Chemical reaction overall order

In the presence of a metal ion (M " ), a metal chalcogenide phase M2Sen will be precipitated upon exceeding the solubility product of [M and [Se ] (or [HSe ]). The concentration of free metal ions must be controlled by an excess of complexing agent, determining the applicable solubility of the metal and the overall competitive chemical reaction, in order to prevent the formation of sulfite, sulfate, and... 

The deposited solid is the final result of all these subprocesses. The rate of the subprocess varies in a wide range. For these sequential reactions or subprocesses the overall deposition rate is controlled by the slowest subprocess. In this section the CH3SiCl3-H2 deposition system has been chosen as the system for discussion in both homogeneous chemical reactions and heterogeneous chemical reactions in order to give a more in-depth understanding of the kinetics of a chosen CVD process. 

The order of a reaction relates to the exponents of the concentration factors in the rate law for a chemical reaction. The order can be stated with respect to a particular reactant (first order in A, second order in B,...) or, more commonly, as the overall order. The overall order is the sum of the exponents. 

Several important points about the rate law are shown in equation A5.4. First, the rate of a reaction may depend on the concentrations of both reactants and products, as well as the concentrations of species that do not appear in the reaction s overall stoichiometry. Species E in equation A5.4, for example, may represent a catalyst. Second, the reaction order for a given species is not necessarily the same as its stoichiometry in the chemical reaction. Reaction orders may be positive, negative, or zero and may take integer or noninteger values. Finally, the overall reaction order is the sum of the individual reaction orders. Thus, the overall reaction order for equation A5.4 isa-l-[3-l-y-l-5-l-8. 

The rate of a process is expressed by the derivative of a concentration (square brackets) with respect to time, d[ ]/dt. If the concentration of a reaction product is used, this quantity is positive if a reactant is used, it is negative and a minus sign must be included. Also, each derivative d[ ]/dt should be divided by the coefficient of that component in the chemical equation which describes the reaction so that a single rate is described, whichever component in the reaction is used to monitor it. A rate law describes the rate of a reaction as the product of a constant k, called the rate constant, and various concentrations, each raised to specific powers. The power of an individual concentration term in a rate law is called the order with respect to that component, and the sum of the exponents of all concentration terms gives the overall order of the reaction. Thus in the rate law Rate = k[X] [Y], the reaction is first order in X, second order in Y, and third order overall. 

The exponents in a rate law depend on the reaction mechanism rather than on the stoichiometry of the overall reaction. The order of reaction often differs from the stoiehiometrie eoejfieient. Consequently, a rate law must always be determined by conducting experiments it can never be derived from the stoichiometry of the overall chemical reaction. 

This is the first example where we have tested to see if the concentration of a product affects the rate of a reaction. It may seem intuitive that products should not be involved in rate laws, but as we show in Section 15-1. a product may influence the rate of a reaction. In careful rate studies, this possibility must be considered. It is common for some reagents in a chemical system to have no effect on the rate of chemical reaction. Although it is unusual for none of the reagents to affect the rate, there are some reactions that are zero order overall. Such reactions have a particularly simple rate law Rate = t. 

Consider the case when the equilibrium concentration of substance Red, and hence its limiting CD due to diffusion from the bulk solution, is low. In this case the reactant species Red can be supplied to the reaction zone only as a result of the chemical step. When the electrochemical step is sufficiently fast and activation polarization is low, the overall behavior of the reaction will be determined precisely by the special features of the chemical step concentration polarization will be observed for the reaction at the electrode, not because of slow diffusion of the substance but because of a slow chemical step. We shall assume that the concentrations of substance A and of the reaction components are high enough so that they will remain practically unchanged when the chemical reaction proceeds. We shall assume, moreover, that reaction (13.37) follows first-order kinetics with respect to Red and A. We shall write Cg for the equilibrium (bulk) concentration of substance Red, and we shall write Cg and c for the surface concentration and the instantaneous concentration (to simplify the equations, we shall not use the subscript red ). 

