Rate constants for homogeneous reactions

ESTABLISHING THE MECHANISM AND MEASURING THE RATE CONSTANTS FOR HOMOGENEOUS REACTIONS BY MEANS OF CYCLIC VOLTAMMETRY AND POTENTIAL STEP CHRONOAMPEROMETRY... 

Values of A , and k may be extracted from the polarographic data, although the treatment is complex. Examples of its use to measure the rate constants for certain redox reactions are given in Refs. 339 and 340 which should be consulted for full experimental details. The values obtained are in reasonable agreement with those from stopped-flow and other methods. The technique has still not been used much to collect rate constants for homogenous reactions. The availability of ultramicroelectrodes has enabled cyclic voltammograms to be recorded at speeds as high as 10 Vs". Transients with very short lifetimes (< ps) and their reaction rates may be characterised. ... 

Rate constants for homogeneous reactions of tip-generated species as they transit between tip and conducting substrate can be determined from steady-state feedback current or TG/SC experiments or by transient measurements (Chapter 7). Generally rate constants can be measured if the lifetime of the species of interest is of the order of the diffusion time between tip and substrate, d2HD. Thus first-order reaction rate constants up to about 105 s and second-order reaction rate constants up to about 10s M 1 s are accessible. 

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

Explicit mechanisms attempt to include all nonmethane hydrocarbons believed present in the system with an explicit representation of their known chemical reactions. Atmospheric simulation experiments with controlled NMHC concentrations can be used to develop explicit mechanisms. Examples of these are Leone and Seinfeld (164), Hough (165) and Atkinson et al (169). Rate constants for homogeneous (gas-phase) reactions and photolytic processes are fairly well established for many NMHC. Most of the lower alkanes and alkenes have been extensively studied, and the reactions of the higher family members, although little studied, should be comparable to the lower members of the family. Terpenes and aromatic hydrocarbons, on the other hand, are still inadequately understood, in spite of considerable experimental effort. Parameterization of NMHC chemistry results when NMHC s known to be present in the atmosphere are not explicitly incorporated into the mechanism, but rather are assigned to augment the concentration of NMHC s of similar chemical nature which the... 

For the relation between the rate constant for homogeneous self-exchange ET process (kex) and the standard rate constant of the corresponding electrode reaction (kg), see 4) in Chapter 9. 

The value of ket > 6 x 108 cm8mol ls - - in the usual units for a bimolecular rate constant for homogeneous solution is > 6 x 105 M-ls l. The ferrocene self-exchange constant is 5 x 106 M-Ts-1 (29). Various cross reactions of substituted ferrocenes and ferricenium derivatives have bimolecular rate constants that exceed 10 M - -s l where the equilibrium constant exceeds unity (30). Further, in the cross reactions, the rate constants varied by almost two orders of magnitude for a change in driving force of -0.25 V (30). Thus, the data in Table II relating to the ferrocene-like molecules is reasonable. 

Specificity of a concrete system accounts for the source of the appearance of a small parameter and for its type. For homogeneous reactions, a small parameter is usually a ratio of rate constants for various reactions some reactions are much faster than the others. For just such a small parameter Vasiliev et al. [25] distinguished a class of chemical kinetic equations for which the application of the quasi-stationarity principle is correct (they considered a closed system). 

A major application of eqn. (47) is to diagnose the presence of catalytic, presumably inner-sphere, electrochemical pathways. This utilizes the availability of a number of homogeneous redox couples, such as Ru(NH3)e+/2+ and Cr(bipyridine) +,2+ that must react via inner-sphere pathways since they lack the ability to coordinate to other species [5]. Provided that at least one of the electrochemical reactions also occurs via a well-defined outer-sphere pathway, the observation of markedly larger electrochemical rate constants for a reaction other than that expected from eqn. (47) indicates that the latter utilizes a more expeditious pathway. This procedure can be used not only to diagnose the presence of inner-sphere pathways, but also to evaluate the extent of inner-sphere electrocatalysis (Sect. 4.6) it enables reliable estimates to be made of the corresponding outer-sphere rate parameters [12a, 116, 120c]. 

Although the homogeneous reaction of sulfide + with oxygen has been accomplished at high O2 pressures only [347], the spontaneous reaction in a zeolite was recently monitored kinetically [348]. The very large rate constant for the reaction between dimethylsulfide + and superoxide, k = 2.3 x lO" s , can be interpreted in terms of rapid ET rather than radical-radical coupling [349]. Rates are also known for the reaction of phosphane + with oxygen [339]. 

For the common circumstance where the transfer coefficient, a, is approximately independent of the electrode potential, a single value of k or k , along with a serves to describe fully the electrochemical kinetics at a given temperature and system composition. As for the rate constants for homogeneous redox reactions, electrochemical rate parameters can be sensitive to electrolyte composition, largely as a result of variations in the structure of the interphasial region (electrochemical double layer) (see 12.3.7.3.). The influence of the electrode material is considered in 12.3.7.5. 

The characteristic lifetime of RX is tk, l-. i and that of li is homogeneous-reaction limited lifetimes rh are lO /fi.. which is at least one order of magnitude less than r, (t, 5 10 - s) when A. > 10 M s. Thus, the minimum value of the rate constant for a reaction that can exhibit reaction-mixing effects is well below the diffusion-control limit. Reactions of Me, with RX might well fall into the range for these effects. 

The Marcus theory also makes predictions about the relation between the rate constants for homogeneous and heterogeneous reactions of the same reactant. Consider the rate constant for the self-exchange reaction,... 

Rate Constants For Homogeneous Electron Transfer Reactions... 

Most workers (3,7,10) are agreed that in the two phase system the nitration reaction with toluene occurs almost exclusively in the acid phase. Batch reactor studies (8,9) show that at low acid strengths the rate is kinetically controlled and given by Rg, = k2[HN03] [T]g, where k2 is the rate constant for homogeneous nitration in the acid phase, and CHNO3] and [Tl are the acid phase concentrations of nitric acid and toluene respectively. 

Kong et al. [90] applied the electrochemical approach to the study of a two-phase azo coupling facilitated by reverse PTC. Cyclic voltammetry and chronoamperometry were employed to evaluate quantitatively the rate constants for the reaction. The process was interpreted in terms of an EC mechanism, i.e., diffusion-controlled electrochemical charge transfer followed by a homogeneous chemical reaction. The authors highlighted the usefulness of this approach based on the factors that enable the estimation of the contributions of the chemical reaction, mass transfer, partitioning, and the adsorption of reactants at the interface to the overall two-phase reaction. 

PHa + O Products. An upper limit of the rate constant for homogeneous removal of PHg by 0 of 1 x1cm3. molecule" s" was used in a study of the reaction of PH3 with O atoms (at 298 K) [22]. Two [23] or four [7] product channels have been proposed ... 

Tab. 4 Homogeneous reaction rate constants for selected reactions involving hydroxyl...

Tab. 4 Rate constants for homogeneous chemical reactions determined using steady state methods...

---