Separation mechanisms equilibrium effect

According to the above mechanism, reverse osmosis separation is governed by two distinct factors, namely (i) an equilibrium effect which is concerned with the details of preferential sorption in the vicinity of the membrane surface, and (ii) a kinetic effect which is concerned with the mobilities of solute and solvent through membrane pores. While the former (equilibrium effect) is governed by repulsive and attractive potential gradients in the vicinity of the membrane surface, the latter (mobility effect) is governed both by the potential gradients (equilibrium effect) and the steric effects associated with the structure and size of molecules relative to those of pores on the membrane surface. 

The adsorptive separation is achieved by one of the three mechanisms steric, kinetic, or equilibrium effect. The steric effect derives from the molecular sieving property of zeolites. In this case only small and properly shaped molecules can diffuse into the adsorbent, whereas other molecules are totally excluded. Kinetic separation is achieved by virtue of the differences in diffusion rates of different molecules. A large majority of processes operate through the equilibrium adsorption of mixture and hence are called equilibrium separation processes. 

In addition to the enhanced diffusivity effect, another issue needs to be taken into account when considering stationary-phase mass transfer in CEC with porous particles. The velocity difference between the pore and interstitial space may be small in CEC. Under such conditions the rate of mass transfer between the interstitial and pore space cannot be very important for the total separation efficiency, as the driving mechanism for peak broadening, i.e., the difference in mobile-phase velocity within and outside the particles, is absent. This effect on the plate height contribution II, s has been termed the equilibrium effect [35], How to account for this effect in the plate height equation is still open to debate. Using a modified mass balance equation and Laplace transformation, we first arrived at the following expression for Hc,s, which accounts for both the effective diffusivity and the equilibrium effect [18] ... 

Secular equilibrium will be obtained only if the system in question remains physically closed, such that radioactive decay is the only process by which a daughter is effectively removed from its parent. Any additional non-radiochemical process that physically removes the daughter will destroy secular equilibrium. We shall see that chemical separation mechanisms prevent a closed system, and this is necessary for useful rate information to be obtained from the radioactive decay series. 

From previous studies and the qualitative nature of the rate data a likely combination appeared to be a controlling surface reaction between adsorbed atomic oxygen and unadsorbed sulfur dioxide. In order to determine ail the constants in the rate equation for this mechanism, it is necessary to vary each partial pressure independently in the experimental work. Thus measuring the rate of reaction at different total pressures but at constant composition is not sufficient to determine all the adsorption equilibrium constants. Similarly, if the data are obtained at constant composition of initial reactants but varying conversions, the partial pressures of the individual components do not vary independently. However, in these cases it is possible to verify the validity of the rate equation even though values of the separate adsorption equilibrium constants cannot be ascertained. Olson and Schuler studied the effect of conversion alone and obtained the data in Table 9-1 at 480°C. 

Liquid-liquid extraction (LLE) is among the oldest sample extraction and preconcentration techniques available in analytical chemistry. LLE is a method whereby two immiscible phases, generahy an organic solvent and an aqueous solution, are brought into contact in order to extract one or more analytes from one phase into the other. If the receiving phase has a smaller volume than the donor phase, preconcentration can be effected. The separation mechanism is, like SPE, based on partitioning. At equilibrium, the partition coefficient of analyte i (Ki) in a two-phase system is given by... 

One strategy that has been employed in our laboratories in an effort to minimize mass discrimination effects has been to couple GPC, either off-line or directly on-line to MS. In GPC, the separation mechanism involves an equilibrium between solutes in the mobile phase and those which can permeate the inner volume of a stationary phase that is porous. Molecules with hydrodynamic volumes (or size in solution) that are smaller than the pore sizes in the stationary... 

We differentiate two distinct regimes for phase separation, depending on whether the process takes place in the metastable or the unstable region of the Temperature-Composition plane (Fig.2.). These are called nucleation and growth and spinodal decomposition , respectively. These mechanisms are competitive in determining the mode of phase-separation, the dominant effect being dependent on how far from the equilibrium binodal the mixture has been thrusted. Polymer-polymer systems, because of the slow diffusion times, can be brought to well beyond the spinodal even at concentrations far from the critical point. 

The reason for this enliancement is intuitively obvious once the two reactants have met, they temporarily are trapped in a connnon solvent shell and fomi a short-lived so-called encounter complex. During the lifetime of the encounter complex they can undergo multiple collisions, which give them a much bigger chance to react before they separate again, than in the gas phase. So this effect is due to the microscopic solvent structure in the vicinity of the reactant pair. Its description in the framework of equilibrium statistical mechanics requires the specification of an appropriate interaction potential. 

It is always important to keep in mind the relative nature of substituent effects. Thus, the effect of the chlorine atoms in the case of trichloroacetic acid is primarily to stabilize the dissociated anion. The acid is more highly dissociated than in the unsubstituted case because there is a more favorable energy difference between the parent acid and the anion. It is the energy differences, not the absolute energies, that determine the equilibrium constant for ionization. As we will discuss more fully in Chapter 4, there are other mechanisms by which substituents affect the energy of reactants and products. The detailed understanding of substituent effects will require that we separate polar effects fiom these other factors. 

Marcus uses the Born-Oppenheimer approximation to separate electronic and nuclear motions, the only exception being at S in the case of nonadiabatic reactions. Classical equilibrium statistical mechanics is used to calculate the probability of arriving at the activated complex only vibrational quantum effects are treated approximately. The result is... 

The statement applies not only to chemical equilibrium but also to phase equilibrium. It is obviously true that it also applies to multiple substitutions. Classically isotopes cannot be separated (enriched or depleted) in one molecular species (or phase) from another species (or phase) by chemical equilibrium processes. Statements of this truth appeared clearly in the early chemical literature. The previously derived Equation 4.80 leads to exactly the same conclusion but that equation is limited to the case of an ideal gas in the rigid rotor harmonic oscillator approximation. The present conclusion about isotope effects in classical mechanics is stronger. It only requires the Born-Oppenheimer approximation. 

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