Determination Of Partial Molar Volumes Research Articles

Determination of partial molar volumes from free energy perturbation theory.

Partial molar volume is an important thermodynamic property that gives insights into molecular size and intermolecular interactions in solution. Theoretical frameworks for determining the partial molar volume (V°) of a solvated molecule generally apply Scaled Particle Theory or Kirkwood-Buff theory. With the current abilities to perform long molecular dynamics and Monte Carlo simulations, more direct methods are gaining popularity, such as computing V° directly as the difference in computed volume from two simulations, one with a solute present and another without. Thermodynamically, V° can also be determined as the pressure derivative of the free energy of solvation in the limit of infinite dilution. Both approaches are considered herein with the use of free energy perturbation (FEP) calculations to compute the necessary free energies of solvation at elevated pressures. Absolute and relative partial molar volumes are computed for benzene and benzene derivatives using the OPLS-AA force field. The mean unsigned error for all molecules is 2.8 cm(3) mol(-1). The present methodology should find use in many contexts such as the development and testing of force fields for use in computer simulations of organic and biomolecular systems, as a complement to related experimental studies, and to develop a deeper understanding of solute-solvent interactions.

Combining in situ FTIR spectroscopy, BTEM analysis, bulk density measurements and DFT for two Diels–Alder reactions. A general approach for partial molar volume and reaction volume analyses

Two organic reactions, namely the reaction of cyclopentadiene (CPD) and dimethyl acetylene dicarboxylate (DMAD) and the dimerization reaction of CPD were conducted in toluene at 298.1 K at atmospheric pressure and measured by in situ FTIR spectroscopy. Band-target entropy minimization (BTEM) analyses were employed for obtaining the pure component spectra of the solutes and their corresponding concentrations. The solute concentrations and the bulk density data were used to evaluate the partial molar volumes of the solute constituents. The partial molar volumes evaluated from this multi-component approach were in good agreement with those determined from independent binary solution measurements. The corresponding volumes of reaction for the CPD + DMAD and dimerization CPD + CPD reactions were determined to be −37 ± 3 cm3 mol−1 and −31 ± 2 cm3 mol−1, respectively. For completeness, DFT calculations were performed and used to rationalize the vibration modes corresponding to the BTEM spectral estimates as well as to provide predictions of the molar volumes of the solutes. The present study demonstrates the usefulness of a combined spectroscopic, signal processing, bulk density measurement and DFT approach to the determination of partial molar volumes and volumes of reaction directly from the multi-component reactive systems.

Determination of Partial Molar Volumes in Aqueous Solutions of Ionic Compounds

Students are given density data for aqueous solutions of three ionic compounds and guided to construct graphs of solution volume versus moles of solute at constant temperature, pressure, and moles of water. They are then asked to fit the data to an equation, use it to find an equation for the partial molar volumes of the solute, and evaluate that PMV at two concentrations.

On the Determination of Partial Molar Volumes, Partial Molar Refractions, Mean Electronic Polarizabilities and Effective Molecular Radii from Dilute Multi-component Data alone using Response Surface Models

A quaternary system consisting of three solutes, namely ethanol, diethylene glycol (DEG) and triethylene glycol (TEG) in benzene at 298.15 K and 1.0125 × 105 Pa was studied. An experimental design in the range of concentration 0.006 < xsolute−i < 0.023 was explored, optimizing the metric distance among the solutes to avoid clustering. On-line simultaneous experimental measurements using a densitometer and a refractometer were utilized to measure bulk solution density and bulk refractive index, respectively. Response surface models describing the total molar volume and total molar refraction were employed to determine the partial molar volumes and the partial molar refractions of each solute from the dilute multi-component data alone. Neither densities nor refractive indices of any of the pure components were used and no binary information was required for the analysis. Definitions for the mean electronic polarizability and the effective molecular radius of a solute based on the partial molar refraction were introduced. Subsequently, the mean electronic polarizabilities and the effective molecular radii for each solute in multi-component solutions, as well as the solvent were determined. The results obtained for the partial molar volumes, partial molar refractions, electronic polarizabilities and the effective molecular radii were in good agreement with those obtained from independent binary experiments as well as those from literature binary data.

