Equations, chemical Quantitative interpretation

The quantitative interpretation of chemical reactions is the part of chemistry called reaction stoichiometry. Recall from Section H that a stoichiometric coefficient in a chemical equation tells us the relative number of moles of a substance that reacts or is produced. Thus, the stoichiometric coefficients in... 

SYMBOLS —FORMULAS —CONSERVATION OF MATTER — CHEMICAL EQUATIONS—QUANTITATIVE INTERPRETATION OF EQUATIONS —PROBLEMS BASED ON EQUATIONS — PROBLEMS. 

A more quantitative interpretation of chemical shift data cannot be made at present, with few exceptions, such as the calculations of ring current shifts. The theory of chemical shifts is by and large inadequate to deal with the subtleties of the observed changes. A priori calculations remain grossly inaccurate, because the large number of parameters contained in the equations cannot be derived from any experimental measurement. Even calculations of ring current shifts involve iterative fitting of these parameters to known crystal structure data. The view of molecular structure derived from a study of chemical shifts thus reveals a wealth of detail blurred in its essentials. 

One of the most important areas of chemical arithmetic is based on balanced chemical equations. Chemists call this area of endeavor stoichiometry (stoy-key-om -ah-tree), which concerns the quantitative relationships between the reactants and products in chemical reactions. Stoichiometric calculations can be used to determine the amount of one reactant needed to completely react with another, or to determine the amount of reactant needed to produce a desired amount of product. The key to understanding how this is done is found in the way balanced chemical equations can be interpreted. So that is the place to begin learning the arithmetic of balanced chemical equations. 

The chemical bonding in iodine compounds is much simpler to describe than that in tin, antimony, or tellurium which precede it in the Periodic Table. This is particularly true where the iodine forms only one bond to another atom. As a result it is possible to develop a quantitative interpretation of the Mossbauer parameters. The equations given here were first formulated by Hafemeister et al. [74] and subsequently revised to a more elegant form by Perlow and Perlow [72]. 

What has been said applies to approximate as well as to ab-initio molecular orbital wavefunctions,i.e. those obtained by solving the self-consistent-field equations exactly. Hence, the localized orbital approach also offers an attractive tool for bridging the gap between rigorous quantitative calculations and qualitative chemical intuition. The experience gained so far has shown that interpretations suggested by the localized orbital picture correspond closely to intuitive chemical thinking. 

There are two general types of aerosol source apportionment methods dispersion models and receptor models. Receptor models are divided into microscopic methods and chemical methods. Chemical mass balance, principal component factor analysis, target transformation factor analysis, etc. are all based on the same mathematical model and simply represent different approaches to solution of the fundamental receptor model equation. All require conservation of mass, as well as source composition information for qualitative analysis and a mass balance for a quantitative analysis. Each interpretive approach to the receptor model yields unique information useful in establishing the credibility of a study s final results. Source apportionment sutdies using the receptor model should include interpretation of the chemical data set by both multivariate methods. 

PHYSICAL CHEMISTRY. Application of the concepts and laws of physics to chemical phenomena in order to describe in quantitative (mathematical) terms a vast amount of empirical (observational) information. A selection of only the most important concepts of physical chemistiy would include the electron wave equation and the quantum mechanical interpretation of atomic and molecular structure, the study of the subatomic fundamental particles of matter. Application of thermodynamics to heats of formation of compounds and the heats of chemical reaction, the theory of rate processes and chemical equilibria, orbital theory and chemical bonding. surface chemistry (including catalysis and finely divided particles) die principles of electrochemistry and ionization. Although physical chemistry is closely related to both inorganic and organic chemistry, it is considered a separate discipline. See also Inorganic Chemistry and Organic Chemistry. 

A more quantitative attempt at interpreting platinum chemical shifts requires that we consider some form of the Ramsey (48) equation, which describes the resonance frequency, v9 in terms of the paramagnetic screening term, o>- QAB is a charge-density, bond-order matrix, AE is the average excitation energy, and r represents a distance from the nucleus for, in this case, a given d electron. 

Thermogravimetry is an attractive experimental technique for investigations of the thermal reactions of a wide range of initially solid or liquid substances, under controlled conditions of temperature and atmosphere. TG measurements probably provide more accurate kinetic (m, t, T) values than most other alternative laboratory methods available for the wide range of rate processes that involve a mass loss. The popularity of the method is due to the versatility and reliability of the apparatus, which provides results rapidly and is capable of automation. However, there have been relatively few critical studies of the accuracy, reproducibility, reliability, etc. of TG data based on quantitative comparisons with measurements made for the same reaction by alternative techniques, such as DTA, DSC, and EGA. One such comparison is by Brown et al. (69,70). This study of kinetic results obtained by different experimental methods contrasts with the often-reported use of multiple mathematical methods to calculate, from the same data, the kinetic model, rate equation g(a) = kt (29), the Arrhenius parameters, etc. In practice, the use of complementary kinetic observations, based on different measurable parameters of the chemical change occurring, provides a more secure foundation for kinetic data interpretation and formulation of a mechanism than multiple kinetic analyses based on a single set of experimental data. 

The present results clearly establish the D parameter of localized triplet diradicals as a reliable spectral tool to probe for electronic factors that control spin delocalization and radical stabilization in the benzyl-type radicals 14. Equation (8) offers us the opportunity to interpret the experimental results through semiempirical MO calculations in terms of the theoretically accessible a-spin-density variations. The spectroscopic AD scale does not suffer from the limitations (polar vs. radical contributions) inherent in the kinetic chemical scales and provides us with over 40 aryl substituents, which is the most comprehensive collection of electronic effects on radicals. Its extension to heteroaryl-substituted diradicals (12) provides for the first time a quantitative experimental measure of delocalization in aromatic n systems. The salient features of this novel method are... 

The concise symbolic notation of modern chemistry, although much less picturesque than alchemical symbolism, enables chemical changes to be represented very simply and fully, particularly by means of chemical equations. These equations embody the leading principle that the chemist must cultivate two-dimensional thou t he must learn to interpret chemical symbolimn both qualitatively and quantitatively. For example, the complete expression of Cavendishes explosion of a mixture of hydrogen and oxygen is given by the equation ... 

P FIGURE 3.15 Interpreting a balanced chemical equation quantitatively. 

We have seen already that chemical equations are always written in terms of the numbers of particles involved. Whether we interpret them in terms of individual molecules or moles of molecules, the stoichiometric coefficients that balance a chemical equation refer to numbers of particles and not to masses. Usually, we can t measure the number of particles directly in the laboratory masses and volume of liquids are the quantities that are more likely to be measurable. Thus if we want to make quantitative calculations for a chemical reaction, fi-equently we need to convert between the measured value of a mass or volume and the desired value of a number of moles. Because such calculations are common and important, chemists have developed a standard approach to overcome this variable mismatch. Although you might think of this approach as an algorithm for solving a particular class of chemistry problems, it is instructive to understand its conceptual... 

---