Molar Isothermal Compressibilities Research Articles

Isothermal compressibility, internal pressure studies of aqueous rare earth nitrate solutions at 298.15 K: An attempt to estimate ionic radii and understand inner– and outer–sphere exchange water structural interactions

In this communication, we report our analysis and results concerning the determination of ionic radii in aqueous solution phase for Lanthanum (La+3), Neodymium (Nd+3), Erbium (Er+3) and Ytterbium (Yb+3) ions in presence of nitrate (NO3-) anion at 298.15 K. The literature data for density, adiabatic compressibility, and specific heat capacity of solutions at constant pressure have been used to compute isothermal compressibility, internal pressure of solutions in limiting concentration range. The apparent molar isothermal compressibility of electrolytes and hydration numbers have been obtained. The electrostriction for rare earth cations and intrinsic volumes have been calculated using thermodynamic equations. The ionic radii of cations have been obtained using the ionic partial molar volume data of NO3- ions and the results are compared with those obtained for rare earth chlorides. The two series affect is also observed for ionic radii and internal pressure. The results have been explained on the basis of water structural effects due to electrostatic field and water dipole interaction between the inner– and outer–sphere water exchange reaction.

Thermodynamic properties of {glycerol (1) + tert-butanol (2)} mixtures at temperatures from 278 K to 323 K and pressures up to 100 MPa

In the present study the densities at atmospheric pressure and the compression coefficients of a binary liquid mixture {glycerol (1) + tert-butanol (2)} were measured within the temperature range from 278.15 K to 323.15 K (278.15, 288.15, 288.15, 308.15 and 323.15) and pressures up to 100 MPa (10, 25, 50, 75 and 100). Due to the limited solubility of tert-butanol in glycerol and the transition of the mixture to the solid phase the measurements at 278.15 K and 100 MPa were carried out up tox2 = 0.45 (x2 is the mole fraction of tert–butanol). The excess molar volumes, molar isothermal compression, molar isobaric thermal expansion, isochoric coefficient of thermal pressure mixtures, as well as the partial molar volumes of the mixture components, including their limit values, were calculated. The excess molar volume values at 323.15 K (the only temperature at which the compression was measured over the entire composition range) were found to be negative. The partial molar volume of glycerol (GL) at 323.15 K was characterized by the presence of a baric inversion region. The limiting partial molar volume of GL was shown to decrease in its own environment as the pressure rose and to increase in the TBA environment. The molar isothermal compression of the mixture varied depending on the composition without extremes, and the partial molar isothermal compression of GL had negative values. The molar isobaric thermal expansion of the mixture in the area of small tert-butanol (TBA) additives changed slightly at low temperatures and pressures and the increase in both the pressure and the temperature led to dispersion of their concentration dependences. The isochoric coefficient of thermal pressure decreased with an increase in x2, forming a small plateau at small TBA additions. The results obtained were discussed from the perspective of solute–solvent and solute–solute interactions.

Thermodynamic and Thermal Analyze of N,N-Dimethylformamide + 1-Butanol Mixture Properties Based on Density, Sound Velocity and Heat Capacity Data.

The present paper contains data on the density (ρ), sound velocity (u), and specific heat capacity cp of the mixture of N,N-dimethylformamide + 1-butanol (DMF + BuOH) determined in the entire concentration range of solution and in the temperature range (293.15-318.15) K. The analysis of thermodynamic functions such as isobaric molar expansion, isentropic and isothermal molar compression, isobaric and isochoric molar heat capacity, as well as their excess functions (Ep,mE,KS,mE,KT,mE,Cp, mE,CV, mE) and also VmE was undertaken. The analysis of changes in the physicochemical quantities was based on consideration of the system in terms of intermolecular interactions and resulting changes in the mixture structure. The results available in the literature were confusing during the analysis and became the reason for our decision to thoroughly examine the system. What is more, for a system whose components are widely used, there is very scarce information in the literature regarding the heat capacity of the tested mixture, which was also achieved and presented in this publication. The conclusions drawn from so many data points allow us to approximate and understand the changes that occur in the structure of the system due to the repeatability and consistency of the obtained results.

