The method of conditional concentrations

Another theoretical method widely applied to describing the kinetics of electron tunneling reactions is based on the employment of the so-called conditional concentrations. This method was first suggested by Galanin [5] in the theory of electron excitation energy transfer and by Antonov-Roma-novskii in the theory of particle recombination [17]. 

The conditional concentration of the donor at time t, n(R,t), is the concentration averaged over all the acceptor particles of those donor particles which are located at distance R from the acceptor particles. In a similar way, 

The first term on the right-hand side of this equation takes into account the decay of the donor by reaction with the acceptor particle which is known to be deliberately located in the origin of coordinates. This is so since, according to the definition of the conditional concentration of the donor, n(R,t), there must be a particle of the acceptor at distance R from the donor, i.e. in the origin of the coordinates. The second term on the right-hand side of eqn. (21) takes into account the decay of donors by reaction with all the remaining acceptor particles. In a similar way, the conditional concentration of the acceptor is described by the equation 

Substituting these ratios again into eqns. (21) and (22) we obtain 

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Kinetic equations for the electron tunneling reactions in the case of non-pair distributions of reagents have been obtained [8-11]. Two methods have been used in the literature to obtain these equations. Both of them have been used earlier to describe the kinetics of energy transfer processes. These are the method of pair density and that of conditional concentrations. It has been shown [15] that these two different methods are, in fact, equivalent and lead to identical results. The detailed description of the pair density method can be found in refs. 3,5,7,13,16, and 33 and that of the method of conditional concentrations in refs. 5,8,15, and 17. 

The method of conditional concentrations also leads to this system of equations. 

The diffusion mechanism is realized when k Kinetic equations for electron tunneling reactions in this case can be obtained, for instance, with the help of the method of conditional concentrations by solving the system of equations... 

The antineuritic vitamin. I. The method of assay, concentration of the vitamin with silver under various conditions, and its solubility in certain organic solvents. Ibid., 94, 765 (1932). With G. R. Cowgill and B. H. Klotz. 

The methods of oxidant consumption are used exclusively in the analysis of residual lignin in unbleached pulps. These procedures are all based on the common principle that lignin consumes the appHed oxidants at a much faster rate than the carbohydrates, and oxidant consumption under carefully specified conditions can be regarded as a measure of lignin concentration in the pulp. 

Significant distinction in rate constants of MDASA and TPASA oxidation reactions by periodate ions at the presence of individual catalysts allow to use them for differential determination of platinum metals in complex mixtures. The range of concentration rations iridium (IV) rhodium (III) is determined where sinergetic effect of concentration of one catalyst on the rate of oxidation MDASA and TPASA by periodate ions at the presence of another is not observed. Optimal conditions of iridium (IV) and rhodium (III) determination are established at theirs simultaneous presence. Indicative oxidation reactions of MDASA and TPASA are applied to differential determination of iridium (IV) and rhodium (III) in artificial mixtures and a complex industrial sample by the method of the proportional equations. 

It is known that Selenium catalyzes reaction of some dye reduction by Sulphide. On this basis spectrophotometric and test-techniques for Selenium determination are developed. Inefficient reproducibility and low sensitivity are their deficiencies. In the present work, solid-phase reagent on silica gel modified first with quaternary ammonium salt and then by Indigocarmine was proposed for Selenium(IV) test-determination. Optimal conditions for the Selenium determination by method of fixed concentration were found. The detection limit of Se(IV) is 10 ftg/L = 2 ng/sample). Calibration curve is linear in the range 50-400 ftg/L of Se(IV). The proposed method is successfully applied to the Selenium determination in multivitamins and bioadditions. 

Cotton linters and viscose grade wood pulp were grafted with acrylamide using the xanthate method. The effects of monomer concentration, reaction time, hydrogen peroxide concentration, reaction temperature, and liquor ratio on the grafting process were studied. Optimum conditions for the grafting reaction were established [26]. 

Once v, is determined under one set of conditions, the procedure is then repeated, varying the concentrations of reactant, catalyst, buffer, etc. The resulting family of v, values can be used to formulate the rate law. This desirable method is probably deserving of wider use in general chemical reactions, just as it is used in biochemical reactions. The method of initial rates is, however, not without its problems. For one thing, the accurate determination of product in the presence of so much substrate is not always feasible. For another, this approach may conceal important effects that come into play only later in the course of the reaction. If the method of initial rates is used, separate experiments must be performed to check these points. 

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