Heterogeneous catalysis isothermal

Influence of the Adsorption Isotherm on the Kinetics of Heterogeneous Catalysis... 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

The problem posed by Eq. (6.22), without the additional complication of the O dependence, is a classical problem in heterogeneous catalysis. The usual approach it to use Langmuir isotherms to describe reactant (and sometimes product) adsorption. This leads to the well known Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics.3 The advantage of this approach is... 

Adsorption of reactants on the surface of the catalyst is the first step in every reaction of heterogeneous catalysis. Flere we focus on gases reacting on solid catalysts. Although we will deal with the adsorption of gases in a separate chapter, we need to discuss the relationship between the coverage of a particular gas and its partial pressure above the surface. Such relations are called isotherms, and they form the basis of the kinetics of catalytic reactions. 

A survey of the literature shows that although very different calorimeters or microcalorimeters have been used for measuring heats of adsorption, most of them were of the adiabatic type, only a few were isothermal, and until recently (14, 15), none were typical heat-flow calorimeters. This results probably from the fact that heat-flow calorimetry was developed more recently than isothermal or adiabatic calorimetry (16, 17). We believe, however, from our experience, that heat-flow calorimeters present, for the measurement of heats of adsorption, qualities and advantages which are not met by other calorimeters. Without entering, at this point, upon a discussion of the respective merits of different adsorption calorimeters, let us indicate briefly that heat-flow calorimeters are particularly adapted to the investigation (1) of slow adsorption or reaction processes, (2) at moderate or high temperatures, and (3) on solids which present a poor thermal diffusivity. Heat-flow calorimetry appears thus to allow the study of adsorption or reaction processes which cannot be studied conveniently with the usual adiabatic or pseudoadiabatic, adsorption calorimeters. In this respect, heat-flow calorimetry should be considered, actually, as a new tool in adsorption and heterogeneous catalysis research. 

The simulation of reacting flows in packed tubes by CFD is still in its earliest stages. So far, only isothermal surface reactions for simplified geometries and elementary reactions have been attempted. Heterogeneous catalysis with diffusion, reaction, and heat transfer in solid particles coupled to the flow, species, and temperature fields external to the particles remains a challenge for the future. 

CI2 evolution reaction, 38 56 electrochemical desorption, 38 53-54 electrode kinetics, 38 55-56 factors that determine, 38 55 ketone reduction, 38 56-57 Langmuir adsorption isotherm, 38 52 recombination desorption, 38 53 surface reaction-order factor, 38 52 Temkin and Frumkin isotherm, 38 53 real-area factor, 38 57-58 regular heterogeneous catalysis, 38 10-16 anodic oxidation of ammonia, 38 13 binding energy quantification, 38 15-16 Haber-Bosch atrunonia synthesis, 38 12-13... 

The specific models we will analyse in this section are an isothermal autocatalytic scheme due to Hudson and Rossler (1984), a non-isothermal CSTR in which two exothermic reactions are taking place, and, briefly, an extension of the model of chapter 2, in which autocatalysis and temperature effects contribute together. In the first of these, chaotic behaviour has been designed in much the same way that oscillations were obtained from multiplicity with the heterogeneous catalysis model of 12.5.2. In the second, the analysis is firmly based on the critical Floquet multiplier as described above, and complex periodic and aperiodic responses are observed about a unique (and unstable) stationary state. The third scheme has coexisting multiple stationary states and higher-order periodicities. 

The Brunauer-Emmett-Teller (or BET) adsorption isotherm applies only to the physisorption of vapours but it is important to heterogeneous catalysis because of its use for the determination of the surface areas of solids. The isotherm is given by the following equation,... 

Chapter 2 describes the evolution in fundamental concepts of chemical kinetics (in particular, that of heterogeneous catalysis) and the "prehis-tory of the problem, i.e. the period before the construction of the formal kinetics apparatus. Data are presented concerning the ideal adsorbed layer model and the Horiuti-Temkin theory of steady-state reactions. In what follows (Chapter 3), an apparatus for the modern formal kinetics is represented. This is based on the qualitative theory of differential equations, linear algebra and graphs theory. Closed and open systems are discussed separately (as a rule, only for isothermal cases). We will draw the reader s attention to the two results of considerable importance. 