Analysis of ultraacoustic behavior of l-aspartic acid in aqueous sodium benzoate and ammonium acetate media

Acoustic study has been carried out on aqueous solutions of l-aspartic acid (ASP) in presence of two food additives sodium benzoate (SB) and ammonium acetate (AA) at 298.15 K. Propagation of ultrasonic sound wave passing through the experimental solutions bears a direct relation with various weak and strong molecular interactions acting between components of the solution. Isentropic compressibility (Ks), apparent molar isentropic compressibility (Ks,ϕ) and isothermal compressibility (KT) decrease with increasing electrostriction of water molecules surrounding the solute and cosolute ions. Although ion–solvent interactions are predominant, reasonable extent of ion-ion, ion/hydrophilic-hydrophilic and ion/hydrophobic-hydrophobic interactions also exists between different segments of solute and cosolute ions. In the process of solvation and ion association reformation of water structure takes place. Various parameters like molar free length (Lf), molar free volume (Vf), relative association (RA), internal pressure (πi), acoustic impedance (Z) and surface tension (γ)derived from density (ρ), viscosity (η) and ultrasonic velocity U advocate for stronger ion- solvent interactions, ion-pair formation and structure building ability of ASP in presence of SB/AA.

Ultraacoustic and conductometric studies on the interactions of l-glutamic acid with potassium sorbate and sodium benzoate in aqueous media

The objective of this investigation is to study and understand the nature of interactions between different ionic, polar and alkyl segments of l-glutamic acid (Glu) and food preservatives with carboxylate ions, e.g. Potassium sorbate (PS) and sodium benzoate (SB), with each other and with water. Acoustic properties were determined by measuring the velocity of ultrasonic sound (U) passing through the aqueous solutions of different concentration of Glu and PS/SB at 298.15 K. Compressibility parameters like isentropic compressibility (Ks), apparent molar isentropic compressibility (Ks,ϕ) and isothermal compressibility (KT) were analysed to elucidate the type of ion–solvent and ion-ion interactions and structural changes of water molecules in the solvation shells with the influence of solute (Glu) and cosolute (PS/SB) ions. Variation of relative association (RA), internal pressure (πi) and acoustic impedance (Z) with concentration of solute and cosolute in the solutions provide knowledge of ion-ion and ion–solvent interactions, structure building/breaking behavior of solute and cosolutes and formation of ion pairs or triplets. Additionally, electrical conductance (К) of the solutions was measured at different temperatures (T = 293.15–313.15 K with 5 K interval). Molar conductance values (Λm), Walden factor (Λm0η0), thermodynamic variables for the process of ion association (ΔGA,ΔHAandΔSA) and energy of activation (EA) for transportation of electrical charges were studied to explore the spontaneity of ion association and mobility of the charged particles through the solution. Critical evaluation of all these physicochemical and thermodynamic data leads to the conclusion that stronger ion–solvent interactions prevail in the solutions, Glu acts as a structure builder in attendance of PS/SB and the process of ion pair formation is spontaneous.

Compressed liquid densities for cyclopentane/n-heptane mixtures from 293.15 K to 363.15 K at pressures up to 70 MPa

The compressed liquid densities of pure cyclopentane, n-heptane and its binary mixtures were measured with the vibrating-tube densimeter. The temperature ranges were from 293.15 K to 363.15 K and the pressures up to 70 MPa. The density data were correlated with the Tammann-Tait equation. The excess molar volumes, isothermal compressibility and isobaric thermal expansivity were calculated and discussed. In addition, the SRK and PR equation of state and the corresponding volume-translation equations were used to predict the densities of the mixtures, and the predictive accuracy was analyzed.

Studies of intrinsic volumes of ethylene glycol and polyethylene glycol–300 molecules in aqueous solutions at 298.15 K: Application of Tammann–Tait–Gibson (TTG) equation of state

