Rate constant, phase-transfer

A 0f is the standard potential difference between phases a and p for this ion, kf is the standard rate constant for transfer of ion / and a is the charge-transfer coefficient. Concentrations c (a) and c (/3) correspond to the immediate vicinity of the phase boundary and are functions of the potential differences in the diffuse double layers according to the Boltzmann relationship... 

Dekker et al. [170] studied the extraction process of a-amylase in a TOMAC/isooctane reverse micellar system in terms of the distribution coefficients, mass transfer coefficient, inactivation rate constants, phase ratio, and residence time during the forward and backward extractions. They derived different equations for the concentration of active enzyme in all phases as a function of time. It was also shown that the inactivation took place predominantly in the first aqueous phase due to complex formation between enzyme and surfactant. In order to minimize the extent of enzyme inactivation, the steady state enzyme concentration should be kept as low as possible in the first aqueous phase. This can be achieved by a high mass transfer rate and a high distribution coefficient of the enzyme between reverse micellar and aqueous phases. The effect of mass transfer coefficient during forward extraction on the recovery of a-amylase was simulated for two values of the distribution coefficient. These model predictions were verified experimentally by changing the distribution coefficient (by adding... 

Intrinsic rate constant Mass transfer coefficient (gas, liquid phase)... 

The curves show clearly the influences of the dimensionless rate constant, mass transfer group and fraction of dilute phase occupied by solids. For slow reactions (kj 0.3), conversion is insensitive to interphase transfer and to whether or not solids are included with the dilute phase. For intermediate reactions (0.3interphase mass transfer group, X, exerts a very significant influence. For fast reactions (kj >10), the group giving the fraction of the bed volume occupied by... 

The equations of combiaed diffusion and reaction, and their solutions, are analogous to those for gas absorption (qv) (47). It has been shown how the concentration profiles and rate-controlling steps change as the rate constant iacreases (48). When the reaction is very slow and the B-rich phase is essentially saturated with C, the mass-transfer rate is governed by the kinetics within the bulk of the B-rich phase. This is defined as regime 1. 

R is rate of reaction per unit area, a is interfacial area per unit volume, S is solubiHty of solute in continuous phase, D is diffusivity of solute, k is rate constant, kj is mass-transfer coefficient, is concentration of reactive species, and Z is stoichiometric coefficient. When Dk is considerably greater (10 times) than Ra = aS Dk. 

The above discussion relates to diffusion-controlled transport of material to and from a carrier gas. There will be some circumstances where the transfer of material is determined by a chemical reaction rate at the solid/gas interface. If this process determines the flux of matter between the phases, the rate of transport across the gas/solid interface can be represented by using a rate constant, h, so that... 

The mass transfer coefficient is calculated for a given diffusivity coefficient and reaction rate constant at the equilibrium concentration of oxygen. When oxygen is continuously transported and removed from the liquid phase we may write ... 

Rushton (R11) in 1954 presented a graph showing contacting efficiency as a function of impeller diameter at constant power input. He found that the rate of mass transfer between phases increased to a maximum and then decreased as the impeller diameter increased. The optimum occurred at a ratio of impeller to tank diameter of about 0.25, a ratio which is much smaller than that found for liquid blending. 

The penetration theory has been used to calculate the rate of mass transfer across an interface for conditions where the concentration CAi of solute A in the interfacial layers (y = 0) remained constant throughout the process. When there is no resistance to mass transfer in the other phase, for instance when this consists of pure solute A, there will be no concentration gradient in that phase and the composition at the interface will therefore at all Limes lie the same as the bulk composition. Since the composition of the interfacial layers of the penetration phase is determined by the phase equilibrium relationship, it, too. will remain constant anil the conditions necessary for the penetration theory to apply will hold. If, however, the other phase offers a significant resistance to transfer this condition will not, in general, be fulfilled. 

