In this section we discuss the major experimental methods used to determine absolute rate constants for gas-phase reactions relevant to atmospheric chemistry. These include fast-flow systems (FFS), flash photolysis (FP), static reaction systems, and pulse radiolysis. The determination of relative rate constants is discussed in Section C.
In general, we use simple bimolecular reactions of the type
as illustrations. However, the techniques can be modified to study termolecular reactions, as discussed earlier, as well as unimolecular reactions.
To study the reaction kinetics of a relatively reactive species A with a reactant B, one normally follows the loss of small amounts of A in the presence of a great excess of B. This requires then that one be able first to generate A and second to monitor its concentration as a function of time. Ideally, to fully elucidate the reaction mechanism, one would also monitor the concentrations of intermediates and products. As we shall see, in practice, for many reactions this proves to be much more difficult than to simply determine the rate constant itself.
1. Kinetic Analysis
The rate law for a simple bimolecular reaction such as (17) is given by
If a small concentration of A is generated in a great excess of B, then even if (f7) is allowed to go to completion, the concentration of B will remain essentially constant at its initial concentration [B](). Integrating (S) and treating [B]0 as constant, one obtains
That is, A decays exponentially with time determined by (k l7[B]„), as if it were a first-order reaction. Thus under these so-called pseudo-first-order conditions, a plot of ln[A] against time for a given value of [B]() should be linear with a slope equal to ( — &I7[B]0). These plots are carried out for a series of concentrations of [B]0 and the values of the corresponding decays determined. Finally, the absolute rate constant of interest, kxl, is the slope of a plot of the absolute values of these decay rates against the corresponding values of [B]0. Some examples are discussed below.
As we have seen earlier, even third-order reactions can be reduced to pseudo-first-order reactions by keeping the concentrations of all species except A constant and in great excess compared to A. This technique of using pseudo-first-order conditions is by far the most common technique for determining rate constants. Not only does it require monitoring only one species, A, as a function of time, but even absolute concentrations of A need not be measured. Because the ratio [A]/[A]0 appears in Eq. (T), the measurement of any parameter that is proportional to the concentration of A will suffice in determining kl7, since the proportionality constant between the parameter and [A] cancels out in Eq. (T). For example, if A absorbs light in a convenient spectral region and Beer's law is obeyed, then the absorbance (Abs) of a given concentration of A, N (number cm-3), is given by
where /„ and I are the intensities of the incident and transmitted light, respectively, / is the optical path length, and a is the absorption cross section of A (to the base e)
Substituting into Eq. (T) for [A] = N = Abs /a I, one obtains
where (Abs) and (Abs)0 are the absorbance of the light by A at times t and t = 0, respectively. For example, 03 has a strong absorption at 254 nm, which can be used to monitor its concentration.
This ability to monitor a parameter that is proportional to concentration, rather than the absolute concentration itself, affords a substantial experimental advantage in most kinetic studies, since determining absolute concentrations of atoms and free radicals is often difficult.
This pseudo-first-order kinetic analysis is generally applied regardless of the experimental system used.
Fast-flow systems (FFS) consist of a flow tube typically 2- to 5-cm in diameter in which the reactants A and B are mixed in the presence of a large amount of an inert "bath gas" such as He or Ar. As the mixture travels down the flow tube at relatively high linear flow speeds (typically 1000 cm s~'), A and B react. The decay of A along the length of the flow tube, that is, with time, is followed and Eq. (T) applied to obtain the rate constant of interest.
The term fast flow comes from the high flow speeds. In most of these systems, discharges are used to generate A or another species that is a precursor to A; hence the term fast-flow discharge system (FFDS) is also commonly applied. Since fast-flow discharge systems have been applied in many kinetic and mechanistic studies relevant to tropospheric chemistry (e.g., see Howard, 1979; Kaufman, 1984), we concentrate on them. However, all fast-flow systems rely on the same experimental and theoretical principles.
Figure 5.4 is a schematic diagram of a typical fast-flow discharge system. The reactive species is generated in a microwave discharge and enters at the upstream
end of the flow tube, and the second reactant is added through one port, C or D, of a movable inlet. The detector is fixed at the downstream end of the flow tube and the reaction time is varied by moving the mixing point for C and D (i.e., the movable inlet) relative to the fixed detector.
For example, OH can be generated by the reaction of H with NO,:
Atomic hydrogen is formed by discharging dilute H2/He mixtures. Then these H atoms are converted to OH by the addition of excess N02, e.g., through port C. By adjusting the concentration of N02 appropriately, essentially all of the H can be converted to OH before the second reactant is added through port D.
Table 5.3 shows some typical sources of reactive species of atmospheric interest used in FFDS, while Table 5.4 shows some of the methods used to detect them.
Under conditions where the plug flow assumption is valid, that is, concentration gradients are negligible so that the linear flow velocity of the carrier gas is the same as that of the reactants, the time (t) for A and B to travel a distance d along the flow tube is given by d t = -.
Here v is the linear flow speed, which can be calculated from the cross-sectional area of the flow tube (ar), the total pressure (p) in the flow tube, the temperature (T), and the molar flow rates idn / dt) of the reactants and the diluent gas:
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