Driving force term

Effects of High Solute Concentrations on Ug and As discussed previously, the stagnant-film model indicates that fcc should be independent of ysM and/cc should be inversely proportional to The data of Vivian and Behrman [Am. Tn.st. Chem. Eng. J., 11, 656 (1965)] for the absorption of ammonia from an inert gas strongly suggest that the film model s predicted trend is correct. This is another indication that the most appropriate rate coefficient to use is fcc. nd the proper driving-force term is of the form (y — yd ysM-... 

Fig. 2.4. The resultant growth rate which is due to a barrier and a driving force term. The driving force increases with l, but at a slower rate than the decrease of the force due to the barrier term. Hence the overall growth rate is positive for l > lmi but decreases to zero at large I, with a maximum in between...

A further paper [167] explains the lamellar thickness selection in the row model. The minimum thickness lmin is derived from the similation and found to be consistent with equilibrium results. The thickness deviation 81 = l — lmin is approximately constant with /. It is established that the model fulfills the criteria of a kinetic theory Firstly, a driving force term (proportional to 81) and a barrier term (proportional to /) are indentified. Secondly, the competition between the two terms leads to a maximum in growth rate (see Fig. 2.4) which is located at the average thickness l obtained by simulation. Further, the role of fluctuations becomes apparent when the dependence on the interaction energy e is investigated. Whereas downwards (i.e. decreasing l) fluctuations are approximately independent... 

Driving Force Term In all rate expressions the driving force must become zero when thermodynamic equilibrium is established. The equilibrium const pt K appearing in equation 6.3.29 can be regarded as the appropriate ratio of partial pressures for the overall reaction. 

In the general case the value of K appearing in the driving force term is the product of the equilibrium constant for the surface reaction Kr and the product of the adsorption equilibrium constants for the reactants divided by the product of the adsorption equilibrium constants for the reaction products. 

We have considered two limiting cases for the kinetics arising from the repulsive interactions in Eqs. (7) and (8). Hence in principle we will find two different model equations for the electromigration experinients when the driving force terms are added. However, as we will see. several basic features of the resulting models are independent of the kinetics when the system is driven far from equilibrium. 

The simplest model equation capable of describing the electromigration experiments arises from Case A (non local mass flow) by adding the driving force term to Eq. (7). Thus we find our basic result ... 

The persistence of these basic features is perhaps most dramatically illustrated by considering the more complicated case that arises when the effects of the repulsions are treated with locally conserved dynamics (Case B). Adding the driving force term Eq. 

It should be noted that equation 3.81 contains a driving force term in the numerator. This is the driving force tending to drive the chemical reaction towards the equilibrium state. The collection of terms in the denominator is usually referred to as the adsorption term, since terms such as KBPB represent the retarding effect of the adsorption of species B on the rate of disappearance of A. New experimental techniques enable the constants KB etc. to be determined separately during the course of a chemical reaction139 and hence, if it were found that the adsorption of... 

This equation also contains a driving force term and an adsorption term. A similar equation may be derived for the case of an Eley-Rideal mechanism and its form is interpreted in Table 3.3. 

For most gas-solid catalytic reactions, usually a rate equation corresponding to one form or another of the Hougen and Watson type described above can be found to fit the experimental data by a suitable choice of the constants that appear in the adsorption and driving force terms. The following examples have been chosen to illustrate this type of rate equation. However, there are some industrially important reactions for which rate equations of other forms have been found to be more appropriate, of particular importance being ammonia synthesis and sulphur dioxide oxidation 42 . 

For more accuracy in the above six equations, we could have used the driving force terms (C... — f(C...)) instead in the above equations, with /(C) more accurately denoting the concentration of the component in play in phase I which is at equilibrium with the concentration in phase II. 

Fig. 6. Marcus relation Free energies of activation as a function of the driving force (terms (A) + (B) in text) corrected for electrostatic work terms (cyano complexes reaction with hydrazine ( ) methylhydrazine (O) 1,2-dimethylhydrazine ( ). Adapted with permission from Dennis et al. (52). Copyright 1987, American Chemical Society.

The driving force represents the chemical affinity of the overall reaction to reach thermodynamic equilibrium. It is proportional to the concentration difference of the reactants with respect to their equilibrium concentrations. The driving force term does not contain parameters associated with the catalyst, consistent with the fact that the catalyst does not affect chemical equilibrium. 

First, the variation in the intrinsic barriers, AG, for related electrochemical reactions can be expected to be closely similar to those for the same series of homogeneous reactions using a fixed coreactant. If the comparison is made at a fixed electrode potential, E, the (often unknown) driving-force terms cancel provided that the free-energy profiles are symmetrical (the symmetry factor a. = 0.5) so that ... 

For the case of a binary electrolyte (i.e., a single salt that dissociates in solution into one cation and one anion species), we can rewrite the molar flux equations for positive and negative ions in terms of a salt concentration gradient diffusion term, a migration term explicit in the current density (as opposed to the VO driving force term in Equation (26.54)), and a bulk convection term ... 

The rate of mass transfer that we introduced in this analysis requires some explanation. The constant Kd is the distribution coefficient for i between the two phases. Km and Ai are the mass transfer coefficient and the interfacial area. But what about the driving force term Why is it written as the difference between the actual concentration of i in the first phase minus the actual concentration of i in the second phase multiplied by Kd ... 

These two terms are the reciprocal holding times for the two phases in the contactor, and The coefficients of the two driving force terms are the ratios of the product of the mass transfer coefficient and the interfacial area to the volume of the phase. Recalhng that Km has dimensions of, we can see that this group is also an inverse time constant, but now this is a reciprocal characteristic time for mass transfer If we multiply through on both sides by the holding time we obtain ... 

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