Simultaneous series reactions

The help command in Maple is invoked to describe Ei. The following description for Ei is given in Maple s help file. 

This classical definition is extended by analytic continuation to the entire complex plane using 

Note that this extension has its branch cut on the negative real axis, but unlike for the 2-argument Ei functions this extension is not continuous onto the branch cut from either above or below. That is, this extension provides an analytic continuation of Ei(z) from the positive real axis, but not in any direction from the negative real axis. If you want a continuation from the negative real axis, use -Ei(l, -z) in place of Ei(z). 

Abramowitz, M. and Stegun, I. Handbook of Mathematical Functions. New York Dover Publications Inc., 1965. 

An additional reference for the function of Ei is F. B. Hildebrand, Advanced Calculus for Applications, 2d Ed, 1976, Prentice-Hall, page 50.[13] 

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Multiple reactions Series or parallel reactions that take place simultaneously in a reactor. For example, A -(- B C and A + D - E are parallel reactions, and A + B C + D E + F arc series reactions. 

Frequently, several reactions proceed simultaneously, and consequently selectivity and yield in networks of parallel and series reactions with respect to a certain desired target component D are essential quantities. 

Fire retardancy of wood involves a complex series of simultaneous chemical reactions, the products of which take part in subsequent reactions. Most FRs used for wood increase the dehydration reactions that occur during thermal degradation so that more char and fewer combustible volatiles are produced. The mechanism by which this happens depends on the particular FR and the thermal-physical environment. The effectiveness of a FR treatment depends upon the performance rating of the treated material when tested in accordance with ASTM E84 (no greater flame spread than 25). 

Complex reactions coupled simultaneous series and parallel... 

Reactions rarely take place in isolation of other reactions. Reversibility is one example of the simultaneity of reaction chemistries. Another classical problem is the one that arises when a reaction is immediately preceded by another reaction. When reactions occur in series, they are referred to as being consecutive. An example would be ... 

Complex Series Reactions. Complex series reactions are those in which there is further reaction between one of the reactants and one of the products so that both series and parallel reactions take place simultaneously. An example of this is... 

A series of simultaneous, complex reactions occurs during acetylation of cellulose and during hydrolysis of cellulose triacetate. Reactions include acetylation of the cellulose, some sulfation of the cellulose, degradation of the cellulose chain and reaction to chain-ends, acetylation of the hemicellulose components, and then random hydrolysis of the acetylated or sulfated product [6-12],... 

The mechanistic detail of surface reactions will be much less complicated than indicated by these global reactions which can never occur as written. Rather, the processes will occur via a series of much simpler, simultaneous/consecutive reactions. The initial state of dispersion of the NaOH is important to maximize the contact between the NaOH and the carbon surface. What is uncertain is the chemical state of the NaOH at temperatures of about 350 °C. Has the —OH become bonded to the carbon surface and is the Na-atom/ ion free to move in and around the carbon, or is there a form of Na—O complex on the surface. At these temperatures, intercalation is possible. The (C) —OH appears not to be stable as such but decomposes to (C) =0 and the hydrogen is abandoned. The hydrogen, which must have originated as an atomic species appears to be unable to be chemisorbed... 

Generai description. Galvanic corrosion refers to the preferential corrosion of the more reactive member of a two-metal pair when the metals are in electrical contact in the presence of a conductive fluid (see Chap. 16, Galvanic Corrosion ). The corrosion potential difference, the magnitude of which depends on the metal-pair combination and the nature of the fluid, drives a corrosion reaction that simultaneously causes the less-noble pair member to corrode and the more-noble pair member to become even more noble. The galvanic series for various metals in sea water is shown in Chap. 16, Table 16.1. Galvanic potentials may vary with temperature, time, flow velocity, and composition of the fluid. 

The only reaction series involving a reaction at a heteroatom which has been extensively studied is the basicity of substituted pyridines. The Hammett equation was first applied to this reaction simultaneously by Brown and co-workers and by Jaffe and Doak. A sampling... 

As stated earlier, catalytic cracking involves a series of simultaneous reaction.s. Some of these reactions are endothermic and some are exothermic. Each reaction has a heat of reaction associated with it (Table 4-4). The overall heat of reaction refers to the net or combined heat of reaction. Although there are a number of exothermic reactions, the net reaction is still endothermic. 

If, for the purpose of comparison of substrate reactivities, we use the method of competitive reactions we are faced with the problem of whether the reactivities in a certain series of reactants (i.e. selectivities) should be characterized by the ratio of their rates measured separately [relations (12) and (13)], or whether they should be expressed by the rates measured during simultaneous transformation of two compounds which thus compete in adsorption for the free surface of the catalyst [relations (14) and (15)]. How these two definitions of reactivity may differ from one another will be shown later by the example of competitive hydrogenation of alkylphenols (Section IV.E, p. 42). This may also be demonstrated by the classical example of hydrogenation of aromatic hydrocarbons on Raney nickel (48). In this case, the constants obtained by separate measurements of reaction rates for individual compounds lead to the reactivity order which is different from the order found on the basis of factor S, determined by the method of competitive reactions (Table II). Other examples of the change of reactivity, which may even result in the selective reaction of a strongly adsorbed reactant in competitive reactions (49, 50) have already been discussed (see p. 12). 

Under the aforementioned circumstances, the two-step reaction 4.53 and the associated eqns. 4.54-4.62 are equally valid on the understanding that HS represents Hcres, etc. further, it must be realized that during titration various amounts of HX and B are simultaneously present. Therefore, from previous measurement of the conductivities (k) of dilution series of the separate acids, bases and salts in m-cresol, the overall constants KHX, KB and KBH+X were calculated by the Fuoss and Kraus method66,67 (with the use of e = 12.5 and viscosity = 0.208 P for m-cresol). For C6H6S03H and HC1 it was necessary to calculate the equivalent conductivity at zero concentration from the equation... 

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