Chemical kinetics rate constant

In fluorescence correlation spectroscopy (FCS), the temporal fluctuations of the fluorescence intensity are recorded and analyzed in order to determine physical or chemical parameters such as translational diffusion coefficients, flow rates, chemical kinetic rate constants, rotational diffusion coefficients, molecular weights and aggregation. The principles of FCS for the determination of translational and rotational diffusion and chemical reactions were first described in the early 1970s. But it is only in the early 1990s that progress in instrumentation (confocal excitation, photon detection and correlation) generated renewed interest in FCS. 

Af Chemical kinetics rate constant c Speed of sound... 

Another consideration in choosing a kinetic method is the objective of one s experiments. For example, if chemical kinetics rate constants are to be measured, most batch and flow techniques would be unsatisfactory since they primarily measure transport- and diffusion-controlled processes, and apparent rate laws and rate coefficients are determined. Instead, one should employ a fast kinetic method such as pressure-jump relaxation, electric field pulse, or stopped flow (Chapter 4). 

Ikeda et al. (1984b) plotted Eq. (4.42) by determining the equilibrium concentrations from adsorption isotherms for S(H), S(NH4), and NH4, and using the pH value to determine [H+]. This plot shows good linearity (Fig. 4.11), which confirms that the mechanism hypothesized in Eq. (4.40) is operational. The kv and k- values for Eq. (4.42) can then be calculated from the slope and intercept of Fig. 4.11, and the kinetic Keq can be determined from the ratio kjk x (Table 4.2). It is important to notice that the values calculated kinetically and statically (equilibrium method) are similar, which indicates that the rate constants one calculates from p-jump experiments are chemical kinetics rate constants. These data also verify... 

Other evidence that would strongly suggest that the rate constants measured by p-jump relaxation are indeed chemical kinetics rate constants was given in the work of Ikeda et al. (1981). In this study, the kinetics of hydrolysis of zeolite 4A surface using p-jump relaxation and conductivity detection was determined. The r 1 could be expressed as... 

Chemical kinetic rate constants for the anodic and cathodic directions of an electrode reaction... 

The superscript T in (3.4)-(3.5) denotes a triplet state. Reaction (3.4) is treated in a coherent manner (hyperfine-induced) rather than with the usual chemical kinetics rate constant formalism. Reactions (3.3) - (3.6) have also been investigated in quinone-free reaction centers, to remove the complications of extra interactions of the Q" spin with those of the other radicals. We focus later on whether (3.1)-(3.2) involves one or two steps. 

Experimentally, the initial solution contains the species P and Ox at equilibrium concentrations. During the reductive sweep. Ox is reduced to Red, and P starts to convert to Ox according to the chemical kinetic rate constants. If the experiment is started with initial concentration of the species Red only, the oxidative CV is an EC mechanism. 

The fundamental principles of chemical kinetics, rate constant estimation and chemical reactor design are the basis of the analysis and study of microkinetics. 

Transient, or time-resolved, techniques measure tire response of a substance after a rapid perturbation. A swift kick can be provided by any means tliat suddenly moves tire system away from equilibrium—a change in reactant concentration, for instance, or tire photodissociation of a chemical bond. Kinetic properties such as rate constants and amplitudes of chemical reactions or transfonnations of physical state taking place in a material are tlien detennined by measuring tire time course of relaxation to some, possibly new, equilibrium state. Detennining how tire kinetic rate constants vary witli temperature can further yield infonnation about tire tliennodynamic properties (activation entlialpies and entropies) of transition states, tire exceedingly ephemeral species tliat he between reactants, intennediates and products in a chemical reaction. 

The next step in understanding the chemical kinetics of this system is the calculation of the kinetic rate constant from a knowledge of the energetics of the reaction system. 

When translational diffusion and chemical reactions are coupled, information can be obtained on the kinetic rate constants. Expressions for the autocorrelation function in the case of unimolecular and bimolecular reactions between states of different quantum yields have been obtained. In a general form, these expressions contain a large number of terms that reflect different combinations of diffusion and reaction mechanisms. 

FRACTAL REACTION KINETICS RATE CONSTANT CHEMICAL KINETICS RATE-CONTRIBUTING STEP RATE-CONTROLLING STEP... 

Both the mass transfer kinetic parameters (diffusion in the phases, D, D j, surface renewal frequency, s) and chemical reaction rate constants (kg, kj) strongly influence enhancement of the absorption rate. The particle size, dp, the dispersed liquid holdup, e and the partition coefficient, H can also strongly alter the absorption rate [42-44,46,48]. Similarly, the distance of the first particle from the gas-liquid interface, 6q is an essential factor. Because the diffusion conditions are much better in the dispersed phase (larger solubility and, in most cases, larger diffusivity, as well) the absorption rate should increase with the decrease of the (5g value. 

Chemical reactions at supercritical conditions are good examples of solvation effects on rate constants. While the most compelling reason to carry out reactions at (near) supercritical conditions is the abihty to tune the solvation conditions of the medium (chemical potentials) and attenuate transport limitations by adjustment of the system pressure and/or temperature, there has been considerable speculation on explanations for the unusual behavior (occasionally referred to as anomalies) in reaction kinetics at near and supercritical conditions. True near-critical anomalies in reaction equilibrium, if any, will only appear within an extremely small neighborhood of the system s critical point, which is unattainable for all practical purposes. This is because the near-critical anomaly in the equilibrium extent of the reaction has the same near-critical behavior as the internal energy. However, it is not as clear that the kinetics of reactions should be free of anomalies in the near-critical region. Therefore, a more accurate description of solvent effect on the kinetic rate constant of reactions conducted in or near supercritical media is desirable (Chialvo et al., 1998). 

