Open pseudo-first-order rate constant

The rate of Sc -promoted photoinduced electron transfer from Ceo to CI4Q determined from the decay rate of the absorbance due to Ceo at 740 nm (inset of Fig. 11) obeys pseudo-first-order kinetics and the pseudo-first-order rate constant increases linearly with increasing the p-chloranil concentration [CI4Q] [135]. From the slope of the linear correlation, the second-order rate constant of electron transfer ( et) in Scheme 15 was obtained. The A et value increases linearly with increasing the Sc + concentration. This indicates that CUQ produced in the photoinduced electron transfer forms a 1 1 complex with Sc + (Scheme 15) [78]. When CI4Q is replaced by p-benzoquinone (Q), the value for electron transfer from Ceo to Q increases with an increase in [Sc " ] to exhibit a first-order dependence on [Sc ] at low concentrations, changing to a second-order dependence at high concentrations, as shown in Fig. 13 (open circles) [135]. Such a mixture of first-order and second-order dependence on [Sc ] was also observed in electron transfer from CoTPP (TPP = tetraphenylporphyrin dianion) to Q... 

Figure 3 Dependence of pseudo-first-order rate constants measured at 0°C for propylene homometathesis, on the Re loading in 10 mg samples of two kinds of supported Re catalysts SnMe4-promoted perrhenate/silica-alumina (solid circles) and MeReOs on HMDS-capped silica-alumina (open circle).

A variety of concave pyridines 3 (Table 1) and open-chain analogues have been tested in the addition of ethanol to diphenylketene (59a). Pseudo-first-order rate constants in dichloromethane have been determined photometrically at 25 °C by recording the disappearance of the ketene absorption [47]. In comparison to the uncatalyzed addition of ethanol to the ketene 59a, accelerations of 3 to 25(X) were found under the reaction conditions chosen. Two factors determine the effectiveness of a catalyst basicity and sterical shielding. Using a Bronsted plot, these two influences could be separated from one another. Figure 4 shows a Bronsted plot for some selected concave pyridines 3 and pyridine itself (50). 

Fig. 23 Pseudo-first-order rate constants for the hydrolysis of NPAlk (n = 2-16) in the absence and in the presence of 1 as a function of alkanoate chain length n, catalyst concentration, and buffer system circles 7.5 x 10-5 molL-1 1 in Tris(hydroxymethyl)amino-methane (7ns) buffer solution closed up triangles 2.5 x 10-5 molL-1 1 in Tris buffer solution closed down triangles 2.5 x 10-5 molL-1 1 in phosphate buffer solution open squares 2.5 x 10-5 molL-1 1 in borate buffer solution open down triangles in Tris buffer solution only closed squares in phosphate buffer solution only open up triangles in borate buffer solution only. (Reprinted with permission from [73]. Copyright 1996 American Chemical Society)...

The pseudo-first-order rate constant kohs monotonously increases with increase in the initial concentration of Ce(NH4)2(N03)6 (cf. the open circles in fig. 4(A)). Here, the pH was kept constant at 2.0. All the experimental points fairly fit solid line (vi) corresponding to the equilibrium concentration of the bimetallic hydroxo-cluster [Ce 2(OH)4] 4. The dotted line (iv) showing the equilibrium concentration of [Ce 2(OH)2] has a similar shape as line (vi). These two species are the candidates for the catalytically active species. On the other hand, line (i) for [Ce ] +, line (ii) for [Ce (OH)] +, line (iii) for [Ce (OH)2] ", and line (v) for [Ce 2(OH)3] + are too flat to model the experimental data, while line (vii) for [Ce 6(OH)i2] " is too steep. These species caimot be the active species. Note that the shapes of these fines are concretely determined only by the Q c,)i values, pH, and [Ce(NH4)2(N03)6]o- On the other hand, the positions of fines are vertically movable by varying the catalytic rate constants of the corresponding species. 

Figure 9.19 Use of Damkholer number (Da, ratio of mixing and process characteristic time) for correlation of data. As the pseudo-first order constant used to model the particle formation rate, is not always known, but is obviously the same for each polymer, (Da/ly) is used to correlate the different sets of data (referring to particles produced using different mixing intensity and different initial polymer concentration in the same mixer) quench volumetric ratio = 0.2. Upper graph PEGylated copolymer in acetone at different inlet concentrations and mixing intensities in Tee mixer (d. = 1 mm). Lower graph comparison of different polymers and solvents (fiUed symbols, acetone open symbols, THF) in CIJ mixer (dj = 1 mm) > PCL = 80,000 , PCL = 14,000 A, PEGylated copolymer O, PHDCA (symbols as in Figure 9.6).

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