Equilibrium between gaseous reactants

Partial molar quantities play an important role in the study of non-ideal mixtures but we have to use them to only a limited extent in elementary thermodynamics. They can usually be replaced by the corresponding molar quantities. Thus, in simple calculations involving perfect gases or ideal solutions, Vi can be replaced by the volume of one mole of pure i in the appropriate physical state. 

This is the simplest type of chemical equilibrium and corresponds to the equilibrium between two isomers such as n-butane and isobutane, f If dnA 

The reaction will proceed until G reaches a minimum value and -rr ) 

This important equation tells us how the position of chemical equilibrium can be defined in terms of the free energies of the reactants and products at 1 atm pressure. Such standard free energies can be determined experimentally and are tabulated for use in this way. We shall consider specific examples later. The equation is also valuable in a qualitative sense. If AG° is negative we know the equilibrium position will correspond to the presence of more product than reactants (lnK. 0). If AG° is positive the reaction will not proceed to such an extent and reactants will predominate in the equilibrium mixture. With this result we have accomplished a major purpose of our study. 

Had our reaction been more complicated we would have obtained essentially the same results. For example for the reaction 

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Phase diagrams can be used to predict the reactions between refractories and various solid, liquid, and gaseous reactants. These diagrams are derived from phase equilibria of relatively simple pure compounds. Real systems, however, are highly complex and may contain a large number of minor impurities that significantly affect equilibria. Moreover, equilibrium between the reacting phases in real refractory systems may not be reached in actual service conditions. In fact, the successful performance of a refractory may rely on the existence of nonequilibrium conditions, eg, environment (15—19). 

From simple measurements of the rate of a photocatalytic reaction as a function of the concentration of a given reactant or product, valuable information can be derived. For example, these measurements should allow one to know whether the active species of an adsorbed reactant are dissociated or not (22), whether the various reactants are adsorbed on the same surface sites or on different sites (23), and whether a given product inhibits the reaction by adsorbing on the same sites as those of the reactants. Referring to kinetic models is therefore necessary. The Langmuir-Hinshelwood model, which indicates that the reaction takes place between both reactants at their equilibrium of adsorption, has often been used to interpret kinetic results of photocatalytic reactions in gaseous or liquid phase. A contribution of the Eley-Rideal mechanism (the reaction between one nonadsorbed reactant and one adsorbed reactant) has sometimes been proposed. 

The quasi-equilibrium between the surface-activated complex and the gaseous reactant is given by... 

A catalyst is a substance that increases the rate at which a chemical reaction approaches equilibrium without, itself, becoming permanently involved in the reaction. The key word in this definition is permanently since there is ample evidence showing that the catalyst and the reactants interact before a reaction can take place. The product of this interaction is a reactive intermediate from which the products are formed. This substratexatalyst interaction can take place homogeneously with both the reactants and the catalyst in the same phase, usually the liquid, or it can occur at the interface between two phases. These heterogeneously catalyzed reactions generally utilize a solid catalyst with the interaction taking place at either the gas/solid or liquid/solid interface. Additional phase transport problems can arise when a gaseous reactant is also present in the liquid/solid system. 

The equilibrium in Equation 1 lies therefore far to the left. This unfavourable situation is ruled by the large difference in entropy between two gaseous reactants and a liquid product that forms very strong intermolecular hydrogen bonds. High pressure and relatively low temperatures will obviously help to shift equilibrium to the right. 

In two-phase systems in which the catalytic reaction takes place in the liquid phase between a liquid reactant and gaseous reactants, the latter have to be transferred over the gas/liquid boundary layer into the liquid phase. In this situation the reaction engineering prediction described above can be performed in an analogous way as long as the rate of transfer of the gaseous reactants into the liquid phase is fast compared with the intrinsic catalytic reaction. Under these circumstances it can usually be assumed that the liquid-phase concentrations of the gaseous reactants correspond to gas/liquid thermodynamic equilibrium. 

