Activated complex, concentration

The production rate of product species is assumed to equal the activated complex concentration times the rate at which C decomposes, which we define as vrc- Motion over the barrier corresponds to passage along a reaction coordinate (RC). Because formation and destruction of C typically involves formation and destruction of a critical bond, moving along the reaction coordinate involves vibrational motion in this special degree of freedom ... 

The activated complex concentration, from a rearranged Eq. (7), can be substituted in the rate equation [Eq. (6)] to give Eq. (8) for the rate of the forward reaction ... 

In the absolute reaction rate theory, the rate of the reaction is proportional to the concentration of activated complex, which is in equilibrium with reactants. Thus, the activated complex concentration can be calculated using the corresponding equilibrium constant and, consequently, the activities. This is the reason why the activity coefficients appear in kinetic equations. 

Molar heat capacity of species j Current efficiency or current yield = ij/i Concentration Lumped kinetic constant Concentrations of an activated complex Concentration of reactant in the continuous phase... 

The reaction rate is given by the quotient of the activated complex concentration in the box over the average lifetime duration t ... 

Note 10.1.- Althongh never written, the resnlt of eqnation [10.28] is identical to the one that wonld have been obtained by writing the eqnilibrinm between activated complex and reactants and deducting the activated complex concentration from the mass action law [10.21]. Numerous authors calculate the reaction rate in this way. Note that the rigorons calculation that we did does not involve any equilibrium, as theoretical considerations show that this cannot exist. The method involving the equihbrium between reactants in an activated complex is actually a mnemonic device to achieve the same result. 

Here we have the formation of the activated complex from five molecules of nitric acid, previously free, with a high negative entropy change. The concentration of molecular aggregates needed might increase with a fall in temperature in agreement with the characteristics of the reaction already described. It should be noticed that nitration in nitromethane shows the more common type of temperature-dependence (fig. 3.1). 

Another problem is that the Nernst equation is a function of activities, not concentrations. As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe "/Fe " redox couple is +0.767 V in 1 M 1TC104, H-0.70 V in 1 M ITCl, and -H0.53 in 10 M ITCl. The shift toward more negative potentials with an increasing concentration of ITCl is due to chloride s ability to form stronger complexes with Fe " than with Fe ". This problem can be minimized by replacing the standard-state potential with a matrix-dependent formal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). 

The reaction between Fe(IlI) and Sn(Il) in dilute perchloric acid in the presence of chloride ions is first-order in Fe(lll) concentration . The order is maintained when bromide or iodide is present. The kinetic data seem to point to a fourth-order dependence on chloride ion. A minimum of three Cl ions in the activated complex seems necessary for the reaction to proceed at a measurable rate. Bromide and iodide show third-order dependences. The reaction is retarded by Sn(II) (first-order dependence) due to removal of halide ions from solution by complex formation. Estimates are given for the formation constants of the monochloro and monobromo Sn(II) complexes. In terms of catalytic power 1 > Br > Cl and this is also the order of decreasing ease of oxidation of the halide ion by Fe(IlI). However, the state of complexing of Sn(ll)and Fe(III)is given by Cl > Br > I". Apparently, electrostatic effects are not effective in deciding the rate. For the case of chloride ions, the chief activated complex is likely to have the composition (FeSnC ). The kinetic data cannot resolve the way in which the Cl ions are distributed between Fe(IlI) and Sn(ll). 

To be consistent with the observed first-order dependences on Pu(VI) and U(IV), it is necessary that steps (13.24) and (13.25) do not occur simultaneously. The rate of reaction decreases with increasing hydrogen-ion concentration. It appears that two activated complexes (and a binuclear intermediate) are involved in the... 

The entity marked with a double dagger is regarded by the authors as an activated complex. Its breakdown (19) may well consist of a sequence of rapid steps rather than the single step implied, which involves a three-electron transfer and double protonation of a transition state subsequent to its formation. Steps (22)-(24 were invoked to explain the complete oxidation of S(IV) to S(VI) at higher Cr(VI) concentrations. 

Since the rate of reaction is proportional to the concentration of the activated complex, it will not be affected by the mobility of the molecules, the diffusion rate, or the viscosity. 

The kinetic equations describing the joint effects of activation and concentration polarization are very complex and we shall consider only the the case of a simple first-order reaction of the type (6.2) proceeding in the presence in the solntion of an excess of a foreign electrolyte. To simplify the appearance of these equations (which even in this case are very cnmbersome), in this section we use a more compact notation that contains two new kinetic parameters ... 

