Experimental measurements and prediction of liquid densities for n-alkane mixtures

We present experimental liquid densities for n-pentane, n-hexane and n-heptane and their binary mixtures from (273.15 to 363.15) K over the entire composition range (for the mixtures) at atmospheric pressure. A vibrating tube densimeter produces the experimental densities. Also, we present a generalized correlation to predict the liquid densities of n-alkanes and their mixtures. We have combined the principle of congruence with the Tait equation to obtain an equation that uses as variables: temperature, pressure and the equivalent carbon number of the mixture. Also, we present a generalized correlation for the atmospheric liquid densities of n-alkanes. The average absolute percentage deviation of this equation from the literature experimental density values is 0.26%. The Tait equation has an average percentage deviation of 0.15% from experimental density measurements.     

Determination of autoprotolysis constants of ternary water—dioxane—methanol solvent systems at 25°C

The thermodynamic autoprotolysis constant K₅ (the sum of the autoprotolysis constants of H₂O and CH₃OH) of various ternary water—dioxane—methanol and the corresponding binary solvent systems (water—dioxane, water—methanol) were determined by potentiometric measurements with a combined glass—calomel electrode. In the ternary mixtures, the results show that the composite medium effect on the pK₅ values, expressed by a parameter b = dpK₅/d_u (u being avariable expressing the solvent composition), depends on the ratio of the organic solvent concentrations. In these mixtures, superposition of the various effects detected in the corresponding binary solvents allows the calculation of the pK₅ value of any ternary mixture by means of a simple equation.     

A semi-empirical equation of state applied to vapor-liquid equilibria calculations

A five-parameter equation of state is proposed to calculate the vapor-liquid equilibria of compounds in binary and multicomponent mixtures. This equation is closely related to a previous equation of state proposed by the author, the main modification being in the entropic term where the parameter m assumes a constant value for all compounds. It is shown that the van der Waals conditions at the critical point and the Morbidelli-Carra' algorithm enable the calculation of three other constants. Rules are given to calculate the remaining constant K which pertains to the enthalpic term. The proposed method only requires knowledge of the critical constants and of the normal boiling temperature as input parameters. A wide application of the new equation to both polar and non-polar binary systems indicates the following: the proposed method is predictive for ideal or nearly ideal mixtures; the correlation of mixtures of hydrocarbons having very different molar volumes can be obtained by optimizing only the binary interaction parameter linked to the enthalpic term; the new equation also correlates well with strongly non-ideal systems which exhibit a miscibility gap; the prediction of multicomponent vapor-liquid equilibria from the binary data alone is also reliable for both polar and non-polar mixtures.     

Burnett—isochoric P—V—T measurements of a nominal 20 mol% hydrogen—80 mol% methane mixture at elevated temperatures and pressures

A new apparatus is described which has been developed to measure P—V—T relations for hydrogen—hdyrocarbon systems at elevated temperatures and pressures. The principal components are three heavy-walled spherical pressure cells with the same outer/internal diameter ratio, a fully submerged differential pressure cell, and measuring equipment including calibrated piston guages and a platinum resistance thermometer. This apparatus was used to measure densities of a 20.05±0.05 mol% hydrogen?79.95±0.05 mol% methane mixture from 273.15 to 600 K and pressures to 72 MPa. Two Burnett isotherms at 273.15 K established fluid densities without direct measurement of either mass or volume. Eight isochores, ranging in density from 1.62 to 14.91 mol dm^?3, were anchored to the Burnett isotherms at 273.15 K where their densities were firmly established. An analytic equation for the thermodynamic surface has been fitted to the resulting P—V—T data, giving a 0.01% root mean square deviation of calculated compressibility factors from experimental results.     

Bubble pressures and saturated liquid molar volumes of trichlorofluoromethane—chlorodifluoromethane mixtures. Representation of refrigerant-mixtures vapor—liquid equilibrium data by a modified form of the Peng—Robinson equation of state

Experimental vapor—liquid equilibrium data and saturated liquid molar volumes of chlorodifluoromethane—trichlorofluoromethane binary mixtures have been obtained at four temperatures (298.15, 323.15, 348.15 and 373.15 K) using apparatus described previously.The experimental vapor—liquid equilibria are represented well by a modified form of the Peng—Robinson equation of state with one interaction parameter, but the mean deviation between the calculated and experimental densities is 5%.Vapor—liquid data for binary refrigerant mixtures from the literature are treated using the modified form of the Peng—Robinson equation of state with one adjusted interaction parameter in the mixing rule for a. The representation is fair and is not improved by introducing an additional parameter in the mixing rule for b.     

