Interacting solute equilibria

Two solutes distribute themselves between the two phases as concentrations Xa and Ya, and Xb and Yb and with rates Qa and Qb, respectively as shown in Fig. 3.32. The corresponding equilibrium concentrations Xa and Xb are functions of both the interacting solute concentrations, Ya and Yb, and can be expressed by functional relationships of the form... 

LIQUID-PHASE BEHAVIOR. The liquid phase contains dissolved substances and contacts the solid phase. For our purposes, the liquid phase is used synonymously with aqueous phase , and all processes discussed in this section take place in aqueous solutions. The dissolved monomers of the solid phase are formed in equilibrium with their uncomplexed components. Such components may be uncomplexed ions (which are charged atoms or molecules) free in solution or ionic complexes in equilibrium with dissociated ions. Concentrations of the uncomplexed ions, therefore, depend upon the concentrations of all chemical substances competing for binding interactions with them. Each complex-ation reaction is defined by either a solution equilibrium constant ... 

This functional is also physically motivated as it expresses the balance of two terms a favorable (negative) solute-solvent interaction energy and an unfavorable (positive) solvent-solvent interaction. At equilibrium the second term is equal to half of the first as expected also from basic electrostatic arguments. 

Saraf, V. P. Kiran, E., "Supercritical Fluid-Polymer Interactions Phase Equilibrium Data for Solutions of Polystyrenes in n-Butane and n-Pentane," Polymer, 29, 2061 (1988). 

The effect of the medium on the position of equilibrium can be considered from two points of view (a) comparison of the gas-phase and solution equilibrium constants, and (b) comparison of the equilibrium constants for different solvents. Unfortunately, few equilibrium reactions have been studied both in the gas and liquid phases [5, 6j. These are primarily non-ionic reactions where the interaction between reacting molecules and solvent is relatively small e.g. the Diels-Alder dimerization of cyclo-pentadiene). In this chapter, therefore, equilibria which have been examined in solvents of different polarity will be the main topic considered (except for acid-base reactions described in Section 4.2.2). 

Intermolecular interactions and complexes Dielectric measurements on interacting solutes in inert solvents provide information about molecule complex formation. Some such dipoles induced by intermolecular interactions and molecular complexes in benzene solution are listed in Table 1.3. The dipole moment of the complex is a function of the relative strengths of the acid and base and the intramolecular equilibrium is described by Eq. (49) ... 

Sardin, M. Schweich, D. Leij, F. J. van Genuchten, M. T. (1991) Modelling the non-equilibrium transport of linearly interacting solutes in porous media A review. Water Resour. Res. 27(9), 2287-2307. 

Confirmation that the side arm participated in complexation when appropriately placed was obtained by comparing the complexation strengths of 8 and 9. Sodium cation is bound in the center of the macrocycle. The side arm of 8 or 9 can reach over the ring, but only 8 has an oxygen donor (methoxy) positioned appropriately to interact. The equilibrium binding constant Ks) for Na by 15-crown-5 at 25°C in methanol solution is 1860. 

When a metal electrode is placed in an electrolyte solution, an equilibrium difference usually becomes established between the metal and solution. Equilibrium is reached when the electrons left in the metal contribute to the formation of a layer of ions whose charge is equal and opposite to that of the cations in solution at the interface. The positive charges of cations in the solution and the negative charges of electrons in the metal electrode form the electrical double layer [4]. The solution side of the double layer is made up of several layers as shown in Fig. 2.7. The inner layer, which is closest to the electrode, consists of solvent and other ions, which are called specifically adsorbed ions. This inner layer is called the compact Helmholtz layer, and the locus of the electrical centers of this inner layer is called the inner Helmholtz plane, which is at a distance of di from the metal electrode surface. The solvated ion can approach the electrode only to a distance d2. The locus of the centers of the nearest solvated ion is called the outer Helmholtz plane. The interaction of the solvated ion with metal electrode only involves electrostatic force and is independent of the chemical properties of the ions. These ions are called non-specifically adsorbed ions. These ions are distributed in the 3D region called diffusion layer whose thickness depends on the ionic concentration in the electrolyte. The structure of the double layer affects the rate of electrode reactions. 

SA2 Saraf, V.P. and Kiran, E., Supercritical fluid-polymer interactions. Phase equilibrium data for solutions of polystyrenes in n-butane and n-pentane, Polymer, 29, 2061, 1988. 

Local equilibrium analysis can be extended to systems with variable interstitial velocity (concentrated gases), interacting solute isotherms such as Eq. (18=8), or finite heats of adsorption (most inportant for... 

The spontaneous aggregation of ionic surfactants produces an array of structures, whose form depends on the surfactant structure and concentration, oil type and concentration, and temperature (Figures 3 and 4). A completely mixed, singlephase micellar solution is at its minimum free energy. This free energy is determined by multiple intermolecular and ionic interactions that include electrostatic, dipole-dipole, ion-dipole, ion-ion, and dispersion (van der Waals) interactions. At equilibrium, the opposing forces are in balance and the net force is zero. The balance determines the size and shape of the micelle. Figure 5(a) is an older conceptual representation of a spherical micelle in aqueous solution... 

According to M.C. Williams, in concentrated solutions intermo-lecular interactions are developed, whose intensity derive from both the potential function and chain segments distribution. Without specifying the nature of intermolecular forces, the author started from the theory of the polymer solutions equilibrium, elaborated by M. Fixman [1008], and proposed the following relation ... 

Solute equilibrium conditions between the mobile and stationary phases are achieved at zero surface coverage of the surface. The chromatogram must be symmetric and the maximum of the chromatographic peak should be independent of the amount of retained adsorbate [20]. The concentration of adsorbate in the gas phase is minimal, and the sorption process is derived from real adsorbate-adsorbent interactions. The adsorbate might be considered as an ideal gas both in the gas phase and in the adsorbed state. At infinite dilution, the net retention volume (Vj,f) is related to the concentration of adsorbate in the gas phase c, as follows ... 

In analytical ultracentrifuges, molecular properties can be modeled through sedimentation velocity analysis or sedimentation equilibrium analysis. In sedimentation velocity analysis, concentrations and solute properties are modeled continuously overtime. Sedimentation velocity analysis can be used to determine the macromolecule s shape, mass, composition, and conformational properties. During sedimentation equilibrium analysis, centrifugation has stopped and particle movement is based on diffusion. This allows for modeling of the mass of the particle as well as the chemical equilibrium properties of interacting solutes. 

In contrast to other modes of chromatography—particularly adsorption chromatography—the enthalpy term can be neglected in this case as the solute and the stationary phase are assumed not to exchange any interaction. The equilibrium constant (K) thus depends exclusively on the entropy term ... 

If it is also assumed the solution is ideal except for intramicellar interactions the equilibrium constant is given by... 

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