Systemic density (ρ) measurements have been carried–out for aqueous solutions of polyethylene glycols (PEG's) with the molar mass 200, 300, 400 and 600 D at (288.15, 293.15, 298.15, 303.15 and 308.15) K and at ambient pressure of 0.1 MPa in dilute solute concentration region (0.0119–0.4941 mol⋅kg−1). The ρ data are used to obtain the apparent molar volume (Vϕ) and partial molar volume (V¯2) of studied PEG's in aqueous solutions at finite concentration as well as at infinitely dilute solutions (Vϕ0) at studied temperatures. The coefficient of thermal expansion (α) for solutions, apparent molar expansivity (Eϕ) and limiting apparent molar expansivity (Eϕ0) for solutes are calculated at 293.15, 298.15 and 303.15 K. The densities of studied PEG's in carbon tetrachloride (CCl4) medium are also measured at 298.15 K. The transfer volume (ΔtrVϕ0) for PEG from pure liquid state to CCl4 and to water as solvent are estimated. The literature data of sound velocity (u), coefficient of thermal expansion (α) and specific heat capacity (CP) for solutions have been utilized to obtain thermodynamic properties like adiabatic compressibility (βad) and isothermal compressibility (βT) in case of aqueous solutions of ethylene glycol (EG) and PEG–300 at 298.15 K. The data are further utilized to obtain apparent molar adiabatic compressibility (KϕS) and apparent molar isothermal compressibility (KϕT) for EG and PEG–300 solute molecules at finite and at infinitely dilute solute concentration (KϕS0 and KϕT0, respectively). Further, the data of KϕT, α and CP data have been utilized to estimate internal pressure Pi (=∂U∂VT) of solutions containing EG and PEG–300 molecules as a function of concentration. The intrinsic volumes (Vint.) of these molecules have been calculated by applying Tammann–Tait–Gibson (TTG) equation of state. It is being observed that intrinsic volume differs appreciably from the value based upon EG and PEG–300 in a liquid state as a standard state. The excess volume change (V¯20E=V¯20-V¯int.0) values are found to be −16.1 and −63.8⋅10–6 m3⋅mol−1 for EG and PEG–300, respectively. Similar calculations made for PEG–300 in CCl4 medium also yield excess volume change of −60⋅10–6 m3⋅mol−1 magnitude. These results are explained on the basis of three dimensional hydrogen bonded structure of EG and the linkage ▪ interaction with solvent water having a presence of helical segments. The inferences drawn will be of help to understand the weak denaturing interactions of glycols in protein denaturation studies.

Liquid phase PVTx properties of {water (1) + 1,3-dimethylurea (2)} mixtures at temperatures from 278.15 to 323.15 K and pressures to 100 MPa

In this study, the compression coefficients k=ΔV/Vo of the binary mixture {water (1) + 1,3-dimethylurea (2)} were measured within the temperature range from 278.15 K to 323.15 K (278.15, 288.15, 288.15, 308.15, 323.15), the pressure range from 10 to 100 MPa (10, 25, 50, 75 and 100) and the composition range up to x2 = 0.19364 (1,3-dimethylurea mole fraction). The molar isothermal compression, KT,m, molar isobaric thermal expansion, EP,m, isochoric coefficient of thermal pressure, βV, and the internal pressure of the mixture, Pint, were calculated. It was demonstrated that the concentration dependences (on the mole fraction of 1,3-dimethylurea (1,3-DMU)) of the molar isothermal compressions of the mixture at low pressures and low temperatures are characterized by a minimum at x2≈0.06 ÷ 0.07, which levels out both with increase in pressure and with increase in temperature. The molar isobaric thermal expansion of the mixture increases with an increase in the 1,3-DMU concentration for all state parameters. At low temperatures, the concentration dependences of the molar expansion are characterized by the presence of a pressure inversion zone. The concentration dependences of the isochoric coefficient of thermal pressure of the mixture indicate the hydrophobic properties of the 1,3-DMU molecule become stronger at high pressures. The obtained results are discussed in terms of solute–solvent and solute–solute interactions.

Studies of internal pressure in aqueous solutions of a surfactant (decyltrimethylammonium bromide) at 298.15 K: Understanding and use of Gibson−Tait equation