Modeling of phase equilibria with CPA using the homomorph approach

For association models, like CPA and SAFT, a classical approach is often used for estimating pure-compound and mixture parameters. According to this approach, the pure-compound parameters are estimated from vapor pressure and liquid density data. Then, the binary interaction parameters, k_ij, are estimated from binary systems; one binary interaction parameter per system. No additional mixing rules are needed for cross-associating systems, but combining rules are required, e.g. the Elliott rule or the so-called CR-1 rule. There is a very large class of mixtures, e.g. water or glycols with aromatic hydrocarbons, chloroform-acetone, esters-water, CO₂-water, etc., which are classified as “solvating” or “induced associating”. The classical approach cannot be used and the cross-association interactions are difficult to be estimated a priori since usually no appropriate experimental data exist, while the aforementioned combining rules cannot capture the physical meaning of such interactions (as at least one of the compounds is non-self-associating). Consequently, very often one or more of the interaction parameters are optimized to experimental mixture data. For example, in the case of the CPA EoS, two interaction parameters are often used for solvating systems; one for the physical part (k_ij) and one for the association part (β^cross). This limits the predictive capabilities and possibilities of generalization of the model. In this work we present an approach to reduce the number of adjustable parameters in CPA for solvating systems. The so-called homomorph approach will be used, according to which the k_ij parameter can be obtained from a corresponding system (homomorph) which has similar physical interactions as the solvating system studied. This leaves only one adjustable parameter for solvating mixtures, the cross-association volume (β^cross). It is shown that the homomorph approach can be used with success for mixtures of water and glycols with aromatic hydrocarbons as well as for mixtures of acid gases (CO₂, H₂S) with alcohols and water. The homomorph approach is less satisfactory for mixtures with fluorocarbons as well as for aqueous mixtures with ethers and esters. In these cases, CPA can correlate liquid-liquid equilibria for solvating systems using two adjustable parameters. The capabilities and limitations of the homomorph approach are discussed.     

Polarography of some sulphur-containing compounds : Part XII.Anodic waves of dialkyldithiocarbamates

Dialkyldithiocarbamates give only a one-electron anodic wave. The various adsorption phenomena are probably caused by varying orientation of the mercury compounds on the electrode surface; the irregular i-t curves recorded at —0.04 V and the anomalous behaviour of the anodic current between +0.2 V and —0.4 V can be interpreted as the behaviour of an adsorbed film at the electrode. Analytical measurements are best made in 60% ethanolic 0.1 M sodium hydroxide media at concentrations of about 10^-5 M dialkyldithiocarbamate; a method is given for the analysis of the monoalkyl and dialkyl compounds in mixtures.     

Pressure and Temperature Effects on the Molecular Rotation in Acetonitrile-Water Mixtures

NMR spin-lattice relaxation time (T ₁) measurements were performed for ¹⁴N of acetonitrile in acetonitrile (CH₃CN)—H₂O mixtures and for ²H of heavy water in CH₃CN—D₂O mixtures at 30°C up to 294.2 MPa together with those for ²H in CH₃CN—D₂O mixtures at 10 and 20°C under atmospheric pressure over the whole composition range of the mixtures. IR absorption spectra for CH₃CN—H₂O and CH₃CN—10 mol% HDO/D₂O mixtures were obtained at 30°C under atmospheric pressure. Densities and viscosities of CH₃CN—H₂O mixtures were also measured under high pressure. The rotational correlation times for D₂O [τ _c (D)] and acetonitrile [τ _c (N)] were determined from T ₁ measurements. Under atmospheric pressure, τ _c (D) exhibits a small maximum around 10 mol% of acetonitrile at each temperature, and the maximum position is almost independent of temperature. These results suggest that the dipole–dipole interaction between acetonitrile and water molecules plays an important role in determining the rotational motion of water molecules in the mixtures. This is supported by the variation of the peak for the bending vibration of water molecules with composition. The decreases in τ _c (D) and τ _c (N) at higher acetonitrile contents are ascribed to the formation of acetonitrile dimer, trimer, and oligomer aggregates. Except for τ _c (D) in the water-rich region, the pressure coefficients of τ _c (D) and τ _c (N) are positive which is understood as a simple compression effect. Furthermore, the composition of mixture at which τ _c (D) and τ _c (N) show a maximum shifted to higher acetonitrile content with increasing pressure. These results are discussed in terms of the pressure effect on the equilibria of acetonitrile monomers with the aggregates of acetonitrile in the mixtures.     

