Thermodynamic equilibrium selectivity factor

There are two principal chemical concepts we will cover that are important for studying the natural environment. The first is thermodynamics, which describes whether a system is at equilibrium or if it can spontaneously change by undergoing chemical reaction. We review the main first principles and extend the discussion to electrochemistry. The second main concept is how fast chemical reactions take place if they start. This study of the rate of chemical change is called chemical kinetics. We examine selected natural systems in which the rate of change helps determine the state of the system. Finally, we briefly go over some natural examples where both thermodynamic and kinetic factors are important. This brief chapter cannot provide the depth of treatment found in a textbook fully devoted to these physical chemical subjects. Those who wish a more detailed discussion of these concepts might turn to one of the following texts Atkins (1994), Levine (1995), Alberty and Silbey (1997). 

For spectra corresponding to transitions from excited levels, line intensities depend on the mode of production of the spectra, therefore, in such cases the general expressions for moments cannot be found. These moments become purely atomic quantities if the excited states of the electronic configuration considered are equally populated (level populations are proportional to their statistical weights). This is close to physical conditions in high temperature plasmas, in arcs and sparks, also when levels are populated by the cascade of elementary processes or even by one process obeying non-strict selection rules. The distribution of oscillator strengths is also excitation-independent. In all these cases spectral moments become purely atomic quantities. If, for local thermodynamic equilibrium, the Boltzmann factor can be expanded in a series of powers (AE/kT)n (this means the condition AE < kT), then the spectral moments are also expanded in a series of purely atomic moments. 

Despite the fact that both normal and monomethyl-substituted paraffins readily enter the pores of ZSM-5 and ZSM-11, preferential sorption of the normal isomer is observed under thermodynamic equilibrium, non-kinetically controlled conditions. Whereas small-pore zeolites, such as 5A and erionite, totally exclude branched hydrocarbons, and large-pore zeolites exhibit little preference, the intermediate pore-size zeolites ZSM-5 and ZSM-11 show a marked preference for sorption of the linear paraffin, even under equilibrium conditions. Competitive liquid phase sorption studies at room temperature indicated selectivity factors greater than ten in favor of n-hexane relative to... 

For these simulations, the primary isomer distribution is chosen according to the thermodynamic equilibrium (sec Table 6). Such a situation would be encountered in practice when neither the reaction mechanism kineti-cally favors a particular isomer nor restricted transition state shape-selectivity effects occur. The disproportionation reaction is assumed to be unaffected by diffusion (i.e. y < 0.01). The effective diffusivities of the ortho and meta isomers are fixed, and assumed to be equal, but by a factor of Ro smaller than the effective diffusivity of the para isomer. 

The primary requirement for an economic separation process is an adsorbent with high selectivity and capacity. The selectivity may depend upon differences in either kinetics or thermodynamic equilibrium of adsorption. Differences in diffusion rates between molecules, due to steric effects, can be large enough to provide transient selectivity. The separation factor is the ratio between the diffusion coefficients of the molecules. 

However, in most cases, selectivity based on differences in adsorption of the components at thermodynamic equilibrium is preferred, the separation factor being then ... 

We first review the thermodynamic principles necessary to describe equilibrium systems. A discussion of electrochemistry is also included. Next, the rates of chemical changes, or chemical kinetics, are examined. Finally, we examine selected natural systems in which thermodynamic and kinetic factors are important. 

In both reactions all three isomers o-, m-, and /i-xylene are formed. The desired product /i-xylene can be obtained with selectivities of over 90 %, although the thermodynamic equilibrium corresponds to a js-xylene fraction of only 24 %. This is explained by the fact that for the slimmer molecule /i-xylene has a rate of diffusion that is faster by a factor of 10 than those of the other two isomers. These isomerize relatively rapidly in the zeolite cavity, and the /i-xylene diffuses out of the cavity. 

Preparing conductive polymer blends with selected localization of CB has attracted considerable research interested with a near continuous stream of publications whose detailed review is outside of the scope of the present book. The thermodynamic and kinetic factors that govern the localization of CB particles at interfaces in polymer blends are rather complex since systems far from equilibrium state are obtained, as recently considered by several authors. ... 

The selective binding of molecules to form productive complexes is of central importance to pharmacology and medicinal chemistry. Although kinetic factors can influence the yields of different molecular complexes in cellular and other non-equilibrium environments,1 the primary factors that one must consider in the analysis of molecular recognition are thermodynamic. In particular, the equilibrium constant for the binding of molecules A and B to form the complex AB depends exponentially on the standard free energy change associated with complexation. 

When the amount of the sample is comparable to the adsorption capacity of the zone of the column the migrating molecules occupy, the analyte molecules compete for adsorption on the surface of the stationary phase. The molecules disturb the adsorption of other molecules, and that phenomenon is normally taken into account by nonlinear adsorption isotherms. The nonlinear adsorption isotherm arises from the fact that the equilibrium concentrations of the solute molecules in the stationary and the mobile phases are not directly proportional. The stationary phase has a finite adsorption capacity lateral interactions may arise between molecules in the adsorbed layer, and those lead to nonlinear isotherms. If we work in the concentration range where the isotherms are nonlinear, we arrive to the field of nonlinear chromatography where thermodynamics controls the peak shapes. The retention time, selectivity, plate number, peak width, and peak shape are no longer constant but depend on the sample size and several other factors. 

Lastly a thermodynamically feasible reaction is not necessarily a commercially viable one, even if the feedstock costs are low. A second factor then comes into play, that of reaction kinetics. If a reaction is unfeasibly slow it will not be commercially viable. For example a very slow reaction may require a reactor so large it may not be economically practical. This is, of course, the role of catalysis, to speed up the rate of formation of a desired product, with a more selective catalyst speeding up the rate of formation of a desired product more than that of unwanted by-products. (We note however, that catalysis cannot change the equilibrium conversion for a reaction, as it is purely a kinetic phenomenon.)... 

In all cases, the selective solvents (entrainers) have the task of altering the partition coefficients in a way that high separation factors and selectivities for the different phase equilibria (extractive distillation vapor-liquid equilibrium (VLE), extraction liquid-liquid equilibrium (LLE), absorption gas-liquid equilibrium (GLE)) are achieved, resulting in a separation of compounds. The required partition coefficients, separation factors and selectivities can be calculated with the help of thermodynamic models (g -models, equations of state). 

Because the activities of species in the exchanger phase are not well defined in equation 2, a simplified model—that of an ideal mixture—is usually employed to calculate these activities according to the approach introduced bv Vanselow (20). Because of the approximate nature of this assumption and the fact that the mechanisms involved in ion exchange are influenced by factors (such as specific sorption) not represented by an ideal mixture, ion-exchange constants are strongly dependent on solution- and solid-phase characteristics. Thus, they are actually conditional equilibrium constants, more commonly referred to as selectivity coefficients. Both mole and equivalent fractions of cations have been used to represent the activities of species in the exchanger phase. Townsend (21) demonstrated that both the mole and equivalent fraction conventions are thermodynamically valid and that their use leads to solid-phase activity coefficients that differ but are entirely symmetrical and complementary. 

Thus the features of the hydrogenation of dialkylacetylenes in the gas phase are largely reproduced when reactions are studied in the liquid phase the cis-olefin is again observed as the major product and the yields of olefins by double bond migration are small. In these reactions the high selectivity is again occasioned by a powerful thermodynamic factor because the isomerization of olefins to their equilibrium proportions and hydrogenation of olefin become important as each alkyne was removed. 

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