Reaction Rates of Solids

Chapter 12. In this chapter we wUl be concerned mosfly with developing suitable rate expressions for the reaction rates of solids in Chapter 12 we will consider the reactor mass and energy equations. 

Batch and semibatch processes are particularly common for processing solids because the conditions of the process can be varied as the reaction proceeds to control the quality of the solid formed. Burned or raw food and defective computer chips are intolerable. 

As with catalytic reactions, our task is to develop pseudohomogeneous rate expressions to insert into the relevant mass-balance equations. For ary multiphase reactor where reaction occurs at the interface between phases, the reactions are pritnarily surface reactions (rate r ), and we have to find these expressions as functions of concentrations and rate and transport coefficients and then convert them into pseudohomogeneous expressions, 

However, now the solid is shrinking, growing, or transforrning as the process proceeds, rather than being unchanged as for solid catalysts. Thus there is a time dependence within the solid in the reactor. 

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Temperature has a marked effect on the kinetics of reaction rates of solid phase sorption/desorption processes [113-116]. Arrhenius noted the following relationship between k and T (Eq. 52) ... 

Figure 8.10 Surface area influences reaction rates of solids. What is the other reactant in this reaction How finely divided is it ...

The rate of solid waste combustion is controlled by diffusion, rather than by reaction kinetics. In general, the time required for combustion of a single particle of waste (1) can be expressed as ... 

A third method, or phenomenon, capable of generating a pseudo reaction order is exemplified by a first-order solution reaction of a substance in the presence of its solid phase. Then if the dissolution rate of the solid is greater than the reaction rate of the dissolved solute, the solute concentration is maintained constant by the solubility equilibrium and the first-order reaction becomes a pseudo-zero-order reaction. 

In contrast, there are fewer limitations from the chemical point of view. The preparation of large, well-defined, libraries that involve amino acid building blocks has been demonstrated many times. Carefully optimized reaction conditions for the preparation of other mixed libraries can also ensure that each desired compound is present in sufficient amount. However, the reaction rates of some individual selectors with the activated solid support may be lower than that of others. As a result, the more reactive selectors would occupy a majority of the sites within the beads. Since the most reactive selectors may not be the most selective, testing of a slightly larger number of specifically designed CSPs may be required to reduce the effect of falsenegative results. 

Measurements of overall reaction rates (of product formation or of reactant consumption) do not necessarily provide sufficient information to describe completely and unambiguously the kinetics of the constituent steps of a composite rate process. A nucleation and growth reaction, for example, is composed of the interlinked but distinct and different changes which lead to the initial generation and to the subsequent advance of the reaction interface. Quantitative kinetic analysis of yield—time data does not always lead to a unique reaction model but, in favourable systems, the rate parameters, considered with reference to quantitative microscopic measurements, can be identified with specific nucleation and growth steps. Microscopic examinations provide positive evidence for interpretation of shapes of fractional decomposition (a)—time curves. In reactions of solids, it is often convenient to consider separately the geometry of interface development and the chemical changes which occur within that zone of locally enhanced reactivity. 

Since 1986, when the very first reports on the use of microwave heating to chemical transformations appeared [147,148], microwave-assisted synthesis has been shown to accelerate most solution-phase chemical reactions [24-27,32,35]. The first application of microwave irradiation for the acceleration of reaction rate of a substrate attached to a solid support (SPPS) was performed in 1992 [36]. Despite the promising results, microwave-assisted soHd-phase synthesis was not pursued following its initial appearance, most probably as a result of the lack of suitable instriunentation. Reproducing reaction conditions was nearly impossible because of the differences between domestic microwave ovens and the difficulties associated with temperature measurement. The technique became a Sleeping Beauty interest awoke almost a decade later with the publication of several microwave-assisted SPOS protocols [37,38,73,139,144]. There has been an extensive... 

Although the use of phase-transfer catalysis (PTC) for manufacturing esters has the merits of a mild reaction condition and a relatively low cost [1], PTC has its limitations, such as the low reactivity of carboxylic ion by liquid-liquid PTC [2], a slow reaction rate by solid-liquid PTC, and the difflculty of reusing the catalyst by both techniques. 

For phase-boundary controlled reactions, the situation differs somewhat. Diffusion of species is fast but the reaction is slow so that the dlfiusing species pile up. That is, the reaction to rearrange the structure is slow in relation to the arrival of the diffusing ions or atoms. TTius, a phaseboundary (difference in structure) focus exists which controls the overall rate of solid state reaction. This rate may be described by ... 

Since the rate of solid state reaction depends upon surface area, we can see that very small particles ought to react much faster than large particles. 

SAMPLE CLOSURE is important since it affects the rate of solid state reaction. Consider the foUowing solid state reaction ... 

The reaction rate of sodium acid pyrophosphate can be controlled by adding calcium ions. While this process happens anyway in the presence of skim milk solids, manufacturers deliberately add calcium ions to sodium acid pyrophosphate to give grades with slower dissolution. 

The rate of solid catalyzed reaction is controlled by external diffusion and surface reaction, with equation... 

Figure 11.32 Influence of essential reaction parameters exerted on the reaction rate of gas-liquid-solid reactions (a, impeller speed b, particle size).

