Quantitative Studies of Chemical Reactions

Near-infrared absorption is therefore essentially due to combination and overtone modes of higher energy fundamentals, such as C-H, N-H, and O-H stretches, which appear as lower overtones and lower order combination modes. Since the NIR absorption of polyatomic molecules thus mainly reflects vibrational contributions from very few functional groups, NIR spectroscopy is less suitable for detailed qualitative analysis than IR, which shows all (active) fundamentals and the overtones and combination modes of low-energy vibrations. On the other hand, since the vibrational intensities of near-infrared bands are considerably lower than those of corresponding infrared bands, optical layers of reasonable size (millimeters, centimeters) may be transmitted in the NIR, even in the case of liquid samples, compared to the layers of pm size which are detected in the infrared. This has important consequences for the direct quantitative study of chemical reactions, chemical equilibria, and phase equilibria via NIR spectroscopy. 

Our objective in this chapter is to begin the subject of stoichiometry, the quantitative study of chemical reactions. This will help us determine, for example, what quantity of oxygen is required for complete combustion of a given quantity of glucose or what mass of carbon dioxide can be obtained. Stoichiometry is a part of chemistry that is fundamental to much of what chemists, chemical engineers, biochemists, molecular biologists, geochemists, and many others do. 

By the seventeenth century, the common strong acids— nitric, sulfuric, and hydrochloric—were known, and systematic descriptions of common salts and their reactions were being accumulated. As experimental techniques improved, the quantitative study of chemical reactions and the properties of gases became more common, atomic and molecular weights were determined more accurately, and the groundwork was laid for what later became the periodic table of the elements. By 1869, the concepts of atoms and molecules were well established, and it was possible for Mendeleev and Meyer to propose different forms of the periodic table. Figure 1.9 illustrates Mendeleev s original periodic table. ... 

Measurements of changes in weight are a characteristic feature of the quantitative study of chemical reactions such measurements reveal one of the most important facts about the chemical combination of substances, namely that it generally involves fixed and definite proportions by weight of the reacting substances. These changes in weight are found to be subject to two fundamental laws ... 

Computer simulation techniques offer the ability to study the potential energy surfaces of chemical reactions to a high degree of quantitative accuracy [4]. Theoretical studies of chemical reactions in the gas phase are a major field and can provide detailed insights into a variety of processes of fundamental interest in atmospheric and combustion chemistry. In the past decade theoretical methods were extended to the study of reaction processes in mesoscopic systems such as enzymatic reactions in solution, albeit to a more approximate level than the most accurate gas-phase studies. 

The application of NMR to the study of chemical reactions has been expanded to a wide range of experimental conditions, including high pressure and temperatures. In 1993, Funahashi et al. [16] reported the construction of a high pressure 3H NMR probe for stopped-flow measurements at pressures <200 MPa. In the last decade, commercial flow NMR instrumentation and probes have been developed. Currently there are commercially available NMR probes for pressures of 0.1-35 MPa and temperatures of 270-350 K (Bruker) and 0.1-3.0 MPa and 270-400 K (Varian). As reported recently, such probes can be used to perform quantitative studies of complicated reacting multicomponent mixtures [17]. 

The problem of chemical composition was directly related to that of chemical combination. Combining chemicals to produce new substances had been a goal of individuals throughout history. Lavoisier s work emphasized the quantitative study of chemical combination. Chemists sought to determine the proportion in which chemicals combined, and how much of one substance it took to react with another. Rather than combining substances using the alchemist s trial and error method, chemists sought to determine the specific ratio of chemicals involved in chemical reactions. 

Since a quantitative measure for chirality is now available, we apply it to the study of chemical reactions. We consider the ensemble of the initial reactants and the ensemble of the final products in both ensembles each molecule is taken as many times as it appears in the balanced stoichiometric equation representing the reaction. These are called the ensembles representing the initial reactants and the final products. With this convention, we can now divide all chemical reactions involving chiral molecules into three mutually exclusive categories ... 

The quantitative study of chemical equilibrium and the rate of chemical reactions will be taken up in Chapter 19. It is often j ssible to reach a useful qualitative conclusion about a chemical system, however, simply by applying Le Chatelier s principle. The example that we are discussing shows that a chemical reaction may be made to proceed first in one direction and then in the opposite direction simply by changing the concentration of one or more of the reacting substances. 

