Partial Molar Volume Of Solute Research Articles

Thermodynamic studies of binary methanol and ethanol solutions of 1-dodecanol and 1-tetradecanol at 25�C

The osmotic coefficients of binary methanol and ethanol solutions of 1-dodecanol and 1-tetradecanol wer measured at 25°C up to 8 mol-kg−1 in methanol and 5.5 mol-kg−1 in ethanol. The activity coefficients of the solute were calculated from Bjerrum's relation. From the osmotic and activity coeficients the excess Gibbs energies of solution as well as the respective partial molar functions of solute and solvent and the virial pair interaction coefficients for the excess Gibbs energies were calculated. In addition, the difference in the Gibbs energy of solvation for the solvent in solution relative to the pure solvent was calculated, as well as the partial molar volumes and excess partial molar volumes of solutes at infinite dilution, and the coefficients of pairwise contributions to the excess volume were determined. The thermodynamic parameters obtained are discussed on the basis of solute-solvent and solute-solute interactions.

Diffusion of a solute in dilute solution in a supercritical fluid

The experimental evidence for the behaviour of the binary diffusion coefficient for a solute in dilute solution in a supercritical fluid (a fluid above its critical temperature and pressure) is reviewed. Measurements at very low dilution, particularly by the Taylor dispersion technique, indicate that, at constant temperature a few degrees above the critical temperature, the product of density and the diffusion coefficient exhibits a small, continuous and undramatic variation from zero density to well above the critical density. However, some measurements made at higher, but still very low concentrations (e.g. with mole fractions around 10 -3 ), show a lowering of the coefficient in the critical region. The equations, based on non-equilibrium thermodynamics, are put into a form in which the behaviour of the binary diffusion coefficient in the critical region, but not very close to the critical point, may be examined using an equation of state. Calculations for naphthalene in solution in carbon dioxide are carried out using the van der Waals equation of state for mixtures to indicate the form and order of magnitude of the ‘anomalous’ lowering of the coefficient, and especially its dependence on concentration. These indicate a substantial effect even at naphthalene mole fractions of 4.0 x 10 -4 or less and a temperatures 1, 3 and 9 K above the critical temperature of the pure solvent. In addition the flux of a solute in a supercritical fluid in the critical region with respect to space or cell-fixed coordinates is discussed. Because of the large and negative partial molar volumes of solutes like naphthalene in this region, the frames of reference, according to which the diffusion coefficients are defined, can be caused to move rapidly, commonly towards the source of concentration. Thus fluxes of solute with respect to space-fixed coordinates are further substantially reduced in the critical region. The combination of the lowering of the diffusion coefficient and barycentric motion can therefore cause a very significant reduction of solute mass transfer in the critical region and may be the explanation of the sometimes very large diffusion anomalies observed experimentally.

Molecular thermodynamics of solute‐polymer‐supercritical fluid systems

AbstractThe distribution coefficients of the solutes (toluene, naphthalene, and phenanthrene) are reported at infinite dilution between silicone rubber and supercriticalfluid carbon dioxide. A new technique is described in which a thin film of polymer is coated and cross‐linked onto silica, and the distribution coefficient is measured rapidly by elution supercritical‐fluid chromatography. Because CO2 significantly enhances the solute's volatility and its diffusion coefficient in the polymer, it is possible to study solute‐polymer interactions at room temperature for nonvolatile compounds which would be difficult to study by conventional techniques such as gas chromatography. These infinite dilution data are used to determine solutepolymer interaction parameters to calculate phase diagrams over a wide concentration range. The residual, combinatorial, and cross‐link contributions to the solute activity coefficient in the polymer are discussed as a function of concentration. In addition, pronounced pressure and temperature effects are described in terms of experimentally measured solute partial molar volumes (to – 14 L/mol) and partial molar enthalpies (to – 850 kJ/mol) in the fluid phase.

Molecular Clustering in Supercritical Solutions

Abstract Molecular explanations have recently identified massive solvent clusters surrounding the dissolved solute as the causative agent of the striking solvent properties of supercritical fluids. Such clusters were first inferred from the large negative values of the solute partial molar volume near the solvent critical point; these clusters were estimated to contain about 100 solvent molecules per solute molecule in excess of the bulk average. Subsequent evidence from visible and ultraviolet absorption and fluorescence spectroscopy and from chemical reaction studies have provided qualitative support for the notion of solvent-solute clusters. Other spcctroscopic evidence suggests the formation of solute-solute aggregates, as well, near the solvent critical point. Such structures on a molecular level are describable in terms of the molecular distribution functions. We present results on the size and radial profile of solvent-solute clusters and on solute-solute aggregation for systems representative of t...

