for reactions (1) and (21, re- spectively, [alkane], and [n-butane],, are the concentrations of the reactant alkane and n-butane, respectively, at time to, and [alkane], and [n-butane], are the corresponding concentrations a t time t. Thus plots of 1n([a1kane],/[a1kane3,) against 1n([n-butane],/[n-butane],)

{ ralkanel,,) = 2 { [n-butaneltO} [n-butane], [alkane],

472 ATKINSON ET AL.

should yield straight lines with a zero intercept and a slope of k , / k z . Plots of eq. (11) are shown in Figures 1-3, and the rate constant ratios k l / k 2 obtained from these plots by least-squares analyses are given in Table I.

In all cases the least-squares intercepts of these plots were within two standard deviations of zero.

Discussion

It can be seen from Figures 1-3 that the experimental data are in good accord with eq. (11). The rate constant ratios k l / k 2 given in Table I can be placed on an absolute basis by using a rate constant for the reaction of OH radicals with n-butane of k2 = 2.58 x 10-l' cm3/molecule . s [8,121, the mean of the absolute literature values (in units of 10-l' cm3/molecule . s) of 2.57 [91, 2.35 2 0.35 I131, 2.72 ? 0.27 [141, and 2.67 2 0.22 [151. The rate constants so derived are also given in Table I along with the available literature data. No previous data have been reported for 2,2-dimethylbutane, 2,4-dimethylpentane, or methylcy- clohexane. For the remaining alkanes investigated it can be seen that the present data are in excellent agreement with the absolute rate constants obtained by Greiner [91 for isobutane, 2,2,3,3-tetramethyl- butane, and 2,2,4-trimethylpentane, and are in general agreement with the previous relative rate data reported for isobutane, 2-meth- ylbutane, 2- and 3-methylpentane, and 2,2,3-trimethylbutane [10,16- 201.

In ( [ n -BUTANE] to / [n-BUTANE]t )

Figure 1. butane, and 2,2,3,3-tetramethylbutane.

Plots of eq, (11) for 2-methylpentane, 2,2,4-trimethylpentane, iso-

OH RADICALS AND BRANCHED ALKANES 473

1.6r

METHYLCYCLOHEXANE

- c. 1.2

2.4-DIMETHYLPENTANE Y

\ 2 0.8

p”

2.2-DIMETHYLBUTANE

0 0.1 0.2 0.3 0.4 0.5 0.6

In ([n-BUTANE] to/[n-BUTANE] t )

Figure 2. Plots of eq. (11) for methylcyclohexane, 2,4-dimethylpentane, 2,2,3- trimethylbutane, and 2,2-dimethylbutane.

Until recently, based on the original work of Greiner 191 and the more recent study of Darnall et al. [lo], it has been assumed that the partial rate constants for abstraction from primary, secondary, or tertiary C-H bonds were the same for all unstrained alkanes [3,7,9- 111. With this assumption, the overall OH radical rate constant is given by

(111) kt0t = npkp + risk, + n,k,

1 . 2 r

-. 3-METHYLPENTANE

w z

Y

2 - METHYLBUTANE

I 0 0.2 0.4 0.6

1 n ( [ n -BUTANE] t,/[n-BUTANE] +) Figure 3. Plots of eq. (11) for 3-methylpentane and 2-methylbutane

474 ATKINSON ET AL.

TABLE I. Rate constant ratios k , /k , and rate constants k , at 297 2 2 K for the reaction of OH radicals with a series of alkanes, together with room temperature literature values.

10'' x k Absolute'

Literature

(cm3 molecule-I 8ec-l)

Alkane kl/kZa This workb Values Relative Literature Values'

Isobutane 0.886 f 0.021 2.29 f 0.06 2.46 I91 3.5 f 0.9 [161; 2.1 1171; 1.86 f 0.21 1181; 2.38 f 0.05 1101

