Dependence of rate constants

Predicting the solvent or density dependence of rate constants by equation (A3.6.29) or equation (A3.6.31) requires the same ingredients as the calculation of TST rate constants plus an estimate of and a suitable model for the friction coefficient y and its density dependence. While in the framework of molecular dynamics simulations it may be worthwhile to numerically calculate friction coefficients from the average of the relevant time correlation fiinctions, for practical purposes in the analysis of kinetic data it is much more convenient and instructive to use experimentally detemiined macroscopic solvent parameters. 

Table 3.3 Solvent Dependence of Rate Constants for AIBMe Decomposition1...

We are now ready to build a model of how chemical reactions take place at the molecular level. Specifically, our model must account for the temperature dependence of rate constants, as expressed by the Arrhenius equation it should also reveal the significance of the Arrhenius parameters A and Ea. Reactions in the gas phase are conceptually simpler than those in solution, and so we begin with them. 

Solution The analysis could be carried out using mole fractions as the composition variable, but this would restrict applicability to the specific conditions of the experiment. Greater generality is possible by converting to concentration units. The results will then apply to somewhat different pressures. The somewhat recognizes the fact that the reaction mechanism and even the equation of state may change at extreme pressures. The results will not apply at different temperatures since k and kc will be functions of temperature. The temperature dependence of rate constants is considered in Chapter 5. 

Figure 19. (a) Cluster size dependence of the rate constants for the reactions of CO2 with the large hydrated hydroxyl anions at T= 130 K O, experimental values for OH (H2O), —, calculated values for 0H (H20)n. (b) Dependence of rate constants on cluster size for the reactions of 0H (H20)n with SO2 at T = 135 K. Taken with permission from ref. 19. 

Fig. 1 Concentration dependence of rate-constant ratios measured by competitive brominations (data from Grosjean et al., 1973).

Dependence of Rate Constant on the Volume of Reactants for Bimolecular Reactions of Nitroxyl Radicals with Phenols in Polymer Matrix [8,10,11]... 

Figure 8.5 Add-base catalysis dependence of rate constant on pH (see text for explanation of cases (a) to (f))...

Kinetic studies on complex formation reactions of the tripodal tetra-mine complex [Co(Me6tren)(H20)]2+ with pyridine, 4-methylpyridine, and imidazole yielded activation parameters AH1, and AS. Activation parameters and dependences of rate constants on incoming ligand concentration indicated that the formation mechanism ranged from dissociative for the weaker and bulkier incoming ligands (py, 4-Mepy) to associative for the more basic and less bulky imidazole 2-methylimida-zole occupies an intermediate position (280). 

The dependence of rate constants for approach to equilibrium for reaction of the mixed oxide-sulfide complex [Mo3((i3-S)((i-0)3(H20)9] 1+ with thiocyanate has been analyzed into formation and aquation contributions. These reactions involve positions trans to p-oxo groups, mechanisms are dissociative (391). Kinetic and thermodynamic studies on reaction of [Mo3MS4(H20)io]4+ (M = Ni, Pd) with CO have yielded rate constants for reaction with CO. These were put into context with substitution by halide and thiocyanate for the nickel-containing cluster (392). A review of the chemistry of [Mo3S4(H20)9]4+ and related clusters contains some information on substitution in mixed metal derivatives [Mo3MS4(H20)re]4+ (M = Cr, Fe, Ni, Cu, Pd) (393). There are a few asides of mechanistic relevance in a review of synthetic Mo-Fe-S clusters and their relevance to nitrogenase (394). 

Figure 5. The pH dependence of rate constant of dopachrome and melanin formation (Q) imidazole-Cu (O) PVIm-Cu (A) PIPo—Cu (9) tyrosinase 30°C, air, phosphate buffer... 

Fig. 6. Ligand dependence of rate constants for photoinitiated ET (k speckled) and thermal ET (k, crosshatched) within the hybrids (a) [ZnP, Fe (L)P] and (b) [MgP, Fe (L)P], For M = Zn, the data refer to 1-methylimidazole rather than imidazole...

Lasaga, 1984), the rates of dissolution can be expected to increase with ajj+ acidic solutions. The experiments, in fact, denote the pH dependency of rate constants as simple proportionalities of type ... 

Temperature dependence of rate constants, ARRHENIUS EQUATION RLOT Temperature-jump method,... 

Fig. 9 Pressure and supporting electrolyte concentration dependences of rate constants feel for the CoWi2O40 electrode reaction in aqueous KCl at 25.0 C, [KCI] = 0.10 ( ), 0.20 ( ), 0.50 (A), and 1.00 (T ) mol L h hollow symbols represent return to low pressure after the pressure cycle. [K6C0W12O40] = 1.0 mmol L (taken from Ref 60).

Termolecular Reactions and Pressure Dependence of Rate Constants... 

Temperature Dependence of Rate Constants a. Arrhenius Expression... 

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