Mixed solvent activity coefficients

It should be emphasised that the use of solvent activity coefficients in investigating the transition state is not limited to one component solvent systems. Provided the thermodynamics of solvent transfer can be established for the reactant solutes in the mixed solvent system then the transfer properties of the transition state can be established. 

The advantage of using solvent activity coefficients in a discussion of the transition state for non-solvolytic reactions in mixed solvent media, is that the solvent activity coefficient is a function of state of the system and can be used to infer transition state properties without cognisance of, or concern for, the structure or detailed identity of the solvation sphere. If on the other hand the mechanism of a bimolecular reaction is clearly defined on other grounds, then the solvent activity coefficients should lead to understanding of the solvent reorganisation upon activation. At this stage very few results have been accumulated in binary solvent mixtures. ... 

The use of mixed solvents for distinguishing associative from dissociative mechanisms has not been successful, since a solvolytic rate proportional to the mole fraction of coordinating solvent in the presence of a non-coordinating solvent can be correlated with either mechan-ism. " It seems likely that delineation could be achieved through solvent activity coefficients in much the same way as Parker has succeeded in the treatment of the solvolysis reactions at carbon centres. ... 

Solvent activity coefficients allow the construction of diagrams such as Fig. 6.2.1 which show the relative free energies of ions in a range of solvents. However, they do not permit us to forecast which solvent is fractionated into the solvation sphere in a mixed solvent environment, since in addition to the ion-solvent interaction we must also consider the solvent-solvent interactions. The preferential solvation of ions such as [Cr(NCS)e] by CH3CN in CH3CN-H2O solvent mixtures is perhaps best regarded as a rejection of CH3CN by the water structure, rather than a predominance of any ion-solvent interactions. 

Classical polymer solution thermodynamics often did not consider solvent activities or solvent activity coefficients but usually a dimensionless quantity, the so-called Flory-Huggins interaction parameter x The % is not only a function of temperature (and pressure), as was evident from its foimdation, but it is also a function of composition and polymer molecular mass. As pointed out in many papers, it is more precise to call it x function (what is in principle a residual solvent chemical potential function). Because of its widespread use and its possible sources of mistakes and rrusinterpretations, the necessary relations must be included here. Starting from Equation [4.4.1b], the difference between the chemical potentials of the solvent in the mixture and in the standard state belongs to the first derivative of the Gibbs free energy of mixing with respect to the amount of substance of the solvent ... 

When a solute is added to an acidic solvent it may become protonated by the solvent. If the solvent is water and the concentration of solute is not very great, then the pH of the solution is a good measure of the proton-donating ability of the solvent. Unfortunately, this is no longer true in concentrated solutions because activity coefficients are no longer unity. A measurement of solvent acidity is needed that works in concentrated solutions and applies to mixed solvents as well. The Hammett acidity function is a measurement that is used for acidic solvents of high dielectric constant. For any solvent, including mixtures of solvents (but the proportions of the mixture must be specified), a value Hq is defined as... 

In principle, Gibbs free energies of transfer for trihalides can be obtained from solubilities in water and in nonaqueous or mixed aqueous solutions. However, there are two major obstacles here. The first is the prevalence of hydrates and solvates. This may complicate the calculation of AGtr(LnX3) values, for application of the standard formula connecting AGt, with solubilities requires that the composition of the solid phase be the same in equilibrium with the two solvent media in question. The other major hurdle is that solubilities of the trichlorides, tribromides, and triiodides in water are so high that knowledge of activity coefficients, which indeed are known to be far from unity 4b), is essential (201). These can, indeed, be measured, but such measurements require much time, care, and patience. 

In this equation x, is the liquid perfume concentration, Mt the molecular weight, R the ideal gas constant, and T the absolute temperature. Equation 2 relates the liquid perfume composition, x, with the human sensory reaction of the evaporated perfume. A key factor of Equation 2 is the activity coefficient, y, because it represents the affinity of a molecule to its neighboring medium. High value of y means an increased inclination for a given substance to be released from the mixture and low value of y means a low concentration in the headspace. This means that the OV values of a particular component can change if it is diluted in different solvents or mixed with different fragrance components. 

MacDougall, F.H. and Bartsch, C.E. The solubility and activity coefficient of silver acetate in mixed solvents, J. Phys. Chem., 40(5) 649-659, 1936. 