The classical approach for discussing adsorption states was through Lennard-Jones potential energy diagrams and for their desorption through the application of transition state theory. The essential assumption of this is that the reactants follow a potential energy surface where the products are separated from the reactants by a transition state. The concentration of the activated complex associated with the transition state is assumed to be in equilibrium... 

APCC, activated prothrombin complex concentrate PCC, prothrombin complex concentrate vWF, von Willebrand factor. 

Treatment algorithm for the management of patients with hemophilia A and factor VIII antibodies. BU, Bethesda unit PCC, prothrombin complex concentrate a PCC, activated prothrombin complex concentrate. 

Addition of the L-732,531 FKBP binary complex to a calcineurin activity assay resulted in increasingly nonlinear progress curves with increasing binary complex concentration. The htting of the data to Equation (6.3) revealed an inhibitor concentration effect on v-, as well as on vs and obs, consistent with a two-step mechanism of inhibition as in scheme C of Figure 6.3. Salowe and Hermes analyzed the concentration-response effects of the binary complex on v, and determined an IC50 of 0.90 pM that, after correction for I.S I/A (assuming competitive inhibition), yielded a A) value for the inhibitor encounter complex of 625 nM. 

Crabtree s catalyst is an efficient catalyst precursor for the selective hydrogenation of olefin resident within nitrile butadiene rubber (NBR). Its activity is favorably comparable to those of other catalyst systems used for this process. Under the conditions studied the process is essentially first order with respect to [Ir] and hydrogen pressure, implying that the active complex is mononuclear. Nitrile reduces the catalyst activity, by coordination to the metal center. At higher reaction pressures a tendency towards zero order behavior with respect to catalyst concentration was noted. This indicated the likelihood of further complexity in the system which can lead to possible formation of a multinuclear complex that causes loss of catalyst activity. 

The reaction rate is then taken to be the product of the frequency at which activated complexes cross the energy barrier and their concentration at the top of the barrier. If (Cx) represents the concentration lying within a region of length dx at the top of the barrier (see Figure 4.2) and if vx is the mean speed at which molecules move from left to right across the barrier, the rate is given by... 

The effect of external pressure on the rates of liquid phase reactions is normally quite small and, unless one goes to pressures of several hundred atmospheres, the effect is difficult to observe. In terms of the transition state approach to reactions in solution, the equilibrium existing between reactants and activated complexes may be analyzed in terms of Le Chatelier s principle or other theorems of moderation. The concentration of activated complex species (and hence the reaction rate) will be increased by an increase in hydrostatic pressure if the volume of the activated complex is less than the sum of the volumes of the reactant molecules. The rate of reaction will be decreased by an increase in external pressure if the volume of the activated complex molecules is greater than the sum of the volumes of the reactant molecules. For a decrease in external pressure, the opposite would be true. In most cases the rates of liquid phase reactions are enhanced by increased pressure, but there are also many cases where the converse situation prevails. 

In one such procedure a rhodium complex concentrate prepared from a 400 ppm rhodium containing hydroformylation catalyst solution, for which catalytic activity had declined to about 30 percent of its initial value, was concentrated in a wiped-film evaporator to about 27,700 ppm rhodium. This concentrate was oxygenated with tertbu-tylhydroperoxide. After isolation and treatment with triphenylphosphine, a 70% yield of [HRh(CO)(PPh3)3] was obtained.[41]... 

Jacobsen et al. reported enhanced catalytic activity by cooperative effects in the asymmetric ring opening (ARO) of epoxides.[38] Chiral Co-salen complexes (Figure 4.27) were used, which were bound to different generations of commercial PAMAM dendrimers. As a direct consequence of the second-order kinetic dependence on the [Co(salen)] complex concentration of the hydrolytic kinetic resolution (HKR), reduction of the catalyst loading using monomeric catalyst leads to a sharp decrease in overall reaction rate. 

Another setup used for the hydrogenation of DMI with Ru-BINAP was equipped with dense PDMS elastomer membranes (Jacobs et al. [48]). The catalyst solution was present in a submerged membrane system, prepared as a sealed PDMS capsule . The catalytically active complex was retained by the membrane while substrate and products, dissolved in the bulk phase, could cross the membrane under the influence of the concentration difference without the need for mechanical pressure. 

Cathodic stripping voltammetry has been used [807] to determine lead, cadmium, copper, zinc, uranium, vanadium, molybdenum, nickel, and cobalt in water, with great sensitivity and specificity, allowing study of metal specia-tion directly in the unaltered sample. The technique used preconcentration of the metal at a higher oxidation state by adsorption of certain surface-active complexes, after which its concentration was determined by reduction. The reaction mechanisms, effect of variation of the adsorption potential, maximal adsorption capacity of the hanging mercury drop electrode, and possible interferences are discussed. 

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