Equilibrium with the Gas Phase

The equilibrium distribution of a volatile solute between gas and liquid phases is described by Henry s law. For the equilibrium A(l) = A(g) in a dilute solution at low gas pressure, 

For some volatile solutes, slow reactions influence the rate of equilibration between the gas and liquid phases. Generally the rate of gas transfer across the liquid-gas interface is the rate-limiting step, as discussed in Section 3.4. But there may also be slow hydration or other reactions in solution that must be allowed for. An important example is the hydration of CO2, whose half-life may be comparable to rates of transfer of CO2 across the air-water interface. 

The kinetics of the hydration and dehydration reactions are slow in comparison with some processes in the water. The reactions are 

Interchange of Solutes between Solid, Liquid and Gas Phases 

Substituting from Table 3.3 for the equilibrium constant for dissociation of H2CO3, which is fast, 

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As discussed in Chapter 6, water forms strong hydrogen bonds and these lead to a number of important features of its atmospheric behavior. All three phases of water exist in the atmosphere, and the condensed phases can exist in equilibrium with the gas phase. The equilibria between these phases is summarized by the phase diagram for water. Fig. 7-9. 

Concentration of ethanol in the compound surface layer in equilibrium with the gas phase First-order reaction constant for the silanization reaction Volumetric flow rate of ethanol from the compound to the gas phase Time... 

The Langmuir adsorption isotherm is easy to derive. Again we assume that the catalyst contains equivalent adsorption sites, and that the adsorbed molecules do not interact. If the adsorbed molecules are in equilibrium with the gas phase, we may write the reaction equation as... 

The results of the unsteady-state reactivity tests and of the catalysts characterization allow us to propose a model for the active layer of VPP under reaction conditions, illustrated in Figure 55.5. In this model, the surface is in dynamic equilibrium with the gas phase, and its nature is a function of both reaction... 

Headspace methods provide an indirect method of sample analysis suitable for the determination of organic volatiles [11,318-323]. The gas diase in contact with the sample and not the sample matrix itself is taken for analysis. If the sample is in thermodynamic equilibrium with the gas phase in a closed thermostated vessel, then this method of analysis is referred to as static headspace. If a carrier gas is passed over the sample and the sample volatiles accumulated in a cryogenic or sorbent trap, then the method is generally referred to as dynamic headspace. If the carrier gas is introduced below the surface of... 

The adsorption capacity of a surface with respect to molecules of a given species is characterized by the total number N of molecules of the particular species retained by unit surface area under the conditions of equilibrium with the gas phase under the given external conditions (i.e., at a given pressure P and temperature T). An expression for N as a function of rf, rr, and 7j+ will be derived in Section II. 

Let us now include an additional component to the Fe-0 system considered above, for instance S, which is of relevance for oxidation of FeS and for hot corrosion of Fe. In the Fe-S-0 system iron sulfides and sulfates must be taken into consideration in addition to the iron oxides and pure iron. The number of components C is now 3 and the Gibbs phase rule reads Ph + F = C + 2 = 5, and we may have a maximum of four condensed phases in equilibrium with the gas phase. A two-dimensional illustration of the heterogeneous phase equilibria between the pure condensed phases and the gas phase thus requires that we remove one degree of... 

In this formula, [H2] is the concentration of hydrogen in the liquid in equilibrium with the gas phase, related by the Henry coefficient. 

The cell potential is simply the work that can be accomplished by the electrons produced in the SOFC, and this potential decreases from the equilibrium value due to losses in the electrodes and the electrolyte. For YSZ electrolytes, the losses are purely ohmic and are equal to the product of the current and the electrolyte resistance. Within the electrodes, the losses are more complex. While there can be an ohmic component, most of the losses are associated with diffusion (both of gas-phase molecules to the TPB and of ions within the electrode) and slow surface kinetics. For example, concentration gradients for either O2 (in the cathode) or H2 (in the anode) can change the concentrations at the electrolyte interface,which in turn establish the cell potential. Similarly, slow surface kinetics could result in the surface at the electrolyte interface not being in equilibrium with the gas phase. 

