Equilibrium solvation energy

This solution, formally expressed as Equation (1.131), is essentially nonlocal in space, although the problem is originally formulated in terms of local Equations (1.119). The spatial nonlocality arises from boundary conditions on S. Simple solutions are available only for spherically symmetrical cases (Born ion or Onsager point dipole). The equilibrium solvation energy is expressed as... 

The molecular theory considers a dipolar liquid where the two constituents are Lennard-Jones spheres each with an embedded dipole moment at the center. The Lennard-Jones parameters (sizes, interaction strength parameters) and also values of the dipole moments are different for the two species. The theoiy properly includes the differing inter- and intramolecular correlations that are present in a binary mixture. As a result, the theory can explain several important aspects of the nonideality of equilibrium solvation energy (broadly known as preferential solvation) observed in experiments. The non-ideality of solvation is found to depend on both the molecular sizes and the magnitude of the dipole moments of the solvent... 

In (32.23) the first term on the right hand side is the required solvation energy of the ion at a distance x from the droplet surface and the second term is the equilibrium solvation energy of the ion at a distance d below the drop s surface. The difference between these two terms gives the solvation energy barrier. 

A preliminary study of the above equilibrium, using 4-31G//MNDO calculations and including thermal and solvation energies [82JPR(324)827], was significantly improved by subsequent calculations. Enchev increased the level of the calculations to 4-31G//STO-3G and considered four other... 

A. Frumkin, and B. Damaskin, Real free solvation energy of an electron in a solution in equilibrium with the electrode and its dependence on the solvent nature,/. Electroanal. Chem. 79, 259-266 (1977). 

Hence, the solvation energy change accompanying the disproportionation can compensate the repulsion term. In weakly solvating media, association with counter ions occurs and the disproportionation equilibrium should be considered, for example, as follows ... 

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, 5 (M+) and B X ), are related to the extraction constant the... 

The investigations of interfacial phenomena of immiscible electrolyte solutions are very important from the theoretical point of view. They provide convenient approaches to the determination of various physciochemical parameters, such as transfer and solvation energy of ions, partition and diffusion coefficients, as well as interfacial potentials [1-7,12-17]. Of course, it should be remembered that at equilibrium, either in the presence or absence of an electrolyte, the solvents forming the discussed system are saturated in each other. Therefore, these two phases, in a sense, constitute two mixed solvents. 

Consider a system of two solvents in contact in which a single electrolyte BA is dissolved, consisting of univalent ions. A distribution equilibrium is established between the two solutions. Because, in general, the solvation energies of the anion and cation in the two phases are different so that the ion with a certain charge has a greater tendency to pass into the second phase than the ion of opposite charge, an electrical double layer appears at... 

So far we have not touched on the fact that the important topic of solvation energy is not yet taken into account. The extent to which solvation influences gas-phase energy values can be considerable. As an example, gas-phase data for fundamental enolisation reactions are included in Table 1. Related aqueous solution phase data can be derived from equilibrium constants 31). The gas-phase heats of enolisation for acetone and propionaldehyde are 19.5 and 13 keal/mol, respectively. The corresponding free energies of enolisation in solution are 9.9 and 5.4 kcal/mol. (Whether the difference between gas and solution derives from enthalpy or entropy effects is irrelevant at this stage.) Despite this, our experience with gas-phase enthalpies calculated by the methods described in this chapter leads us to believe that even the current approach is most valuable for evaluation of reactivity. 

The source of some of the difficulties encountered in trying to explain the effects of structural changes on ionization rates may be due to the different parts played by the solvent, as for example, the sulfur dioxide of the trityl chloride equilibrium experiments and the aqueous acetone of the benzhydryl chloride rate data. The solvent is bound to modify the effect of a substituent, and although the solvent is usually ignored in discussing substituent effects this is because of a scarcity of usable data and not because the importance of the solvent is not realized "... solvation energy and entropy are the most characteristic determinants of reactions in solution, and... for this class of reactions no norm exists which does not take primary account of solvation. 220 Precisely how best to take account of solvation is an unanswered problem that is the subject of much current research. 

The coefficients c, in solution correspond to the global minimum of the free energy (note that this is not the equilibrium solvation condition), and satisfy the system of equations... 

Although in principle one could choose a set of arbitrary values for the solvent coordinates sm, solve the eigenvalue equation (2.23), and compute the free energy (2.12), in practice a preliminary aquaintance with the equilibrium solvation picture for the target reaction system serves as a computationally convenient doorway for the calculations in the nonequilibrium solvation regime. We show this below in the section dedicated to an illustration of the method for a two state case reported in BH-II. 

Since the reverse of the reaction Nl is the ionisation of the ester, the equilibrium position for any one system depends critically on the nature, especially the polarity, of the solvent, which determines the AHS terms. The accumulation of the necessary thermochemical data is essential to a rationalisation of the relation between cationic and pseudocationic polymerisations but the prevalence of the former at low temperatures and of the latter at high temperatures is surely related to the fact that the dielectric constant, and with it solvation energies, increases as the temperature of a polar solvent is reduced, so that decreasing temperature favours ionisation. 

The solvation energy described by the Born equation is essentially electrostatic in nature. Born equations 8.116 and 8.120 are in fact similar to the Born-Lande equation (1.67) used to define the electrostatic potential in a crystal (see section 1.12.1). In hght of this analogy, the effective electrostatic radius of an ion in solution r j assumes the same significance as the equilibrium distance in the Born-Lande equation. We may thus expect a close analogy between the crystal radius of an ion and the effective electrostatic radius of the same ion in solution. 

A linear solvation energy relationship (LSER) has been developed to predict the water-supercritical CO2 partition coefficients for a published collection of data. The independent variables in the model are empirically determined descriptors of the solute and solvent molecules. The LSER approach provides an average absolute relative deviation of 22% in the prediction of the water-supercritical CO2 partition coefficients for the six solutes considered. Results suggest that other types of equilibrium processes in supercritical fluids may be modeled using a LSER approach (Lagalante and Bruno, 1998). 

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