Mass-action

Micelle formation can be treated as a mass action equilibrium, for example. 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

Complex chemical mechanisms are written as sequences of elementary steps satisfying detailed balance where tire forward and reverse reaction rates are equal at equilibrium. The laws of mass action kinetics are applied to each reaction step to write tire overall rate law for tire reaction. The fonn of chemical kinetic rate laws constmcted in tliis manner ensures tliat tire system will relax to a unique equilibrium state which can be characterized using tire laws of tliennodynamics. 

For a closed chemical system witli a mass action rate law satisfying detailed balance tliese kinetic equations have a unique stable (tliennodynamic) equilibrium, In general, however, we shall be concerned witli... 

In particular if the reaction rate depends only on Cj, which is the case, for example, if the reaction is irreversible with mass,-action kinetics, then these reduce further to a pair of equations, namely... 

In the fumace/ketde batch process, a charge of drossed blast furnace buUion is treated in a reverberatory furnace or a kettie (see Fig. 12). Oxygen is supphed in the form of compressed air or as lead oxide blown into the bath through submerged pipes. The formation of lead oxide serves by mass action to assure the removal of the impurities to the desired low concentrations. The softening reactions are... 

The mass action law or Saha equation for thermal ionisation of seed atoms is... 

In the early twentieth century, the law of mass action was appHed to the basic pathway of dmg—receptor interaction. Assuming that response, R, is proportional to the concentration of the dmg—receptor complex, ITT, and that maximum response, occurs when all receptors are occupied (2,6,10),... 

In an undoped, intrinsic semiconductor the equiHbrium concentrations of electrons, and holes,/), are described by a lever rule derived from the law of mass action (eq. 3) ... 

The carrier concentrations in doped or extrinsic semiconductors to which donor or acceptor atoms have been added can be deterrnined by considering the chemical kinetics or mass action of reactions between electrons and donor ions or between holes and acceptor ions. The condition for electrical neutraHty is given by equation 6. When the predominant dopants are donors, the semiconductor is... 

The extent of displacement depends on the relative stabiUties of the complexes and the mass action effect of an excess of M For equivalent total amounts of M and M, K must be on the order of 10 for 99% complete displacement to occur. Similar considerations apply for the displacement of L from ML by U. The situation is quite analogous to the familiar competition of two bases for the hydrogen ion. 

This was first demonstrated ia 1862 by Berthelot and Saint-Gibes (32), who found that when equivalent quantities of ethyl alcohol and acetic acid were abowed to react, the esterification stopped when two-thirds of the acid had reacted. Sinularly, when equal molar proportions of ethyl acetate and water were heated together, hydrolysis of the ester stopped when about one-third of the ester was hydroly2ed. By varyiag the molar ratios of alcohol to acid, yields of ester >66% were obtained by displacement of the equbibrium. The results of these tests were ia accordance with the mass action law shown ia equation 5. 

The law of mass action, the laws of kinetics, and the laws of distillation all operate simultaneously in a process of this type. Esterification can occur only when the concentrations of the acid and alcohol are in excess of equiUbrium values otherwise, hydrolysis must occur. The equations governing the rate of the reaction and the variation of the rate constant (as a function of such variables as temperature, catalyst strength, and proportion of reactants) describe the kinetics of the Hquid-phase reaction. The usual distillation laws must be modified, since most esterifications are somewhat exothermic and reaction is occurring on each plate. Since these kinetic considerations are superimposed on distillation operations, each plate must be treated separately by successive calculations after the extent of conversion has been deterrnined (see Distillation). 

Law of Mass Action The effect of concentration on the rate is isolated as... 

The rates of many reactions are not represented by application of the law of mass action on the basis of their overall stoichiometric relations. They appear, rather, to proceed by a sequence of first- and second-order processes involving short-lived intermediates which may be new species or even unstable combinations of the reaclants for 2A -1- B C, the sequence could be A -1- B AB followed by A -1- AB C. 

Ion Exchange A useful tool is provided by the mass action law for describing the general exchange equilibrium in fully ionized exchanger systems as... 

Separation Factor By analogy with the mass-action case and appropriate for both adsorption and ion exchange, a separation factor / can be defined based on dimensionless system variables [Eq. (16-10)] by... 

Mass Action Here the equilibrium reladons, consistent with Eq. (16-25), are... 

FK . 16-8 Ideal mass-action equilibrium for three-component ion exchange with unequal valences. K a,c — 3.06 K b,c = 3.87. Diiolite C-20 polystyrenesiil-fonate resin, with Ca as A, Mg as B, and Na as C. [Klein et al, Ind. Eng. Chem. Fund., 6, 339 (1967) repiinted with permission.)... 

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