In Hammett correlations, the descriptors, such as a.(or a.,J and o, can be used to derive equations for aromatic and aliphatic compounds, respectively. For aromatic compounds, the a., descriptor formulated better Hammett correlations than the om descriptor. Given the value of a molecular descriptor, a Hammett correlation for a particular chemical class may be used to predict kinetic rate constants for compounds with similar chemical structure. The QSAR models for each class of compounds studied by elementary hydroxyl radicals are summarized in Table 5.12. 

The result of QSAR models can be rationalized in terms of oxidation necessary for the activation energy of these chemicals, because HOMO is a measure of the ability of a molecule to release electrons, and hydroxyl radicals serve as oxidants that accept electrons. As the energy of the HOMO increases, the ability of organic compounds to behave as nucleophiles increases therefore, the increased oxidation activity of compounds with hydroxyl radicals increases and leads to higher kinetic rate constants. 

Clearly, molecular structure influences the reaction kinetics of organic compounds during their photocatalytic oxidation. This relationship between degradability and molecular structure may be described using quantitative structure-activity relationship (QSAR) models. QSAR models can be developed to predict kinetic rate constants for organic compounds with similar chemical structures. The following section discusses QSAR models developed by Tang and Hendrix (1998) as well as those developed by other researchers. 

The QSAR models can be used to estimate the treatability of organic pollutants by SCWO. For two chemical classes such as aliphatic and aromatic compounds, the best correlation exists between the kinetic rate constants and EHOMO descriptor. The QSAR models are compiled in Table 10.13. By analyzing the behavior of the kinetic parameters on molecular descriptors, it is possible to establish a QSAR model for predicting degradation rate constants by the SCWO for organic compounds with similar molecular structure. This analysis may provide an insight into the kinetic mechanism that occurs with this technology. 

This device has been used for many years to measure diffusion coefficients and, more recently, to study the rates of chemical reactions involving solids. In the latter case, a circular pellet of reactant is embedded in the disc. For a dissolving solid which reacts with first-order kinetics (rate constant ki) in the receiving phase (Fig. 5.18) the flux j is given by Equation 5.13 [13] ... 

Landrum et al. (1992) developed a kinetic bioaccumulation model for PAHs in the amphipod Diporeia, employing first-order kinetic rate constants for uptake of dissolved chemical from the overlying water, uptake by ingestion of sediment, and elimination of chemical via the gills and feces. In this model, diet is restricted to sediment, and chemical metabolism is considered negligable. The model and its parameters, as Table 9.3 summarizes, treat steady-state and time-variable conditions. Empirically derived regression equations (Landrum and Poore, 1988 and Landrum, 1989) are used to estimate the uptake and elimination rate constants. A field study in Lake Michigan revealed substantial differences between predicted and observed concentrations of PAHs in the amphipod Diporeia. Until more robust kinetic rate constant data are available for a variety of benthic invertebrates and chemicals, this model is unlikely to provide accurate estimates of chemical concentrations in benthic invertebrates under field conditions. 

Thomann et al. (1992) developed a steady-state food web bioaccumulation model that combines kinetic and bioenergetic parameters to quantify chemical uptake and elimination by zooplankton, benthic invertebrates and fish. First-order kinetic rate constants quantify uptake of freely-dissolved chemical from interstitial water and overlying water and total chemical elimination from gills and feces. Various physiological and bioenergetic parameters quantify chemical uptake from diet and growth dilution. 

Because kinetic rate constants are not readily available in the literature, Thomann et al. (1992) used a set of formulas to estimate the gill uptake rate constant and an excretion rate constant. The uptake rate constant is a function of the respiration rate of the organism and the efficiency of chemical transfer across the organism s membrane. The excretion rate constant is related to the uptake rate constant and Kow. 

Chemical kinetic models provide information on reaction rates that cannot otherwise be obtained in chemical thermodynamics. However, in many situations information such as kinetic rate constants, needed for such models, are not available. The basic premise in kinetics is to relate the rate of a process to the concentration of reactants. For example, we can examine the formation and dissociation of species AB as it relates to reactants A and B in the following reactions ... 

Sufficient experimental data from several laboratories now exist to describe the conditions under which the radiation-induced ionic propagation of many pure liquid vinyl monomers can be observed. The kinetic data and electrical conductivity measurements establish the ionic nature of the reaction scavenger studies appear to establish the preponderant role played by the carbonium ion in propagating the polymerization. On the basis of a single propagating species, it is possible to write a simple mechanism to describe the process. Limiting values of several of the kinetic rate constants can be estimated, notably the rate constant for reaction between a bare carbonium ion and a vinyl double bond. These rate constants are compared with similar constants arrived at in chemically initiated free radical, carbonium ion and carbanion polymerization. Several shortcomings of the present scheme are discussed. 

Derivation of kinetic rate constants for chemicals or congeners outside of the training set, but within the chemical class, is possible through QSAR and molecular modeling calculations based on appropriate descriptors (e.g., physicochemical and quantum chemical properties of the chemicals, as well as enzyme active site conformation). 

At the energies required for conformational conversions and other exchange processes which are amenable to study by NMR spectroscopy, the reacting molecules have state densities which are much lower than those of molecules undergoing isomerization and decomposition reactions which are generally found to obey RRKM kinetics. Whether these systems can be modeled with RRKM theory is a question of current interest. Table 8 lists molecules for which pressure-dependent gas-phase chemical exchange rate constants have been obtained. 

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