Aqueous-Phase Chemical Equilibria

FIGURE 7.3 Aqueous fraction of a species as a function of the cloud liquid water content and the species Henry s law constant. 

On dissolution in water a number of species dissociate into ions. This dissociation is a reversible reaction that reaches equilibrium rapidly. In Chapter 12 we will discuss the timescale needed to achieve such equilibrium. 

Water itself ionizes to form a hydrogen ion, H+, and a hydroxide ion, OH-  

TABLE 7.4 Thermodynamic Data for Aqueous Equilibrium Constants 

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AQUEOUS -PHASE CHEMICAL EQUILIBRIA 347 and the total dissolved carbon dioxide is given by... 

Gas/Aqueous-Phase Distribution Factor 343 Aqueous-Phase Chemical Equilibria 344... 

Several gases, after dissolving in the aqueous-phase, ionize and establish an aqueous-phase chemical equilibrium system. For example, for S02,... 

Wet deposition encompasses the removal of gases and particles from the atmosphere by precipitation events, through incorporation into rain, snow, cloud, and fog water, followed by precipitation (Hales, 1986). As in the case of dry deposition, wet deposition is a complex phenomenon which in this particular case involves transport to the surface of a droplet, absorption, and possible aqueous-phase chemical conversion. Wet removal of gases is frequently approximated by assuming that the species is in equilibrium between the gas and aqueous phases. The equilibrium partitioning is represented in terms of a washout ratio, Wg = [C]drop/[C]air, where [C]drop and [C]ajr are the concentrations of the chemical in the aqueous and gas phases (Mackay, 1991). 

Figure 12.5 depicts schematically the gas- and aqueous-phase concentrations of A in and around a droplet. The aqueous-phase concentrations have been scaled by HART, to remove the difference in the units of the two concentrations. This scaling implies that the two concentration profiles should meet at the interface if the system satisfies at that point Henry s law. In the ideal case, described by (12.45), the concentration profile after the scaling should be constant for any r. However, in the general case the gas-phase mass transfer resistance results in a drop of the concentration from cA(oo) to cA(Rp) at the air-droplet interface. The interface resistance to mass transfer may also cause deviations from Henry s law equilibrium indicated in Figure 12.5 by a discontinuity. Finally, aqueous-phase transport limitations may result in a profile of the concentration of A in the aqueous phase from [A(/ ,)J at the droplet surface to [A(0)] at the center. All these mass transfer limitations, even if the system can reach a pseudo-steady state, result in reductions of the concentration of A inside the droplet, and slow down the aqueous-phase chemical reactions. 

To ensure a net flux of A from the gas phase to the liquid phase, the bulk liquid-phase concentration of A must not be in equilibrium with the bulk gas-phase partial pressure pAa and cAl < HApAc. (If the reverse is true, then the net flux of A is from the liquid to the gas.) The absence of equilibrium can be a result of aqueous-phase chemical reaction of A or simply the fact that water is undersaturated relative to the atmospheric concentration of the gas. (We do not consider here the enhancement of deposition that arises from chemical reaction in the liquid phase.)... 

DYNAMIC BEHAVIOR OF SOLUTIONS WITH AQUEOUS-PHASE CHEMICAL REACTIONS 387 and dissociation equilibrium is... 

These steps must occur during the production of sulfate or for other aqueous-phase chemical reactions within cloud drops. In Chapter 6 we studied the aqueous-phase kinetics of a number of reactions, corresponding to the last step in the above series of processes. Chapter 6 provided the tools for the calculation of the sulfate production rate at a given point inside a cloud drop, provided that we know the reactant concentrations at this point. For some of the Chapter 6 calculations we assumed that the cloud droplets were saturated with reactants, or equivalently that the concentration of the species inside the droplet is uniform and satisfies at any moment Henry s law equilibrium with the bulk gas phase. In mathematical terms we assumed that the aqueous-phase concentration of a species A at location r, at time /, satisfies... 