p-V-T parameters of propylencarbonate and cis-,trans-decahydronaphthalene in temperature and pressure ranges of 20–50°C and 1–1000 bar

The condensability of propylencarbonate and cis-,trans-decalin (40: 60 wt %) were measured using the liquid weighting method in the temperature and pressure ranges of 20–50°C and 1–1000 bar, respectively. The Tait equation coefficients C and B for this temperature interval were calculated. Taking pro-pylencarbonate as an example, it was demonstrated that equation 1/β _T = 0.9759 × (1000V ₀/ΔV _{1 kbar}) — 4386 proposed earlier for liquids allows us to predict C and B coefficients with good precision.     

High-pressure density measurements for choline chloride: Urea deep eutectic solvent and its aqueous mixtures at T = (298.15 to 323.15) K and up to 50 MPa

New measurements are reported for the densities of choline chloride: urea (REL) deep eutectic solvent and its aqueous mixtures over the temperature range (298.15 to 323.15) K and pressures up to 50 MPa. The experimental data were used to derive other properties such as isothermal compressibility, isobaric expansivity and excess molar volume. A Tait-type equation was used to correlate accurately the high-pressure density data to temperature, T, pressure, P, and composition, x. The excess molar volumes of {REL (1) + H₂O (2)} mixtures were also investigated and represented as a function of all three variables, T, P, x, using an empirical equation. Results indicate that the correlations used in this work can be satisfactorily used to predict the densities of the studied systems at different conditions of temperature, pressure and composition.     

A Correlation Between Solvatochromic Solvent Polarity Parameters and the Ionization Constants of Various Phenols in 1,4-Dioxane–Water Mixtures

Precise thermodynamic ionization constants K for 3-nitrophenol, 3,4-dichlorophenol, and 4-cyanophenol have been obtained in 1,4-dioxane-water mixtures (0–70% volume fraction in dioxane) at 25°C using a potentiometric method. The same information for another twelve cationic, neutral, and anionic phenols were taken from the literature. Three different methods were used to study the effects of the solvents on the ionization constants: one involves a single polarity parameter, E _T(30); the next involves the Kamlet–Taft multiparametric method; and the last involves the preferential solvation model. The pK values follow the preferential solvation model, but the parameters obtained are highly correlated. Using the data for the phenol molecule as reference, a linear correlation between ΔpK and E _T(30) has been used to develop a new method of obtaining pK values for any binary solvent composition, with only the pK in water known. The pK(s) values correlate with the molecular parameters for the dipolarity/polarizability of the solvent π* and its hydrogen-bond donor ability α. The preferential solvation parameter, f _12/1, correlates with the parameter for the hydrogen-bond donor ability of the solvent. All the phenols follow Hammett's equation and the reaction constants have been calculated for the different water–dioxane mixtures.     

Measurement,correlation and estimation of binary vapor—liquid equilibria for alcohol—chlorobenzene systems

Experimental VLE of chlorobenzene—1-pentanol binary mixtures are determined at 101.08 kPa. Also, the activity coefficients at infinite dilution (γ^∞) for some alcohol—chlorobenzene systems are determined from ebulliometric measurements. The Wilson equation is tested for 10 binary alcohol—chlorobenzene systems. The results show that this model represents the data well. There is good comparison between experimental γ^∞,s and γ^∞,s computed from Wilson parameters. Further, the VLE data for the above-mentioned mixtures are estimated by the UNIFAC method.     

β-Aluminas and water

TG, DSC and X-ray measurements were made to characterize the water absorption process by Li (50%) — Na (50%)β-alumina. The equilibrium water content, dehydration enthalpies and lattice parameter values have been determined and compared with those previously obtained for pure Li and Naβ-aluminas. The mixedβ-alumina is shown to be very similar to Liβ-alumina as concerns the dehydration enthalpy and the temperature range in which the dehydration occurs, while it seems to be very similar to Naβ-alumina with respect to the equilibrium water content andc-axis values.     