Recently reported literature density (ρ), thermal coefficient of expansion (α) data for aqueous solutions of decyltrimethylammonium bromide (C10TAB) in limiting concentration range (0.01 to 0.15 mol kg−1 comprising both pre-micellar and post-micellar regions) have been used and combined with literature density, adiabatic compressibility (βS) and specific heat capacity data (Cp), to calculate isothermal compressibility (βT) and internal pressure (Pi) properties of solutions. The variations of apparent molar adiabatic compressibility (Kϕs) of solute, apparent molar isothermal compressibility (KϕT) of solute and internal pressure (Pi) of solutions are studied and used to obtain infinite dilution parameters such as limiting apparent molar adiabatic compressibility (KϕS0) of C10TAB. The Tammann−Tait−Gibson (TTG) model is applied to calculate the excess volume change for the electrolyte (ΔV¯2E) and intrinsic volume (Vint.) of the cationic surfactant both in pre-micellar and post-micellar regions of concentration. A new method based on internal pressure of solutions and an approach by Tanford incorporating alkyl chain volume, length and head group is developed and used to obtain radius of the micelle and aggregation number. From these data, it is concluded that the micelles are small, spherical and incorporating the surface area of the head group. Our proposed method provides a framework for examining the thermodynamic properties of surfactant in terms of equilibria of the monomer (in limiting range of concentration) and the micelle aggregates after critical micelle formation (cmc) (post-micellar region). In pre-micellar region, water structural changes are important and the hydration of the cations is determined by hydrophobic van der Waal's forces, of which extent increases after cmc, resulting in self-assembly in the form of micelle. Volume changes due to transfer of an electrolyte C10TAB from a liquid hydrocarbon like environment to aqueous solutions and to interior of micelle are also estimated and found to be of positive magnitude.

P-ρ-T data and modelling for (2-methylpropan-1-ol + n-octane or n-decane) between 313.15 K–353.15 K and 0.1–20 MPa

Isothermal measurements for 2-methylpropan-1-ol (1) + n-octane (2) and 2-methylpropan-1-ol (1) + n-decane (2) were conducted utilizing an Anton Paar DMA HP densimeter. Measurements include the entire mixture composition range and were conducted in the pressure range (0.1–20) MPa for 5 different temperatures between 313.15 and 353.15 K. The data were successfully correlated for each composition with the modified Toscani-Szwarc equation using 5 unique parameters. The data were also fit to the Peng-Robinson equation of state using a single binary interaction parameter, however quantitative results were poor. Mixture density predictions were also made by the PC-SAFT model, which also yielded mostly qualitative results. Three derived thermodynamic properties, namely excess molar volume, thermal expansivity and isothermal compressibility, were also computed using the regressed parameters.

Density, Speed of Sound, Compressibility and Related Excess Properties of Methane + n-Heptane at T = 303.15 K and p = 10 to 70 MPa

Density and speed of sound of methane + n-heptane binary mixtures were measured at a temperature equal to 303.15 K and at pressures ranging from 10 MPa to 70 MPa. The measurements were performed in pure n-heptane and eight different mixtures with methane molar percentage ranging from 20 % to 95 %. Speed of sound data was obtained by a pulse-echo technique working at 3 MHz whereas density data were acquired from a vibrating U-tube densimeter. Isothermal and isentropic compressibilities were derived from both measurements in the same conditions. Finally, partial molar volumes, excess molar volume, excess isothermal compressibility as well as excess speed of sound and excess isentropic compressibility were estimated at the same conditions and the relative excess properties were represented as a function of methane content. From these measurements, it was observed that the large difference in compressibility of pure components provoked significant deviations to ideal behavior with relative excess values that can reach − 20 %, − 100 % and 200 % of the ideal properties for molar volume, isothermal compressibility and speed of sound, respectively. Moreover, a small clustering effect at high dilution of n-heptane at 30 MPa was brought forth to light by evaluating the partial molar volumes.

Volumetric properties of n-hexadecane/ethyl octanoate mixtures from 293.15 K to 363.15 K and pressures up to 60 MPa

The densities of pure ethyl octanoate and n-hexadecane/ethyl octanoate mixtures were measured from 293.15 K to 363.15 K and up to 60 MPa using U-shape vibrating-tube densimeter. The results were correlated as Tait equation, the excess molar volumes, isothermal compressibilities, and isobaric thermal expansivities of the mixtures were calculated and analyzed. In addition, the parameters in the PC-SAFT equation for ethyl octanoate were obtained based on the high-pressure densities obtained in this work and the vapour pressure in the literatures. The densities of the mixtures were predicted by PC-SAFT equation, the absolute average deviations between the experimental results and those calculated were less than 0.52%.

