Pure solvents, thermodynamic

Surfactants are compounds that exhibit surface activity, or more generally, interfacial activity, and migrate to the interface when placed in solution. This migration results in lowering the solution surface tension (interfacial tension) as compared to the surface tension of the pure solvent. Thermodynamically, adsorption of a surfactant is deLned by the Gibbs adsorption equation ... 

The argument made above not withstanding, the pure solvent thermodynamics, including coexistence curve location, critical parameters, and dielectric constant are, in fact, rather well reproduced by the SPC models, and SPC/E in particular[54, 55]. Further, when the SPC/E model is applied to SCW, the calculated structural results agree with recent experimental neutron scattering data approximately as well in SCW as in ambient water[15, 16]. Hence, the SPC models have shown themselves to be remarkably robust caricatures of fluid water, and well supported for our studies of SCW. 

Osmotic pressure is one of four closely related properties of solutions that are collectively known as colligative properties. In all four, a difference in the behavior of the solution and the pure solvent is related to the thermodynamic activity of the solvent in the solution. In ideal solutions the activity equals the mole fraction, and the mole fractions of the solvent (subscript 1) and the solute (subscript 2) add up to unity in two-component systems. Therefore the colligative properties can easily be related to the mole fraction of the solute in an ideal solution. The following review of the other three colligative properties indicates the similarity which underlies the analysis of all the colligative properties ... 

Whether AH for a projected reaction is based on bond-energy data, tabulated thermochemical data, or MO computations, there remain some fundamental problems which prevent reaching a final conclusion about a reaction s feasibility. In the first place, most reactions of interest occur in solution, and the enthalpy, entropy, and fiee energy associated with any reaction depend strongly on the solvent medium. There is only a limited amount of tabulated thermochemical data that are directly suitable for treatment of reactions in organic solvents. Thermodynamic data usually pertain to the pure compound. MO calculations usually refer to the isolated (gas phase) molecule. Estimates of solvation effects must be made in order to apply either experimental or computational data to reactions occurring in solution. 

This effect is explained by a structuring of the solvent surrounding the apolar solute. Table 2 shows a comparison of the thermodynamical excess quantities for mixing the pure solvent with the pure solute to an infinitely diluted solution for hydrophobic and non-hydrophobic solutes, according to Chan et al. 42). 

Because osmosis is a thermodynamic property, we can expect it to be related to the effect of the solute on the enthalpy and entropy of the solution solvent flows until the molar Gibbs free energy of the solvent is the same on each side of the membrane We have already seen several times that a solute lowers the molar Gibbs free energy of the solution below that of the pure solvent, and solvent therefore has a tendency to pass into the solution (Fig. 8.33). 

In the osmotic pressure method, the activity of the solvent in the dilute solution is restored to that of the pure solvent (i.e., unity) by applying a pressure m on the solution. According to a well-known thermodynamic relationship, the change in activity with pressure is given by... 

The solubility parameter 5 of a pure solvent defined initially by Hildebrand and Scott based on a thermodynamic model of regular solution theory is given by Equation 4.4 [13] ... 

A great many electrolytes have only limited solubility, which can be very low. If a solid electrolyte is added to a pure solvent in an amount greater than corresponds to its solubility, a heterogeneous system is formed in which equilibrium is established between the electrolyte ions in solution and in the solid phase. At constant temperature, this equilibrium can be described by the thermodynamic condition for equality of the chemical potentials of ions in the liquid and solid phases (under these conditions, cations and anions enter and leave the solid phase simultaneously, fulfilling the electroneutrality condition). In the liquid phase, the chemical potential of the ion is a function of its activity, while it is constant in the solid phase. If the formula unit of the electrolyte considered consists of v+ cations and v anions, then... 

Equilibrium phenomenon, operative in polymer solutions, in multicomponent solvents, and in polymer networks swollen by multicomponent solvents, that produces differences in solvent composition in the polymer-containing region and in the pure solvent which is in thermodynamic equilibrium with that region. 

Both AGt(x)e and AGt(x)e mix refer to a neutral solute species or a neutral combination of ions X. These quantities may be determined thermodynamically from emf measurements on suitable cells or from solubility studies in the mixed or pure solvents. The splitting of these quantities into separate contributions from the ions has been the subject of much speculation (8). We may regard Equations 16 and 17 as valid if the species X bears a charge, provided the ionic contributions are added to obtain the values for a neutral combination of ions. 

