Info

"The parameters B and C give the temperature dependence in the form k = BT"e where C = E.A/R. From Atkinson (1997a).

h The parameters D and F = E.d/R are for the temperature dependence in the form recommended by Donahue et al. (1998a): k(T) = De-F/r/[T( 1 - e-lMv'/r)2{\ - e~ lMv^r)], where two bends at r, = 300 cm"1 and one bend at r2 = 500 cm"1 are treated explicitly.

' Kramp and Paulson (1998).

temperature dependence consistent with a simplified form of transition state theory:

where u{ is the degenerate C-H-O bend frequency (cm-1) and v2 is the H-O-H bend frequency (cm-1). Table 6.2 also shows the parameters D and F = Ed/R for this form of the temperature dependence using l'i = 300 cm-1 and u2 = 500 cm-1.

The first thing that stands out in Table 6.2 is that the OH-CH4 rate constant, 6.2 X 10"15 cm3 molecule-1 s-1, is much smaller than those for the higher alkanes, a factor of 40 below that for ethane. This relatively slow reaction between OH and CH4 is the reason that the focus is on "non-methane hydrocarbons" (NMHC) in terms of ozone control in urban areas. Thus, even at a typical peak OH concentration of 5 X 106 molecules cm-3, the calculated lifetime of CH4 at 298 K is 373 days, far too long to play a significant role on urban and even regional scales. Clearly, however, this reaction is important in the global troposphere (see Chapter 14.B.2b).

Second, the room temperature rate constants increase with increasing size and complexity of the alkane and are of the order of 10"11 cm3 molecule-1 s"1 for the largest alkanes. To put this in perspective, a diffusion-controlled reaction, i.e., one that occurs on every collision of the reactants, is of the order of ~ (3-5) X fO"10 cm3 molecule-1 s"1. Thus for the larger alkanes, reaction occurs in approximately one in 10 collisions, which is quite a fast process.

As discussed in Chapter 5, kinetic theories predict that the preexponential factor should have a temperature dependence that manifests itself in curved Arrhe-nius plots if the reactions are studied over a sufficiently broad temperature range. This is the case for OH-al-kane reactions, where there has been great interest in the high-temperature kinetics for combustion systems. Table 6.2 also shows the temperature dependence for the OH reactions in the form k = BT"e~c/1, where C = E.JR and in the form recommended by Donahue et al. (f 998a).

The C-H bond strength is largest for primary C-H bonds at ~ 101 kcal mol"1, decreasing to ~98 kcal mol"1 for secondary and ~96 kcal mol-1 for tertiary C-H bonds (Lide, 1998-1999). Hence one expects that, all else being equal, a tertiary C-H will react faster than a secondary C-H, which in turn will react faster than a primary C-H. Greiner (1970), whose measurements of the absolute rate constants for OH reactions in the mid-1960s provided the first clue of the potential importance of OH in the troposphere, suggested that the rate constant for the overall reaction, could be treated as the sum of contributions from each type of abstractable hydrogen in the following manner:

k , ks, and k{ represent rate constants for the abstraction of primary, secondary, and tertiary hydrogens, respectively, and N , Ns, and Nt are the corresponding numbers of each kind of hydrogen. If the rate constants (&"") for a number of simple alkanes are known, the experimental data can be fit to obtain best values for kp, ks, and kt. These can then be used to predict the rate constant for the reaction of OH with an alkane where experimental measurements have not been made.

This type of structure-reactivity relationship (SRR) works reasonably well for the simple alkanes. However, clearly one would expect that the nature of adjacent groups would also have an effect on the rate constant, albeit a smaller one than the type of C-H bond. A variant of the approach in Eq. (A) is to use rate constants per primary, secondary, or tertiary group modified by factors reflecting the adjacent groups. In this case,

£'p(CH3X) = k*F(X), £'S(CH2XY) = k*F(X)F( Y), &;(CHXYZ) = k*F(X)F(Y)F(Z), where k*, k*, and k* are the rate constants for the CH3- group, the -CH2- group, and the >CH- group, respectively, and the F factors reflect how the rate constants for the individual groups are modified by adjacent groups, X, Y, and Z. Recommended values (Kwok and Atkinson, 1995; Atkinson, 1997a) of these group rate constants are k* = 1.36 X 10"13, k* = 9.34 X 10"l3, and k* = 1.94 X 10"12 cm3 molecule"1 s"1 at 298 K. The modifying F parameters at 298 K are taken as 1.00 for X = CH3 and f .23 for all of the other simple alkyl groups, -CH2-, >CH-, and >C< . Other correction factors must be included for cyclic compounds (Atkinson, 1997a).

For example, the rate constant for the reaction of OH with 2-methylbutane,

0 0

Post a comment