Temperature, rate constant

Fig. 1. Examples of temperature dependence of the rate constant for the reactions in which the low-temperature rate-constant limit has been observed 1. hydrogen transfer in the excited singlet state of the molecule represented by (6.16) 2. molecular reorientation in methane crystal 3. internal rotation of CHj group in radical (6.25) 4. inversion of radical (6.40) 5. hydrogen transfer in halved molecule (6.16) 6. isomerization of molecule (6.17) in excited triplet state 7. tautomerization in the ground state of 7-azoindole dimer (6.1) 8. polymerization of formaldehyde in reaction (6.44) 9. limiting stage (6.45) of (a) chain hydrobromination, (b) chlorination and (c) bromination of ethylene 10. isomerization of radical (6.18) 11. abstraction of H atom by methyl radical from methanol matrix [reaction (6.19)] 12. radical pair isomerization in dimethylglyoxime crystals [Toriyama et al. 1977].

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

Note that only Er, which is actually the sum of the reorganization energies for all degrees of freedom, enters into the high-temperature rate constant formula (2.62). At low temperature, however, in order to preserve E, one has to fit an additional parameter co, which has no direct physical sense for a real multiphonon problem. 

Carrying out the LFER with values of log k or AG, rather than with A//, is advantageous because they are known very accurately at a given temperature. The values of AG typically have a precision of 0.1-0.2 kJ mol-1. These quantities are temperature-dependent, however, and the ordering of the high-temperature rate constants can even invert at low temperature. To avoid this, the quantity chosen for cor-... 

Edney, E.O., Kleindienst, T.E., Corse, E.W. (1986) Room temperature rate constants for the reaction of OH with selected chlorinated and oxygenated hydrocarbons. Int J. Chem. Kinet. 18, 1355-1371. 

We now turn to the addition of hydrogen to 3Fe(CO)3. This is hypothesized to be the process that leads to the short-lived species formed in sc Ar upon photolysis of iron pentacarbonyl in the presence of H2 (24). It is however possible that Fe(CO)3 is present instead in the form of the weakly bound 3Fe(CO)3(Ar) species under these conditions. However, the reaction has also been studied in the gas phase, where a room-temperature rate constant of 2.7 x 10 11cm3molecule 1s 1 was reported (49,55), again corresponding to a very large, near collision-limit value. 

The oxidative solvolysis steps (Eq. 31/30) have previously been demonstrated to occur, and the room temperature rate constant given (kj = 3.5 x lO s" ) is in good agreement with that measured on producing the -chloroalkyl radical by the addition route (Eq. 29). 

When an aqueous solution containing 1,4-dichlorobenzene (190 pM) and a nonionic surfactant micelle (Brij 58, a polyoxyethylene cetyl ether) was illuminated by a photoreactor equipped with 253.7-nm monochromatic UV lamps, photoisomerization took place, yielding 1,2- and 1,3-dichlorobenzene as the principal products. The half-life for this reaction, based on the first-order photodecomposition rate of 1.34 x 10 /sec, is 8.6 min (Chu and Jafvert, 1994). A room temperature rate constant of 3.2 x lO cmVmolecule-sec was reported for the vapor-phase reaction of 1,4-dichlorobenzene with OH radicals (Atkinson, 1985). 

Photolytic. A rate constant of 3.7 x 10 L/molecule-sec was reported for the reaction of propylbenzene with OH radicals in the gas phase (Darnall et al, 1976). Similarly, a room temperature rate constant of 5.7 x lO cm /molecule-sec was reported for the vapor-phase reaction of propylbenzene with OH radicals (Atkinson, 1985). At 25 °C, a rate constant of 6.58 x 10 cmVmolecule-sec was reported for the same reaction (Ohta and Ohyama, 1985). 

Photolytic. Glyoxal, methylglyoxal, and biacetyl were produced from the photooxidation of 1,2,3-trimethylbenzene by OH radicals in air at 25 °C (Tuazon et al., 1986a). The rate constant for the reaction of 1,2,3-trimethylbenzene and OH radicals at room temperature was 1.53 x 10 " cmVmolecule-sec (Hansen et al., 1975). A rate constant of 1.49 x 10 L/molecule-sec was reported for the reaction of 1,2,3-trimethylbenzene with OH radicals in the gas phase (Darnall et al., 1976). Similarly, a room temperature rate constant of 3.16 x 10 " cm /molecule-sec was reported for the vapor-phase reaction of 1,2,3-trimethylbenzene with OH radicals (Atkinson, 1985). At 25 °C, a rate constant of 2.69 x lO " cm /molecule-sec was reported for the same reaction (Ohta and Ohyama, 1985). 2,3-Butanedione was the only products identified from the OH radical-initiated reaction of 1,2,4-trimethylbenzene in the presence of nitrogen dioxide. The amount of 2,3-butanedione formed decreased with increased concentration of nitrogen dioxide (Bethel et al., 2000). 

