Liquid phase reactions ideal solutions

The discussion so far has been restricted to gas-phase reactions. One reason for this is that a large number of reactions, including many high-temperature reactions (except metallurgical reactions), occur in the gas phase. Also, the identification of the equilibrium state is easiest for gases, as nonidealities are,.generally less important than in liquid-phase reactions. However, many reactions of interest to engineers occur in the liquid phase.- The prediction of the equilibrium state in such cases can be complicated if the only information available is iifa or since liquid solutions are rarely ideal,... 

The second approach is to formulate rules for the correlation of the enthalpies and entropies of liquids and gases so that by the use of established correlations of the parameters for the gases, those for the corresponding liquids may be estimated. A recent paper by Patrick [398] has considerably clarified this approach. Assuming ideal thermodynamic behaviour of the solution components, it was concluded that for reactions involving no change in the number of molecules, i.e. transfer reactions of the present type, the ratio of equilibrium constants of the gas and liquid phase reactions is unity. This would appear to be most simply explained if the forward and reverse rate coefficients (fef(liq.), kf(gas), k (liq.) and fer(gas)) were equal, i.e. fef(liq.) = fef(gas) and fer(hq-) = fer(gas), but this remains to be confirmed experimentjdly. 

The impact of these liquid phase reactions on the phase equilibrium properties is thus an increased solubility of NH3, CO2, H2S and HCN compared with the one calculated using the ideal Henry s constants. The reason for the change in solubility is that only the compounds present as molecules have a vapour pressure, whereas the ionic species have not. The change thus depends on the pH of the mixture. The mathematical solution of the physical model is conveniently formulated as an equilibrium problem using coupled chemical reactions. For all practical applications the system is diluted and the liquid electrolyte solution is weak, so activity coefficients can be neglected. 

As mentioned in 7 3 it is always possible to discuss the equilibrium of a reaction in solution in terms of the partial pressures in the saturated vapour above the solution (provided that this vapour is a perfect mixture). However, for many purposes it is more useful to express the equilibrium constant of a liquid phase reaction directly in terms of the composition of the liquid. This is done by substituting in equation (10 1) any of the appropriate expressions for the chemical potential of a component of a solution which have been developed in the last two chapters. It will save space if the equations are developed in a general form applicable to a non-ideal solution. The limiting forms of these expressions appljdng to reaction equilibrium in an ideal solution may be obtained by putting the activity coefficients equal to unity. 

In order to use the W-P criterion successfully, it is important to accurately determine the effective diffusivity of the reactant in a given catalyst system. In the case of liquid-phase reactions, the pores of the catalyst are filled primarily with solvent, if one is used, and the molecular diffusivity of the reactant solute can be several orders of magnitude lower in a liquid-phase system compared to a vapor-phase system. Apart from the decrease in bulk diffusivities, there can also be liquid-phase non-idealities, adsorption phenomena, and other unknown factors influencing the effective diffusivity [24]. If the size of the diffusing molecules is comparable to the pore size, diffusion in the pores is hindered [25-28]. A different situation arises when the diffusing species has a strong affinity for the catalytic surface, which can lead to surface diffusion and migration [2,29] however, this consideration will not be of importance in liquid-phase reactions [30]. 

Equation (1) may be applied to the equilibrium between vapor and liquid of a pure substance (X = vapor pressure) or to the equilibrium between an ideal dilute solution and the pure phase of a solute X = solubility) or to the equilibrium of a chemical reaction (X = equilibrium constant). 

If one confines one s attention to the liquid phase, however, these idealized reactions apparently never occur. The proton, H+, does not exist free in solution,... 

For ideal solutions, the partial pressure of a component is directly proportional to the mole fraction of that component in solution and depends on the temperature and the vapor pressure of the pure component. The situation with group III-V systems is somewhat more complicated because of polymerization reactions in the gas phase (e.g., the formation of P2 or P4). Maximum evaporation rates can become comparable with deposition rates (0.01-0.1 xm/min) when the partial pressure is in the order of 0.01-1.0 Pa, a situation sometimes encountered in LPE. This problem is analogous to the problem of solute loss during bakeout, and the concentration variation in the melt is given by equation 1, with l replaced by the distance below the gas-liquid interface and z taken from equation 19. The concentration variation will penetrate the liquid solution from the top surface to a depth that is nearly independent of zlDx and comparable with the penetration depth produced by film growth. As result of solute loss at each boundary, the variation in solute concentration will show a maximum located in the melt. The density will show an extremum, and the system could be unstable with respect to natural convection. 

For the given reaction with an ideal solution in the liquid phase, Eq. (13.33) becomes ... 

When liquid and gas phases are both present in an equilibrium mixture of reacting species, Eq. (11.30), a criterion of vapor/liquid equilibrium, must be satisfied along with the equation of chemical-reaction equilibrium. There is considerable choice in the method of treatment of such cases. For example, consider a reaction of gas A and water B to form an aqueous solution C. The reaction may be assumed to occur entirely in the gas phase with simultaneous transfer of material between phases to maintain phase equilibrium. In this case, the equilibrium constant is evaluated from AG° data based on standard states for the species as gases, i.e., the ideal-gas states at 1 bar and the reaction temperature. On the other hand, the reaction may be assumed to occur in the liquid phase, in which case AG° is based on standard states for the species as liquids. Alternatively, the reaction may be written... 

In Chap. 6 we treated the thermodynamic properties of constant-composition fluids. However, many applications of chemical-engineering thermodynamics are to systems wherein multicomponent mixtures of gases or liquids undergo composition changes as the result of mixing or separation processes, the transfer of species from one phase to another, or chemical reaction. The properties of such systems depend on composition as well as on temperature and pressure. Our first task in this chapter is therefore to develop a fundamental property relation for homogeneous fluid mixtures of variable composition. We then derive equations applicable to mixtures of ideal gases and ideal solutions. Finally, we treat in detail a particularly simple description of multicomponent vapor/liquid equilibrium known as Raoult s law. 

