Indirect reaction, calculations

Knowing the reaction rate constants of the direct and indirect reactions and the concentrations, the total reaction rate can be calculated. Unfortunately some data continue to be generated that fail to distinguish between the direct ozone reaction and hydroxyl radical chain reaction. Knowledge of independent rate constants for each pathway is useful to predict competition effects. In drinking water the direct oxidation kinetic is often negligible compared with the indirect, in waste water there is often no clear preference and both pathways can develop simultaneously. This was found for example in the ozonation of 4-nitroaniline at pH = 2, 7 and 11 (T = 20 °C) (Saupe, 1997 Saupe and Wiesmann, 1998). 

Modeling in drinking water applications is largely confined to describing chemical processes. The mathematical models used in this area are based on the reaction rate equation to describe the oxidation of the pollutants, combined with material balances on the reaction system to calculate the concentrations of the oxidants as a function of the water matrix. As noted above, the reaction rate equation is usually simplified to pseudo-first order. This is based on the assumption of steady-state concentrations for ozone and the radicals involved in the indirect reaction. 

RRKM theory, an approach to the calculation of the rate constant of indirect reactions that, essentially, is equivalent to transition-state theory. The reaction coordinate is identified as being the coordinate associated with the decay of an activated complex. It is a statistical theory based on the assumption that every state, within a narrow energy range of the activated complex, is populated with the same probability prior to the unimolecular reaction. The microcanonical rate constant k(E) is given by an expression that contains the ratio of the sum of states for the activated complex (with the reaction coordinate omitted) and the total density of states of the reactant. The canonical k(T) unimolecular rate constant is given by an expression that is similar to the transition-state theory expression of bimolecular reactions. 

Acetic acid formation cannot be directly detected via DEMS due to its low vapor pressure, while ethyl acetate formation can be detected (through the m/z = 61 fragment) at high (> 0.5 M) ethanol concentrations. Therefore, acetic acid yields are determined indirectly by calculating the difference between the measured Faradaic current and the partial currents for ethanol oxidation to CO2 and acetaldehyde. This calculation is based on the assumption that only three reaction products, namely CO2, acetaldehyde, and acetic acid, are formed during ethanol oxidation. 

The enthalpy, entropy and free energy changes for an isothennal reaction near 0 K caimot be measured directly because of the impossibility of carrying out the reaction reversibly in a reasonable time. One can, however, by a suitable combination of measured values, calculate them indirectly. In particular, if the value of... 

In this paper the electtode anodic reactions of a number of dihydropyridine (DHP) derivatives, quantum-chemical calculations of reactions between DHP cation-radicals and electrochemiluminescers anion-radicals (aromatic compounds) and DHP indirect ECL assay were investigated. The actuality of this work and its analytical value follow from the fact that objects of investigation - DHP derivatives - have pronounced importance due to its phaiTnacology properties as high effective hypertensive medical product. 

Levy (Chapter 6) has also explored the use of supercomputers to study detailed properties of biological macromolecule that are only Indirectly accessible to experiment, with particular emphasis on solvent effects and on the Interplay between computer simulations and experimental techniques such as NMR, X-ray structures, and vltratlonal spectra. The chapter by Jorgensen (Chapter 12) summarizes recent work on the kinetics of simple reactions In solutions. This kind of calculation provides examples of how simulations can address questions that are hard to address experimentally. For example Jorgensen s simulations predicted the existence of an Intermediate for the reaction of chloride Ion with methyl chloride In DMF which had not been anticipated experimentally, and they Indicate that the weaker solvation of the transition state as compared to reactants for this reaction In aqueous solution Is not due to a decrease In the number of hydrogen bonds, but rather due to a weakening of the hydrogen bonds. 

Experimentally, the measurement of reaction rates consists in investigating the rate at which starting materials disappear and/or products appear at a particular (constant) temperature, and seeking to relate this to the concentration of one, or all, of the reactants. The reaction may be monitored by a variety of methods, e.g. directly by the removal of aliquots followed by their titrimetric determination, or indirectly by observation of colorimetric, conductimetric, spectroscopic, etc., changes. Whatever method is used the crucial step normally involves matching the crude kinetic data against variable possible functions of concentration, either graphically or by calculation, until a reasonable fit is obtained. Thus for the reaction,... 