Analysis of infinite dilution partial molar volumes using a distribution function theory

We present a theoretical investigation of the partial molar volumes of binary mixtures in which one component is at the limit of infinite dilution. The study is based upon the Percus-Yevick integral equation theory applied to mixtures in which the intermolecular forces are modeled using Lennard-Jones 12-6 potentials. The Kirkwood-Buff equations are used to determine the thermodynamic properties from the pair correlation functions of the mixture. We focus especially upon the dependence on solvent density of the solute partial molar volume along isotherms close to the critical temperature of the solvent. The predictions are compared with both results from Monte Carlo computer simulations of Lennard-Jones 12-6 mixtures and experimental data for naphthalene-carbon dioxide mixtures. These comparisons show that the integral equation theory provides a useful and very economical approach to the analysis of these systems. We relate the extrema in the partial molar volume near the solvent critical density to the behavior of the solute-solvent and solvent-solvent pair correlation functions. Our results demonstrate that the important density dependent effect is the growth of long ranged correlations in the solvent. We use our results to examine the concept of ‘clustering’ which has recently been used in connection with these phenomena.

Attractive, weakly attractive, and repulsive near-critical systems

Mixtures composed of trace amounts of a solute in the vicinity of a solvent’s critical point exhibit one of three types of behavior: repulsive, weakly attractive, or attractive. Each regime is characterized by the signs of the diverging solute partial molar volume (and enthalpy), and of the correlations between solute and solvent concentration fluctuations at infinite dilution. Attractive behavior, in which the former quantity is negative and the latter positive, underlies all of the actual or proposed applications of supercritical fluids to processes ranging from precipitation polymerization to activated carbon regeneration. The presence of trace amounts of a solute within a solvent characterized by long-ranged density fluctuations gives rise to a cooperative phenomenon which, for attractive systems, involves the formation of a large solvent-rich region around each solute molecule. Likewise, for repulsive behavior, the cooperative phenomenon involves the formation of a large solvent-deficient region around each solute molecule. The calculated volume, enthalpy, and entropy changes per solvent molecule are very similar to the corresponding condensation (attractive behavior) and evaporation (repulsive behavior) effects for the pure solvent at subcritical temperatures. This suggests a qualitative description of near-critical cooperative phenomena as induced phase transitions.

The molecular basis of temperature effects in supercritical extraction

AbstractThe behavior of solute partial molar enthalpies in dilute supercritical mixtures gives rise to the well‐known phenomenon of retrograde solubility (equilibrium solubility decreasing with increasing temperature at constant pressure). A mechanistic interpretation of this phenomenon in terms of the formation of large clusters of solvent molecules around solute molecules is consistent with experimentally observed retrograde behavior. Cluster formation occurs as a consequence of the unbounded increase in the solvent's compressibility arbitrarily close to the latter's critical point. At infinite dilution, the solute's partial molar volume and enthalpy grow linearly with cluster size. This means that the negative divergence of these quantities is simply a macroscopic manifestation of a “condensation” in which an increasing number of solvent molecules cluster around solute molecules. Arbitrarily close to the solvent's critical point, scaling relationships show that the decay of both solvent‐solvent and solute‐solvent correlation functions exhibits the same radial dependence. This functionality is thus solute‐independent, and is determined exclusively by the proximity to the solvent's critical point. The locus along which thermal effects associated with cluster formation are maximized is arbitrarliy close to the solvent's critical isochore as the latter's critical point is approached.

Interpretation of free energies of transfer and solute partial molar volumes in mixed solvents using Kirkwood–Buff theory

Using the Kirkwood–Buff theory for partial molar volumes in ternary mixtures and the Hall formulation of the same theory for free energies of transfer, we have demonstrated how one may obtain separately the two solute–solvent Kirkwood–Buff radial distribution function integrals for an infinitely dilute solute in a binary solvent mixture. As an example, the parameters are calculated for NaCl in MeOH–H2O.