P–ρ–T Data and Modeling for Butan-1-ol + n-Octane or n-Decane between 313.15–353.15 K and 0.1–20 MPa

Density measurements conducted for the binary systems of butan-1-ol (1) + n-octane (2) and butan-1-ol (1) + n-decane (2) at high pressures are presented in this work. These measurements were conducted utilizing an Anton Paar DMA HP densitometer and encompass the entire composition range, with a temperature and pressure range of T = (313.15–353.15 K) and P = (0.1–20 MPa), respectively. The modified Toscani–Szwarc equation of state was employed to successfully correlate the experimental density data. The measured data were observed to comply with general expected trends with regards to the relationship between density, temperature, and pressure. Derived thermodynamic properties, namely, excess molar volumes, thermal expansivity, and isothermal compressibility, are also presented. Deviations from ideality are attributed to differing molecule sizes and shapes as well as intermolecular interactions between components constituting the mixture.

The (p-Vm-T-x) properties of {water (1) + acetamide (2)} mixtures in the range 278.15–323.15 K and 0.10–100 MPa

The density ρ at atmospheric pressure and compression ratios k=ΔV/Vo of the {water (1) + acetamide (2)} mixture in the range of temperature from 278.15 K to 323.15 K (278.15, 288.15, 298.15, 308.15, 323.15), pressures from 10 to 100 MPa (10, 25, 50, 75 and 100) and in a wide range of compositions (maximum mole fraction of acetamide (AA) x2 = 0.3875) were measured in the work. The partial molar volumes of both components V¯1 and V¯2 in the mixture, molar isothermal compression KT,m, molar isobaric thermal expansion EP,m, isochoric coefficient of thermal pressure βV, and internal pressure of the mixture Pint were calculated. The volume characteristics for an infinitely dilute AA solution in water: limiting partial molar volumes V¯2∞, limiting partial molar isothermal compression K¯T,2∞, and limiting partial molar isobar expansion E¯P,2∞ were calculated. The obtained results are discussed from the standpoint of interactions of solute-solvent and solute-solute. The obtained results are discussed in terms of solute-solvent and solute-solute interactions.

Kirkwood-Buff integration: A promising route to entropic properties?

Kirkwood-Buff integration (KBI) is implemented into the massively-parallel molecular simulation tool ms2 and assessed by molecular dynamics simulations of binary liquid mixtures. The formalism of Krüger et al. (P. Krüger et al., J. Phys. Chem. Lett. 4: 235–238, 2013) that adopts NVT ensemble data to the μVT ensemble is employed throughout. Taking advantage of its linear scaling with inverse system size, the extrapolation to the thermodynamic limit is analyzed. KBI are calculated with standard radial distribution functions (RDF) and two corrected RDF forms. Simulations in the NVT ensemble are carried out in the entire composition range for four Lennard-Jones mixtures, studying system size dependence by varying N = 4000, 8000 and 16000 molecules. Moreover, four mixtures of “real” components are considered with N = 4000. Thermodynamic factor, partial molar volumes and isothermal compressibility are calculated from KBI and compared with benchmark data from NpT ensemble simulations. The assessment shows that the formalism of Krüger et al. greatly improves KBI and that extrapolation is important, particularly for smaller systems.

Density and Speed-of-Sound Measurements for Dilute Binary Mixtures of Diethylammonium-Based Protic Ionic Liquids with Water

Physicochemical properties of diethylammonium (DEA)-based protic ionic liquids and their aqueous solutions were obtained using experimental measurements of density (ρ) at different temperatures from T = (293.15 to 313.15) K and the speed of sound (w) at 298.15 K. Four DEA-based protic ionic liquids (PILs) with carboxylates as anions were synthesized. The standard entropy (S0) and lattice potential energy (UPOT) for pure PILs were estimated from molecular volumes at 298.15 K obtained using experimental density data. Apparent molar volumes (ϕV), isobaric expansivity (α), isentropic compressibility (βS), and isothermal compressibility (βT) have been obtained for aqueous solutions of PILs using experimental density and speed-of-sound data. These data have been further used to understand the electrostriction and concentration dependence of internal pressure. The Passynski method has been used to estimate concentration-dependent hydration numbers of PILs. The results obtained have been discussed in terms of con...