We have a first-order homogeneous reaction, taking place in an ideal stirred tank reactor. The volume of the reactor is 20 X 10 3 m3. The reaction takes place in the liquid phase. The concentration of the reactant in the feed flow is 3.1 kmol/m3 and the volumetric flow rate of the feed is 58 X 10 m3/s. The density and specific heat of the reaction mixture are constant at 1000 kg/m3 and 4.184kJ/(kg K). The reactor operates at adiabatic conditions. If the feed flow is at 298 K, investigate the possibility of multiple solutions for conversion at various temperatures in the product stream. The heat of reaction and the rate of reaction are... 

Ideally, biphasic catalysis is performed in such a way that mass-transfer from one phase to the other does not restrict the rate of the reaction. An elegant solution to overcome this potential limitation is reversible two phase-single phase reaction conditions. An example of a temperature-controlled reversible ionic liquid-water partitioning system has been demonstrated for the hydrogenation of 2-butyne-l,4-diol, see Figure 3.2.1251... 

Phase equilibria of vaporization, sublimation, melting, extraction, adsorption, etc. can also be represented by the methods of this section within the accuracy of the expressions for the chemical potentials. One simply treats the phase transition as if it were an equilibrium reaction step and enlarges the list of species so that each member has a designated phase. Thus, if Ai and A2 denote liquid and gaseous species i, respectively, the vaporization of Ai can be represented stoichiometrically as —Aj + A2 = 0 then Eq. (2.3-17) provides a vapor pressure equation for species i. The same can be done for fusion and sublimation equilibria and for solubilities in ideal solutions. 

Few experiments allow one to bridge gas-phase electron transfer mechanism to liquid (or condensed)-phase electron transfer reactions. The major problem is to model the so-called solvent coordinates in the gas phase. Of course, clusters seems to be the ideal medium to build solvent effects in a stepwise manner. However, clusters are much colder than liquids, with the consequence that only a limited number of isomers are explored, as compared with the room temperature configurations involved in liquid processes. Discrepancies are observed in the case of cluster solvation of ionic molecules in clusters Nal remains at the surface of water clusters whereas it dissolves in bulk water [275]. Clusters thus do not allow one to explore in a single step all the aspects of a liquid-phase electron-transfer reaction. Their main advantage arises from this limitation since they allow one to study separate aspects of the solution processes. 

Substituting the appropriate ideal expression for the activity of gaseous or dissolved species from Equation 14.8a or 14.8b leads to the forms of the mass action law and the equilibrium constant K already derived earlier in Section 14.3 for reactions in ideal gases or in ideal solutions. We write the mass action law for reactions involving pure solids and liquids and multiple phases by substituting unity for the activity of pure liquids or solids and the appropriate ideal expression for the activity of each gaseous or dissolved species into Equation 14.9. Once a proper reference state and concentration units have been identified for each reactant and product, we use tabulated free energies based on these reference states to calculate the equilibrium constant. 

Solubility equilibria resemble the equilibria between volatile liquids (or solids) and their vapors in a closed container. In both cases, particles from a condensed phase tend to escape and spread through a larger, but limited, volume. In both cases, equilibrium is a dynamic compromise in which the rate of escape of particles from the condensed phase is equal to their rate of return. In a vaporization-condensation equilibrium, we assumed that the vapor above the condensed phase was an ideal gas. The analogous starting assumption for a dissolution-precipitation reaction is that the solution above the undissolved solid is an ideal solution. A solution in which sufficient solute has been dissolved to establish a dissolution-precipitation equilibrium between the solid substance and its dissolved form is called a saturated solution. 

A mass balance does not apply directly to volume. If the densities of the materials entering into each term are not the same, or mixing effects occur, then the volumes of the material will not balance. Also, chemical reactions can result in a change in the number of moles in the system (H2 plus O2 reacting to form H2O is one example). For gas-phase reactions in which pressure and temperature remain constant, the volume can change (refer to the ideal gas law). Non-constant volumes can also apply to liquid-phase systems. For example, one classic mixing experiment is to mix equal volumes of alcohol and water. The resulting solution does not have twice the volume. 

SOLUTION Ideal gas behavior is a reasonable approximation for the feed stream. The inlet concentrations are 287 mol m of methane and 15 mol m of carbon dioxide. The column pressure drop is mainly due to the liquid head on the trays and will be negligible compared to 8 atm unless there is an enormous number of trays. Thus the gas flow rate F will be approximately constant for the column as a whole. With fast reaction and a controlling gas-side resistance, c = 0. The liquid phase balance gives everything that is necessary to solve the problem ... 

Relative to the levels of the species we have been considering, water vapor is at a high concentration in the atmosphere. Liquid water, in the form of clouds and fog, is frequently present. Small water droplets can themselves be viewed as microscopic chemical reactors where gaseous species are absorbed, reactions take place, and species evaporate back to the gas phase. Droplets themselves do not always leave the atmosphere as precipitation more often than not, in fact, cloud droplets evaporate before coalescing to a point where precipitation can occur. In terms of atmospheric chemistry, droplets can both alter the course of gas-phase chemistry through the uptake of vapor species and act as a medium for production of species that otherwise would not be produced in the gas phase or would be produced by different paths at a lower rate in the gas phase (Fig. 10). Concentrations of dissolved species in cloud, fog, and rain droplets are in the micromolar range, and therefore one usually assumes that the atmospheric aqueous phase behaves as an ideal solution. 

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