Effect of the partial molar volume of the solute in the stationary phase on retention in supercritical fluid chromatography

Retention in supercritical fluid chromatography is a dynamic mechanism, involving intermolecular interactions in the mobile and stationary phases. A simple thermodynamic model, describing solute retention, has been investigated on the basis of macroscopic thermodynamic variables of the solute partial molar volume in the stationary and mobile phases. Solute-solvent interactions in the mobile phase are dominant at lower pressures. Solute-stationary phase interactions have an important role in solute retention in capillary supercritical fluid chromatography. The interaction of the solute with the five different stationary phases reflects the polarizability differences between these phases, as shown by the partial molar volume of the solute in the stationary phase.

Numerical solutions for diffusion-controlled growth of spheres from finite initial size

Efficient numerical methods have been developed to predict the diffusion-controlled growth of an isolated sphere of finite intial size in conditions of spherical symmetry. Analytical solutions for growth from zero size have also been re-examined and it is shown that Scriven's assumption of constant density is unnecessary; it is only required that the partial molar volumes of solute and solvent be independent of concentration. Detailed comparisons of analytical predictions and numerical results for both size and concentration profile confirm the accuracy of the numerical techniques for wide ranges of the parameters concerned.

Clustering in dilute, binary supercritical mixtures: A fluctuation analysis

Solute-solvent concentration fluctuation correlations at infinite dilution are a statistical measure of the excess number of solvent molecules surrounding a given solute molecule, with respect to a uniform distribution at the prevailing density. This leads to the concept of a cluster which, in dilute supercritical mixtures (trace solute(s) in the vicinity of a solvent's critical point) acquires mechanistic and not merely statistical significance. Experimental measurements of solute partial molar volumes at infinite dilution in such systems are shown to be equivalent, when analyzed in the light of fluctuation theory, to a cluster size determination. This quantity can be either positive or negative. Calculations based on experimental measurements of infinite dilution partial molar volumes of organic solids in supercritical fluids indicate the existence of clusters of ca 100 solvent molecules per solute molecule. The fluctuation approach cannot be used arbitrarily close to the solvent's critical point, since it is based on the assumption of a finite solvent compressibility. Asymptotic laws for the behavior of solute fluctuations in dilute mixtures within differently defined regions of space (constant volume; constant solvent mass) are derived. Finally, it is shown that there is a univocal relationship between cluster formation and the experimentally observed solubility enhancement in dilute mixtures of non-volatile solutes in supercritical solvents.

Densities and partial molar volumes of supercooled aqueous solutions

Density measurements of aqueous solutions of ethanol, t-butanol, and hydrazine in the temperature range from 50 °C down to nucleation are presented. From these data, solute partial molar volumes and temperatures of maximum density are determined. The partial molar volumes of the alcohol solutions at low concentration become small below −30 °C, and the characteristic minimum in the partial molar volume vs concentration curve vanishes. The hydrazine solutions display similar behavior except no minimum is observed. It is also found that the temperature of maximum density washes out at finite concentrations and solutions with higher concentration do not seem to nucleate but may be forming glasses. These results are discussed in terms of a liquid clathrate structural model of water which becomes multiply connected to fill all space as the water is supercooled.

Retention volume in high-pressue gas chromatography : I. Thermodynamics of the specific retention volume

Formal thermodynamic relationships were derived for the specific retention volume of the solute in the solute-carrier gas-stationary liquid ternary system, applicable at higher pressures and with a negligible pressure drop across the column. Special attention has been paid to the effects of the solubility of the carrier gas in the stationary phase and to the non-ideal behaviour of the carrier gas. The relationships derived show that the pressure dependence of the specific retention volume alone can give only approximate information on binary solute-carrier gas systems. If more precise data are to be obtained, it is necessary to know additional parameters (the partial molar volume of solute in the solute-carrier gas-stationary liquid ternary system, activity coefficients of the dissolved carrier gas and their dependence on the composition, and the molar fraction of dissolved carrier gas), which cannot be obtained reliably from chromatographic data.

Volumetric properties of alcohols in dilute aqueous solutions

The densities of dilute (mole fraction concentration < 2 × 10–3) aqueous solutions of the four isomeric butanols have been determined at 0.5, 5, 25 and 40°, and solute partial molar volumes and expansibilities have been evaluated. Extrapolations of volume data to infinite dilution are analyzed, and the limiting volumes and expansibilities are interpreted in terms of the effects of alcohols on the structural properties of water. The concentration and temperature dependences of the partial volumes indicate the presence of long-range interactions between hydrated solute molecules.