Aqueous-Phase Reaction Rates

Rates of reaction of aqueous-phase species are generally expressed in terms of moles per liter (M) of solution per second. It is often useful to express aqueous-phase reaction rates on the basis of the gas-phase properties, especially when comparing gas-phase and aqueous-phase reaction rates. In this way both rates are expressed on the same basis. 

To place our discussion on a concrete basis, let us say we have a reaction of S(IV) with a 

The moles per liter of air can be then converted to equivalent S02 partial pressure for 1 atmosphere total pressure by applying the ideal-gas law to obtain 

FIGURE 7.14 Nomogram relating aqueous reaction rates, in pMs to equivalent gas-phase reaction rates in ppbh-1, at T = 288 K, p — 1 atm, and given liquid water content. 

Reaction rates are sometimes also expressed as a fractional conversion rate in %h l. The rate R given above can be converted to a fractional conversion rate by dividing by the mixing ratio, E,s02, of S02 in ppb and multiplying by 100 

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FIGURE 7.16 Rate of aqueous-phase oxidation of S(IV) by ozone (30 ppb) and hydrogen peroxide (I ppb), as a function of solution pH at 298 K. Gas-aqueous equilibria aie assumed for all reagents. R/ so. represents the aqueous phase reaction rate per ppb of gas-phase SOj. R/L represents rate of reaction referred to gas-phase SO2 pressure per (gm 3) of cloud liquid water content. 

Given an aqueous-phase reaction rate Ra (Ms 1), show that with a liquid water mixing ratio wL, the comparable gas-phase rate in ppb h 1 is... 

The reactants for aqueous-phase atmospheric reactions are transferred to the interior of cloud droplets from the gas phase by a series of mass transport processes. We would like to compare the rates of mass transport in the gas phase, at the gas-water interface, and in the aqueous phase in an effort to quantify the mass transport effects on the rates of aqueous-phase reactions. If there are no mass transport limitations, the gas and aqueous phases will remain at Henry s law equilibrium at all times. Our objective will be to identify cases where mass transport limits the aqueous-phase reaction rates and then to develop approaches to quantify these effects. 

We now compare the rate of each mass transport step to the aqueous-phase reaction rate. If the mass transport rate exceeds the aqueous-phase reaction rate, then mass transport does not limit the aqueous-phase kinetics. 

Let us return to our reacting system, where a species A diffuses around a droplet of radius Rp and then reacts with an aqueous-phase reaction rate Rliq (M s 1). We assume here that interfacial and aqueous-phase transport are so rapid that we can neglect them. At steady-state, the diffusion rate to the particle will be equal to the reaction rate, or... 

As long as the aqueous-phase reaction rate is less than the value specified by (12.84), the reaction will not be limited by gas-phase diffusion. 

In the criteria (12.85), (12.86), and (12.93), e is the fractional reduction in aqueous-phase reaction rate due to mass transport limitations that triggers our concern. Satisfaction of these inequalities for, say, e = 0.1, indicates that the decrease of the aqueous-phase reaction rate by the corresponding mass transfer process is less than 10%. 

The discussion above indicates that appreciable mass transport limitation is absent under most atmospheric conditions of interest, although instances of substantial limitations under certain conditions of pH, temperature, and reagent concentrations exist. In the latter cases we would like to estimate the aqueous-phase reaction rate taking into account reductions in these rates due to the mass transport limitations. The graphical method presented in the previous sections is a useful method to estimate if there are mass transport limitations present. Our goal in this section is to derive appropriate mathematical expressions to quantify these rates. 

This equation indicates that when the aqueous-phase reaction rate is limited by gas-phase mass transport, at steady-state the aqueous-phase reaction rate is only as fast as the mass transport rate. 

Interfacial Limitation The solution of the steady-state problem for only interfacial limitation is given by (12.91). The aqueous-phase reaction rate is then... 

The aqueous-phase reaction rate between 03 and S(1V) can be calculated using the kinetic expressions given in Chapter 7. 

Carbon Dioxide/Water Equilibrium 345 Sulfur Dioxide 348 Ammonia/Water Equilibrium 353 Nitric Acid/Water Equilibrium 355 Equilibrium of Other Important Atmospheric Gases Aqueous-Phase Reaction Rates 361 S(IV) to S(VI) Transformation and Sulfur Chemistry 363... 

From the measurements of the effective uptake coefficient, the aqueous phase reaction rate constant can be calculated, as long as the gas phase and liquid phase diffusion coefficients and the Henry constant are known. As mentioned, a gas transfer into droplets is characterized by the continuum regime. The unsteady-state diffusion flux (it means that depends on t as well as on x) of species A along the x-axis to the stationary droplet (Fig. 4.20) was described by Seinfeld and Pandis (1998), where c x, t) is the concentration, depending on time and location ... 

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