When nonnegligible concentrations of the electrolyte are present in the organic solvent, ion-ion interactions superimpose on the ion-solvent ones, or the secondary medium ejfect. Although an equation similar to Eq. (2.43) may be used for determining the activity coefficient in the new medium, it is necessary to employ the appropriate value of A in this equation that depends on the relative permittivity of the medium A(org) = A(aq)(eaq/e ,g) Unless very water-rich mixed solvents are used, different numerical values of the parameters in the denominator and the second term on the right-hand side of Eq. (2.43) have to be employed. 

A common sitnation is that the electrolyte is completely dissociated in the aqueons phase and incompletely, or hardly at all, in the organic phase of a ternary solvent extraction system (cf. Chapter 3), since solvents that are practically immiscible with water tend to have low valnes for their relative permittivities e. At low solnte concentrations, at which nearly ideal mixing is to be expected for the completely dissociated ions in the aqneons phase and the undissociated electrolyte in the organic phase (i.e., the activity coefficients in each phase are approximately nnity), the distribntion constant is given by... 

The papers in the second section deal primarily with the liquid phase itself rather than with its equilibrium vapor. They cover effects of electrolytes on mixed solvents with respect to solubilities, solvation and liquid structure, distribution coefficients, chemical potentials, activity coefficients, work functions, heat capacities, heats of solution, volumes of transfer, free energies of transfer, electrical potentials, conductances, ionization constants, electrostatic theory, osmotic coefficients, acidity functions, viscosities, and related properties and behavior. 

Here 113 is completely defined by the variables Z and N3. For any given values of Z and N3, the reference of the activity coefficient will be chosen as the extremely dilute state (N3 = 0) of the given solute in a binary mixed solvent of the same composition Z. By the definition, the chemical potential of the reference state varies with Z. Hence, one obtains for the 1-1 salts... 

The mean ionic activity coefficients of hydrobromic acid at round molalities (calculated by means of Equation 2) are summarized in Tables XI, XII, and XIII for x = 10, 30, and 50 mass percent monoglyme. Values of —logio 7 at round molalities from 0.005 to 0.1 mol-kg-1 were obtained by interpolating a least squares fit to a power series in m which was derived by means of a computer. These values at 298.15° K are compared in Figure 2 with those for hydrochloric acid in the same mixed solvent (I) and that for hydrobromic acid in water (21). The relative partial molal enthalpy (H2 — Hj>) can be calculated from the change in the activity coefficient with temperature, but we have used instead the following equations ... 

The activity coefficients of hydrobromic acid in the mixed solvents are lower, as expected, than those in water (20). Hydrobromic acid completely dissociates in the mixed solvents (e = 49.5 at 298.15° K for the 50 mass percent monoglyme) under investigation. Figure 2 clearly indicates that at a particular molality, the stoichiometric activity coefficient of hydrochloric acid is lower than that of hydrobromic acid in the same mixed solvent, and the heat capacity changes (Cp — Cp) also suggest that there are no ion-pair formations. 

Activity Coefficients of Electrolytes in Water-Polyethylene Glycol Mixed Solvent by Isopiestic Method... 

With the use of thermodynamic relations and numerical procedure, the activity coefficients of the solutes in a ternary system are expressed as a function of binary data and the water activity of the ternary system. The isopiestic method was used to obtain water activity data. The systems KCl-H20-PEG-200 and KBr-H20-PEG-200 were measured. The activity coefficient of potassium chloride is higher in the mixed solvent than in pure water. The activity coefficient of potassium bromide is smaller and changes very little with the increasing nonelectrolyte concentration. PEG-200 is salted out from the system with KCl, but it is salted in in the system with KBr within a certain concentration range. 

The trend of activity coefficients of potassium chloride and potassium bromide is different in measured mixed solvent. The activity coefficient of potassium chloride is higher in the mixed solvent than in the pure water and rises smoothly with the nonelectrolyte content. The minimum value, about 2.0-3.0m in pure water, can be observed in the mixed solvent also. Because of the activity coefficient of the nonelectrolyte in the ternary system (also higher than that in pure water), both components are mutually salted out. 

The activity coefficient of potassium bromide is smaller in the mixed solvent than in pure water and changes very little with the increasing nonelectrolyte concentration. 