The direct determination of partial molar volumes and reaction volumes in ultra-dilute non-reactive and reactive multi-component systems using a combined spectroscopic and modified response surface model approach

Two experimental multi-component organometallic systems were studied, namely, (1) a non-reactive system consisting of [Mo(CO)(6)], [Mn(2)(CO)(10)], and [Re(2)(CO)(10)] in toluene under argon at 298.15 K and 0.1 MPa and (2) a reactive system consisting of [Rh(4)(CO)(12)] + PPh(3)--> [Rh(4)(CO)(11)PPh(3)] + CO in n-hexane under argon at 298.15 K and 0.1 MPa. The mole fractions of all solutes were less than 140 x 10(-6) in system (1) and less than 65 x 10(-6) in system (2). Simultaneous in-situ FTIR spectroscopic measurements and on-line oscillatory U-tube density measurements were performed on the multi-component solutions. A newly developed response surface methodology was applied to the data sets to determine the individual limiting partial molar volumes of all constituents present as well as the reaction volume. The limiting partial molar volumes obtained for system (1) were 176.4 +/- 2.5, 265.1 +/- 2.4, and 276.8 +/- 2.4 cm(3) mol(-1) for [Mo(CO)(6)], [Mn(2)(CO)(10)], and [Re(2)(CO)(10)], respectively and are consistent with independent binary experiments. The limiting partial molar volumes obtained for system (2) were 310.7 +/- 2.7, 219.8 +/- 2.2 and 461.5 +/- 4.5 cm(3) mol(-1) for [Rh(4)(CO)(12)], PPh(3) and [Rh(4)(CO)(11)PPh(3)], respectively. In addition, a reaction volume Delta(r)V equal to -17.0 +/- 5.7 cm(3) mol(-1) was obtained. The present results demonstrate that both partial molar volumes and reaction volumes can be obtained directly from multi-component organometallic solutions. This development provides a new tool for physico-chemical determinations relevant to a variety of solutes and their reactions.

Gas permeation through a glassy polymer membrane: chemical potential gradient or dual mobility mode?

The flux equation for gas transport through a glassy polymer membrane is expressed in terms of a chemical potential gradient. It is an implicit function of the operating pressure. By studying the specific properties of this function, it can be simplified to an explicit form, which is mathematically identical to the expression proposed by the dual mobility model. Using this new model, all the data obtained by the dual mobility model can be described adequately. However, the physical significance of the parameters of the present model is completely different from the parameters of a dual mobility model. The present model assumes that only the molecules sorbed by the Henry mode contributed to the flux, and those sorbed by the Langmuir mode remained completely immobilized. This model provides an indirect method for the determination of partial molar volumes of gases in polymer membranes. It has been shown that the steady-state flux depends on the sorption rate at the interface, and not on the Henry constant. It has been found that the contribution of pressure in the diffusional transport of gases is of the same order and may be even higher than that of the concentration, which contradicts the popular perception that ‘the diffusion process is related basically to the concentration gradient’.

Experimental determination of partial molar volumes of Ga 2O 3 and GeO 2 in silicate melts: implications for the pressure dependence of metal–silicate partition coefficients

In this study, densities of gallium and germanium bearing silicate liquids were determined using the double bob Archimedian method. The silicate base components of the liquids were sodium disilicate (NS2) and anorthite–diopside eutectic composition (AD). Densities were converted to molar volumes and plotted against mole fractions of Ga 2O 3 or GeO 2. The mixing behavior of volumes is linear in all systems except in the NS2+Ga 2O 3 liquids where a strong non-linearity is observed. In this case, the partial molar volume at infinite dilution was determined by the common tangent method. At 1600 K, the partial molar volume of Ga 2O 3 is 50±8 cm 3/mol in the NS2 liquid and 36.3±0.3 cm 3/mole in the AD liquid. For GeO 2 a partial molar volume of 29.7±0.2 cm 3/mol is found independent of silicate composition. The knowledge of the partial molar volumes of Ga 2O 3 and GeO 2 in silicate melts allows first order predictions of the pressure dependence of metal/silicate partition coefficients. Such data are important in deciding between homogeneous and inhomogeneous accretion models of the Earth. Using the partial molar volumes of Ga 2O 3 and GeO 2 measured in this study combined with literature data on the metallic components, the volume change of the exchange reaction x 2 Fe met + MO x/2 sil = x 2 FeO sil + M met was calculated (M=Ga or Ge). Volume changes for Ga-bearing AD liquids are positive and increase with temperature leading to a decrease in siderophility of Ga relative to Fe with increasing pressure whereas the corresponding change in the Ge-bearing AD liquids is negative implying higher siderophility of Ge with pressure. The decrease of the metal–silicate partition coefficient of Ga with pressure is consistent with models of core formation by global metal–silicate equilibrium at some depth. The increase of the metal/silicate partition coefficient of Ge with pressure is incompatible with global core mantle equilibrium. However, there is some ambiguity regarding the valence state and the coordination of Ge during core formation. Either Ge was present as GeO or as GeO 2 while the experimental results obtained in this study are only applicable for GeO 2. Our extrapolations are only valid as long as the coordination of Ge does not change because the partial molar volumes depend strongly on the coordination number.