The double layer at the interface between two immiscible electrolyte solutions: Part II. Structure of the water/nitrobenzene interface in the presence of 1:1 and 2:2 electrolytes

From fast galvanostatic pulse measurements at 25°C the capacitance of the water/nitrobenzene interface was evaluated as a function of the interfacial potential difference Δ_o^w? for systems consisting of NaBr, LiCl or MgSO₄ in water and tetrabutylammonium tetraphenylborate, tetraphenylarsonium tetraphenylborate or tetraphenylarsonium dicarbollylcobaltate in nitrobenzene. The modified Verwey—Niessen model, in which an inner layer of solvent molecules separates two space-charge regions (the diffuse double layer), describes the structure of the water/nitrobenzene interface well at electrolyte concentrations above ca. 0.02 mol dm^?3, provided that the ions are allowed to penetrate into the inner layer over some distance. For all the systems studied the zero-charge potential difference was found at Δ^w_o?_pzc ≈ 0 on the basis of the standard potential difference Δ^w_o?⁰_TMA + = 0.035 V for tetramethylammonium cation which was used as a reference ion. At zero surface charge a comparison was made with the theoretical capacitance calculated using the mean spherical approximation for a model consisting of two ion and dipole mixtures facing each other. The effect of ion penetration on the interfacial capacitance was estimated from the solution of the linearized Poisson-Boltzmann equation for a triple dielectric model with a continuous distribution of the point ions. The concentration-independent inner layer potential difference and capacitance can only be inferred from the capacitance data if the ion size effect is taken into account. A non-iterative procedure based on the hypernetted-chain equation was used for the evaluation of the potential drop across the diffuse double layer. The extend of the penetration into the inner layer appears to be a function of ion solvation, e.g. the more hydrated ion the less extensive ion penetration is likely.     

Equation of state and the thermodynamic properties of liquid polymers: Application of the Hirai-Eyring model

It is shown that the Hirai-Eyring model for the liquid state is capable of accurately describing the p, V, T behavior of liquid polymers in the temperature range over which measurements are now made, and below. Once the parameter choices necessary to accomplish the fit are made for a particular polymer, the excess thermodynamic functions (differences in properties, liquid less solid) are determined by the same parameters. Above the glass transition temperature T_g the volume, excess enthalpy, and square of the excess entropy are predicted by the model to be essentially linear with temperature, in agreement with experiment. Below T_g, these functions do not remain linear (as is usually assumed in extrapolating the equilibrium behavior to low temperatures), but instead they rapidly approach zero in a continuous way as the temperature is lowered. These remarks apply to glass-forming materials composed of small molecules, as well as to polymers. The “paradox” raised by Kauzmann is thus resolved, and the Gibbs-DiMarzio second-order transition appears to be unnecessary.     

Thermodynamic behaviour of some glycol—water mixtures. Excess and partial volumes

Densities of water—glycol (mono- di-, tri- and tetraethyleneglycol) mixtures have been measured over the entire composition range at 298. 15 K. Mixtures involving monoethyleneglycol (MEG) have also been studied at different temperatures from 308.15 to 288.15 K. Deviations, V^E, from ideal volumes of mixing have been calculated: negative values are observed for all systems. They increase with the number of ether functions present in the organic molecule; a slight dependence of V^E towards temperature has been shown in the water—MEG mixtures. Partial molal volumes have also been calculated for both components of each system; they exhibit an extremum in the water-rich region.     

Study on the relationship between the ternary interaction parameter and the structure of water by the effect of aliphatic alcohols and phenol on the swelling behavior of poly(ethylene-co-vinyl alcohol) membrane in aqueous solution

The effect of very low concentrations of ethanol, 2-propanol and phenol on the swelling degree of poly(ethylene-co-vinyl alcohol) (EVAL) in water was investigated. The effect of phenol on the swelling degree of EVAL was remarkably large compared to that of ethanol and that of 2-propanol. Theoretical analysis on the basis of Flory-Huggins theory using three binary interaction parameters could appropriately predict the EVAL swelling degree in ethanol/water and 2-propanol/water mixtures. However, the theoretical swelling degree of EVAL in phenol/water mixtures needed a ternary interaction parameter (χ_T) to match with experimental data points. An optimum value of χ_T for the water-phenol-EVAL system was found to be −3.3. The relationship between the ternary interaction parameter and the structure of water from observations of the effect of phenol on the EVAL swelling was discussed. Based on the analysis of low-frequency Raman spectroscopy reported by Suzuki et al. [J. Chem. Phys. 107 (1997) 5890], the contribution of χ_T to the EVAL swelling was attributed to the increase of the entropy in bulk water due to the effect of phenol on the disruption of the tetrahedral hydrogen-bonded networks of water molecules. This, in turn, induced an increase of water absorption in EVAL.