The subject of interest is a gel swollen by solvent. Let F be the Gibbs free energy change after mixing of solvent and an initially unstrained polymer network [1]. When the gel is isotropic and is immersed in a pure solvent with a fixed pressure Po, F is a thermodynamic potential dependent on the temperature T, the pressure p inside the gel, and the solvent particle number Ns inside the gel. It satisfies... 

To understand why a solute lowers the vapor pressure, we need to look at the thermodynamic properties of the solution. We saw in Section 8.2, specifically Eq. 1, that at equilibrium, and in the absence of any solute, the molar free energy of the vapor is equal to that of the pure solvent. We now need to consider the molar free energies of the solvent and the vapor when a solute is present. We shall consider only nonvolatile solutes, which do not appear in the vapor phase, and limit our considerations to ideal solutions. 

An interesting property of resins impregnated with oximes or oxines is that the selectivity of, for example, copper over iron(III), approaches that of a pure solvent-extraction process only when an inert solvent is present in the pores of the resin.396 Thus, in a /S-hydroxyoxime SIR, the selectivity for copper over iron(III) improved by a factor of 20 when the solvent perchloroethylene was introduced into the SIR, and by a factor of 700 in a similar resin impregnated with 8-hydroxy-quinoline.396 This is believed to be due to kinetic and thermodynamic restrictions in the extraction of iron(III), but not of copper, at an aqueous—organic boundary.396 397... 

The derivation of the law of mass action from the second law of thermodynamics defines equilibrium constants K° in terms of activities. For dilute solutions and low ionic strengths, the numerical values of the molar concentration quotients of the solutes, if necessary amended by activity coefficients, are acceptable approximations to K° [Equation (3)]. However, there exists no justification for using the numerical value of a solvent s molar concentration as an approximation for the pure solvent s activity, which is unity by definition.76,77... 

I well remember my shock when I recognized that COSMO-RS was not thermodynamically consistent, just after having quit my safe position at Bayer AG and had started my own company. But within an hour I had located the origin of the inconsistency in the solvent-size correction, and within a day I found an expression for the size correction that ensures Gibbs-Duhem consistency, while leaving the limits of pure solvents unchanged compared with our original COSMO-RS expression ... 

The thermodynamic consistency of this expression follows directly from the fact that the chemical potential corrections are now calculated as composition derivatives of a thermodynamic potential. Since this expression left the limits of pure solvents unchanged, and since almost only these limits are of importance for our COSMO-RS parameterization data set, we could use the existing COSMO-RS parameterization in combination with the new Gibbs-Duhem-consistent solvent size correction. 

Thus, the standard state of the solvent is the pure solvent and is identical to the reference state for the solvent in all of its thermodynamic properties. 

When the infinitely dilute solution, with respect to all solutes, is used as the reference state of the solution at all temperatures and pressures, Ap c approaches zero as all cfs approach zero. Thus, the standard state of the solvent is the pure solvent at all temperature and pressures and is identical to the reference state of the solvent for all thermodynamic functions. 

The definition is completed by assigning a value to m and (f>c in some reference state. To conform with the definitions made in Sections 8.9 and 8.10, the infinitely dilute solution with respect to all molalities or molarities is usually used as the reference state at all temperatures and pressures, and both m and c are made to approach unity as the sum of the molalities or molarities of the solutes approaches zero. The standard state of the solvent is again the pure solvent, and is identical to its reference state in all of its thermodynamic functions. 

When changing force field parameters of a compound, overall exactness of the model is determined by the parameterization criteria. As this work was parameterized to reproduce the solubility, which is related to the thermodynamic quantity of free energy, this raises the question of solvent structure, as the structure-energy relationship is evident even in the gas phase interactions. One way to test the solvent structure is to check the density of the aqueous solution as a rough estimate of the ability of the model to reproduce the correct intermolecular interaction between the solute and the solvent. For this purpose, additional MC simulations were carried out on the developed models to test their ability to reproduce the experimental density of solution, at the specified concentration. The density was calculated using the experimentally derived density equations for carbon dioxide in aqueous solution from Teng et al., which is calculated from the fyj, of the C02(aq) and the density of the pure solvent [36, 37]. 