Determination of the partial molar volume of SiO 2 in silicate liquids at elevated pressures and temperatures: a new experimental approach

This study presents a new approach for determining the partial molar volume and its pressure derivative for a silicate liquid component through an experimental determination of the isothermal pressure dependence of the solubility in the liquid of a crystalline phase having the composition of the component. Because this approach allows the determination of partial molar volumes of liquid components at elevated pressure, it has the potential to detect pressure-induced structural changes associated with particular components in silicate liquid through their influence on partial molar volumes. To illustrate the approach, an experimental determination of the solubility of quartz in a rhyolitic liquid was used to determine the partial molar volume of SiO 2 at pressures up to 35 kbar and a temperature of 1350°C. The 1 bar partial molar volume for SiO 2 determined in this way, 2.635 ± 0.009 J/bar, is slightly smaller than the 2.690 ± 0.006 J/bar determined by Lange and Carmichael (1987) (all uncertainties are 1σ). The isothermal pressure dependence of the partial molar volume of SiO 2 at 10 to 35 kbar (−8.69 × 10 −6 ± 6.1 × 10 −7 J/bar 2) is approximately one-half of the value determined by Kress and Carmichael (1991) at 1 bar (−1.96 × 10 −5 ± 0.2 × 10 −6 J/bar 2). Our high pressure determination can be reconciled with the existing 1 bar volume and compressibility data if the isothermal pressure dependence of the partial molar volume of SiO 2 in silicate liquids decreases rapidly between 1 bar and 10 kbar, then remains approximately constant to at least 35 kbar.

Correlation and prediction of infinite-dilution partial molar volumes of organic solutes in SC CO 2 using the Peng-Robinson and PHCT equations of state and the LCVM EOS/G E model

An extensive infinite-dilution partial molar volume (PMV) data base of various liquid and solid solutes in supercritical carbon dioxide, including the very recent experimental partial molar volume data reported by Spicka et al. [B. Spicka, A. Cortesi, M. Fermeglia, I. Kikic, Determination of partial molar volumes at infinite dilution using SFC technique, J. Supercrit Fluids 7 (1994) 171] and Cortesi et al. [A. Cortesi, I. Kikic, B. Spicka, K. Magoulas, D. Tassios, Determination of partial molar volumes at infinite dilution of alcohols and terpenes in supercritical carbon dioxide, J. Supercrit. Fluids 9 (1996) 141] is used for a comprehensive study of the capabilities of three different thermodynamic models for the prediction of infinite-dilution partial molar volume data. The models are two equations of state, i.e. the well-known Peng-Robinson cubic EoS and the perturbed hard-chain theory (PHCT) EoS, and an EoS/G E model, the recently proposed LCVM group-contribution model. Correlation of the whole data base has been also considered with the Peng-Robinson EoS in order to determine the capability of a cubic equation of state to describe PMV data. Generally, all models were found to be semi-quantitative in the PMV prediction, especially in the range of the PMV minimum. Satisfactory prediction results are obtained using the Peng-Robinson EoS with interaction parameters from phase equilibrium data, and the fully predictive LCVM model. Both LCVM and the PHCT models tend to overpredict the PMV of n-alkanes in carbon dioxide in the high-pressure region, while PHCT always gives less satisfactory prediction results.

Structural Volume Changes in Photoinduced Electron Transfer Reactions. Laser-Induced Optoacoustic Studies of Speciation during the Quenching Reaction of Excited Ru(bpy)32+ by Fe(III) in Aqueous Solutions

Laser-induced optoacoustic spectroscopy has been applied to the photoinduced electron-transfer reaction between Ru(bpy)32+ and various salts of Fe(III) [Fe(ClO4)3, Fe2(SO4)3, and FeCl3]. The reaction volume changes associated with photoinduced ligand exchange derived from these measurements allowed the determination of partial molar volumes at high dilutions of several species such as FeSO4, FeSO4+, Fe(SO4)2-, Fe(OH)2+, FeCl+, FeCl2+, and FeCl2+, not attainable from other techniques. The volume change of oxidation of Ru(bpy)32+ to Ru(bpy)33+ at high dilution was also calculated.