The activated-complex theory provides a plausible explanation of the first-order rate of unimolecular gaseous reactions. In such a reaction the reacting molecules gain the energy of activation by colhsion with other molecules. This might be thought of as a second-order process, since the number of collisions is proportional to the square of the concentration. However, Lindemann showed in 1922 that activation by collision could result in first-order rates. If A is an activated molecule of reactant, the equilibrium between A and A and reaction to products B can be represented as... 

In the case of a three-phase electrocatalytic system, such as those of fuel cells, the cylindrical pore model is not applicable since it does not consider the problem of the partial pressure of the reactant in the gas phase. In this case, an equilibrium between the gaseous pressure inside the pore (which tends to force the electrolyte out of it) and the capillary forces of the electrolyte (which tend to flood the electrolyte away from the pore) must occur. This is known as the stable meniscus condition ... 

Figure 17.13 For the reaction between CO and H2 at constant temperature, changing the volume of the reaction vessel changes the concentrations of gaseous reactants and products. Increasing the pressure shifts the equilibrium to the right and increases the amount of product. 

Table I. Equilibrium (a) and kinetic (b) isotopic fractionation factors (a) of importance to nitrogen cycling in lakes (Collister Hayes, 1991). As a first approximation, an a value of, for example, 1.020 implies a difference in of ca. 20%o between the reactant and product. In the case of N2 gas dis.solution, therefore, differs by less than l%o between the gaseous and aqueous phases, whereas gaseous ammonia liberated during ammonia volatilisation will be ca. i4%o lighter than the aqueous ammonia.

What would happen to the gaseous equilibrium mixture of reactants and products represented in Fig. 6.3, parts (c) and (d), if we injected some H20(g) into the box To answer this question, we need to be sure we understand the equilibrium condition The concentrations of reactants and products remain constant at equilibrium because the forward and reverse reaction rates are equal. If we inject some H2O molecules, what will happen to the forward reaction H2O + CO —> H2 -I- CO2 It will speed up because when there are more H2O molecules there will be more collisions between H2O and CO molecules. This in turn will form more products and will cause the reverse reaction H2O + CO H2 + CO2 to speed up. Thus the system will change until the forward and reverse reaction rates again become equal. Will this new equilibrium position contain more or fewer product molecules than are shown in Fig. 6.3(c) and (d) Think about this carefully. If you are not sure of the answer now, keep reading. We will consider this type of situation in more detail later in this chapter. 

As depicted in Figure 2.2, the dissolved gaseous reactant has to overcome the resistance offered by the liquid-solid film before it reaches the solid catalyst surface where the reaction between the adsorbed reactive species takes place. The intrinsic capacity of a catalyst is realized when all mass transfer processes are at equilibrium. Therefore, it is required to know the rate of the solid-liquid mass transfer step. Such an estimate should reveal the relative importance of this step and also establish the controlling step in an overall process. In a multiphase system, the mass transfer between the liquid and particulate phases is considered to be good when there is an intimate mixing between the two phases. In the case of solid-liquid mass transfer, the minimum desirable condition is suspension of the solid in the liquid or in the gas-liquid dispersion as the case may be. 

As can be observed, the main difference between conventional three-phase reactors and catalytic membrane reactors hes in the relative positions of the mass transfer resistances with respect to the catalytic phase. In a conventional porous catalyst the catalytic sites in the pores have only one way or path of access. The gaseous reactant will encounter the first two mass transfer resistances at the gas-liquid interface, where the solvation equilibrium of the species from one phase to the other wiU take place. The dissolved species will diffuse towards the surface of the catalytic pellet for quite a long path in the hquid phase and will meet an additional mass transfer resistance at the hquid-sohd catalyst interface. It then needs to diffuse and react in the porous structure of the catalyst as well as the other reactant already present in the liquid phase. In the case of a traditional three-phase reactor (Fig. 4.3a), the concentration of at least one of the reacting species is hmited by its solubility and diffusion in the other fluid phase with a long diffusion path and in some cases unknown interfadal area (e.g., bubbles with variable size depending on the type of the gas feeding and distribution device in slurry reactors, not uniform phase contact and distribution in trickle-bed reactors). 