Effect of high pressure and temperature on the volume properties of the liquid-phase mixture of {water (1) + formamide (2)}

Compression, k = Δv/vo, was measured for the {water (1) + formamide (2)} binary mixture within the whole range of the component ratio at temperatures from 278.15 K to 323.15 K and pressure up to 100 MPa. Molar isothermal compressions, molar isobaric thermal expansions, isochoric coefficient of thermal pressure and internal pressure were calculated. Concentration dependences (from formamide content) of molar isothermal compressions for water + formamide mixtures at low pressure and temperature (close to 278.15 K) were featured with the minimum at x2 ≈ 0.1, which was smoothed over with both pressure and temperature increase. Molar isobaric thermal expansions of the mixture increased with the increase of formamide content in it at all state parameters; pressure increase resulted in temperature inversion in its concentration dependence, which shifted to the area of lower formamide (FA) concentration with the pressure increase. Isochoric coefficient of thermal pressure of the mixture drastically increased in the area of small FA additions. The temperature effect on the thermal pressure coefficient was opposite in the mixtures with high water and high formamide content. Calculated values for pure components were also compared.

Density and volumetric properties of the aqueous solutions of urea at temperatures from T = (278 to 333) K and pressures up to 100 MPa

Abstract This paper highlights the values of densities of aqueous solutions of urea in the concentration range m (from 0.1809 to 12.801) mol·kg−1 at T = (278.15, 288.15, 298.15, 308.15, 323.15 and 333.15) K and at p = (0.101, 10, 25, 50, 75 and 100) MPa. The densities were also measured for dilute aqueous solutions m (from 0.093 to 2.505) mol·kg−1 with temperature from 274.15 to 283.15 K, with increment of 1 K at atmospheric pressure, in order to study the effect of urea on the temperature of the maximum water density. Volumetric properties calculated from the density, such as apparent molar volumes of urea, Vɸ,2, molar isothermal compressions, KT,m, and molar isobaric thermal expansions, EP,m, of solution are considered depending on concentration, temperature and pressure. Also, certain volumetric characteristics for infinitely diluted urea in water were obtained: the limiting partial molar volumes, V 2 ∞ ; limiting partial molar isothermal compressions, K T , 2 ∞ ; and limiting partial molar isobaric thermal expansions, E P , 2 ∞ . Obtained results are discussed from the standpoint of solute – solute and solute – solvent interactions. With the help of various approaches based on volumetric characteristics, the character of the disturbing effect of urea on the water structure was described.

High-pressure densities and derived properties of binary {methyl tert-butyl ether (MTBE) + alcohols} mixtures

In this study, density of binary liquid mixtures of {methyl tert-butyl ether (MTBE) + ethanol, or + 1-propanol, or + 1-butanol} has been determined as a function of composition at temperature 290 K and pressure up to 35 MPa. Densities data were measured using an Anton Paar DMA 4500 vibrating tube densimeter coupled to an external Anton Paar DMA HP high-pressure cell. A Tait equation was used to correlate experimental densities with pressure. The experimental results have been used to calculate the derived volumetric properties such as excess molar volumes ( $$V_{\text{m}}^{\text{E}}$$ ), apparent molar volumes ( $$V_{{\upphi{\text{i}}}}$$ ), partial molar volume ( $$\bar{V}_{\text{i}}$$ ) and isothermal compressibility (κ T). The thermodynamic results suggest that the structural effects and intermolecular interactions must outweigh other possible effects present in the mixtures studied.

Densities and Volumetric Properties of Aqueous Solutions of {Water (1) + N-Methylurea (2)} Mixtures at Temperatures of 274.15–333.15 K and at Pressures up to 100 MPa

Densities of the mixture {water (1) + N- methylurea (2)} in the concentration range to mole fraction x2 = 0.07071 (or to the solution molality concentration m2 = 4.22335 mol·kg–1) at atmospheric pressure in the temperature range from 274.15 to 333.15 K and compression k = ΔV/V0 at pressures to 100 MPa (10, 25, 50, 75, and 100) in the temperature range from 278.15 to 323.15 K (278.15, 288.15, 288.15, 308.15, 323.15) in the same concentration range were calculated in this study. The apparent molar volumes of N-methylurea Vϕ,2 and the partial molar volumes of both components V̅1 and V̅2 in the mixture, molar isothermal compressibilities KT,m, molar isobaric thermal expansions EP,m, and isochoric coefficients of thermal pressure β of the mixture were calculated. Moreover, volumetric measures for the infinitely dilute solution of N-methylurea solution were calculated: limiting partial molar volumes V̅2∞, the limiting partial molar isothermal compressibilities K̅T,2∞, and the limiting partial molar isobaric thermal expansions E̅P,2∞. The results obtained are discussed from the point of view of solute–solvent and solute–solute interactions.