2-Uethylbutane 1.54 f 0.04 3.97 f 0.11

2,Z-Dimethylbutane 1.03 f 0.03 2.66 f 0.08

3.0 f 0.6 1191, 3.57 f 0.07 [I01

2-Methylpentane 2.20 f 0.09 5.68 f 0.24 4.8 f 1.0 1191

3-Hethylpentane 2.24 f 0.04 5.78 f 0.11 6.5 f 1.1 I191

2,2,3-Trinethylbutane 1 . 6 3 f 0.03 4.21 f 0.08 5.05 (91 3.6 f 0.7 [201

2,4-Dimethylpentane 2.04 f 0.04 5.26 f 0.11

Methylcyclohexane 4.12 f 0.10 10.6 f 0.3

2,2.3,3-TeC~'~.ethylb~fane 0.410 f 0.030 1.06 t 0.08 1.12 [91

2,2.4-Trimethylpentane 1.42 f 0.06 3.66 f 0.16 3.73 [91

a At 297 -t 2. The indicated errors are two least-squares standard deviations of the slopes of the plots shown in Figures 1-3.

cm'/molecule . s 18,121, the mean of the absolute literature values ( X 10" cm3/molecule . s ) of 2.57 [91, 2.35 i 0.35 1131, 2.72 i 0.27 [141, and 2.67 -t 0.22 [151.

Taken from \ 111, which should be consulted for details. The data of 110,191, which are relative to n-butane, have been adjusted to be consistent with the presently used n-butane rate constant.

Placed on an absolute basis using a rate constant k , of 2.58 x 10-

where ktot is the OH rate constant for a molecule with np, n,, and n, primary, secondary, and tertiary carbon atoms, and kp, k,, and k, are their respective group rate constants. However, the rate constant data for the C,-C,, n-alkanes recently obtained in these laboratories 181 showed that for the secondary -CH,- groups involved in these n- alkanes this assumption is an oversimplification, and that the -CH,- rate constants depend on the identity of the neighboring groups. Thus for the C,C,, n-alkanes, the overall OH radical rate constants at room temperature were predicted to a high degree of accuracy by the expression [81

ktot = 2klCH33 + 2k[CH,(CH31(CH,)1 + (n - 4) k[CH2(CH2),1

where n is the number of carbons in the n-alkane, k[CH31 is the partial rate constant for H-atom abstraction from a -CH3 group [i.e., k, in eq. (11111, and k[CH,(CH,)(CH,)] and k[CH,(CH,),I are group rate con- stants for abstraction from -CH,- groups bonded to one -CH3 and one -CH2-, and to two -CH,-- groups, respectively. Similarly, for propane, the overall OH radical rate constant is given by [81:

k(propane) = 2k[CH31 + k[CH,(CH3),1

OH RADICALS AND BRANCHED ALKANES 475

The CH3- and -CH,-- group rate constants determined at room temperature from this previous study [SI are given in Table 11. In a totally analogous manner, values of k[CH,(CH,),I, k[CH,(CH,)(C)l, k[CH(CH,),], k[CH(CH,),(CH)I, and k[CH(CH,),(C)I can be derived from the OH radical rate constants obtained in the present work and previously [121 for cyclohexane [121, 2,2-dimethylbutane, isobutane, 2,3-dimethylbutane [12], and 2,2,3-trimethylbutane, respectively. The values for these group rate constants are also given in Table 11.

Unfortunately, for the other branched alkanes, methylcyclohexane, and the bicyclo[4.4.01decanes, the group rate constants involved cannot be unambiguously derived from the available data. However, it can be seen from Table I1 that the -CH,-- and >CH- group rate constants increase by an approximately constant factor upon replacing a neigh- boring CH3- group by a -CH,- group, a -CH2-- group by a >CH- group, and a >CH- group by a -Ctgroup. Thus quantities k:,

= ky

= k:Fs

= kp

= k: F ,

where Fs and F, are the factors involved in replacing a neighboring CH,- group by a -CH,- group for secondary and tertiary groups,

TABLE 11. kinetic data for normal and branched alkanes and cyclohexane.

Group rate constants which can be directly derived from the available

Group lo1‘ x Group Rate Constant Derived from

(cm3 molecule-’ sec-1)

0.19 neopentane and 2,2,3,3-tetramethylbutane

C5-Cl0 n-alkanes cyclohexane

476 ATKINSON ET AL.

respectively. The data in Table I1 further indicate that to a good approximation the other group rate constants can be expressed by, for example,

kTCH2(CH2),1 = k[CHJCHJ(CH)l = kTCHZ(CH3)(CH2)1 F , = k: F:

kLCH,(CHJ(C)I = kTCH,(CH2)(CH)I = k[CH2(CH3)(CH)I F, = k: F:

k[CH(CH&(CH)I = k[CH(CH&(CH,)I F, = ky F:, and so on. I t may be noted that the above formulism is equivalent to assuming that

