Separating equilibria

An increase in the temperature was found to reduce the retention times and the plate count. This had a net effect of decreasing the resolution and increasing the peak height. The temperature dependence is likely to be dependent on the thermodynamics of the separation equilibria. 

As stated above, the term 9t T In c, represents a contribution to chemical potential stemming from the entropy associated with the dilution and concentration of components (see Section 1.6). Dilution and concentration processes are fundamental to separations, so it is clear that this term lies at the roots of separative equilibria. 

Essentially all separative equilibria, therefore, involve adjustments in concentration to such relative levels that the general equilibrium criterion /if = fx is satisfied. These adjustments differ from component to component because different intermolecular interactions give different A/i° values, thus giving the unequal concentration distributions that ultimately yield separation. 

Martin and Synge (3) introduced the important concept of theoretical plates into chromatography. Their concept was derived from partition theory and random statistics, and was related to similar ideas developed for extraction and fractional distillation. They supposed that the column could be divided into a number of sections called theoretical plates, and that solutes (dissolved compounds) could be expected to achieve equilibrium between the two phases (mobile and stationary) that exist within each plate. The chromatographic process, like an extraction process, can be visualized to occur when mobile phase (solvent) is transferred to the next plate, where a new equilibrium is established. Theoretical plate numbers of 1000 or more are common for HPLC columns, which means that 1000 separate equilibria must be established to obtain the same degree of separation by solvent... 

Figure 4-1. Separation equilibria. Separation in a separating funnel (left) in which a compound is distributed differentially between two immiscible phases, and analogous behaviour in a chromatography column (right) where a compound exhibits differing affinities to the stationary and the mobile phases.

Formally, two separate equilibria can be written, one for the transfer of electrons, and one for that of ions ... 

We seek perturbations of Hamiltonian dynamics with separable equilibria, i.e., such that p = p (//(z))p( ) is a stationary solution. 

Like precipitation, solvent extraction involves the removal of a substance from one phase (usually aqueous) into another (usually organic). A study of how the extent of extraction varies with experimental conditions is based on equilibrium considerations. In this chapter as well as in Chapters 16 and 17, the elementary relationships describing phase separation equilibria developed in Chapter 14 will be used. 

Two types of phase equilibria are superimposed phase separation equilibria in amorphous and ciystalhne phases. The thermodynamic equilibrium of the system presented in Figure 6.2 corresponds to polymer crystallization. The amorphous phase is metastable. It can exist fi om the beginning of crystalline phase nucleation through subsequent crystallization imtil the equilibrium state for the crystalline polymer is reached. A system can degenerate into many simple systems for polymers that erystallize readily in dilute solutions where polymer segregates into separate crystallites. Polymers, capable of partial crystallization at the ejq)ense of the formation of local regular blocks of chains (e.g., PVC) can exist as a metastable amorphous-erystalhne system. In such cases, one phase repre-... 

Since the simplifications will depend on the pressure range to be considered for a given case, we shall consider separately equilibria calculations for high and for low pressures. 

The prediction and correlation of energy requirements, heat exchanger duty, chemical equilibria, and separation equilibria requires a knowledge of the enthalpy, compressibility, fugacity, and vapor-liquid equilibrium properties of these compounds and their mixtures. 

The relation between the extent of separation and the extent of reaction is briefly considered in Section 5.1. How chemical reactions alter the separation equilibria in gcts-liquid, vapor-liquid, liquid-liquid, solid-liquid, surface adsorption equilibria, etc., is described in Section 5.2. The role of chemical reactions in aitering the separation in... 

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