Empirical Concepts

Heterogeneity could also be expressed and described by elementary operations with empirical models. The only difference between (7.1) and (7.2) lies in the coefficient of c (t) on the right-hand side of the differential equations. This allows someone to infer empirically that these equations could be unified as 

Moreover, combinations of these models can also be used to roughly describe physiological considerations. For instance, if the drug is metabolized by the liver and simultaneously eliminated by the kidney, a gamma profile is obtained as solution of (7.3), where the a/t term expresses the structural heterogeneity of the liver, and the term j3, the homogeneous elimination process from the kidney. 

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The number of chemical species involved in a single elementary reaction is referred to as the molecularity of that reaction. Molecularity is a theoretical concept, whereas stoichiometry and order are empirical concepts. A simple reaction is referred to as uni-, bi-, or termolecular if one, two, or three species, respectively, participate as reactants. The majority of known elementary steps are bimolecular, with the balance being unimolecular and termolecular. 

Despite the fact that Milner s theory was originally developed for miktoarm-star copolymers, it can also be adopted for more complex branched structures. This empirical concept termed constituting-block copolymers approximates the architecture of branched molecules to be composed of an array of A2B and A2B2 miktoarms. This approach is capable of predicting the morphology of architectures as complex as centipedes or barbed wires, as shown in a very recent publication [125]. 

It would be highly desirable to reduce the individual facts in an information retrieval system to general principles just as the chemist has done in devising his empirical concepts mentioned pre-r viously. Such a reduction of information to its essential contents asks for insights, to transform information to knowledge. 

With chemical reactions, the exponents in a rate expression are usually integers. However, the exponents can be fractions or even negative depending on the complexity of the reaction. Reaction order should not be confused with molecularity. Order is an empirical concept whereas molecularity refers to the actual molecular process. However, for elementary reactions, the reaction order equals the molecularity. See Chemical Kinetics Molecularity First-Order Reactions Rate Constants... 

Our basic empirical concept is that chemical systems coupled via a metal atom behave like fragments directly joined with one another by o-bonds. In Scheme 2.2-1 the formal procedure for the linkage of orpnic moieties is compared with that re-... 

Of all the concepts used in chemistry, that of the chemical bond is one of the most useful and, at the same time, one of the most difficult. It is useful because it helps us to understand the structures of compounds and their properties, and it is difficult because it is not easy to relate it to the physical theories, such as quantum mechanics, that underlie chemistry. This is not to say that people have not attempted to find a connection between the chemical bond and quantum mechanics. The Lewis (1923) electron pair model and the orbital overlap model (Coulson 1961) are, perhaps, among the better known attempts, but all are a posteriori rationalizations, trying to explain the properties of the empirical nineteenth-century chemical bond in terms of twentieth-century physical concepts. It is unlikely that, left to themselves, theoretical chemists in the twentieth century would have ever created the idea of a chemical bond had not the concept already been central to the language of structural chemistry. To this day the chemical bond remains largely an empirical concept. 

It was not long before this empirical concept of chemical affinity became associated with the concept of Newtonian short-range interparticle forces, an identihcation best expressed in Bergman s 1775 monograph, A Dissertation on Elective Attractions, and in attempts, now known to be flawed, by such chemists as Guyton de Morveau, Wenzel, and Kirwan to quantitatively measure these forces—attempts which also culminated in an early precursor of the chemieal equation known as an affinity diagram (Figure 3). 

It should be mentioned that, as is often the case in a first draft, the author based his treatment of the turbulent convection on certain assumptions which in fact were not necessary, in particular the semi-empirical concept of L. Prandtl. Moreover, even in the analysis of laminar convection, the author [cf., for example the transition from equation (9) to equation (10)], to derive the asymptotic laws, resorts to simplifications of the equations which are really not necessary. Actually, it is possible to manage without these assumptions so that Zeldovich s asymptotic laws (8), (8a), (11), and (11a) may be obtained by simple dimensional analysis under the most general assumptions. 

The well-known Irving-Williams series1661 and the hard and soft acids and bases (HSAB) principle1671 are established empirical concepts related to the stability of... 

The theory underlying influences 1) and 2) is that of adsorption. General discussions of this theory can be found in (89). The theory of 3) and 4) was articulated by Arrhenius, and has been developed to include the concept of a transition state, intermediate between products and reactants. The theory of reaction kinetics is summarized at an elementary level in (88, 90-91) Theories of energized surface chemical reactions, 5) of which PEC is the best developed (44-48) are relatively recent, and can not be considered to be complete. Stabilization by surfaces, 6) is an empirical concept, for which no general theory has been developed, nor may even be possible. 

