Reaction rate laws heterogeneous reactions

The rates of heterogeneous reactions do not usually follow rate laws of homogeneous reactions instead, they involve multisteps and are controlled by the... 

As with homogeneous reactions, rate laws for heterogeneous reactions are kinetic statements and must be determined experimentally. The exponents (called orders) of a rate law depend on the reaction mechanism. 

Heterogeneous gas-solid surface adsorption reaction processes can frequently be treated using the same reaction rate law approach used for homogeneous chemical reactions. In such cases, surface sites are often a key reactant, and their concentration is often represented in terms of a fractional occupancy or availability [e.g., O or (1 - O)]. Using these principles, as an example, the rate at which a Pt surface is poisoned by CO gas adsorption can be modeled as 4> = 1 - (1 - 3>o)c where O is the fraction of the Pt surface that is poisoned... 

Finally, inserting the Ti reaction rate law (Equation 5.9 ) into this expression allows for the etching rate to be calculated as a function of the heterogeneous reaction rate... 

One of the factors limiting the rate of heterogeneous reactions such as (9), (10) and (11) is the availability of the second reactant at the surface. For a trace species like HCl, this may be determined by the solubility of the species in sulfuric acid. Measurements of the effective Henry s law constant for HCl in sulfuric acid solutions between 50 wt.% and 60 wt.% [24] have been made. Because the solubility is low, the range of temperatures and compositions over which the Knudsen cell experiment could be performed is limited. However, extrapolation to room temperature measurements [28] looks reasonable, and the agreement with the results of other groups [29,30] is good. 

Analysis In most heterogeneous catalytic reactions, rate laws are expressed in terms of partial pressures instead of concentration. However, we see that through the use of the ideal gas law we could easily express the partial pressure as a function of concentration then conversion in order to express the rate law as a function of conversion. In addition, for most all heterogeneous reactimis you will usually find a term like (1 + + K Pg +, ..) in the denominator of the rate law, as will be... 

In the above derivation a power-law kinetic expression was assumed for the intrinsic chemical reaction. For the systems where large concentration differences occur between the bulk fluid and the interior of the porous solid, the Langmuir-Hinshelwood type rate expression should be used because this provides a better description of the rate of heterogeneous reactions. 

Althou the rate of heterogeneous reactions is usually expressed according to the Langmuir-Hinshelwood mechanisms (Walker et al. (18)), a simpler power law expression is recommended for most of the char-gas reactions. This is to reduce the mathemati- cal complexity in reactor modelling and the number of parameters needed to be determined by experimentation. Accordingly, the rate e q>ression for a volumetric reaction can be described in the following forms ... 

Heat of vaporization, 66 see also Vaporization Helium, 91 boiling point, 63 heat of vaporization, 105 interaction between atoms, 277 ionization energy, 268 molar volume, 60 on Sun, 447 source, 91 Hematite, 404 Hemin, structure of, 397 Hess s Law, 111 Heterogeneous, 70 systems and reaction rate, 126 n-Hexane properties, 341 Hibernation, 2 Hildebrand, Joel H.. 163 Holmium, properties, 412 Homogeneous, 70 systems and reaction rate, 126 Hydration, 313 Hydrazine, 46, 47, 231 Hydrides of third-row elements, 102 boiling point of. 315 Hydrocarbons, 340 unsaturated, 342... 

In this chapter we consider the problem of the kinetics of the heterogeneous reactions by which minerals dissolve and precipitate. This topic has received a considerable amount of attention in geochemistry, primarily because of the slow rates at which many minerals react and the resulting tendency of waters, especially at low temperature, to be out of equilibrium with the minerals they contact. We first discuss how rate laws for heterogeneous reactions can be integrated into reaction models and then calculate some simple kinetic reaction paths. In Chapter 26, we explore a number of examples in which we apply heterogeneous kinetics to problems of geochemical interest. 

Propose a rate law based on the Langmuir-Hinshelwood model for each of the following heterogeneously catalyzed reactions ... 

