surface reaction rate, ax is the activity of the solution-phase reactant, and ps is a probability parameter between 0 and 1. Another approach is described by Hanson (1997, 1998).

Similarly, there is some experimental evidence for surface reactions of organics. For example, Schweitzer et al. (1998) report evidence for a surface reaction (probably protonation) of glyoxal, (CHO)2, on acid surfaces at temperatures below 273 K.

Although this area of reactions at interfaces is relatively new and not well understood, it may potentially be more significant than previously recognized. Because of the unique characteristics of such processes both kinetically and mechanistically compared to bulk aqueous-phase or gas-phase reactions, we suggest the term "fourth phase" be used to describe this chemistry at gas-liquid interfaces in the atmosphere.

In short, when treating the uptake of gases into particles, clouds, and fogs in the atmosphere and their reactions either at the interface or in the bulk, one must take into account all of the processes depicted in Fig. 5.12. While exact solutions for the series of coupled differential equations describing the individual steps are not always possible, approximate solutions have been derived for most situations of atmospheric interest in which the various steps can be treated as decoupled processes. In extrapolating values for the various steps derived from laboratory studies to particles in the atmosphere, one must take into account differences in conditions, including particle size. Summing up, if the fundamental parameters such as the

Henry's law constants, diffusion coefficients, and rate constants are known, extrapolation to the atmosphere can be carried out reliably and reasonably accurately.

We now turn to a brief description of typical laboratory techniques used to determine kinetic parameters that characterize heterogeneous reactions in the atmosphere.

2. Knudsen Cells

Much of the data on heterogeneous reactions in the atmosphere, particularly the earliest work, were generated using Knudsen cells (Golden et al., 1973; Caloz et al., 1997; Fenter et al., 1997). Figure 5.21 is a schematic diagram of a Knudsen cell. Gases flow into the cell, which has an orifice of known size connected to a low-pressure system. Gases exiting the Knudsen cell through this orifice are detected and measured, usually by mass spectrometry. When the gas is exposed to a surface that takes up the gas, the concentration of the gas in the cell and hence the amount exiting the orifice decrease. From the change, the net uptake of the gas by the surface can be determined in the following manner.

Let the flow of molecules into the Knudsen cell be F (molecules s-1). In the absence of the reactive surface, these molecules are removed when they strike the escape aperture into the mass spectrometer. Let kcx be the effective first-order rate constant (s-1) for escape of the gas from the cell through this orifice, which can be measured experimentally. Alternatively, kcsc can be calculated from kinetic molecular theory since the number of collisions per second, js, of a gas on a

Where The Mass Spec Orifice

Mass Spectrometer

FIGURE 5.21 Schematic of a Knudsen cell.

Mass Spectrometer

FIGURE 5.21 Schematic of a Knudsen cell.

surface of area As, or equivalently, /h a hole of surface area Ah, is given by i.e.,

Here um is the average speed of the molecules of molecular weight M at temperature T and is given by Mav = (8kT/irM)l/2, where k = 1.381 X 10"23 J K"1, N is the number of molecules in the cell, and V is the cell volume.

Under steady-state conditions, the flow into the cell is balanced by escape from the orifice, and the number of gas molecules in the cell in the absence of the reactive surface, Na, remains constant, i.e., dN{)

When the gas is exposed to the reactive surface, some of the gas-phase molecules are removed with an effective first-order rate constant kr, thus reducing the number of molecules in the cell to Nr. A new steady-state is established such that dNr

Combining these two equations and rearranging, one obtains k r — k

The first-order rate constant kr (s-1) for the heterogeneous reaction is related to the rate of gas-surface collisions, /s, and the fraction of those collisions that lead to uptake, yncl, since krNr = ync,/s. Since /s is also equal to As(Nr/VXu.dV/4), then y„c,'s = ynctAs(Nr/V)(u3V/4) = krNr, i.e., kT = 4). (YYY)

Combining Eqs. (VVV), (XXX), and (YYY), the net uptake probability is given by

Since the ratio of the number of gas molecules in the cell in the presence and absence of the reactive surface

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