Basic routes

Ethylene oxide has been produced commercially by two basic routes the ethylene chlorohydrin and direct oxidation processes. The chlorohydrin process was first iatroduced dufing World War I ia Germany by Badische Anilin-und Soda-Eabfik (BASE) and others (95). The process iavolves the reaction of ethylene with hypochlorous acid followed by dehydrochlofination of the resulting chlorohydrin with lime to produce ethylene oxide and calcium chloride. Union Carbide Corp. was the first to commercialize this process ia the United States ia 1925. The chlorohydrin process is not economically competitive, and was quickly replaced by the direct oxidation process as the dominant technology. At the present time, all the ethylene oxide production ia the world is achieved by the direct oxidation process. 

Congress charged the Environmental Protection Agency (EPA) to administer TSCA and, in assigning authority provided two basic routes for implementation. In the first case, Congress spelled out in the act what information EPA was to provide and made such... 

Figure 7.53 Hydrolysis and polymerization of a generic alkoxide Si(OR)4 involving both (a) acid and (b) basic routes. Reprinted, by permission, from H. Yanagida, K. Koumoto, and M. Miyayama, The Chemistry of Ceramics, p. 148. Copyright 1996 by John Wiley Sons, Inc.

Another series of monomers that was prepared began with the displacement of an unactivated aryl halide with phenate anion in the presence of a copper catalyst [113-115], Figure 46 outlines the basic route followed for the preparation of 114a. The sequence of reactions started with 4-bromobenzocyclobu-tene, 2 which was reacted with the phenate of p-acetamidophenol, 112a in the presence of copper (I) chloride as a catalyst, to afford the ether linked product 113a in a yield of 50-75%. 

Other, preferable compounds are from the class of amino phospohonates (21). The preparation of several phosphoramidate compounds has been described in detail (68). The basic route of synthesis is shown in Figure 8.3. 

It can be shown algebraically that the number of basic routes, P, is determined by... 

A linear independence of routes does not imply linear independence of the respective overall equations. For instance, as mentioned, the basic routes of the reaction (35) result in the same overall equation. A more complicated... 

If, for some stage rs r s > the stage is called fast, it may also be called a quasi-equilibrium stage. In addition, strictly equilibrium stages are also possible namely, if stoichiometric numbers of a stage for all basic routes are zero, then rs = r s (i.e., = 0). Herewith rs and r s may be... 

If the number of basic overall equations, Q, is smaller than that of basic routes, P, it is expedient to use a stoichiometric basis of routes for a description of the reaction. In this case we need to know only Q rates along nonempty basic routes the remaining P — Q rates are not required (but this by no means implies that they equal zero). 

It has been already noted that the rate of a steady-state reaction can be regarded as a vector in the P-dimensional space specified by its components, which are the rates along the basic routes. In terms of linear algebra, the above result means that when the basis of routes is transformed the reaction rate vector along these routes is transformed contravariantly. 

The equations determining the kinetics of a steady-state reaction comprise, together with unknown rates along the basic routes, unknown concentrations of intermediates. Only the rates as functions of the concentrations of reaction participants are usually required therefore, the unknown concentrations are to be excluded from the equations. In many cases this is made easier by application of an equation that is obtained as follows (33). We form an identity including the rates of m stages with numbers, s2, s2, sm, chosen arbitrary from the total number of stages, S ... 

Generally speaking, the concept of forward and reverse reaction rates is inapplicable to many-route reactions, but it can be applied in some particular cases. Such is the case of a double-route reaction with one of basic routes being at equilibrium (35). 

Another case occurs if a mechanism of a many-route reaction includes a block that has only one basic route then, as was explained in Section VII, the equation of single-route steady-state reactions and, consequently, the concept of forward and reverse rates can be applied. 

While the reaction is described by two overall equations, the number of basic routes is three. The basis of the routes in scheme (220) is chosen so that the overall equation of route Art3) is 0 = 0 i.e., A 3) is an empty route. Thus, the basis of routes is stoichiometric. Therefore, kinetic equations are required only for two rates namely that along routes AK1) and AK2). 

In the range of temperatures and pressures where the reaction is substantially reversible, the kinetics is much more complicated. There is no grounds to consider chemical changes described by (272) and (273) as independent, not interconnected, reactions. Conversely, if processes (272) and (273) occur on the same surface sites, then free sites will act as intermediates of both processes. Thus one must use the general approach, treating (272) and (273) as overall equations of a certain single reaction mechanism. But if a reaction is described by two overall equations, its mechanism should include at least two basic routes hence, the concept of reaction rate in the forward and reverse directions can be inapplicable in this case. However, experiments show that water-gas equilibrium (273) is maintained with sufficient accuracy in the course of the reaction. Let us suppose that the number of basic routes of the reaction is 2 then, as it has been explained in Section VIII, since one of the routes is at equilibrium, the other route, viz., the route with (272) as overall equation, can be described in terms of forward, r+, and reverse, r, reaction rates. The observed reaction rate is then the difference of these... 

Basic route N(l) is a block (i.e., has with basic route JV(2) no common stages) therefore, (71) may serve for the derivation of the kinetic equation, with only the stages of the block included. 

The reaction is described by two basic routes in (391) they are chosen so that carbon enters the reaction only in route A 1, and route N<2) results in the conversion of a part of CO formed in route N(1) into C02. With such a choice of the basis of routes, r u, the rate of the reaction along route Nil) is the rate of carbon gasification i.e., corresponds to symbol r(1) in (390). 

It is evident that the choice of stoichiometric numbers is ambiguous. In principle, one can obtain an infinitive number of routes by obtaining them as linear combinations of routes entering into the basic route. 

The theory of steady-state reactions operates with the concepts of "a path of the step , "a path of the route , and "the reaction rate along the basic route . Let us give their determination in accordance with ref. 16. The number of step paths is interpreted as the difference of the number of elementary reaction acts in the direct and reverse directions. Then the rate for the direct step is equal to that of the paths per unit time in unit reaction space. One path along the route signifies that every step has as many paths as its stoichiometric number for a given route. In the case when the formation of a molecule in one of the steps is compensated by its consumption in the other step, the steady-state reaction process is realized. If, in the course of this step, no final product but a new intermediate is formed, then it is this... 

The application of the concept of "the rate along the basic route provides a possibility of obtaining a new formulation for the quasi-stationary conditions in terms of the Horiuti theory which is different from the ordinary one, i.e. "the formation of an intermediate is equal to that of its consumption . Temkin called the equations obtained "the conditions for the statio-narity of steps . In matrix form they are represented as... 

Here v is the matrix of the Horiuti (stoichiometric) numbers and v and w the vector-columns of the rates along basic routes and of the step rates, respectively. Thus the rate of every step is represented as a linear combination of the rates along the basic routes. Here it is recommended that a simple hydrodynamic analogy be used. The total liquid flow along the tube (step) is the reaction rate. This flow consists of individual streams which are the rates along the routes. 

---