Ideal Solution Theory Research Articles

The vapour-pressure behaviour and the association of isomeric propylamines and n-deuteriopropylamines in mixtures with n-hexane

In isothermal measurements between 283 and 343 K, the vapour pressures of n-hexane mixtures with CH3CH(NH2)CH3 and CH3CH(N2H2)CH3 are found to exceed by almost a factor of two the vapour pressures of n-hexane mixtures with C3H7NH2 and C3H7N2H2. The vapour-pressure differences for the n-hexane mixtures with C3H7NH2 and with C3H7N2H2 and for those with CH3CH(NH2)CH3 and with C3H7(N2H2)CH3 are both less than 3%.Considering the representation of the measurements according to Wilson, the coefficients λ12 − λ11 (1 = amine, 2 = hexane) for the systems containing the isocompounds are smaller by 5 – 10% than those for the systems containing the normal compounds. The differences in the coefficients λ12 − λ11 which result from deuteration fall within the error limits. Similarly, noticeable differences between the normal and isocompounds, but only insignificant differences between the deuterated and non-deuterated compounds, are observed for the activity coefficients, gas phase compositions, excess Gibbs free energies, heats of vaporization and association constants calculated according to the theory of ideal associated solutions. The normal vapour-pressure isotope effect for CH3CH(NH2)CH3 and CH3CH(N2H2)CH3 is weaker than that for C3H7NH2 and C3H7N2H2, and the constants of the AB equations between 283 and 333 K for isopropylamine (A = 8142 K2 and B = 21.4 K) are distinctly smaller than for propylamine (A = 9501 K2 and B = 24.6 K). All the differences enumerated can be explained by the fact that the isocompounds are more weakly associated, owing to the stronger shielding of their amino groups. This weaker association leads to an increase of the maximum excess entropy of 0.20 J K−1 for the non-deuterated and of 0.23 J K−1 mol−1 for the deuterated isomers.

A scanning calorimetric study of small molecule-lipid bilayer mixtures.

The influence of small molecules on the main phase transition of dimyristoyl phosphatidylcholine was observed by high-sensitivity differential scanning calorimetry. The variation with temperature of the excess heat capacity is markedly affected by solid solution formation, which appears to be of frequent occurrence in solutions in lipid bilayers. The experimental results are in some cases in reasonable agreement with ideal solution theory.

Adsorption of surfactants on mineral oxide surfaces from aqueous solutions: II: Binary mixtures of anionic surfactants

Individual surfactant adsorption was measured for well defined mixtures of two isomerically pure alkylbenzene sulfonates adsorbing from aqueous solutions onto both alumina and kaolinite. An adsorption model, which includes two-dimensional phase transitions resulting from lateral interactions, is shown to describe the observed isotherms. The phase transitions result in the formation of mixed hemimicelles (high-density aggregates of surfactant mixtures on the surface). The environment for methylene groups in the mixed hemimicelle is slightly less favorable than that in either pure surfactant hemimicelle. For solution compositions below the mixed Critical Micelle Concentration (CMC), the surfactant having the least tendency to adsorb exhibits greatly increased adsorption because of the presence of the mixed hemimicelles. The adsorption of the surfactant having the greatest tendency to adsorb is not greatly different from the pure component adsorption. Since only monomer adsorbs significantly, monomer-micelle equilibrium had to be considered simultaneously with the adsorption model to predict results above the CMC. Ideal solution theory was shown to be a good approximation for this equilibrium. Above the CMC, conditions are described which result in minima and maxima in total adsorption isotherms.

MICELLE FORMATION IN MIXTURES OF ANIONIC AND NONIONIC SURFACTANTS

ABSTRACT The critical micelle concentration of mixtures of anionic and nonionic surfactants was measured. The anionic surfactants were alkylbenzene sulfonates and the nonionic surfactants were polyoxyethylene nonylphenols and a polyoxy-ethylene alcohol. The effect of added electrolyte, the number of ethylene oxide units in the polyethoxylate, and the anionic alkyl chain length were studied. All systems showed substantial negative deviations (lower CMC) from ideal solution theory. The results can be represented by regular solution theory. Charge separation appears to be the source of the nonideality. This considers the reduction of electrostatic repulsion between the ionic surfactant head groups in the mixed micelle, due to the insertion of nonionic hydrophilic groups between these charged groups, to be the cause of enhanced micelle formation. The physical basis of regular solution theory was shown to be consistent with the charge separation effect.