A recent study performed by Mello et al. focuses on a comparison of n-hexane and cyclohexane in the polymerization of BD with the catalyst system NdV/D I BAH/f BuCl. In this study Mello et al. use the pure solvents and mixtures of n-hexane and cyclohexane [423]. Cyclohexane yields BR with a significantly lower molar mass than n-hexane. According to Mello et al. this effect is due to the thermodynamically better solvent quality of cyclohexane. The authors found no strong influence of the cyclohexane/n-hexane ratio neither on catalyst activity nor on microstructure. 

Figure 51.1 illustrates some of the relevant thermodynamic features relating to the addition of solute to a pure solvent to form a solution and its corresponding effect on the melting point, Tm and boiling point, ZJ,. 

The Boltzmann law computes to a configurational AS governed by Eq. (3.22). A configurational AS represents dissolution of a perfectly ordered, pure solid polymer in pure solvent (Allcock and Lampe, 1981). van Oss (1991) cautions against designating physical processes as AH- or AS-driven unless careful microcalorimetric measurements have been made, because many thermodynamic suppositions (imputed to modeling or intuition) have not been substantiated by experimentation. Although descriptive analyses of... 

The topic of interactions between Lewis acids and bases could benefit from systematic ab initio quantum chemical calculations of gas phase (two molecule) studies, for which there is a substantial body of experimental data available for comparison. Similar computations could be carried out in the presence of a dielectric medium. In addition, assemblages of molecules, for example a test acid in the presence of many solvent molecules, could be carried out with semiempirical quantum mechanics using, for example, a commercial package. This type of neutral molecule interaction study could then be enlarged in scope to determine the effects of ion-molecule interactions by way of quantum mechanical computations in a dielectric medium in solutions of low ionic strength. This approach could bring considerable order and a more convincing picture of Lewis acid base theory than the mixed spectroscopic (molecular) parameters in interactive media and the purely macroscopic (thermodynamic and kinetic) parameters in different and varied media or perturbation theory applied to the semiempirical molecular orbital or valence bond approach [11 and references therein]. 

Alot of information about the free energies of transfer of single ions between pure solvents has been accumulated. Less numerous are determinations in mixed solvents, and the ionic enthalpies of transfer and entropies of transfer as function of mole fraction are known as an exception only. In Table 1 ions and solvent mixtures are listed for which free energies of transfer and some other thermodynamic quantities have been determined. 

The most important property of micelles in aqueous or nonaqueous solvents is their ability to dissolve substances that are insoluble in the pure solvent. In aqueous systems, nonpolar substances are solubilized in the interior of the micelles, whereas polar substances are solubilized in the micellar core in nonaqueous systems. This process is called solubilization. It can be defined as the formation of a thermodynamically stable isotropic solution with reduced activity of the solubilized material (8). It is useful to further differentiate between primary and secondary solubilization. The solubilization of water in tetrachloroethylene containing a surfactant is an example of primary solubilization. Secondary solubilization can be considered as an extension of primary solubilization because it refers to the solution of a substance in the primary solubilizate. 

Electromotive force measurements of the cell Pt, H2 HBr(m), X% alcohol, Y% water AgBr-Ag were made at 25°, 35°, and 45°C in the following solvent systems (1) water, (2) water-ethanol (30%, 60%, 90%, 99% ethanol), (3) anhydrous ethanol, (4) water-tert-butanol (30%, 60%, 91% and 99% tert-butanol), and (5) anhydrous tert-butanol. Calculations of standard cell potential were made using the Debye-Huckel theory as extended by Gronwall, LaMer, and Sandved. Gibbs free energy, enthalpy, entropy changes, and mean ionic activity coefficients were calculated for each solvent mixture and temperature. Relationships of the stand-ard potentials and thermodynamic functons with respect to solvent compositions in the two mixed-solvent systems and the pure solvents were discussed. 

We haven t discussed activities, vapor pressure and other aspects of the thermodynamics of liquids (optimistically assuming you ve done all this in P. Chem). Nevertheless, we are sure that you recall that the vapor pressure of the solvent in a polymer solution relative to the vapor pressure of the pure solvent may, to a first approximation, be equated to the activity of the solvent, which in turn is related to the chemical potential by ... 

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