Mayer, S. W., Schieler, L., and Johnston, H. S., Computation of high-temperature rate constants for bimolecular reactions of combustion products, in 11th Symposium (Inti) on Combustion." The Combustion Institute, Pittsburgh, 1967, p, 837. 

A number of studies of the kinetics of this reaction were carried out in the 1960s and the early 1970s, and the room temperature rate constants, measured at total pressures up to 200 Torr in inert gases such as He, Ar, and N2, were generally in good agreement with kl4 1.5 X 10 13 cm3 molecule 1 s 1 at room temperature. In fact, this reaction was often used to test whether a newly constructed kinetic apparatus was functioning properly. 

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 10 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. 

The room temperature rate constants for the reactions of 03 with some alkenes are given in Table 6.9. While the values are many orders of magnitude smaller than those for the corresponding OH reactions, the fact that tropospheric ozone concentrations are so much larger makes these reactions a significant removal process for the alkenes. 

TABLE 6.13 Room Temperature Rate Constants and Temperature Dependence11 for the Gas-Phase Reactions of the NOs Radical with Some Alkenesb... 

Table 6.16 shows the room temperature rate constants for the reactions of OH with some simple aromatics as well as the branching ratio for abstraction, i.e., the ratio kM/(kbi + kb2). Abstraction accounts for less than about 10% of the reaction at room temperature for those alkylbenzenes studied to date. It is noteworthy that the reactions are all quite fast, even that for benzene being within approximately two orders of magnitude of diffusion controlled. 

As seen in Table 6.1, the reactions of the nitrate radical with the simple aromatic hydrocarbons are generally too slow to be important in the tropospheric decay of the organic. However, one of the products of the aromatic reactions, the cresols, reacts quite rapidly with NO,. o-Cresol, for example, reacts with N03 with a room temperature rate constant of 1.4 X 10 " cm3 molecule-1 s-1, giving a lifetime for the cresol of only 1 min at 50 ppt N03. This rapid reaction is effectively an overall hydrogen abstraction from the pheno-... 

GAS-PHASE REACTIONS IN IRRADIATED ORGANIC-NO,-AIR MIXTURES TABLE 6.19 Room Temperature Rate Constants (cm3 molecule 1 s — 1) for the Reactions of Some Oxygen-Containing Organics" ... 

Thus, it is the carboxylic hydrogen that is ultimately abstracted by this channel. This is consistent with the decrease in the room temperature rate constant upon deuterium substitution from 5.2 X 10 11 to 4.9 X 10 11 to 1.4 X 10 cm3 molecule-1 s for OH + CH3COOH vs OH + CD3COOH vs OH +... 

TABLE 6.22 Room Temperature Rate Constants for the Reactions of OH with Some Simple Alkyl Nitrates at 298 K ... 

Reaction with OH is, however, reasonably rapid as might be expected and is of the same order of magnitude as the OH-alkane reactions. Table 6.22, for example, shows the room temperature rate constants for the reactions of OH at 298 K with some alkyl nitrates. With 2-butyl nitrate as an example, the lifetime with... 

The room temperature rate constant is 1.6x10"13 cm3 molecule"1 s"1 (DeMore et al., 1997 Atkinson et al., 1997a, 1997b), giving an estimated lifetime for NH3 of 72 days with respect to reaction with OH at a typical average daytime concentration of 1 X 106 radicals cm"3. 

TABLE 10.35 Room Temperature Rate Constants, k, for the Gas-Phase Reactions of Selected PAHs and Nitro-PAHs with the... 

While the F02 reactions with NO and NOz are moderately fast, with room temperature rate constants of the order of 10 12 and 10 13 cm3 molecule-1 s-1, respectively (Sehested et al., 1994 Li et al., 1995b), the concentrations of NO and NOz are sufficiently small that they do not represent major atmospheric loss processes for F02. It is interesting, however, that the F02 + NO reaction proceeds by transfer of the F atom to form FNO (which photolyzes) rather than by transfer of an oxygen atom, which is more common for... 

CH, Br reacts with OH with a room temperature rate constant of 2.9 X 10 14 cm3 molecule 1 s. ... 

With an overall room temperature rate constant of k3 = 1.3 X 10-11 cm3 molecule-1 s-1 (Wallington and Nielsen, 1991), the lifetime of CF3CHFOO is only about half a minute at 0.1 ppb NO. At very small concentrations of NO, reaction with HOz (or other ROz) can occur, e.g.,... 

Although an appreciable amount of termination is found at elevated temperatures, rate constants can be calculated from the initial slope of the first-order time-conversion curve. The concentration of living ends is calculated from the linear plot of the number-average degree of polymerization vs. conversion.which still remains linear when termination occurs, since the total number of chains remains unaltered., provided nor intermolecular termination (grafting) nor transfer occurs. 

Figure 5. Low-temperature rate constants for capture by ions of HC1 (o), HCN (x) and CS ( ) [SACM calculations from Ref. 15 dashed curve Eqs. (32H34)].

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