In a continuous steady state reactor, a slightly soluble gas is absorbed into a liquid in which it dissolves and reacts, the reaction being second order with respect to the dissolved gas. Calculate the reaction rate constant on the assumption that the liquid is semi-infinite in extent and that mass transfer resistance in the gas phase is negligible. The diffusivity of the gas in the liquid is 10" 8 m2/s, the gas concentration in the liquid falls to one half of its value in the liquid over a distance of 1 mm, and the rate of absorption at the interface is 4 x 10"6 kmol/m2 s. 

Presumably the most important kinetie parameter used in the deseription of the kineties of an eleetrode is the exchange current density or the almost equivalent rate constant. It indicates the speed of the heterogeneous process of charging or discharging species at the phase boundary, i.e. the charge transfer process. Its value is influenced by numerous factors of the investigated system. For both applied and fundamental aspects of electrochemical research a list of reported values should be helpful. It concludes this volume. 

The above explanation of autoacceleration phenomena is supported by the manifold increase in the initial polymerization rate for methyl methacrylate which may be brought about by the addition of poly-(methyl methacrylate) or other polymers to the monomer.It finds further support in the suppression, or virtual elimination, of autoacceleration which has been observed when the molecular weight of the polymer is reduced by incorporating a chain transfer agent (see Sec. 2f), such as butyl mercaptan, with the monomer.Not only are the much shorter radical chains intrinsically more mobile, but the lower molecular weight of the polymer formed results in a viscosity at a given conversion which is lower by as much as several orders of magnitude. Both factors facilitate diffusion of the active centers and, hence, tend to eliminate the autoacceleration. Final and conclusive proof of the correctness of this explanation comes from measurements of the absolute values of individual rate constants (see p. 160), which show that the termination constant does indeed decrease a hundredfold or more in the autoacceleration phase of the polymerization, whereas kp remains constant within experimental error. 

The total wet deposition flux consists of 2 contributory factors. The first derives from the continuous transfer of Hg to cloud water, described by chemistry models. There are 2 limiting factors 1) the uptake of gas phase Hg(0), which is regulated by the Hemy s corrstant and 2) the subsequent oxidation of Hg(0) to Hg(ll), which is governed by reaction rate constants and the irritial concentratiorrs of the oxidant species. The total flirx depends on the hquid water content of the cloud and the percentage of the droplets in the cloud that reach the Earth s surface. 

For a batch system, with no inflow and no outflow, the total mass of the system remains constant. The solution to this problem, thus involves a liquid-phase, component mass balance for the soluble material, combined with an expression for the rate of mass transfer of the solid into the liquid. 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

The driving force for the transfer process was the enhanced solubility of Br2 in DCE, ca 40 times greater than that in aqueous solution. To probe the transfer processes, Br2 was recollected in the reverse step at the tip UME, by diffusion-limited reduction to Br . The transfer process was found to be controlled exclusively by diffusion in the aqueous phase, but by employing short switching times, tswitch down to 10 ms, it was possible to put a lower limit on the effective interfacial transfer rate constant of 0.5 cm s . Figure 25 shows typical forward and reverse transients from this set of experiments, presented as current (normalized with respect to the steady-state diffusion-limited current, i(oo), for the oxidation of Br ) versus the inverse square-root of time. 

M sulfuric acid to air [34]. As discussed above, for the aqueous-DCE interface, the rate of this irreversible transfer process (with the air phase acting as a sink) was limited only by diffusion of Bt2 in the aqueous phase. A lower limit for the interfacial transfer rate constant of 0.5 cm s was found [34]. 

The theory presented above accounts for the electrostatic effects on the apparent rate constant for ion transfer by relating the observed changes in to changes in c"(0), or equivalently to 0(0). In the following, we present the simulated electrical potential distributions and the corresponding enhancement factors for a cation transferring from the aqueous phase across the water-l,2-DCE interface (s" = 78.39, s° = 10.36). The rela-... 

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