Reverse rate constant

As = surface area of a semiconductor contact [A ] = concentration of the reduced form of a redox couple in solution [A] = concentration of the oxidized form of a redox couple in solution A" = effective Richardson constant (A/A ) = electrochemical potential of a solution cb = energy of the conduction band edge Ep = Fermi level EF,m = Fermi level of a metal f,sc = Fermi level of a semiconductor SjA/A") = redox potential of a solution ° (A/A ) = formal redox potential of a solution = electric field max = maximum electric field at a semiconductor interface e = number of electrons transferred per molecule oxidized or reduced F = Faraday constant / = current /o = exchange current k = Boltzmann constant = intrinsic rate constant for electron transfer at a semiconductor/liquid interface k = forward electron transfer rate constant = reverse electron transfer rate constant = concentration of donor atoms in an n-type semiconductor NHE = normal hydrogen electrode n = electron concentration b = electron concentration in the bulk of a semiconductor ... 

Adsorption of vapors on test chamber walls has been previously described by means of models including two or three rate constants for adsorption/desorption processes in the ease of dynamic experiments (Dunn et al., 1988 Colombo et al., 1993) and with three adsorption/desorption constants in the case of static experiments (Colombo et al., 1993). Two rate constants describe a reversible sink whereas three rate constants describe a reversible and an irreversible (i.e. leak type) sink. However, these models did not adequately describe the sorption process(es), especially in the case of long-term tests, as resulted from two observations (Colombo et al., 1993) (a) the model with three sorption rate constants (reversible + irreversible sink) provided a better description of the experimental data than the one-sink model and (b) desorption experiments following adsorption gave strong indications that the irreversible sink was in fact slowly rever-... 

Reaction Rate constant Forward reaction Rate constant Reverse reaction... 

The exponential fiinction of the matrix can be evaluated tln-ough the power series expansion of exp(). c is the coliinm vector whose elements are the concentrations c.. The matrix elements of the rate coefficient matrix K are the first-order rate constants W.. The system is called closed if all reactions and back reactions are included. Then K is of rank N- 1 with positive eigenvalues, of which exactly one is zero. It corresponds to the equilibrium state, witii concentrations r detennined by the principle of microscopic reversibility ... 

Low temperatures strongly favor the formation of nitrogen dioxide. Below 150°C equiUbrium is almost totally in favor of NO2 formation. This is a slow reaction, but the rate constant for NO2 formation rapidly increases with reductions in temperature. Process temperatures are typically low enough to neglect the reverse reaction and determine changes in NO partial pressure by the rate expression (40—42) (eq. 13). The rate of reaction, and therefore the... 

The exchange current is directiy related to the reaction rate constant, to the activities of reactants and products, and to the potential drop across the double layer. The larger the more reversible the reaction and, hence, the lower the polarization for a given net current flow. Electrode reactions having high exchange currents are favored for use in battery apphcations. 

In the presence of 6-iodo-l-phenyl-l-hexyne, the current increases in the cathodic (negative potential going) direction because the hexyne catalyticaHy regenerates the nickel(II) complex. The absence of the nickel(I) complex precludes an anodic wave upon reversal of the sweep direction there is nothing to reduce. If the catalytic process were slow enough it would be possible to recover the anodic wave by increasing the sweep rate to a value so fast that the reduced species (the nickel(I) complex) would be reoxidized before it could react with the hexyne. A quantitative treatment of the data, collected at several sweep rates, could then be used to calculate the rate constant for the catalytic reaction at the electrode surface. Such rate constants may be substantially different from those measured in the bulk of the solution. The chemical and electrochemical reactions involved are... 

This expression has been obtained by Skinner and Trommsdorf [1988]. The rate constants for the direct (Jc) and reverse (Jc) transition at / > 1 are proportional to ij( ), and n( ) + 1, respectively, and the relaxation rate equals... 