In the pressure range 0.05 < P/P < 0.35, the quantity [V(P /P) — 1] 1 increases linearly with P/P from the slope s" and intercept "i", one obtains bm0n0 = 1 /(s + i) and c = 1 + s/i. Thus, the BET isotherm measures the effective specific surface of a particulate solid support substances like silica gel, zeolite, and so on, can have a specific surface useful for heterogeneous catalysis, provided that it exceeds 200 m2 g... 

In some cases, adsorption of analyte can be followed by a chemical reaction. The Langmuir-Hinshelwood (LH) and power-law models have been used successfully in describing the kinetics of a broad range of gas-solid reaction systems [105,106]. The LH model, developed to describe interactions between dissimilar adsorbates in the context of heterogeneous catalysis [107], assumes that gas adsorption follows a Langmuir isotherm and that the adsorbates are sufficiently mobile so that they equilibrate with one another on the surface on a time scale that is rapid compared to desorpticm. The power-law model assumes a Fre-undlich adsorption isotherm. Bodi models assume that the surface reaction is first-order with respect to the reactant gas, and that surface coverage asymptotically approaches a mmiolayer widi increasing gas concentration. 

Of course, other types of adsorption isotherms commonly represent the adsorption processes in heterogeneous catalysis, for example, the Freundlich isotherm and, especially in electrode processes, the Temkin and Frumkin isotherms (99). In the latter case... 

To study a class of mechanisms for isothermal heterogeneous catalysis in a CSTR, Morton and Goodman (1981-1) analyzed the stability and bifurcation of simple models. The limit cycle solutions of the governing mass balance equations were shown to exist. An elementary step model with the stoichiometry of CO oxidation was shown to exhibit oscillations at suitable parameter values. By computer simulation limit cycles were obtained. 

Adsorption isotherms. Adsorption is an important facet of kinetics of heterogeneous catalysis. Adsorption isotherms, showing the equilibrium concentration of a species on a solid as a function of the concentration in the contacting fluid at constant temperature, may have different shapes, usually classified as Types I through V [18] (see Figure 2.4). 

In continuous stirred-tank reactors (CSTRs), complex kinetics may give rise to multiple steady states even in isothermal operation, especially in heterogeneous catalysis. However, to unravel the causes may be difficult. Here, Feinberg s network theory can help [3]. It operates with a deficiency index that is a readily calculated zero or positive integer. The most useful result of the theory is ... 

For batch, plug flow, and CSTR. Includes gas-phase isothermal, nonisothermal, and nonisobaric reactions, heterogeneous catalysis, and thermochemical database for calculation of equilibrium constants. Many subprograms for special situations (shock waves, flames, partially stirred reactors, etc.) are available. 

The adsorption/desorption equilibrium constant for each component is Kf = 0.25 atm and forward is the kinetic rate constant for the forward chemical reaction on the catalytic surface with units of moles per area per time. The reason that forward has the same units as Ehw is because rate laws for heterogeneous catalysis are written in terms of fractional surface coverage by the adsorbed species that participate in the reaction. Langmuir isotherms are subsequently used to express fractional surface coverage of the reacting species in terms of their partial pressures. The best value for the pseudo-first-order kinetic rate constant is calculated from... 

Following Drazer and Zanette, we assume that, although the whole system is not at equilibrium, in different local areas of the column there is a local equilibrium. We invoke the homottatic patch approximation in heterogeneous catalysis [20], according to which the overall adsorption isotherm is made up of a contribution of local Langmuir adsorption isotherms ... 

One of the most conamon uses of the BET isotherm is for determining the surface area of finely divided solids by physical adsorption. Such information can be of great importance in a number of areas including heterogeneous catalysis and various sorption applications. While the BET model for multilayer adsorption contains several potential sources of error due to the assumptions of the absence of lateral interactions between adsorbed molecules, the... 

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