Section 2 deals with reactions involving only one molecular reactant, i.e. decompositions, isomerisations and associated physical processes. Where appropriate, results from studies of such reactions in the gas phase and condensed phases and induced photochemically and by high energy radiation, as well as thermally, are considered. The effects of additives, e.g. inert gases, free radical scavengers, and of surfaces are, of course, included for many systems, but fully heterogeneous reactions, decompositions of solids such as salts or decomposition flames are discussed in later sections. Rate parameters of elementary processes involved, as well as of overall reactions, are given if available. 

As can be concluded from this short description of the factors influencing the overall reaction rate in liquid-solid or gas-solid reactions, the structure of the stationary phase is of significant importance. In order to minimize the transport limitations, different types of supports were developed, which will be discussed in the next section. In addition, the amount of enzyme (operative ligand on the surface of solid phase) as well as its activity determine the reaction rate of an enzyme-catalyzed process. Thus, in the following sections we shall briefly describe different types of chromatographic supports, suited to provide both the high surface area required for high enzyme capacity and the lowest possible internal and external mass transfer resistances. 

Figure 5.4 Effect of gas flow rate on (a) the SSP reaction rate of PET at temperatures of 190 and 220 °C, and (b) the rate of increase of the intrinsic viscosity of PET at various temperatures [13]. Reprinted from Polymer, 39, Huang, B. and Walsh, J. J., Solid-phase polymerization mechanism of polyethylene tereph-thalate) affected by gas flow velocity and particle size, 6991-6999, Copyright (1998), with permission from Elsevier Science...

Although, as described by Bjerle et alS13 liquid jet-type absorbers are also used, one relatively recent application of mass transfer in agitated tanks with chemical reaction is the absorption of pollutants from flue gases and, in particular, the scrubbing of sulphur dioxide by a slurry containing fine limestone particles. In this case, the concentration of sulphur dioxide is usually very low and the mechanism of the absorption is complicated due to the presence of solids in the liquid phase where the rate of solid dissolution may significantly affect the absorption rate. 

There are four main processes (i.e., bulk transport chemical reaction film and particle diffusion) which can affect the rate of solid phase chemical reactions and can broadly be classified as transport and chemical reaction processes [10, 31,103 -107]. The slowest of these will limit the rate of a particular reaction. Bulk transport process of a certain pollutant(s), which occurs in the aqueous phase, is very rapid and is normally not rate-limiting. In the laboratory, it can be eliminated by rapid mixing. The actual chemical reaction at the surface of a solid phase (e.g., adsorption) is also rapid and usually not rate limiting. The two remaining transport or mass transfer processes (i.e.,film and particle diffusion processes), either singly or in combination, are normally rate-limiting. Film diffusion invol-... 

Aboul-Kassim [1] studied the characterization, chemodynamics, and environmental impact assessment of organic leachates from complex mixtures. He reported that an important factor in controlling the rate of solid phase adsorption reactions is the type and quantity of solid phase components as well as the time period (i. e., short vs long) over which the organic contaminant has been in contact with the solid phase. 

The main reasons for investigating the rates of solid phase sorption/desorption processes are to (1) determine how rapidly reactions attain equilibrium, and (2) infer information on sorption/desorption reaction mechanisms. One of the important aspects of chemical kinetics is the establishment of a rate law. By definition, a rate law is a differential equation [108] as shown in Eq. (32) ... 

Sabatier and Balandin had predicted a relationship between catal)dic activity and heat of adsorption. If a solid adsorbs the reactants only weakly, it will be a poor catalyst, but if it holds reactants, intermediates or products too strongly, it wiU again perform poorly. The ideal catalyst for a given reaction was predicted to be a compromise between too weak and too strong chemisorption. Balandin transformed this concept to a semiquantitative theory by predicting that a plot of the reaction rate of a catal)Tic reaction as a function of the heat of adsorption of the reactant should have a sharp maximum. He called these plots volcano-shaped curvesl This prediction was confirmed by Fahrenfort et al." An example of their volcano-shaped curve is reproduced in Fig. 9.1. They chose the catalytic decomposition of formic acid... 

Figure 15 Overall reaction rate and its approximations step 2 is rate-limiting. Dots represent the exact reaction rate dependence, solid line is the first-term hypergeometric approximation, dashed line corresponds to the reaction-rate equation that assumes the limitation of step 2 and dash-dots represent the equilibrium approximation. Hypergeometric approximation survives the 100-times increase in rate-limiting stage kinetic parameters and it works when there is no rate-limiting step at all. Parameters r, = 5, fj = 15, rj = 10 t2 = 0.2, fj = 0-1 (a) rj = 2,fj = - (b) t2 = 20, = 10, (c).

When ions migrate through a solid electrolyte, they diffuse from this onto the gas-exposed surface of the metal electrode. These ions form a double layer (and hence a potential difference) at the metal/gas interface. I Iowcver, this potential difference (which varies with the electrode potential) in turn changes the work function at the gas/metal interface. The ease of availability of electrons in the bonding of radicals adsorbed from the gas phase onto the electrode increases as the electronic work function of the solid decreases. The chemical reaction rate of the catalyzed reaction depends on the bonding strength of these radicals to the electrode catalyst, which involves electrons from the metal and is therefore dependent on the work function of the metal this itself is a function of the electrode potential. In this way, a dependence of the rate of the chemical reaction upon the potential of the working electrode can be rationalized. 

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