Figure 13.23. Examples of vapor-liquid equilibria in presence of solvents, (a) Mixture of-octane and toluene in the presence of phenol, (b) Mixtures of chloroform and acetone in the presence of methylisobutylketone. The mole fraction of solvent is indicated, (c) Mixture of ethanol and water (a) without additive (b) with 10gCaCl2 in 100 mL of mix. (d) Mixture of acetone and methanol (a) in 2.3Af CaCl2 ip) salt-free, (e) Effect of solvent concentration on the activity coefficients and relative volatility of an equimolal mixture of acetone and water (Carlson and Stewart, in Weissbergers Technique of Organic Chemistry IV, Distillation, 1965). (f) Relative volatilities in the presence of acetonitrile. Compositions of hydrocarbons in liquid phase on solvent-free basis (1) 0.76 isopentane + 0.24 isoprene (2) 0.24 iC5 + 0.76 IP (3) 0.5 iC5 + 0.5 2-methylbutene-2 (4) 0.25-0.76 2MB2 + 0.75-0.24 IP [Ogorodnikov et al., Zh. Prikl. Kh. 34, 1096-1102 (1961)].

These equations are used whenever we need an expression for the chemical potential of a strong electrolyte in solution. We have based the development only on a binary system. The equations are exactly the same when several strong electrolytes are present as solutes. In such cases the chemical potential of a given solute is a function of the molalities of all solutes through the mean activity coefficients. In general the reference state is defined as the solution in which the molality of all solutes is infinitesimally small. In special cases a mixed solvent consisting of the pure solvent and one or more solutes at a fixed molality may be used. The reference state in such cases is the infinitely dilute solution of all solutes except those whose concentrations are kept constant. Again, when two or more substances, pure or mixed, may be considered as solvents, a choice of solvent must be made and clearly stated. 

At equilibrium the ratio of concentrations of P in a mixed solvent and in water will be equal to the inverse of the transfer activity coefficient,... 

Studies of the solution properties of heteropoly acids have been somewhat spares despite the general interest in these compounds for many years. Deterents to such studies have been primarily the instability of the compounds and the uncertainty concerning their composition. Conductivity and pH measurements on the heteropoly acids H4[PMonVO40] and H5[PMoi0V2O40] in aqueous solutions and mixed solvents has already been discussed. The acids are strong 1-4 and 1-5 electrolytes, respectively. Activity coefficients of ammonium 6-heteropolymolybdates have been reported and shown these to be 1 3 electrolytes197. ... 

Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially non-ideal behavior. The electrolyte components represent reaction products of absorbed gases or dissociation products of dissolved salts. There are two basic models applied for the description of electrolyte-containing mixtures, namely the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model [37-39] is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed solvent electrolyte systems based on the binary pair parameters. The model reduces to the well-known NRTL model when electrolyte concentrations in the liquid phase approach zero [40]. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

In solvents that are chemically similar to the solute (i.e., naphthalene/toluene), the experimental solubility of the solute is very close to the ideal value. Either negative or positive deviation from the ideal value occurs when the solute and the solvent are chemically dissimilar. The nonideal behavior results from the differences in the interactions between the solute and the solvent molecules (i.e., solute-solute, solvent-solvent, and solute-solvent). The sum of these interactions usually becomes positive, and having an incomplete mixing of all components results in a finite solubility of the solute in the solvent. These deviations from ideal solution behavior can be expressed by the activity coefficient of the nonideal solution. The activity, a2, of a solute in a nonideal solution is the product of concentration, x2, and the activity coefficient, y2, as ... 

Assuming that it is only van der Waals forces which are acting in the solute/ solvent system, and that the heat of mixing is responsible for all deviations from ideal behaviour, as well as the fact that the solute/solvent interaction energy is the geometric mean of solute/solute and solvent/solvent interactions, Hildebrand [228, 229] and Scatchard [230] were able to develop the following expression for the activity coefficient f of the nonelectrolyte solute i dissolved in a solvent s (mole fraction basis), referred to a standard state of pure liquid solute (not infinite dilution) ... 

The standard potential of the silver-silver bromide electrode has been determined from emf measurements of cells with hydrogen electrodes and silver-silver bromide electrodes in solutions of hydrogen bromide in mixtures of water and N-methylacetamide (NMA). The mole fractions of NMA in the mixed solvents were 0.06, 0.15, 0.25, and 0.50, and the dielectric constants varied from 87 to 110 at 25°C. The molality of HBr covered the range 0.01-0.1 mol kg 1. Data for the mixed solvents were obtained at nine temperatures from 5° to 45°C. The results were used to derive the standard emf of the cell as well as the mean ionic activity coefficients and standard thermodynamic constants for HBr. The information obtained sheds some light on the nature of ion-ion and ion-solvent interactions in this system of high dielectric constant. 

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