Thus, in contrast to what occurred in the jar, in an EPS the overall chemical reaction occurs in the form of two spatially separated partial electrochemical reactions. Electric current is generated because the random transfer of electrons is replaced by a spatially ordered overall process. 

It is apparent from the last example cited in previous section that there is not necessarily a connection between the kinetic order and the overall stoichiometry of the reaction. This may be understood more clearly if it is appreciated that any chemical reaction must go through a series of reaction steps. The addition of these elementary steps must give rise to the overall reaction. The reaction kinetics, however, reflects the slowest step or steps in the sequence. An overall reaction is taken as for an example ... 

In general, the overall reaction process may comprise several individual steps, as shown in Figure 3.24. It could be seen that these steps pertain to (i) mass transfers of reactants and the products between the bulk of the fluid and the external surface of the solids (ii) transport of reactants and the products within the pores of the solid and (iii) chemical reaction between the reactants in the fluid and those in the solid. In order to be able to determine the rate-controlling step and to ascertain whether more than a single step should be consid-... 

The proportionality constant k, called the rate constant, has a constant value for a given reaction at a given temperature. The terms in square brackets are concentration terms (compare Chap. 14), and x and y are exponents which are often integral. The exponent x is called the order with respect to A, and y is called the order with respect to B. The sum x +y is called the overall order of the reaction. The values for x and y can be 0, 1, 2, 3 or 0.5, 1.5, or 2.5, but never more than 3. These values must be determined by experiment, and do not necessarily equal the values of a and b in the chemical equation. 

The Hatta criterion compares the rates of the mass transfer (diffusion) process and that of the chemical reaction. In gas-liquid reactions, a further complication arises because the chemical reaction can lead to an increase of the rate of mass transfer. Intuition provides an explanation for this. Some of the reaction will proceed within the liquid boundary layer, and consequently some hydrogen will be consumed already within the boundary layer. As a result, the molar transfer rate JH with reaction will be higher than that without reaction. One can now feel the impact of the rate of reaction not only on the transfer rate but also, as a second-order effect, on the enhancement of the transfer rate. In the case of a slow reaction (see case 2 in Fig. 45.2), the enhancement is negligible. For a faster reaction, however, a large part of the conversion occurs in the boundary layer, and this results in an overall increase of mass transfer (cases 3 and 4 in Fig. 45.2). 

In this expression, k is the rate constant—a constant for each chemical reaction at a given temperature. The exponents m and n, called the orders of reaction, indicate what effect a change in concentration of that reactant species will have on the reaction rate. Say, for example, m = 1 and n = 2. That means that if the concentration of reactant A is doubled, then the rate will also double ([2]1 = 2), and if the concentration of reactant B is doubled, then the rate will increase fourfold ([2]2 = 4). We say that it is first order with respect to A and second order with respect to B. If the concentration of a reactant is doubled and that has no effect on the rate of reaction, then the reaction is zero order with respect to that reactant ([2]° = 1). Many times the overall order of reaction is calculated it is simply the sum of the individual coefficients, third order in this example. The rate equation would then be shown as ... 

The fact that diffusion models describe a number of chemical processes in solid particles is not surprising since in most cases, mass transfer and chemical kinetics phenomena occur simultaneously and it is difficult to separate them [133-135]. Therefore, the overall kinetics of many chemical reactions in soils may often be better described by mass transfer and diffusion-based models than with simple models such as first-order kinetics. This is particularly true for slower chemical reactions in soils where a fast reaction is followed by a much slower reaction (biphasic kinetics), and is often observed in soils for many reactions involving organic and inorganic compounds. 

In considering chemical stability of a pharmaceutical, one musf evaluate the reaction order and reaction rate. The reaction order may be the overall order (the sum of the exponents of the concentration terms of fhe rate expression), or fhe order with respect to each reactant (the exponent of the individual concentration term in the rate expression). The reaction rate expression is a description of the drug concentration with respect to time. Most commonly, zero- and first-order reactions are encountered in pharmacy. 

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

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