Rate constants, intrinsic

As the pre-equilibria in Schemes 5-10 and 5-11 are not identical and their equilibrium constants are therefore likely to be different from one another, the rate constants k - and are not intrinsic rate constants of the corresponding slow dissociation steps, but are dependent in addition on the constants of these pre-equilibria. 

Assuming that reactions 1 and 2 are reversible and are fast in comparison with reaction 5, the measured rate constants ( obs) at pH 8.2-9.8 are related to the intrinsic rate constant k5 according to Scheme 5-16, as shown by Ritchie and Wright (1971a). ... 

Broxton and Roper measured the rate of dissociation (A 3) of the (ii)-diazo ether, A 2, and the rate of the protection reaction (A p), i.e., the transformation of the (Z)-into the (ii)-ether ( protection because the diazo ether is protected against dediazoniation almost completely if present as the ( >isomer). Rate constants kx and k are known from Ritchie and Virtanen s work (1972). The results demonstrate firstly that the initial reaction of the diazonium ion takes place in such a way that almost exclusively the (Z)-ether is formed directly (ki/k3 = 120). The protection rate constant kp is a simple function of the intrinsic rate constants as shown in Scheme 6-4. 

In addition to the influence of the complexation equilibrium constant K, the observed reaction rate of arenediazonium salts in the presence of guest complexing reagents is influenced by the intrinsic reaction rate of the complexed arenediazonium ion. This system of reactions can be rationalized as in Scheme 11-1. Here we are specifically interested in the numerical value of the intrinsic rate constant k3 of the complexed diazonium ion relative to the rate constant k2 of the free diazonium ion. 

Does this model give us a practical solution for the synthesis of monosubstitution products in high yields The model teaches us that reactions are not disguised by micromixing if the intrinsic rate constant (in Scheme 12-84 k2o and k2v>) is significantly less than 1 m-1s-1. As discussed in Section 12.7, the intrinsic rate constant refers to unit concentrations of the acid-base equilibrium species involved in the substitution proper, not to analytical concentrations. Therefore, if the azo coupling reaction mentioned above is not carried out within the range of maximal measured rates (i.e., with the equilibria not on the side of the 1-naphthoxide ion and... 

According to the method as described by Hiromi et al [5,6] the measured parameters Km and Umax were used for the calculation of the subsite affinities A - and the intrinsic rate constant. The calculated subsite affinities are summarized in Table 3. 

The material balance was calculated for EtPy, ethyl lactates (EtLa) and CD by solving the set of differential equation derived form the reaction scheme Adam s method was used for the solution of the set of differential equations. The rate constants for the hydrogenation reactions are of pseudo first order. Their value depends on the intrinsic rate constant of the catalytic reaction, the hydrogen pressure, and the adsorption equilibrium constants of all components involved in the hydrogenation. It was assumed that the hydrogen pressure is constant during... 

Figure 6.3 Dependence of the apparent rate constants, determined by fitting the experimental transients with (6.5), on the step fraction. The final potentials are 0.73 V (triangles), 0.755 V (diamonds), 0.78 V (squares), and 0.805 V (circles). The value of the step fraction for Pt(lll) was estimated using a procedure described in [Lebedeva et al., 2002c]. The inset shows the independence of the apparent intrinsic rate constant per step.

Figure 6.4 Dependence of the apparent rate constants and the apparent intrinsic rate constant on the potential ( Tafel plots ), determined by fitting the experimental transients with (6.5).

The first equation gives the rate of gas consumption as moles of gas (n) versus time. This is the only state variable that is measured. The initial number of moles, nO is known. The intrinsic rate constant, K is the only unknown model parameter and it enters the first model equation through the Hatta number y. The Hatta number is given by the following equation... 

In electrochemical literature the standard rate constant fe is often designated as fes h or fe9, called the specific heterogeneous rate constant or the intrinsic rate constant. According to eqns. 3.5 and 3.6, we have... 

Calculate the intrinsic rate constant from the input parameters, using equation 12.3.24. 

Compare the measured rate constant k / with the product of the assumed rj and the intrinsic rate constant determined in step 3. If the two are equal, the assumption in step 1 was correct if they are unequal, one assumes a new... 

Formation of products in paraffin cracking reactions over acidic zeolites can proceed via both unimolecular and bimolecular pathways [4], Based on the analysis of the kinetic rate equations it was suggested that the intrinsic acidity shows better correlation with the intrinsic rate constant (kinl) of the unimolecular hexane cracking than with the apparent rate constant (kapp= k K, where K is the constant of adsorption equilibrium). In... 

The intrinsic barriers for the reaction of [12+] correspond to intrinsic rate constants of ( mcoh)o = 1 x 108m-1 s-1 and (kp)0 = 450 s-1 (equation 4). This analysis shows that the thermoneutral addition of methanol to [12+] is an intrinsically fast reaction, with a rate constant that is only 50-fold smaller than that for a diffusion-limited reaction.16... 

Our problem now is to determine the functional form of this experimental free energy curve for the intrinsic rate constant ki for electron transfer. In addition to the Marcus eq 4, two other relationships are currently in use to relate the activation free energy to the free energy change in electron transfer reactions (15, JL6). 

Figure 11. Free energy relationship for the intrinsic rate constant (log kt) for heterogeneous electron transfer.

Figure 13. Test for the consistency of AG evaluated from the intrinsic rate constant (log kj using Marcus Equation 4 (a), Rehm-Weller Equation 17 (b), and Marcus-Levine-A gmon Equation 18 (c) at various potentials.

Flere, As is the mineral s surface area (cm2) and k+ is the intrinsic rate constant for the reaction. The concentrations of certain species Aj, which make up the rate law s promoting and inhibiting species, are denoted m , and P- are those species exponents, the values of which are derived empirically. Qg is the activity product for Reaction 16.1 (Eqn. 3.41). In the absence of promoting and inhibiting species, the units of the rate constant are mol cm-2 s-1, and in any case these are the units of the product of k+ and the n term. 

The conversion of butane is based on the difference in the moles between the feed and the products. Intrinsic rate constants, shown in the third column of Table II, are based on BET surface areas (m2/g) measurements (101). 

We find from separate e qperiments with ZSM-5 catalyst that the intrinsic rate constant for isomerization, kj, is much faster than that for disproportionation, kD at 482°C, kj/kD > 7000, i.e. kj/kD is much faster than it is for the synthetic faujasite catalyst. 

We have also determined the intrinsic rate constant kirrtr for TDP... 

The activity in terms of 1st order rate constant khcalc was calculated in Table 2 from (8) and (9) with effective diffusivity Dejf=5.3-10 6 m2/s and intrinsic rate constant =33000 Nm3/h/m3 = 23 s"1 fitted to the measurements. This simple and useful method models the measured influence of particle size satisfactorily for a first optimization of particle size and shape. The 35% higher activity measured for the 9-mm Daisy compared to the 12-mm Daisy, however, exceeds the 25% expected from (8), and this illustrates the importance of measuring the activity of the actual shape. 

Defining intrinsic rate constants as rate constants that would be observed in the absence of an electric field leads to... 

What remains is to relate the surface potential to activation potentials for the adsorption/desorption reaction steps. Defining the activation potentials as iji, ijjf for the activation required to overcome the EDL potential for the adsorption, desorption steps, respectively, allows the intrinsic rate constants to be directly related to the rate constants k, k (4), i.e.,... 

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