Calculations showed that this indirect photolysis occurs between 2.5 and 4 times faster than the processes occurring in the upper atmosphere. Analogous reactions were described by Clarke and Ferris (1997) ... 

Figure 19.19 An Ellman s assay may be done to determine the maleimide activation level of SMCC-derivatized proteins. Reaction of the activated carrier with different amounts of 2-mercaptoethanol results in various levels of sulfhydryls remaining after the reaction. Detection of the remaining thiols using an Ellman s assay indirectly indicates the amount of sulfhydryl uptake into the activated carrier. Comparison of the Ellman s response to the same quantity of 2-mercaptoethanol plus an unactivated carrier indicates the absolute amount of sulfhydryl that reacted. Calculation of the maleimide activation level then can be done.

The luminol reaction has also been used for the CL determination of organic substances such as penicillins [32] and tartrate ion [30] in pharmaceutical preparations by their inhibitory effect on the luminol-iodine and luminol-periodate-manganese(II)-TEA system, respectively. As can be seen from Table 1, the results were quite satisfactory. In the indirect determination of penicillins by their inhibitory effect on the luminol-iodine system, the stopped-flow technique improves the accuracy and precision of the analytical information obtained, and also the sample throughput [32], Thus, in only 2-3 s one can obtain the whole CL signal-versus-time profile and calculate the three measured parameters formation and... 

The chemistry of carbenes in solution hits been extensively studied over the past few decades.1-5 Although our understanding of their chemistry is often derived from product analyses, mechanistic details are often dependent on thermodynamic and kinetic data. Kinetic data can often be obtained either directly or indirectly from time-resolved spectroscopic methods however, thermochemical data is much less readily obtained. Reaction enthalpies are most commonly estimated from calculations, Benson group additivities,6 or other indirect methods. 

Equation (1) is generally used to estimate the rate constant, kin the micellar pseudophase, but for inhibited bimolecular reactions it provides an indirect method for estimation of otherwise inaccessible rate constants in water. Oxidation of a ferrocene to the corresponding ferricinium ion by Fe3 + is speeded by anionic micelles of SDS and inhibited by cationic micelles of cetyltrimethylammonium bromide or nitrate (Bunton and Cerichelli, 1980). The variation of the rate constants with [surfactant] fits the quantitative treatment described on p. 225. Oxidation of ferrocene by ferricyanide ion in water is too fast to be easily followed kinetically, but the reaction is strongly inhibited by anionic micelles of SDS which bind ferrocene, but exclude ferricyanide ion. Thus reaction occurs essentially quantitatively in the aqueous pseudophase, and the overall rate depends upon the rate constant in water and the distribution of ferrocene between water and the micelles. It is easy therefore to calculate the rate constant in water from this micellar inhibition. 

As mentioned in the introduction to controlled potential electrolysis (Section 2.3), there are various indirect methods to calculate the number of electrons transferred in a redox process. One method which can be rapidly carried out, but can only be used for electrochemically reversible processes (or for processes not complicated by chemical reactions), compares the cyclic voltammetric response exhibited by a species with its chronoamperometric response obtained under the same experimental conditions.23 This is based on the fact that in cyclic voltammetry the peak current is given by the Randles-Sevcik equation ... 

The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed for orienting molecules prior to collision (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) bmte force orientation of polar molecules in extremely strong electric fields. Several chemical reactions have been studied with one of the reagents oriented prior to collision. ... 

These species, and in particular the Ti derivative, have a fundamental significance, being related to the Sharpless epoxidation reaction. In fact, despite the many attempts made in order to isolate and characterize the titanium tartrate peroxide derivative involved in that enantioselective process, only indirect evidence in solution and theoretical calculation clues have been obtained so far . ... 

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