The temperature dependency is described by the van t Hoff equation (4.94) where the reaction enthalpy must be replaced by the enthalpy of solution A oiH. The derivation of (4.209) follows from the equality of the chemical potentials in the gas and aqueous phases in equilibrium, q ig) + RTlnPa = q (aq) + i Tln [A] from which [A] = Pa constant follows. In close relation to the Henry s law constant are the Bunsen absorption coefficient a (the volume of gas absorbed by one volume... 

We will later see when discussing the dry deposition (Chapter 4.4.1) that a similar conception is applied to explain the partial conductance the first term on the right side in Eq. (4.302) denotes the resistance of diffusion and the second the interfacial transfer. The steps that follow after interfacial transfer are the (fast) salvation and/or protolysis reactions until reaching the equilibrium, the diffusion within the droplet (until reaching steady-state concentrations or, in other words, a well-mixed droplet) and finally the aqueous phase chemical reactions. Let us first consider a pseudo-first-order reaction ... 

Once a stable particle is formed, it can grow or shrink owing to mass transfer processes between the gas and the particle phase. These processes are governed mainly by the actual particle size, by the ratio of mean free path and particle diameter (Knudsen number), by the molecular diffusion coefficient, and most importantly, by the difference between the gas phase and the particle surface equilibrium vapor pressures of the transferred chemical species. Vapor pressures in the gas phase that are higher than the equilibrium vapor pressure at the particle surface result in a net mass flux toward the particle surface (i.e., the particle gains mass and growth takes place). Gas-phase vapor pressures that are lower than the equilibrium vapor pressure at the particle surface cause a net mass flux directed away from the particle (i.e., the particle loses mass and shrinks). The most important mechanisms that influence the equilibrium vapor pressure at the particle surface are the Kelvin effect, the effect of nonvolatile solute, aqueous-phase chemical reactions, and latent heat release. 

Absorption, Dissociation, and Aqueous-Phase Chemical Reactions The diffusive penetration of gases or gas mixtures into a condensed phase (e g., droplet) is called absorption. In equilibrium, the absorbed gas is dissolved at a certain concentration inside the droplet and the equilibrium vapor pressure over the droplet surface is proportional to the concentration at the droplet surface (Henry s law). The concentration inside the droplet itself can be influenced by dissociation or chemical reactions (sulfur production by oxidation of dissolved SO2 to SOt ). If these processes represent a sink for the solute, the concentration inside the droplet and, consequently, the vapor pressure at the droplet surface is decreased (i.e., mass transfer is enhanced). Typical gases that dissolve into atmospheric water droplets are CO2, SO2, NH3, H2O2, and O3. 

In the present work, the technique of XO and MTB immobilization onto silica gel in the form of its complexes with Fe(III) and Bi(III) respectively were found. The acid - base and chemical-analytical characteristics of solid-phase reagents were examined. The optimal conditions of quantitative recovery of Pb(II) and Zn(II) from diluted solutions, such as acidity of aqueous phase, the mass of the sorbents, the volume of solutions and the time of equilibrium reaching, were found. The methods of and F" detenuination were based on a competitive reactions of Zr(IV) with immobilized MTB and or F". Optimal conditions of 0,0 and F" determination in solution using SG, modified ion associates QAS-MTB (pH = 1,5, = 5-10 mol/1). 

It is known that the order of acidity of hydrogen halides (HX, where X = F, Cl, Br, I) in the gas phase can be successfully predicted by quantum chemical considerations, namely, F < Cl < Br < I. However, in aqueous solution, whereas hydrogen chloride, bromide, and iodide completely dissociate in aqueous solutions, hydrogen fluoride shows a small dissociation constant. This phenomenon is explained by studying free energy changes associated with the chemical equilibrium HX + H2O + HjO in the solu-... 