(IV) k, (np) = k: F:"

and

(V) k,(n,) = kp,:,,

where nP is the total number of carbons in the /3 position relative to the group center (i.e., the number of next nearest neighbors), and k,(n,) and k,(n,) are the corresponding -CH2-- and >CH- group rate constants. Therefore, the overall alkane OH radical rate constant is given by

(VI) kWt = npk, + 2 n,(n,)k: FZP + 2 n,(n&)ky F;a

where n,(np) is the number of -CH2-- groups in the molecule with n,, next nearest neighbors, and n,(n;) is the number of >CH- groups with n; next nearest neighbors. With this approximation only five parameters, namely, k,, k:, k; , F, and F,, are required to derive the overall room-temperature rate constant for any alkane that does not have significant ring strain 121) or steric hindrance.

These five parameters were derived from weighted nonlinear least- squares analyses [221 using the OH radical rate constants for acyclic and nonstrained cyclic alkanes measured in this and our previous [8,12,21 J kinetic studies. The experimental data used are listed in Table 111. For these weighted nonlinear least-squares analyses, the alkanes in Table I11 were grouped into two sets: set A being the acyclic alkanes except for 2,4-dimethylpentane and 2,2,4-trimethylpentane, and set B consisting of set A together with the four unstrained cy- cloalkanes. 2,4-Dimethylpentane and 2,2,4-trimethylpentane were ex- cluded from these analyses since they have anomalously low OH radical rate constants, probably due to steric hindrance restricting access of the OH radical to the central -CH2- group.

From the weighted nonlinear least-squares analyses of sets A and B i t was observed that the parameters obtained from the analysis of

B max 11 P max rr

ng = 0 n b - 0

OH RADICALS AND BRANCHED ALKANES 477

TABLE 111. Room temperature rate constants from this work and previous studies in these laboratories [8,12,21 I for the reactions of OH radicals with alkanes, together with predicted values.

10” x k (cm3 molecule-’ sec-l) Alkane Observeda Calculatedb

Set A ( A % ) Set B ( A X )

n-Alkanes

Propane n-Butane n-Pentane n-Hexane >-He? tane n-Octane n-Xonane n-Decane

Sranchel. Alkanes

I sobu t ane Teopentane 2-?(ethylbutane 2-Yethylpentane 3-Yethylpentane 2,2-3imethylbutane 2,3-Dimethylbutane 2,2,3-Trimethylbutane 2,4-Dimethylpentanec 2,2,3,3-Tetramethylbutane 2,2, 4-Trimethylpentanec

Unstralned Cycloalkanes

Cyclohexane Yethylcyclohexane cis-Bicyclo[4.4.0]decane trans-Bicyclo[4.4.0]decane

1.22 f 0.05 2.58 4.13 f 3.08 5.70 f 0.09 7.30 -f 0.17 9.01 f 0.19 10.7 f 0.4 11.4 f 0.6

2.29 f 0.06 0.77 f 3.05 3.97 f 0.11 5.68 f 3.24 5.78 f 3.11 2.66 + 0.09 6.26 t 0.06 4.21 0.38 5.26 f 0.11 1.06 f 0.08 3.66 f 0.16

7.57 f 0.05 10.6 f 3.3 20.1 f 1.4 20.6 f 1 .2

1.27 2.68 4.15 5.63 7.10 8.57 10.0 11.5

2.23 0.71 4.15 5.71 6.20 2.58 6.15 4.33 7.37 1.07 6.03

8.84 11.0 22.1 22.!

(4.1) (3.9) (0.5) (-1.2) (-2.7) (-4.9) (-6.5) (0.9)

(-2.6) (-7.8) (4.5) (0.5) (7.3) (-3.0) (-1 .A) (2.9) (40.1) (0.9) (64.8)

(16.8) (3.8) (10.0) (7.3)

1.32 2.59 3.90 5.22 6.53 7.84 9.15 10.5

2.46 0.83 4.15 5.51 5.92 ? . 4 ! 6.17 4.26 7.17 1.24 5.55

7.88 10.0 19.4 19.4

(8.2) ( 0 . 4 ) (-5.6) (-8.4) (-10.5) (-13.0) (-14.5) (-7.9)

(7.4) (7.8) (4.5)

(-3.0) (2.4) (-9.4) ( - 1 . 4 ) (1.2) (36.3) (17.0) (51.6)

(b.1) (-5.7) (-3.5) (-5.8)

’ All based on a rate constant for the reaction of OH radicals with n-butane of 2.58 x 10. l 2 cm:’/molecule . s [8,121. Data a re from this work and [8,12.21].

