Formal mixed solvents

Several other reaction types have also appeared in the literature but are sometimes purely formal schemes dating from the time when the solvent was (incorrectly) thought to undergo self-ionic dissociation into SO + and S03 or SO " and S205 . More recently it has been shown that, whereas neither SO2 nor OSMe2 (dmso) react with first-row transition metals, the mixed solvent smoothly effects... 

For the mixed solvent layer formalism, the preexponential parameter was estimated by extension of the Newton and Sutin approach [61],... 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

In ternary systems composed of one polymer and two liquids or of two polymers and one solvent, the total Gibbs mixing function of the system can be written in terms of the g interaction parameters of the corresponding binary pairs, according to the I lory - Huggins formalism [11], When studying polymers in mixed solvents, it has been customary to introduce an additional interaction parameter, called ternary,... 

Fig. 8. Dependence of the logarithm of the standard rate constant in mixed solvents related to the rate in aqueous solution (w) on the formal potential for the following systems (1) Pb(II)/Pb(Hg) (2) Zn(II)/Zn(Hg) and (3) Mn(II)/Mn(Hg).

Superscripts m and w relate to mixed solvent and water, respectively, and the rate constants (Arth) are calculated at constant potential, on the solvent-independent scale. Such formal adoption of Eqs. (57) and (58) gives equations which can be valid only when there is no difference between the composition of the bulk and the surface phases, as in pure solvents where the validity of Eqs. (57) and (58) was proved. 

The Kirkwood—Buff formalism was used to derive an expression for the composition dependence of the Henry s constant in a binary solvent. A binary mixed solvent can be considered as composed of two solvents, or one solvent and a solute, such as a salt, polymer, or protein. The following simple expression for the Henry s constant in a binary solvent (H2t) was obtained when the binary solvent was assumed ideal In = [In f2,i(ln V — In V ) + In i 2,3(ln Vj — In V)]/ (In — In V ). In this expression, i 2,i and i 2,3 are the Henry s constants for the pure single solvents 1 and 3, respectively V is the molar volume of the ideal binary solvent 1—3 and and Vs are the molar volumes of the pure individual solvents 1 and 3. The comparison with experimental data for aqueous binary solvents demonstrated that the derived expression provides the best predictions among the known equations. Even though the aqueous solvents are nonideal, their degree of nonideality is much smaller than those of the solute gas in each of the constituents. For this reason, the ideality assumption for the binary solvent constitutes a most reasonable approximation even for nonideal mixtures. 

In this paper, the Kirkwood—Buff formalism was used to relate the Henry s constant for a binary solvent mixture to the binary data and the composition of the solvent. A general equation describing the above dependence was obtained, which can be solved (analytically or numerically) if the composition dependence of the molar volume and the activity coefficients in the gas-free mixed solvent are known. A simple expression was obtained when the mixture of solvents was considered to be ideal. In this case, the Henr/s constant for a binary solvent mixture could be expressed in terms of the Henry s constants for the individual solvents and the molar volumes of the individual solvents. The agreement with experiment for aqueous solvents is better than that provided by any other expression available, including an empirical one involving three adjustable parameters. Even though the aqueous solvents considered are nonideal, their degrees of nonideality are much lower than those of the solute gas in each of the constituent solvents. For this reason, the assumption that the binary solvent behaves as an ideal mixture constitutes a reasonable approximation. 

The aim of the present paper is to develop a theoretical approach for the description of the gas solubility in a solvent containing a salt. To achieve this goal, the Kirkwood—Buff formalism for ternary mixtures will be used. Recently, such a formalism has been used to predict the gas solubility in mixed solvents (mixture of two nonelectrol5rtes) in terms of the solubilities in the individual solvents. A similar approach will be employed here. 

The Kirkwood-Buff formalism can be also used to derive the composition dependence of the Henry constant for a sparingly soluble gas dissolved in a mixed solvent containing water-r electrolyte [27]. The obtained equation requires information about the molar volume and the mean activity coefficient of the electrolyte in the binary (water-H electrolyte) mixture. Several expressions for the mean activity coefficient of the electrolyte were tested and it was concluded that the accuracy in... 

By combining Equations 10.8 and 10.9, one obtains an expression for the derivative of the activity coefficient of an infinitely dilute solute with respect to the cosolvent mole fraction in terms of characteristics of the solute-free binary solvent (y, c,°, and c°) and the parameters Aj2 and A23, which characterize the interactions of an infinitely dilute solute with the components of the mixed solvent. Even though Equation 10.8 constitutes a formal statistical thermodynamics relation in which all... 

In many centred molecules the interactions between the electro-active centres in a given molecule modify the spacing of the formal Standard Potentials of the successive processes by an amount that depends in the case of coulombic forces in part on the dielectric properties of the local surrounding electrolyte solution. This feature has been observed in Ae case of bimetallic complexes in mixed solvent systems of relatively low bulk dielectric constants, has been used to ascertain Ae impact of electrolyte concentration in particular ion-pairing on electrolyte dielectric behaviour. 

The TEAF system can be used to reduce ketones, certain alkenes and imines. With regard to the latter substrate, during our studies it was realized that 5 2 TEAF in some solvents was sufficiently acidic to protonate the imine (p K, ca. 6 in water). Iminium salts are much more reactive than imines due to inductive effects (cf. the Stacker reaction), and it was thus considered likely that an iminium salt was being reduced to an ammonium salt [54]. This explains why imines are not reduced in the IPA system which is neutral, and not acidic. When an iminium salt was pre-prepared by mixing equal amounts of an imine and acid, and used in the IPA system, the iminium was reduced, albeit with lower rate and moderate enantioselectivity. Quaternary iminium salts were also reduced to tertiary amines. Nevertheless, as other kinetic studies have indicated a pre-equilibrium with imine, it is possible that the proton formally sits on the catalyst and the iminium is formed during the catalytic cycle. It is, of course, possible that the mechanism of imine transfer hydrogenation is different to that of ketone reduction, and a metal-coordinated imine may be involved [55]. 

Flory [3] formalized the equation of state for equilibrium swelling of gels. It consists of four terms the term of rubber-like elasticity, the term of mixing entropy, the term of polymer solvent interaction and the term of osmotic pressure due to free counter ions. Therefore, the gel volume is strongly influenced by temperature, the kind of solvent, free ion concentrations and the degree of dissociation of groups on polymer chains. 

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