First, the simple thermodynamic description of pe (or Eh) and pH are both most directly applicable to the liquid aqueous phase. Redox reactions can and do occur in the gas phase, but the rates of such processes are described by chemical kinetics and not by equilibrium concepts of thermodynamics. For example, the acid-base reaction... 

Distribution coefficient (Kd)—Describes the distribution of a chemical between the solid and aqueous phase at thermodynamic equilibrium, is given as follows ... 

The surface is a very minor part of the entire Earth, but being heated from the interior and energised by the Sun s radiation can not only maintain an approximately constant temperature but it can allow activated chemical reactions that create especially energised organic compounds not at equilibrium These processes gave rise to life, apparently starting in the aqueous phase. 

Fig. 4. Plots of initial mineralization rates (IMR) versus equilibrium aqueous phase concentrations for biphenyl-degrading bacteria. Cap B, Sch A, Cap A, and Col A indicate soils used in the study. Letters A and B indicate A and B soil horizon, respectively. Cap, Sch, and Col represent Capac, Schoolcraft, and Colwood soil, respectively. Reprinted with permission from Feng et al. (2000). Copyright (2000) American Chemical Society.

Because the chemical potentials of water distributed in two phases (i.e., solution and vapor) must be equal, the water activity of a food can be measured by bringing the food into equilibrium with the air above it. At equilibrium, under conditions of constant temperature and pressure, the aw values of the aqueous phase of a food (aw l) and of the air (aw v) are equal and can be estimated from the ratio of the partial vapor pressure of water above the food (pv) to the vapor pressure of pure water (p") at the same temperature (Walstra, 2003) ... 

Equilibrium between simple salts and aqueous solutions is often relatively easily demonstrated in the laboratory when the composition of the solid is invariant, such as occurs in the KCI-H2O system. However, when an additional component which coprecipitates is added to the system, the solid composition is no longer invariant. Very long times may be required to reach equilibrium when the reaction path requires shifts in the composition of both the solution and solid. Equilibrium is not established until the solid composition is homogeneous and the chemical potentials of all components between solid and aqueous phases are equivalent. As a result, equilibrium is rarely demonstrated with a solid solution series. 

Stoichiometric saturation defines equilibrium between an aqueous solution and homogeneous multi-component solid of fixed composition (10). At stoichiometric saturation the composition of the solid remains fixed even though the mineral is part of a continuous compositional series. Since, in this case, the composition of the solid is invariant, the solid may be treated as a one-component phase and Equation 6 is the only equilibrium criteria applicable. Equations 1 and 2 no longer apply at stoichiometric saturation because, owing to kinetic restrictions, the solid and saturated solution compositions are not free to change in establishing an equivalence of individual component chemical potentials between solid and aqueous solution. The equilibrium constant, K(x), is defined identically for both equilibrium and stoichiometric saturation. 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

The solubility of gaseous weak electrolytes in aqueous solutions is encountered in many chemical and petrochemical processes. In comparison to vapory-liquid equilibria in non reacting systems the solubility of gaseous weak electrolytes like ammonia, carbondioxide, hydrogen sulfide and sulfur dioxide in water results not only from physical (vapor-liquid) equilibrium but also from chemical equilibrium in the liquid phase. 

The reaction order of one is also in good accordance with the film theory, where the rate of mass transport linearly correlates with the equilibrium concentration of citral in the aqueous phase. As a matter of fact, the mass transport rate is of first order regarding the substrate concentration in the organic phase. Therefore, what is measured is in fact the rate of mass transport and not the rate of chemical reaction. This result is in our opinion a good example of how kinetic parameters could be falsified when the reaction is limited by mass transport and not kinetics. 

All chemicals used were of very high purity grade (>99 %). The quaternary systems were mixed and allowed to reach equilibrium over a week at constant temperature, with occasional stirring. The oil phase (top phase) was placed in the measuring cell of the pendant drop apparatus. The bottom (aqueous) phase was filled in the syringe for the measurement. 

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