’Calculated using (see text): Set A - k , = 0.178, k:‘ - 0.918, k:’ : 1.695, F. 7

F , = 1.267; set B-k, , = 0.207, k:l = 0.902. k: -- 1.834, F , = F, = 1.206 (these values of k,,, kr, and kP are in units of 10

Rate constants anomalously lower than expected, possibly due to steric hindrance. cmJ/molecule . s ) .

set A alone fitted the experimental data, within the cited error limits, for significantly more alkanes than did those obtained from analysis of set B. However, the parameters obtained from the analysis of set B fitted the experimental data for cyclohexane and the isometric bi- cyclo[4.4.0ldecanes somewhat better than did the parameters obtained from analysis of set A alone, as expected.

The coefficients k,, k:, ky, F,, and Ft obtained from these analyses of the data of OH radical rate constants of sets A and B are given in Table IV. I t can be seen that the values of F, and F, are very similar, overlapping within the error limits. Hence further analyses of the set

478 ATKINSON ET AL.

TABLE IV. Parameters used in eq. (VII to predict room temperature OH radical rate constants for alkanes as derived by weighted nonlinear least-squares analyses.

x 10'~ (cm3 molecule-' sec-l)

Alkanes kFJ k: k: Fs Ft

Set A 0.178tG.014 0.877i0.047 1.745f0.090 1.304*0.042 1.247i0.030 Se: B 0.201i0.025 0.98310.093 1.74&0.166 1.152i0.057 1.244i0.054

Set A 0.178~0.014 0.918L0.032 1.695f3.078 1 .267f0.025a Sec B 9.207i0.025 0.932f0.058 1.834f0.148 1.206i0 .040a

'I Obtained by setting F. = F,

A and B data were carried out with F , = F, = F , and the values of k,, k:, k:, and F derived on this basis are also given in Table IV. The rate constants predicted with F, = F, and F , # F, for the alkanes listed in Table I1 were identical within -5%, indicating that the simpler expression with F, = F, may be used with no significant adverse effect on the predictive capabilities.

The predicted rate constants calculated using eq. (VI) with the pa- rameters derived assuming that F , = F, and using data from both sets A and B are given in Table 111, where they can be compared with the experimental data. It can be seen that in general the agreement between predicted and experimental data is excellent, with only 2,4- dimethylpentane and 2,2,4-trimethylpentane being in obvious disa- greement for both analyses. Using the parameters derived from the set A or the set B data, the experimental data, apart from the two alkanes noted above, are fitted to within -17% (with most being predicted to within -10%). While there is little to differentiate these two sets of parameters utilized for the calculations in Table 11, we would recommend the use of those obtained from set A alone, since this set of parameters gives a significantly better fit to most of the acyclic alkanes, and gives acceptable fits to methylcyclohexane and the bicyclo[4.4.0]decanes. Thus we recommend use of eq. (VI) with

h, = 1.8 x 10 cm:'/molecule . s hy = 9.2 x 10 cm"/molecule . s kp = 1.7 x 10 '* cm'/molecule . s F , = F , = 1.27

for the a priori estimation of rate constants for the reaction of OH radicals with acyclic alkanes and unstrained cycloalkanes.

As indicated above, the OH radical rate constants predicted for 2,4- dimethylpentane and 2,2,4-trimethylpentane do not agree well with the experimental values. This is probably due to steric hindrance

OH RADICALS A N D BRANCHED ALKANES 479

affecting the rate of OH attack on the central -CH2- group. If i t is assumed that the CH3- and >CH- group rate constants for these alkanes are the same as those derived above, then values of'

k 1CH2(CH),1 = 0.25 x 10 cm"/molecule . s

kICH,(CH)(C)] = 0.62 x 10 l 2 cm"/molecule . s

may be obtained for these "sterically hindered" -CH2- groups. These "sterically hindered" group rate constants can be compared with the expected values of 2.37 x 10- " and 3.00 x lo- ' ' cm3/molecule . s derived using eq. (IV). For these groups the values given above, rather than those derived from eq. (IV), should probably be used for predictive purposes. Although the value of k[CH,(C), 1 is not known, it is reasonable to assume that it is also small compared to the value predicted by eq. (IV). The possibility of steric effects obviously should also be con- sidered when estimating rate constants for certain tertiary groups (e.g., 1 CH(CH:, )CC),l, etc.), especially since eq. (V) predicts relatively high rate constants for these groups, while their actual group rate constants may be quite low.

