## Laboratory Techniques For Determining Relative Rate Constants For Gasphase Reactions

Many of the rate constants for gas-phase reactions of atmospheric interest reported in the literature were actually determined not as absolute values but rather as a ratio of rate constants. Thus if the absolute value for one of the rate constants has been determined independently, the second one can then be calculated from the experimentally determined ratio.

In the simplest case, determining relative rate constants for a reactive species A is based on a competition between two reactions:

X, and X2 are the reactants that compete for A, and P, and P2 are the respective products of these reactions. By monitoring the concentrations of the reactants X, and X2, the concentrations of the products P, and P2, or the change in the concentration of one of these as the second reactant is added with time, one can obtain the rate constant ratio kl/k2.

For example, if X, and X2 are monitored, the relevant rate laws are as follows:

Rearranging one obtains

Combining (CC) and (DD) to eliminate [A] yields Eq. (EE):

kx dt k2 dt

Integrating from time t = 0 when the initial concentrations are [X,],, and [X2]0, respectively, to time t when the concentrations are [X,], and [X2], gives Eq. (FF)

Thus the concentrations of X, and X2 as a function of reaction time, plotted as given by Eq. (FF) (i.e., InflXJo/tX,],) versus ln([X2]„/[X2]()), can be used to derive the rate constant ratio ki/k2. If an absolute value is known for one of the two rate constants from independent studies, then an absolute value for the second one can be obtained.

For example, Figure 5.11 shows typical results from a relative rate experiment on the reaction of chlorine atoms with some simple alkanes (Beichert et al., 1995). The chlorine atoms in this case were produced by the

FIGURE 5.11 Plots of the relative decays of pairs of organics (Eq. (FF)) in the presence of chlorine atoms at room temperature (adapted from Beichert et al., 1995).

FIGURE 5.11 Plots of the relative decays of pairs of organics (Eq. (FF)) in the presence of chlorine atoms at room temperature (adapted from Beichert et al., 1995).

blacklamp photolysis of Cl2. The reaction vessel was a 50-L Teflon collapsible chamber into which Cl2 and the alkanes were introduced as a dilute mixture in air. The mixture was sampled periodically into a gas-sampling valve interfaced to a gas chromatograph so that the concentrations of the alkanes were measured as a function of photolysis time.

The most common sources of OH used for relative rate studies include the photolysis of HONO (e.g., see Cox, 1975) or alternatively methyl nitrite (CH3ONO) in air in the presence of NO (Atkinson et al., 1981):

CH3ONO + hv CH30 + NO, (22) CH30 + 02 -» HCHO + H02, (23) HOz + NO -> OH + NOz. (24)

Determination of OH relative rate constants for compounds that photolyze significantly in actinic radiation requires a nonphotolytic source of OH. Three such OH sources are H202-N02-C0 mixtures (Campbell et al., 1975, 1979; Audley et al., 1982), the thermal decomposition of H02N02 in the presence of NO (Barnes et al., 1982), and 03-hydrazine reactions (Tuazon et al., 1983) or 03-alkane reactions in the dark (Finlayson-Pitts et al., 1993). However, in these cases, the reactant must not react with 03, HOz, or H202, and care must be taken in interpreting the data since these systems have the potential of being rather complex. Indeed, the rate constants derived have not always agreed well with literature values. Until the general features of the mechanisms involved in the production of OH in these systems have been fully elucidated, the simultaneous production of other highly reactive species, and hence possible interfering secondary reactions, cannot be firmly ruled out.

Relative rate techniques have the advantage that such relative measurements can be made with greater precision than absolute rate constant measurements because only relative, not absolute, concentrations of X, and X2 need be measured. Indeed, precisions of 5% or better are common using these techniques. Note, however, that increased precision does not necessarily imply increased accuracy.

Another advantage is that the species A, which is frequently a highly reactive free radical such as OH which is difficult to measure, need not be monitored in such experiments; only X, and X2, which are usually stable and easily measured molecules, such as hydrocarbons, are followed. Finally, relative rate experiments can often be carried out under conditions directly relevant to the atmosphere, e.g., low concentrations of the reactants in high pressures of air.

The accuracy of the results, however, depends critically on knowing enough of the mechanistic details of the reaction system to be sure that the kinetic analysis, which is not always straightforward in complex systems, is valid. Furthermore, obtaining an accurate rate constant from the rate constant ratio (k]/k2) requires accurate knowledge of the second, reference rate constant.