Hydrogen transfer in excited electronic states is being intensively studied with time-resolved spectroscopy. A typical scheme of electronic terms is shown in fig. 46. A vertical optical transition, induced by a picosecond laser pulse, populates the initial well of the excited Si state. The reverse optical transition, observed as the fluorescence band Fj, is accompanied by proton transfer to the second well with lower energy. This transfer is registered as the appearance of another fluorescence band, F2, with a large anti-Stokes shift. The rate constant is inferred from the time dependence of the relative intensities of these bands in dual fluorescence. The experimental data obtained by this method have been reviewed by Barbara et al. [1989]. We only quote the example of hydrogen transfer in the excited state of... 

Enzyme and substrate first reversibly combine to give an enzyme-substrate (ES) complex. Chemical processes then occur in a second step with a rate constant called kcat, or the turnover number, which is the maximum number of substrate molecules converted to product per active site of the enzyme per unit time. The kcat is, therefore, a rate constant that refers to the properties and reactions of the ES complex. For simple reactions kcat is the rate constant for the chemical conversion of the ES complex to free enzyme and products. 

If kj and kj denote tlie forward and reverse rate constants respectively, die general rate of disappearance (-r ) for any type of reaction is defined as ... 

Although a closed-form solution can thus be obtained by this method for any system of first-order equations, the result is often too cumbersome to lead to estimates of the rate constants from concentration-time data. However, the reverse calculation is always possible that is, with numerical values of the rate constants, the concentration—time curve can be calculated. This provides the basis for a curve-... 

If a reaction system consists of more than one elementary reversible reaction, there will be more than one relaxation time in general, the number of relaxation times is equal to the number of states of the system minus one. (However, even for multistep reactions, only a single relaxation time will be observed if all intermediates are present at vanishingly low concentrations, that is, if the steady-state approximation is valid.) The relaxation times are coupled, in that each relaxation time includes contributions from all of the system rate constants. A system of more than... 

D-Methylmalonyl-CoA, the product of this reaction, is converted to the L-isomer by methylmalonyl-CoA epunerase (Figure 24.19). (This enzyme has often and incorrectly been called methylmalonyl-CoA racemase. It is not a racemase because the CoA moiety contains five other asymmetric centers.) The epimerase reaction also appears to involve a carbanion at the a-position (Figure 24.20). The reaction is readily reversible and involves a reversible dissociation of the acidic a-proton. The L-isomer is the substrate for methylmalonyl-CoA mutase. Methylmalonyl-CoA epimerase is an impressive catalyst. The for the proton that must dissociate to initiate this reaction is approximately 21 If binding of a proton to the a-anion is diffusion-limited, with = 10 M sec then the initial proton dissociation must be rate-limiting, and the rate constant must be... 

This is the general expression for film growth under an electric field. The same basic relationship can be derived if the forward and reverse rate constants, k, are regarded as different, and the forward and reverse activation energies, AG are correspondingly different these parameters are equilibrium parameters, and are both incorporated into the constant A. The parameters A and B are constants for a particular oxide A has units of current density (Am" ) and B has units of reciprocal electric field (mV ). Equation 1.114 has two limiting approximations. 

An interesting method, which also makes use of the concentration data of reaction components measured in the course of a complex reaction and which yields the values of relative rate constants, was worked out by Wei and Prater (28). It is an elegant procedure for solving the kinetics of systems with an arbitrary number of reversible first-order reactions the cases with some irreversible steps can be solved as well (28-30). Despite its sophisticated mathematical procedure, it does not require excessive experimental measurements. The use of this method in heterogeneous catalysis is restricted to the cases which can be transformed to a system of first-order reactions, e.g. when from the rate equations it is possible to factor out a function which is common to all the equations, so that first-order kinetics results. 

Rate constants for ring-opening of dioxolan-2-yl radicals have been measured by Barclay et a/.241 as 103-104 s 1 at 75 °C (Scheme 4.29). There is also evidence that ring-opening is reversible.24 244 Thus, isomerization of the initially formed product to one more thermodynamically favored is possible if propagation is slow. 

This equation can be solved numerically to give values of Clr and Ctr.404 For reversible addition-fragmentation chain transfer (RAFT) (Scheme 6.5), the rate constant for the reverse reaction is defined as shown in eq. 22 ... 

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