Using bulk average composition to assess the chemistry of fogs and clouds can be misleading in other respects as well. For example, Pandis and Seinfeld (1991, 1992) show that the bulk mixture formed from drops with different pH values that are each in equilibrium with the gas phase does not itself conform to Henry s law, with the bulk mixture being supersaturated with respect to species such as weak acids and... 

In a similar vein, the time scales to achieve equilibrium for inorganics have been examined by Meng and Seinfeld (1996), who show that small (submicron) particles can come to equilibrium with the gas phase in less than a few hours typically but that larger particles may not. The major factors determining the time needed to reach equilibrium are the aerosol size distribution,... 

K is the overall mass-transfer coefficient based on the liquid phase. A is the total interfacial area in the gas-liquid dispersion. C is the concentration in the liquid phase. C thus corresponds to equilibrium with the gas phase of composition y. H is the Henry coefficient for the gas. In the case of oxygen or a sparingly soluble compound, H is large and resistance to mass transfer is located in the liquid phase. 

In this model, A2 molecules are first adsorbed on the surface non-dissociatively. The A2 molecular precursor might dissociate if there is a free active site adjacent to it, and if it is capable of climbing the dissociation energy barrier due to thermal excitation, or the precursor could be thermally activated to desorb as A2 into the gas phase again. It is still assumed that the dissociation (now from the precursor state and not from the gas phase) is the rate-determining step. If the reaction proceeds to a steady-state, but the over-all gas phase reactants and products are kept out of equilibrium, the precursor state will be in equilibrium with the gas phase reactant, but not with the dissociated state. This model will have a turnover frequency given by ... 

If the oxygen at the interfaces is in equilibrium with the gas phase oxygen, i.e. there is no chemical reaction, and oxygen behaves as an ideal gas, this reduces to,... 

Slopes (mr) of these plots derived from ambient air sampling data are often different from the expected value of -1 (Equation 8) possibly because of kinetic limitations and/or sampling artifacts or thermodynamic factors (Pankow and Bidleman, 1992). Goss and Schwartzenbach (1998) and Simcik et al. (1998) argued that slopes differing from -1 do not necessarily mean that the aerosols are out of equilibrium with the gas phase. In these situations, the intercept (br) partly depends on the slope and cannot be used to estimate 0 (Pankow and Bidleman, 1992). Table 10.2 lists reported values of these parameters. 

If the sorption and dissociation of hydrogen molecules is a rapid process, then the hydrogen atoms on the membrane surface are in equilibrium with the gas phase. The concentration, c, of hydrogen atoms on the metal surface is given by Sievert s law ... 

The interest in this equation is that it affords the calculation of the composition of the condensed phase in equilibrium with the gas phase when the values of the derivative, yA, yB, and yAB can be determined [32]. 

At point a, die solid metal is in equilibrium with the gas phase consisting of the vapour... 

Multiphase reactors include, for instance, gas-liquid-solid and gas-liq-uid-liquid reactions. In many important cases, reactions between gases and liquids occur in the presence of a porous solid catalyst. The reaction typically occurs at a catalytic site on the solid surface. The kinetics and transport steps include dissolution of gas into the liquid, transport of dissolved gas to the catalyst particle surface, and diffusion and reaction in the catalyst particle. Say the concentration of dissolved gas A in equilibrium with the gas-phase concentration of A is CaLt. Neglecting the gas-phase resistance, the series of rates involved are from the liquid side of the gas-liquid interface to the bulk liquid where the concentration is CaL, and from the bulk liquid to the surface of catalyst where the concentration is C0 and where the reaction rate is r wkC",. At steady state,... 

Ruether and Puri (1973) presented another method, which separates ksas by examining the catalytic gas-liquid-solid reaction at low (i.e., limiting) concentrations of the liquid reactant, CBL, as a function of the inverse of the partial pressure of the gaseous reactant. In this case, Cal, the concentration of the gaseous reactant in the suspension, is always at equilibrium with the gas phase, not only at the gas-liquid interface but also at the catalyst surface, i.e.,... 

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