Determination of partial molar volumes at infinite dilution of alcohols and terpenes in supercritical carbon dioxide

The use of supercritical fluid chromatography for determining partial molar volumes of alcohols and terpenes at infinite dilution in supercritical CO 2 is presented and discussed. Partial molar volumes at infinite dilution are obtained from the variation of the retention properties with the density of mobile phase at 313.15 K and in the pressure range from 85 to 280 bar.

Determination of partial molar volumes at critical end points

There has been considerable interest in the volumetric behavior of supercritical binary (and higher) fluid mixtures near the solvent critical point. It is in the vicinity of this critical point that supercritical extraction processes are generally considered to be most effective. In the case of a solvent + solute system that exhibits liquid-liquid-vapor (llg) partial miscibility, properties of the dense gas phase near an ll = g upper critical end point are most interesting. The partial molar volumes of the solvent and solute at these conditions are difficult to measure directly. In this note, we show that the solvent and solute partial molar volumes of the critical phase of a binary critical end point are readily determined from the associated three-phase liquid-liquid-vapor (llg) volume-composition data.

Determination of partial molar volumes at infinite dilution using SFC technique

The use of supercritical-fluid chromatography for determining partial molar volumes of some substances (linear, cyclic and aromatic hydrocarbons, benzaldehyde) at infinite dilution in supercritical C02 is presented and discussed. Partial molar volumes at infinite dilution are obtained from the variation of the retention properties with the density of mobile phase at 313.15 K and in the pressure range from 80 to 280 bar.

Determination of Individual Partial Molar Volumes of Ions in Water from Measurements of Ultrasonic Vibration Potentials

Abstract A new apparatus for measurements of ionic vibration potentials generated by the propagation of ultrasonic waves through electrolyte solutions was constructed, and used for the determination of partial molar volumes of ions in aqueous solutions of uni-univalent electrolytes. The apparatus, based on the method of ultrasonic vibration potentials (Zana and Yeager), was improved in two points through the introduction of the Doppler effect: a small measuring cell (about 50 cm3) and very low noises (50 nV). Then, measurements of temperature variation of ultrasonic vibration potentials have become possible. Partial molar volumes of hydrogen, alkali metal, and halide ions in water were determined in the range of temperature, 15–45 °C.

Binding of metal ions to polysaccharides III. Partial molar volumes of chondroitin sulphate systems

Determination of partial molar volumes provides information on the solvation of species in solution. As such this quantity is an obvious tool to distinguish between specific and atmospheric binding. We found that in aqueous systems of chondroitin sulphate and copper(II) ions specific binding effects play an important role. Binding to only one charged group (carboxylate or sulphate) could be ruled out on the basis of our results. However, a distinction between possible modes of binding to two charged groups could not be made merely from the partial molar volumes. Nevertheless, for the binding of divalent metal ions the involvement of two carboxylate groups, or one carboxylate group and one sulphate group, appears most likely.

Utilisation d'une méthode d'ajouts pour la détermination précise des volumes molaires partiels des constituants dans un solvant mixte. Application au système eau–méthanol

The determination of partial molar volumes of each component in a binary mixture is usually the result of the derivation of the polynomial function which describes the whole excess curve. The accuracy of the present available densimeters (vibrating densimeter Piker type) allows direct access to the values of partial molar volume by a method requiring successive additions of various components. The method of calculation is discussed in this paper and applied for the water–methanol system. Partial molar volumes of water and methanol are calculated for different phase compositions, and each variation is described by polynomial functions which are related to each other by thermodynamic rules. This technique may be extended to mixtures which contain different solvents and highly concentrated solutes.

Partial molar volumes of gases dissolved in liquids. Part II. A dilatometer for measuring infinite-dilution partial molar volumes, and results for 40 liquid-gas systems

Abstract A dilatometer with an imprecision of less than 0.4% is described for the determination of partial molar volumes of gases dissolved in liquids. Measurements at 298.15 K are reported for 40 liquid-gas systems having n-alkanes and 1-alkanols as the liquid component. The results are interpreted in terms of a number of empirical and semiempirical correlations.