Free energy reduction rate

The borohydride reduction rate data are paralleled by the rate data for many other carbonyl addition reactions. In fact, for a series of ketones, most of which are cyclic, a linear free-energy correlation of the form... 

An estimate for the activation energy can be obtained by the consideration that for r = 2, the charge reduction reaction must proceed at a rate similar to that for the single solvent molecule dissociation, which means that the activation free energies for the two reaction are of similar magnitude. Neglecting the difference between AG and AH we obtain,... 

Eqs. 9 and 10 make clear predictions about the dependence of quenching rate constants on the free energy change in the quenching step. One way of testing the theory is to observe the quenching of the excited state by a series of related quenchers where the parameters kq(0), K, and k j) should remain sensibly constant and yet where the potentials of the quenchers as oxidants or re-ductants can be varied systematically. Such experiments have been carried out, most notably with the MLCT excited state, Ru(bpy)3 + (1). The experiments have utilized both a series of oxidative nitroaromatic and alkyl pyridinium quenchers, and a series of reductive quenchers based on aniline derivatives. From the data and known redox potentials for the quenchers, plots of RTlnk q vs. 

The cyclodimers are liberated from the respective elimination products 8a and 10a via successive substitution processes with incoming butadiene, that regenerates the active catalyst la in an overall exergonic process. For the rate determining reductive elimination step of the C8-channel free-energy activation barriers of 20.1-24.1 kcalmol-1 are predicted for catalysts TTV, that are in excellent agreement with experimental estimates.43 Thus, moderate reaction conditions are required for the catalytic cyclodimerization of 1,3-butadiene.6... 

The forward and reverse rate constants are thus equal at zero standard free energy. However, this will be difficult to check in practice, for both reactions are very slow, since a bond-breaking/bond-forming process endowed with a quite large internal reorganization is involved. The result is that dissociative electron transfer reactions are usually carried out with electron donors that have a standard potential largely negative to the dissociative standard potential. The reoxidation of the R, X- system is thus possible only with electron acceptors, D +, that are different from the D,+ produced in the reduction process (they are more powerful oxidants). There is no reason then that the oxidation mechanism be the reverse of the... 

Nucleation is defined as the point where the protonucleus is sufficiently large that its surface area to volume ratio exceeds a critical point, and further growth results in a reduction in global free energy surface effects are now small compared to the inside of the crystal. This is the point where enthalpy dominates over entropy. Subsequent crystal growth and further nucleation events will occur until thermodynamic equilibria is reached, as defined by Eq. 3. The rate of nucleation is defined as the rate at which clusters grow through this critical point. 

The experimental kinetic data obtained with the butyl halides in DMF are shown in Fig. 13 in the form of a plot of the activation free energy, AG, against the standard potential of the aromatic anion radicals, Ep/Q. The electrochemical data are displayed in the same diagrams in the form of values of the free energies of activation at the cyclic voltammetry peak potential, E, for a 0.1 V s scan rate. Additional data have been recently obtained by pulse radiolysis for n-butyl iodide in the same solvent (Grim-shaw et al., 1988) that complete nicely the data obtained by indirect electrochemistry. In the latter case, indeed, the upper limit of obtainable rate constants was 10 m s", beyond which the overlap between the mediator wave and the direct reduction wave of n-BuI is too strong for a meaningful measurement to be carried out. This is about the lower limit of measurable... 

Dos Santos Alfonso and Stumm (1992) suggested that the rate of reductive dissolution by H2S of the common oxides is a function of the formation rate of the two surface complexes =FeS and =FeSH. The rate (10 mol m min ) followed the order lepidocrocite (20) > magnetite (14) > goethite (5.2) > hematite (1.1), and except for magnetite, it was linearly related to free energy, AG, of the reduction reactions of these oxides (see eq. 9.24). A factor of 75 was found for the reductive dissolution by H2S and Fe sulphide formation between ferrihydrite and goethite which could only be explained to a small extent by the difference in specific surface area (Pyzik Sommer, 1981). 

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