Ionic Strength Vs Rate Constant

Products, the rate of the reaction is given by k [X *], where [X *] is the concentration of the activated complex in the transition state. The concentration of the activated complexes can be obtained from the equilibrium assumed between the reactants and the transition state:

Thus

Rate = kpK

= *[A][B], where the reaction rate constant is given by

TaTB 7x#

Using the Debye-Hiickel limiting law for the relationship between the activity coefficients y and the ionic strength of the solution, one finds log k = log k{) + log yA + log yu - log yx * , = log + 2BZaZu/'/2.

With B = 0.51 Ll/2 mol~l/2 for aqueous solutions at 25°C, this becomes log k = log Jt0 + 1.02ZaZu/'/2.

Thus a plot of log k against 7I/2 should give straight lines of slope f.02ZAZU and intercepts of log k{). The constant k() is seen to be the rate constant in a solution of zero ionic strength, that is, at infinite dilution. Equation (NN) also predicts that reactions between ions of the same sign should speed up as the ionic strength increases, whereas reactions between oppositely charged ions should slow down with increasing ionic strength. For reactions between an ion and an uncharged molecule (Zu = 0), ionic strength should not alter the rate constant. These relationships have been confirmed for solutions that are sufficiently dilute so that the Debye-Hiickel law is applicable (Fig. 5.14). As might be expected, deviations are observed at higher ionic strengths (e.g., see the text by Benson, 1960, for a more detailed discussion).

This effect of ionic strength on solution rate constants is very important in studying reactions relevant to atmospheric chemistry. Thus care must be taken to study the effects of ionic strength over a range that FIGURE 5.14 Variation of rate constant with ionic strength (/) of the solution for reactants having different charges. Reactions: (A) [Co(NH3)5Br]2 + + Hg2+ + H20 -> [Co(NH3)5(H20)F++(HgBr) + ; (B)S20^-+ I~-> (intermediates) -> I3 + 2S042- (not balanced); (C) [02NNC00Et]-+ OH-^ N20 + + EtOH; (D) cane sugar + OH--» invert sugar (hydrolysis reaction); (E) H202 + H++ Br~ -> H20 + l/2Br2 (not balanced); (F) [Co(NH3)5Br]2 + +

FIGURE 5.14 Variation of rate constant with ionic strength (/) of the solution for reactants having different charges. Reactions: (A) [Co(NH3)5Br]2 + + Hg2+ + H20 -> [Co(NH3)5(H20)F++(HgBr) + ; (B)S20^-+ I~-> (intermediates) -> I3 + 2S042- (not balanced); (C) [02NNC00Et]-+ OH-^ N20 + + EtOH; (D) cane sugar + OH--» invert sugar (hydrolysis reaction); (E) H202 + H++ Br~ -> H20 + l/2Br2 (not balanced); (F) [Co(NH3)5Br]2 + +

Br"

Fe approximates those found in the atmosphere. Aerosols in polluted urban areas can be highly concentrated solutions with ionic strengths in the range of 8-19 M (Stelson and Seinfeld, 1981); reactions in these solutions will not follow the "ideal" relationships discussed earlier. On the other hand, cloud water and rainwater in clean areas contain much lower solute concentrations; for example, from the ionic composition of precipitation samples in the maritime area of Cape Grim, Australia (Ayers, 1982), the ionic strength can be calculated to be -10"3 M.

4. Experimental Techniques Used for Studying Solution Reactions

The approaches to studying reaction kinetics in the liquid phase are analogous to those in the gas phase, that is, the use of various spectroscopic techniques to follow the loss of one reactant in the presence of a large excess of the second reactant. UV-visible spectroscopy is a primary tool for following both stable species and radicals in solution.

As discussed in Chapters 7, 8, and 9, there are a number of free radical species whose reactions in the aqueous phase drive the chemistry of clouds and fogs. These include OH, H02, N03, halogen radicals such as Cl2, sulfur oxide radicals, and R02. Generation of these radicals in the liquid phase for use in kinetic studies is typically carried out using either flash photolysis or pulse radiolysis.

Flash photolysis can be carried out using either broadband light sources in the 200- to 300-nm range, with pulse durations of the order of microseconds, or lasers with specific wavelengths and pulse durations of nanoseconds to femtoseconds. The advantages of lasers lie in the use of specific wavelengths, which minimizes the simultaneous photolysis of reactants or products at other wavelengths that can occur with broadband light sources, and in the availability of higher light intensities to generate larger radical concentrations. Excimer lasers have proven especially useful: ArF at 193 nm, KrF at 248 nm, XeCl at 308 nm, and XeF at 351 nm.

Pulse radiolysis relies on the interaction of high-energy ionizing radiation to generate free radicals during a short (¡xs to ns) radiation pulse (see Pagsberg et al., 1995). The hydroxyl radical can be easily generated through processes described shortly, and other species by secondary reactions of OH. With water as a solvent, bombardment with ionizing radiation generates electrons (e~), H20+, and excited water molecules, H20*. The electrons either form hydrated electrons, e~ , or ionize additional water molecules. The hydroxyl radical is generated from reactions of H20+ and H20*:

Higher OH yields can be obtained if the solution contains N20:

To generate other free radicals, OH can be reacted with other species (e.g., see Zellner and Herrmann, 1995). For example,

ClOH

In the case of the chlorine reactions, the involvement of H+ in the second step means that these reactions are efficient sources of chlorine atoms only at a pH less than about 4. Br- can be converted to Br atoms in reactions analogous to those for chlorine, but in this case, generation of atomic bromine occurs up to a pH of about f f (Zellner and Herrmann, 1995).

Photodiode array detector

Photodiode array detector FIGURE 5.15 Schematic of typical apparatus used to study kinetics of reaction in the liquid phase (adapted from Zellner and Herrmann, 1995).

The reaction of OH with nitrate ion is endothermic so OH cannot be used to generate NO-, in solution. It is often generated by reactions such as

or the photolysis of eerie ammonium nitrate solutions at 350 nm (e.g., Alfassi et al, f 993):

CeIV(N03)fi" + hv -» N03 + Cem(N03);:~ . (36)

Figure 5.15 is a schematic diagram of a typical apparatus used to study aqueous-phase kinetics (Zellner and Herrmann, 1995). An excimer laser is used to generate the free radical species of interest which is located in a cavity with White cell optics used to obtain long total path lengths (e.g., 60 cm) using a shorter base path (see Chapter ll.A.lc). The time dependence of the concentrations of the free radical reactant can be followed using its absorption of light from a halogen or D2 lamp. In this particular apparatus, a photodiode array detector is used so that a range of wavlengths can be followed, rather than a single wavelength. This allows several different reactants and products to be monitored simultaneously, or if only one absorbing species is present, its absorption spectrum can be obtained.