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FIGURE 5.22 Typical uptake of gaseous HNO, by solid NaCl (monitored at m/e = 46) and increase in the gaseous HCI product (monitored at m/e = 36) (adapted from Beichert and Finlayson-Pitts, 1996).

is needed to calculate ynel, the measurement need not be one of absolute concentrations but rather just relative values. Hence the relative signals measured using mass spectrometry in the presence and absence of the reactive surface are typically used to obtain yncl.

Knudsen cells are operated at low pressures, typically < 10 mTorr, so that the mean free path (L) of the gas molecules is much larger than the diameter of the escape orifice. Since L = l/[2{]-5vd2(N/V)], where d is the molecular diameter of the gas, at fO mTorr N2, L = 0.5 cm, for example.

Figure 5.22 shows the results of a typical Knudsen cell experiment for the uptake of HNO-, by crystalline NaCl powder. The parent peak at m/e = 63 is weak, so the peak at m/e = 46 is followed instead. Both the loss of HN03 and the release of the product HCI into the gas phase can be followed and are seen to occur simultaneously as expected for the reaction

In Knudsen cell studies, as in other techniques, care must be taken to avoid surface "saturation," i.e., complete reaction of the surface so that one is no longer measuring uptake by the original surface. For example, at 10 mTorr there are approximately 10lx collisions per cm2 per second of the gas with the surface. For typical areas of reactive surface that are convenient to use in these systems, the surface will have of the order of fOlft surface sites. Thus if every collision leads to uptake and there is no reevaporation from the surface, it will be completely reacted in only 10 ms!

Another important factor to recognize is that the net uptake coefficient determined using Knudsen cells may not represent the true uptake or trapping of the gas by the surface if reevaporation into the gas phase occurs, which must be taken into account in such cases. In principle, the mass accommodation coefficient is the uptake measured as t —> 0 or, equivalently, as the aqueous-phase concentration of the gaseous species of interest approaches zero.

For some typical examples of the applications of Knudsen cells to atmospheric reactions, see Quinlan et al. (1990), Fenter et al. (1994), Beichert and Finlayson-Pitts (1996), and De Haan and Finlayson-Pitts (1997).

3. Flow Tube Studies

As discussed earlier, flow tubes have been applied for many years to obtaining absolute rate constants for a variety of gas-phase reactions, especially with highly reactive free radical intermediates such as OH and CI. More recently, the same approach has been applied to studying reactions of gases with both solid and liquid surfaces (e.g., McMurry and Stolzenburg, 1987).

The flow tube walls can be coated with the condensed phase of interest, and the gaseous reactant added through a movable injector. As the distance between the injector tip and the detector is increased, the gas is increasingly removed at the walls of the flow tube, and a pseudo-first-order rate constant for removal of the gas, ks, is measured. From Eq. (UUU), the number of collisions per second per unit area is given by (N/V)(um/4), where (N/V) is the concentration of the gas and Mav the mean molecular speed. If the net uptake probability is yncl, the number of gas molecules removed at the surface per second in a flow tube of radius r and length I is ynci(N/V)(uiiV/4X2irrl) and the change in the concentration per second is d(N/V)/dt = ynjN/V)(u.dV/4)(2TTrl)/(Trr2l) = (ynclMav/2r)(iV/V). Thus the first-order rate constant for loss of the gas at the surface is ks = yncl«av/2r; i.e., the net uptake probability yncl is given by

"av where r is the flow tube radius and Mav is the mean thermal speed of the molecules.

ft is often inconvenient and/or experimentally impossible to coat the walls of the flow tube with the condensed phase, e.g., for horizontally mounted flow tubes. In this case, the liquid can be held in a rectangular container on the bottom of the flow tube. While the principle of the experiment is the same, corrections for only a portion of the surface area being reactive must be made. The same approach has been applied to studying the reactions of gases with solids, if the solid sample is in the form of a powder, there are usually multilayers of the crystalline grains in the sample container, which makes determination of the effective surface area available for reaction much more complex. For some typical applications of flow tubes to studying heterogeneous reaction kinetics, see Hanson and Rav-ishankara (1993b), Zhang et al. (1994), and Leu et al. (1995).

4. Falling-Droplet Apparatus

A technique for obtaining the mass accommodation coefficients for the uptake of gases into liquid droplets is the falling-droplet apparatus, which has been applied to a number of atmospherically relevant species (e.g., see Gardner et al., 1987; Worsnop et al., 1989; Nathanson et al., 1996; and Robinson et al., 1998). Figure 5.23 shows a schematic of a typical falling-droplet apparatus. The droplets are generated using a vibrating orifice generator and are ejected into a flow tube at linear flow speeds of about f500-4500 cm s-1. As the stream of droplets flows down the tube, it interacts with the gas of interest, which can be added at various positions along the length of the flow tube. The gas concentration is measured using techniques such as mass spectrometry or tunable diode infared laser spectroscopy at the downstream end of the flow tube after it has interacted with the droplets of known surface area for a known time; alternatively, the droplets can be collected and their composition determined (e.g.,

Helium Water Vapor

Droplet Generation Chamber

Vibrating Orifice

Helium Water Vapor

Droplet Generation Chamber

Vibrating Orifice

Water Helium Vapor

Coolant In

Collection Flask

FIGURE 5.23 Schematic diagram of typical falling-droplet apparatus used for studying heterogeneous atmospheric reactions (adapted from Jayne et al., 1992).

Water Helium Vapor

Coolant In

Collection Flask

FIGURE 5.23 Schematic diagram of typical falling-droplet apparatus used for studying heterogeneous atmospheric reactions (adapted from Jayne et al., 1992).

Ponche et al., 1993). The droplet flow can be turned off and on to measure the change in the gas concentration caused by the droplets, or alternatively, the change in the gas concentration when the droplet surface area is changed can be measured. From the change in the gas concentration, the uptake of the gas by the liquid can then be extracted in the following manner.

If the flow of the carrier gas (e.g., He) is given by F (cm3 s-1) and An is the change in the trace gas concentration due to uptake by the droplets, then the number of gas molecules taken up per second is just FgAn. The number of gas-droplet collisions per second per unit area is given (Eq. PP) as /' = N u.dV/4, where N is the number of gas molecules per unit volume and Mav is the mean molecular (thermal) speed. If Ad is the surface area of one droplet and there are N* droplets to which the gas is exposed, then the total available surface area is (N*Ad), the total number of gas-droplet collisions is J' = (N*Ad)NgudV/4, and the measured mass accommodation coefficient becomes

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