When chemical reaction presents the major resistance to the overall progress of reaction, the concentration of the fluid reactant will be constant everywhere and the reaction will occur uniformly throughout the volume of the solid. If, on the other hand, pore diffusion presents the major resistance, the reaction will occur in a narrow boundary between the unreacted and the completely reacted zones, where the gaseous reactant concentration becomes zero (or takes on its equilibrium value in the case of reversible reaction). This latter case is identical to the diffusion-controlled shrinking unreacted-core system of a nonporous solid, which was discussed in detail in Chapter 3. 

In most circumstances, it can be assumed diat die gas-solid reaction proceeds more rapidly diaii die gaseous transport, and dierefore diat local equilibrium exists between die solid and gaseous components at die source and sink. This implies diat die extent and direction of die transport reaction at each end of die temperature gradient may be assessed solely from diermodynamic data, and diat die rate of uansport across die interface between die gas and die solid phases, at bodi reactant and product sites, is not rate-determining. Transport of die gaseous species between die source of atoms and die sink where deposition takes place is die rate-determining process. 

Since the partial pressure is the mole fraction in the vapor phase multiplied by the total pressure, (i.e., p, = y, P), the equilibrium constant Keq is expressed as Keq = Ky PAn, where An = (2 - 1 - 3), the difference between the gaseous moles of the products and the reactants in the ammonia synthesis reaction. 

Consider the effect of surface diffusion on the effectiveness factor for a first-order, irreversible, gaseous reaction on a porous catalyst. Assume that the intrinsic rates of adsorption and desorption of reactant on the Surface are rapid with respect to the rate of surface diffusion. Hence equilibrium is established between reactant iii the gas in the pore and reactant adsorbed on the surface. Assume further that the equilibrium expression for the concentration is a linear one. Derive an equation for the effectiveness factor for each of the following two cases ... 

Theoretical Consideration The decomposition temperature is an important, if not the most important kinetic parameter used in studies of the decomposition processes. It defines the upper limit of reactant stability and the onset of a decomposition reaction. However, temperature is most commonly used only as an additional factor in determination of the Arrhenius parameters. (For instance, Galwey [1] used an average decomposition temperature in his estimations of A values basing on E parameters, known for various substances.) No quantitative definition of the concept of an initial decomposition temperature has been developed, based on a certain specified value of the decomposition rate J, or on parameters related to it (the rate constant k, or the equilibrium pressure of gaseous products Pb)- The detailed interrelation between the decomposition temperature and the molar enthalpy,... 

The magnitude of the ratio Tjn/ (K mol kJ ) for all reactants is very close to the expected (theoretical) value Tgub/ r-f T = 3.62 0.22K mol kJ The mean value T- /E is 3.61 0.39K mol kJ for reactants in Table5.2 and 3.62 0.37K mol kJ for those in Table 5.3. No difference is observed in the mean values of E-ajE for substances that decompose to gaseous products and those that decompose to solid and gaseous products. The only difference between the experimental values of T-m/E and the theoretical (for equilibrium sublimation) value Tgub/ r T i somewhat higher (by a factor of... 

Results and Discussion The values of the above-mentioned parameters and the compositions of the primary products, found from their comparison, are listed in Table 16.64. The discrepancies between the calculated and experimental values of AyH do not exceed 5% for Ag, Ni, and Mn oxalates and 10% for Hg and Pb oxalates. For the latter two reactants, the discrepancies are most likely due to underestimation of the initial parameter E. This is confirmed by the overestimated experimental values of the Tm/E ratio for these oxalates (Table 16.63). When determining the optimal composition of the primary gaseous products, the similarity of the decomposition schemes for the reactions yielding similar solid products (metals or oxides) was taken into account. The most unexpected result was that the primary gaseous products contained, instead of equilibrium CO2 molecules, a mixture of CO and 02 molecules for Ag, Ni, Mn, and Pb oxalates and a mixture of CO and O for Hg oxalate. The corresponding differences in the enthalpies are 283 and 532 kJ moP, respectively, exceeding by an order of magnitude the possible measurement and calculation errors. 

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