X 0_6[l+(l«g[(1.4x 1«"12)/(1.5X lO"12)])2]"1

This is almost a factor of two smaller than at 300 K and 760 Torr pressure.

In summary, rate constants for addition reactions in the atmosphere can be estimated as a function of temperature and pressure if values are available for the low- and high-pressure limiting rate constants as a function of temperature, that is, if /c(30", &300, n, m, and Fc are known.

At first glance, it might appear that the vast majority of the bimolecular reactions with which one deals in the troposphere are simple concerted reactions, that is, during the collision of the reactants there is a reorganization of the atoms, leading directly to the formation of the products. However, it has become increasingly apparent in recent years that some important reactions that appeared to be concerted exhibit characteristics such as pressure dependencies that are not consistent with a direct concerted process.

A classic case is the reaction of OH with CO:

This reaction appears to be an elementary bimolecular reaction involving a simple transfer of an oxygen atom from OH to CO. In accord with the definition of an elementary reaction, one can imagine that it occurs during one collision of an OH radical with a CO molecule.

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 k~ 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.

However, a variety of studies since the mid-1970s has established that it is not, in fact, a simple bimolecular reaction as implied by reaction (14) but rather involves the formation of an excited HOCO* intermediate (e.g., see Fulle et al., 1996; Golden et al., 1998; and references therein):

In (15), HOCO is the radical adduct of OH + CO, and HOCO* is the adduct containing excess internal energy resulting from the energy released by bond formation between OH and CO. As described earlier, M is any molecule or atom that collides with the HOCO*, removing some of its excess energy; in practice, it is usually an inert bath gas such as He or Ar that is present in great excess over the reactants.

Reactions such as (15), which proceed with the formation of a bound adduct between the reactants, are known as indirect or nonconcerted reactions. The

FIGURE 5.3 Typical potential energy diagram proposed for reaction of OH with CO (adapted from Mozurkewich et al., 1984). Note the well corresponding to formation of the (HOCO) intermediate.

adduct is "stable" in the sense that it corresponds to a well on the potential energy surface connecting the reactants and products (Fig. 5.3); as such it has a finite lifetime and should be capable of being detected using appropriate techniques. Because of the complex nature of the mechanism, such reactions can exhibit a relatively complex temperature dependence. In addition, if the rate of collisional stabilization of the excited adduct is comparable to its rate of decomposition, a pressure dependence may result, as in the OH + CO reaction. The distinction between bimolecular and termolecular reactions blurs in such cases. In any event, the OH + CO rate constant at 1 atm in air is now thought to be ~2.4 X 10"13 cm3 molecule-1 s~', significantly greater than the low-pressure value, 1.5 X 10"13 cm3 molecule s-1, that had been widely accepted at one time.

3. Temperature Dependence of Rate Constants a. Arrhenius Expression

The temperature dependence of many rate constants can be fit over a relatively narrow temperature range by the exponential Arrhenius equation k=Ae-';"/RT, (F)

where R is the gas constant and the temperature T is in kelvin (K = °C + 273.15). A, the preexponential factor, and E.d, the activation energy, are parameters characteristic of the particular reaction.

To a first approximation over the relatively small temperature range encountered in the troposphere, A is found to be independent of temperature for many reactions, so that a plot of In k versus T~x gives a straight line of slope — £a/R and intercept equal to In A. However, the Arrhenius expression for the temperature dependence of the rate constant is empirically based. As the temperature range over which experiments could be carried out was extended, nonlinear Arrhenius plots of In k against T~1 were observed for some reactions. This is not unexpected when the predictions of the two major kinetic theories in common use today, collision theory and transition state theory, are considered. A brief summary of the essential elements of these is found in the following sections, as we refer to them periodically throughout the text.

For many reactions, the temperature dependence of A is small (e.g., varies with Ti/2) compared to the exponential term so that Eq. (F) is a good approximation, at least over a limited temperature range. For some reactions encountered in tropospheric chemistry, however, this is not the case. For example, for reactions in which the activation energy is small or zero, the temperature dependence of A can become significant. As a result, the Arrhenius expression (F) is not appropriate to describe the temperature dependence, and the form k = BT"e-':'/Rr (G)

is frequently used, where B is a temperature-independent constant characteristic of the reaction and n is a number adjusted to provide a best fit to the data.

While most reactions with which we deal in atmospheric chemistry increase in rate as the temperature increases, there are several notable exceptions. The first is the case of termolecular reactions, which generally slow down as the temperature increases. This can be rationalized qualitatively on the basis that the lifetime of the excited bimolecular complex formed by two of the reactants with respect to decomposition back to reactants decreases as the temperature increases, so that the probability of the excited complex being stabilized by a collision with a third body falls with increasing temperature.

An alternate explanation can be seen by treating termolecular reactions as the sum of bimolecular reactions, as was illustrated in Section A.2 for the OH + S02 + M reaction. Recall that the third-order, low-pressure rate constant km can be expressed as the product of the three rate constants k.d, kh, and kK for the three individual reaction steps (12), ( — 12), and (13):

Expressing each of the component rate constants in the Arrhenius form, A:"1 becomes

Thus the activation energy for the reaction, Ew, is a combination of the activation energies for the individual steps, (£a + Ec - Eh). If Eh > (E.d + Ec), that is, if

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