For strained cycloalkanes we have previously shown 1211 that overall ring strain energies of 54-5 kcal/mol have no significant effect on the rate constants, but that for overall ring strain energies 25 kcal/mol the rate constant decreases approximately exponentially with increasing strain energies. In particular, for E,,,.,,,, > 5 kcal/mol the data were reasonably well fit by 1211:

and

) = 0.27 - 0.062ESLr,,, (VI I ) 1 n( hstraintrdikunstraine~

where EStra,,, is the total ring strain energy in kcal/mol and is the predicted rate constant [e.g., using eq. (VI)] for the

unstrained system. Thus the use of this relationship together with the predictive technique derived in this work for unstrained alkanes allows the estimation of the room temperature OH radical rate constants for all alkanes, acyclic and cyclic, including strained cycloalkanes, but excluding alkanes with significant steric hindrance.

The estimation of OH radical reaction rate constants for alkanes at temperatures other than -298 K is more difficult since the available experimental data are not sufficient to derive the temperature de- pendences of the five parameters (k,,, k;, kp. FA, and F, ) involved in eq. (VI). Until sufficiently precise and extensive data become available, we assume that the effect of increasing the number of next nearest neighbors on both secondary and tertiary groups is to reduce the Arrhenius activation energy, rather than to increase the preexponential factor, for that group rate constant. Thus

k u n n t r i t i n ~ 4

480 ATKINSON ET AL.

k, = A, exp( - E,/RT)

k, = A: exp[ - (EP - np R T In F,)/RTl

k, = A: exp[ - (E: - n; R T In F,)/RTl

where A,, A:, and A: are the preexponential factors for primary, secondary, and tertiary groups, respectively, and E,, E:, and EP are the Arrhenius activation energies (in cal/mol) for primary, CH,(CH, 12, and CH(CH3I3 groups, respectively. Thus since Fs = F, = 1.27 at 298 K, then each next nearest neighbor reduces the Arrhenius activation energy by 0.140 kcal/mol,

k, = A: exp[ - (E: - 140n,)/RTl

k, = A: exp[ - (EP - 140n;)/RTl

The only available literature data for the >C, alkanes a t other than room temperature are those of Greiner I91 for propane, butane, 'iso- butane, neopentane, cyclohexane, 2,3-dimethylbutane, 2,2,3-tri- methylbutane, 2,2,3,3-tetramethylbutane, n-octane, and 2,2,4-trime- thylpentane, and of Perry et al. [14] for n-butane. Based upon the data of Greiner for neopentane and 2,2,3,3-tetramethylbutane 191, an Arrhenius activation energy for primary groups of E, = 1.635 kcal/mol can be derived [9-111, and hence

cm'/molecuIe . s k, = 2.85 x 10 - 12 e- - 163A:HT

Similarly, based upon the reported temperature dependences for propane [91, n-butane [9,14], and cyclohexane [9], an Arrhenius activation energy for CH,(CH,), groups of E: = 1.05 kcal/mol may be derived, and hence

cm3/molecule . s k, = 3.87 10- 1 2 e-rioso - I ~ O ~ ~ J ; R T

Finally, from the data of Greiner [ 91 for isobutane, 2,3-dimethylbutane, and 2,2,3-trimethylbutane, an essentially zero (though with a significant uncertainty) Arrhenius activation energy for the CH(CH, group may be obtained,

10 12 e (140n,,:.'RT cm:'/molecule . s k, = 1.7

The use of these temperature-dependent group rate constants then allows the estimation of OH radical rate constants for alkanes which do not exhibit steric hindrance and for unstrained cycloalkanes over the temperature range of -295-500 K. However, further experimental data concerning the temperature dependences of these reactions, es- pecially for alkanes containing tertiary >CH- groups, are clearly needed.

OH RADICALS A N D BRANCHED ALKANES 48 1

Acknowledgment

This work was supported by the California Air Resources Board under contract A2-115-32 (Project Monitor, Dr. Jack Suder) and by the U.S. Environmental Protection Agency under cooperative agreement CR-809247-02 (Project Officer, Bruce W. Gay, Jr.).

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Received August 27, 1983 Accepted September 12, 1983