In Section 9.3, we focus more on the intrinsic rates for reactions involving solids, since there are some modem processes in which mass transport rates play a relatively small role. Examples in materials engineering are chemical vapor deposition (CVD) and etching operations. We describe some mechanisms associated with such heterogeneous reactions and the intrinsic rate laws that arise. 

The mechanisms, and hence theoretically derived rate laws, for noncatalytic heterogeneous reactions involving solids are even less well understood than those for surface-catalyzed reactions. This arises because the solid surface changes as the reaction proceeds, unlike catalytic surfaces which usually reach a steady-state behavior. The examples discussed here are illustrative. 

In analyzing the kinetics of surface reactions, it will be illustrated that many of these processes are rate-controlled at the surface (and not by transport). Thus, the surface structure (the surface speciation and its microtopography) determine the kinetics. Heterogeneous kinetics is often not more difficult than the kinetics in homogeneous systems as will be shown, rate laws should be written in terms of concentrations of surface species. 

Basically, whenever isotopic exchanges occur between different phases (i.e., heterogeneous equilibria), isotopic fractionations are more appropriately described in terms of differential reaction rates. Simple diffusion laws are nevertheless appropriate in discussions of compositional gradients within a single phase— induced, for instance, by vacancy migration mechanisms, such as those treated in section 4.10—or whenever the isotopic exchange process does not affect the extrinsic stability of the phase. 

Some gas—solid heterogeneous reactions follow a similar rate law. Under certain conditions, the rate of hydrogenation of ethene is described by the equation... 

In heterogeneous reactions we frequently find relations between rate of reaction and concentration quite different from those which the law of mass action would indicate to be valid for a homogeneous system. It is a little difficult, at first sight, to see how, by equating the rates of the forward and reverse reactions, we are still to arrive at the correct equilibrium relations. The general problem is very complex, but one simple example may be given to illustrate the manner in which conflict with the second law of thermodynamics is avoided. 

Because reactions in solids tend to be heterogeneous, they are generally described by rate laws that are quite different from those encountered in solution chemistry. Concentration has no meaning in a heterogeneous system. Consequently, rate laws for solid-phase reactions are described in terms of a, the fraction of reaction (a = quantity reacted -r- original quantity in sample). The most commonly encountered rate laws are given in Table 1. These rate laws and their application to solid-phase reactions are described elsewhere. 1 4 10-12 Unfortunately, it is often merely assumed that solid-phase reactions are first order. This uncritical analysis of kinetic data produces results that must be accepted only with great caution. 

The increase A will occur at interface A/AB if LA/LR< 1, and it will occur at AB/B if La >Lr (Fig. 1-5). We conclude that parabolic rate laws in heterogeneous solid state reactions are the result of two conditions, the prevalence of a linear geometry and of local equilibrium which includes the phase boundaries. 

Heterogeneous solid state reactions occur when two phases, A and B, contact and react to form a different product phase C. A and B may be either chemical elements or compounds. We have already introduced this type of solid state reaction in Section 1.3.4. The rate law is parabolic if the reacting system is in local equilibrium and the growth geometry is linear. The characteristic feature of this type of reaction is the fact that the product C separates the reactants A and B and that growth of the product proceeds by transport of A and/or B through the product layer. 

The experimental quantity used to characterize heterogeneous reaction rates is the "reaction probablity", y, which is defined as the fractional collision frequency that leads to reactive loss. Kinetic data for the generally irreversible reactive uptake of trace gas species on condensed surfaces are expressed in terms of uptake experiments, where the disappearance of the species under consideration and/or the appearance of one or more reaction products has been observed. Such processes may not be rate limited by Henry s law constraints, however the fate of the uptake reaction products may be subject to saturation limitations. 

These considerations can be extended to reversible processes. They also apply to single phase, liquid systems. For the case, rather common in heterogeneous catalysts, in which one reactant is in a gas phase and the others and the products are in a liquid phase, application of the principles given above is straightforward provided that there is mass transfer equilibrium between gas phase and liquid phase, i.e., the fugacity of the reactant in the gas phase is identical with its fugacity in the liquid phase. In such case, a power rate law for an irreversible reaction of the form... 

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