Precision, concept

The modem theory of valency is not simple—it is not possible to assign in an unambiguous way definite valencies to the various atoms in a molecule or crystal. It is instead necessary to dissociate the concept of valency into several new concepts—ionic valency, covalency, metallic valency, oxidation number—that are capable of more precise treatment and even these more precise concepts in general involve an approximation, the complete description of the bonds between the atoms in a molecule or crystal being given only by a detailed discussion of its electronic structure. Nevertheless, these concepts, of ionic valency, covalency, etc., have been found to be so useful as to justify our considering them as constituting the modern theory of valency. 

The systems approach providers a conceptual framework for organizing knowledge about states of consciousness and a process for continually improving knowledge about the structures/subsystems. The ten subsystems sketched in chapter 8 are crude concepts at this stage of our knowledge and should eventually be replaced with more precise concepts about the exact nature of a larger number of more basic subsystems and about their possibilities for interaction to form systems. 

With this precise concept it is easy to understand that... 

More Precise Concepts. The concept of valence as discussed above is not rigorously defined, and many puzzling questions may present themselves. Thus elementary hydrogen may be considered to have either the valence 0, since it is not combined with any other element, or the valence 1, since the molecule may be assigned the structural formula H—H. Similarly oxygen in hydrogen peroxide, H Oo, may be taken As univalent, since.it is combined with an equal number of... 

A substantially macroscopic (in the thermodynamic sense) character of the parameter called the rate constant is its fundamental feature. Rigorously speaking, it is a statistical value (as well as temperature is) and can be applied only if the equilibrium distribution of Maxwell Boltzman type is kept (see Knyazev and Tsang, 1999). Unfortunately, the requirement of using the more precise concept, namely reaction cross-section, in everyday practice would not... 

A mathematically more precise concept associated to this property is ergodicity. The stroboscopic map is ergodic if all of its invariant sets (i.e. those that satisfy r(A) = A) have zero measure or their complement has zero measure. A stronger property is mixing that requires that for any two sets A and B the measure n (area or volume) of the intersection satisfies n B) —> /j,(A)/j,(B) for... 

The only mathematical restriction on /x° and f° in equation (12.1) is that they both refer to the same integration limit, or in physical terms, that they refer to the same equilibrium state. This state has been referred to in various places thus far as a reference state, which it is. We now consider it in more detail, with a more exact definition, and we refer to this more precise concept as a standard state. The exact nature of this state is completely a matter of definition, although a few definitions have themselves become standard because of their utility. We have used it in discussions of thermodynamic properties such as G°, H°, etc. to signify that the substance is in its pure state, and we have seen in the two conventions discussed in Chapter 7 that the pressure and temperature of the standard state could be different in different cases. With the introduction of the activity concept, standard states take on added importance because of their use in a wide variety of solutions, temperatures, and pressures, both fixed and variable, and we must now pay more attention to their definition than we have done so far. 

Reliability It is rather difficult to use the accuracy and precision concepts as these capital and basic properties are closely related in qualitative analysis. Their combination has produced a new property called reliability, which is defined as the proportion (percentage) of right yes or no answers provided by individual tests carried out on n aliquots of the same sample to identify an analyte or a family of the analytes. This definition represents the positive side of the errors in qualitative analysis false positives and false negatives. The reliability of the binary response is not an independent property as it strongly depends on the basic properties of sensitivity and selectivity. Moreover, it is in contradiction with productivity-related properties. Reliability is equivalent to certainty and, in quantitative analysis, the uncertainty of a result is a parameter associated with reliability. Indeed, the term is included in the definition of traceability as every experimental datum is affected by specific variations or doubts. As it directly affects the quality of an analytical result, it is necessary to find out an equivalent method to express vmcertainty in qualitative analysis. The term unreliabifity can be... 

Especially, Faraday s merit was that through introduction of precise concepts and definitions, he formed the basis of the quantitative description of the electrochemical phenomena known today. Thus, Faraday introduced such concepts as ion, anion, cation, anode, cathode and electrolyte. 

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