The quantitative study of photochemical reactions requires knowledge of the concentrations of reactants and products as well as the number and energy of photons absorbed by the sample. The determination of the number of photons absorbed by the sample is known as actinometry. In some cases these measurements are made by irradiating the sample and a standard chemical reference system simultaneously. Alternatively, the measurements may be made with electronic devices. ... 

In order to simplify and rationalize the studies of chemical reactions it would be useftil to identify the central properties of any molecule that determine whether and how it would react with any other molecule. Some approaches in this direction were discussed in Section 7 but we saw that this field is not yet mature and, although some trends are emerging (including those based on the HSAB principle and on the Fukui function), the approaches can still not be used in a quantitative manner. 

Wood, P.M., Ross, J. A quantitative study of chemical waves in the Belousov- Zhabotinsky reaction. J. Chem. Phys. 82, 1924 (1985)... 

A major challenge in quantum dynamics is to develop quantitatively accurate methods for practical computational study of chemical reactions involving polyatomic molecules. Currently, rigorous quantum dynamics calculations are limited to those systems involving no more than four atoms. In order to perform a quantitatively accurate quantum dynamics study for the vast majority of chemical reactions that are of chemical or biological interest, it is necessary to develop practical computational methods to treat the reaction dynamics of polyatomic molecules. To this end, some reduced dimensionality methods have been proposed to treat polyatomic systems (tetra-atomic systems in particular) by reducing the dynamical degrees of freedom from six to three. 

P.M. Wood and J. Ross "A quantitative Study of Chemical Waves in the Belousov Zhabotinsky Reaction," submitted to J.Chem.Phys. 

Before beginning a quantitative treatment of enzyme kinetics, it will be fruitful to review briefly some basic principles of chemical kinetics. Chemical kinetics is the study of the rates of chemical reactions. Consider a reaction of overall stoichiometry... 

Chemistry is a quantitative science. This means that a chemist wishes to know more than the qualitative fact that a reaction occurs. He must answer questions beginning How much. . . The quantities may be expressed in grams, volumes, concentrations, percentage composition, or a host of other practical units. Ultimately, however, the understanding of chemistry requires that amounts be related quantitatively to balanced chemical reactions. The study of the quantitative relationships implied by a chemical reaction is called stoichiometry. 

These observations remind us of Chapter 8, in which we considered the factors that determine the rate of a chemical reaction. Of course, the same ideas apply here. We can draw qualitative information about the mechanism of the reaction by applying the collision theory. With quantitative study of the effects of temperature and concentration on the rate, we should be able to construct potential energy diagrams like those shown in Figure 8-6 (p. 134). 

With growing interest in the chemical behaviour of actinide ions in the environment (1), the complexation of these ions with carbonate anions has been recently attracting particular attention (2-10) due to the ubiquitous presence of carbonate ions in nature (11, 12) and their pronounced tendency to form complexes with heavy metal ions (7, 10-14). In spite of the carbonate complexation of actinides being considered important chemical reactions for understanding the chemistry of actinides in natural fluids, not many experiments have been devoted up to now to the quantitative study of the subject, though numerous qualitative observations are discussed in the literature. Although there are a few papers reporting the formation constants of carbonate complexes... 

Chemical kinetics deals with quantitative studies of the rates at which chemical processes occur, the factors on which these rates depend, and the molecular acts involved in reaction processes. A description of a reaction in terms of its constituent molecular acts is known as the mechanism of the reaction. Physical and organic chemists are primarily interested in chemical kinetics for the light that it sheds on molecular properties. From interpretations of macroscopic. kinetic data in terms of molecular mechanisms, they can gain insight into the nature of reacting systems, the processes by which chemical bonds are made and broken, and the structure of the resultant product. Although chemical engineers find the concept of a reaction mechanism useful in the correlation, interpolation, and extrapolation of rate data, they are more concerned with applications... 

Mechanisms of dissolution kinetics of crystals have been intensively studied in the pharmaceutical domain, because the rate of dissolution affects the bioavailability of drug crystals. Many efforts have been made to describe the crystal dissolution behavior. A variety of empirical or semi-empirical models have been used to describe drug dissolution or release from formulations [1-6]. Noyes and Whitney published the first quantitative study of the dissolution process in 1897 [7]. They found that the dissolution process is diffusion controlled and involves no chemical reaction. The Noyes-Whitney equation simply states that the dissolution rate is directly proportional to the difference between the solubility and the solution concentration ... 

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