Five Generalizations

Based on more than a century of experimental and theoretical study of the kinetics of many different chemical reactions, some rules of thumb concerning the form of the rate equation have evolved. There are important exceptions to each of these ndes-of-thumb. Nevertheless, the following five generalizations permit chemical engineers to attack many practical problems in reactor design and analysis. 

For single reactions that are essentially irreversible, the rate of disappearance of reactant A can be expressed as 

This equation tells us that the effects of temperature and concentration frequently can be separated. The term k T) does not depend on any of the concentrations and is called a rate constant. The term F(aU C,) depends on the concentrations of the various species but not on temperature. 

There are two major theories of chemical kinetics, collision theory (CT) and transition-state theory (TST). Both theories lead to rate equations that obey Generalization I, i.e., the effects of temperature and concentration are separable. Unfortunately, both CT and TST apply to a very limited category of reactions known as elementary reactions. An elementary reaction is one that occurs in a single step on the molecular level exactly as written in the balanced stoichiometric equation. The reactions that chemists and chemical engineers deal with on a practical level almost never are elementary. However, elementary reactions provide the link between molecular-level chemistry and reaction kinetics on a macroscopic level. Elementary reactions will be discussed in some depth in Chapter 5. For now, we must look at Eqn. (2-1) as an empirical attempt to extrapolate a key result of CT and TST to complex reactions that are outside the scope of the two theories. 

Despite its lack of a strong theoretical justification, Eqn. (2-1) is very useful in a practical sense. It frequently provides a reasonable starting point for the analysis of experimental kinetic data as well, as for reactor design and analysis. 

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Odor perception and description are highly subjective in nature. Nevertheless, there is a generally agreed-upon odor vocabulary that is used to characterize individual ingredients and finished fragrances. Table 1 shows some commonly used odor descriptors grouped into five general classifications. 

Types of Insulation Ciyogenic insiilations have generally been divided into five general categories high vacuum, multilayer insulation, powder, foam, and specif insulations. Each is discussed in turn in the following sections. 

Five general types of isotherms have been observed, and the shapes of these eharaeteristic isotherms are shown in Fig. 6 [29]. The Type I isotherm represents systems where only monolayer adsorption occurs, while Type 11 indicates the... 

There are five general eategories of emergeney response personnel who respond to speeifie types of emergeneies ... 

Table 4-3 Symmetric Laminate with Five Generally Orthotropic Layers...

It is important to recognize that different types of inhibitors often function by different mechanisms, and that a given antioxidant may react in more than one way. Thus, a material that acts as an antioxidant under one set of conditions may become a pro-oxidant in another simation. The search for possible synergistic combinations of antioxidants can be conducted more logically and efficiently if we seek to combine the effects of different modes of action. Five general modes of oxidation inhibition are commonly recognized ... 

In studying dissolution and precipitation, geochemists commonly consider that a reaction proceeds in five generalized steps ... 

Five general cases have been described in the literature for AB diblocks with one crystallizable block ... 

Viral vaccines may have their strength expressed as one of five general forms. 

Five general categories of what can go wrong with self-reactive materials are ... 

Section 409(b)(2) of the Act describes the statutory requirements for food additive petitions. Briefly, these encompass five general areas of information ... 

There are five general methods known for the preparation of 1,2,4-oxadiazoles ... 

The ability to catalyze reactions leading to enantiomerically pure products is one of the most important features of enzymes. Therefore there is a special need for the analysis of optical activity of substrates or products of bio catalytic conversions. The methods for the estimation of enantioselectivity of bioconversions can be divided into five general classes ... 

The robustness of TMSP-type catalysts allows one to address many of the limitations regarding the development of optimal catalysts for homogeneous selective oxidation, including the five general limitations articulated above (1) inadequate... 

FIG. 9.4 Qualitative shapes of the five general types of gas adsorption isotherms. (See text for a discussion of their physical significance.)... 

I consider that there are five general conditions which are to be met in hydrogen bonding, and only there ... 

The major classes of photochemical reaction for aromatic compounds are nucleophilic substitution and a range of processes that lead to non-aromatic products—valence isomerization, addition or cycloaddition reactions, and cyclization involving 6-electron systems. These five general categories of reaction will be described in the following sections, together with a few examples of more specific processes. 

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