Even the layout of the periodic table of the elements cannot be derived from quantum theory without assuming an empirical concept, known as the Pauli exclusion principle. An alternative derivation (4.6.1) through number theory predicts the correct periodicity, without assuming the exclusion principle. In fact, the operation of an exclusion principle can be inferred from this periodic structure and reduced to a property of space, but it remains impossible to reconstruct or predict from more basic principles. 

Discontinuing the unwarranted allocation of precision to empirical concepts ... 

Elimination of the dependence on the antiquated, admittedly empirical, concept of "oxidation number" in inorganic chemistry, as well as reliance on the (not admitted) topologically inappropriate concept of smallest set of smallest rings in organic chemistry — whose mathematical raison d etre is a two dimensional world view ... 

The well known Irving-Williams series1253 2561 and the HSAB principle1257-1 are established empirical concepts related to the stability of metal complexes, and the question of whether these are accounted for in a general molecular mechanics approach have not always been appreciated when metal ion selectivities have been modeled via empirical force field calculations. The assumption that the position of the minima and the steepnesses of the potential energy functions for the metal-ligand bonds for varying metal ions and constant donor sets accurately reflect var-... 

The answer to the first question is of an empirical nature and will be sought in terms of the nature of the inversion process, the structural factors affecting it and the rationalization of the results through more or less empirical or semi-empirical concepts and schemes. 

Since the ionic radius is an empirical concept and furthermore its value is only constant to a rough approximation (p. 39) these differences of a few 0.01 A are without significance. 

Theoretical chemistry must search for realistic models and alternative interpretations of basic theory that accord with the time-honoured empirical concepts of chemistry. Above all chemistry needs a theory of the electron, the one object at the heart of all chemical change. 

However, the analysis of experimental data on flow birefringence and the use of some theoretical (sometimes semi-empirical) concepts allows important conclusions... 

The nature of the chemical bond and the principles of molecular structure were formu lated along time ago to systematize an immense body of chemical knowledge. With the advent of quanmm mechanics, it became possible to actually derive the concepts of chemical bonding from more fundamental laws governing matter on the atomic scale. Remarkably, many of the empirical concepts developed by chemists have remained valid when reexpressed in terms of quantum-mechanical principles. 

Alchemy The study and manipulation of matter based on a belief that matter can be transformed from one form to another by physical, spiritual or magical processes, or a combination of such processes. Although alchemical ideas extend back to at least 5000 b.c.e and existed in all civilizations, there was a great expansion of alchemical activities between 800 and 1600 c.E. after which time alchemical ideas were gradual replaced with empirical concepts of matter. Alchemy was often directed toward the making of gold from base metals or the creation of an elixir of life that gave immortality. 

Other empirical concepts have been used to consolidate data. These include the isoelectronic principle, electronegativity correlations, the relationship to absorption spectra, and the effects of single and multiple substitutions of functional groups on molecules. A similar change in the electron affinities is observed when the more electronegative nitrogen atom replaces a CH group in aromatic molecules. Statistical techniques are used to establish these correlations. Because they are empirical and require additional data for their application, the results are less certain. 

It should perhaps be stressed that tbe notion of chemical substances is completely different from the metaphysical concept of substance that figures in the philosophical tradition since Aristotle (Witt, 1989 Hoffman Rosenkrantz, 1994). As will appear, the chemical notion of substance is, at least as presented in this chapter, an empirical concept, whose referent is wholly defined in terms of laboratory procedures, and cannot be given an essentialist definition. 

The reaction order is an empirical concept. Its value has to be determined, since it cannot readily be derived from the stoichiometry, often... 

X-ray diffraction does not separate atoms that are Periodic Table neighbours well, as the scattering factors of these species are so similar. Thus, problems such as the distribution of Fe2+ and Fe3+ over the available sites in a crystal structure may be unresolved by conventional structure determination methods. The bond valence model is an empirical concept that correlates the strength of a chemical bond between two atoms and the length of the bond. Because crystal structure determinations yield accurate interatomic distances, precise values of the bond strength, called the experimental bond valence, can be derived. 

In spite of years of experience with catalysts and the vast number of pubhcations concerning catalytic processes, there is stiU no fundamental theory of catalysis. As is often the case in chemistry, empirical concepts are used to explain experimental results or to make predictions about new reactions, with greater or lesser degrees of success. 

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