Phase Diagrams of Binary Liquid Crystal Mixtures

Abstract A series of four binary mixtures of smectic liquid crystalline compounds was prepared and their thermodynamic properties measured by differential thermal calorimetry. Calculations using ideal solution theory were carried out and were compared to the experimental phase diagrams. Plots of ideal ΔH and ΔS values for the mixtures were also prepared and were compared to experiment. It is concluded that large deviations from ideality are caused by a great variety of very subtle electronic and geometric forces present in the mixtures, and that no one of the explanations put forward to date is of itself adequate to describe the observed deviations from ideality.

LPE of LuLaSmGaFe garnet from a PbO-V2O5 flux

A flux for garnet systems prepared from a PbO and V2O5 mixture has been found advantageous for thin film growth by LPE. There is reduced garnet solubility which leads to slower growth rates. A study of growth kinetics which are interpreted in terms of published models indicates a reduced kinetic constant. Melt equilibrium of the LuLaSmGaFe garnet in the PbO-V2O5 flux system was extensively examined over a wide temperature range. Relationships between film and melt compositions are interpreted in the context of an ideal solution theory for liquid and solid. The relationship between La and Ga interaction in this melt system is examined to reveal effects of growth temperature. Suggested modes for empirical adjustment of the equilibrium model to encompass growth rate effects are briefly discussed.

Phase diagram and single crystal growth of the CuInSe2xS2(1−x) solid solutions

AbstractThe phase diagram of the CuInSe2‐CuInS2 system is plotted using DTA and the solidus and liquidus lines by the approximation of the theory of regular and ideal solutions are calculated. The single crystals of the CuInSe2xS2(1−x) solid solutions are first grown by chemical transport.

Gel filtration of solubilized systems. V. Effects of sodium chloride on micellar sodium lauryl sulfate solutions solubilizing alkylparabens.

The present investigation was undertaken to examine the effects of added sodium chloride on solubilized systems of sodium lauryl sulfate (SLS) micellar solutions solubilizing alkylparabens by gel filtration. The results showed that the addition of sodium chloride decreased the distribution coefficients of alkylparabens between the SLS micellar and aqueous phases. The factors causing the decrease of distribution coefficients were investigated. Activity coefficients of SLS and alkylparabens in mixed micelles were estimated on the basis of ideal solution theory. The activity coefficients suggested that the addition of sodium chloride hardly changed the SLS-alkylparaben interaction in the mixed micelles. The decrease in the surface area per SLS molecule in the micelles on addition of sodium chloride seems to be an important factor.

The distribution of alkyl paraben in aqueous sodium lauryl sulfate micellar solutions: III. The gel filtration of solubilized systems

The apparent distribution coefficients, K a, for methyl-, ethyl-, and butylparabens between the sodium lauryl sulfate (SLS) micellar and aqueous phases were measured from the elution curves of SLS and alkyl paraben obtained by the tail analysis on Bio Gel P-4. The results show that the K a was a linear function of the molar fraction of alkyl paraben in the micellar phase ( X s m ). In view of this relationship, the distribution coefficients, K t, were estimated from the K a values on the basis of ideal solution theory. The free energy change of a solubilizate for a transition from the aqueous to micellar phase, ΔG t, was calculated from the K t. The solubilized system was analyzed thermodynamically on the basis of the ΔG t. The results show that an approximately linear relationship exists between the ΔG t and the carbon number of the alkyl paraben. Furthermore, the CMC decreasing effect which describes stabilization of micelle on solubilization was confirmed experimentally to be correlated with ΔG t.

Liquid mixtures involving complex formation : Extensions of the ideal associated solution theory

Extensions of the ideal associated solution theory which take into account intermolecular interaction and/or size factors are derived and applied to triethylamine+ CHCl3 and diethyl ether+CHCl3. Evidence is presented for non-hydrogen-bonding specific interactions between the unlike molecules in these systems. Theories that do not take this into consideration are likely to be unsatisfactory for the determination of hydrogen-bond properties. With respect to the evaluation of ?net complex formation? properties, the extensions considered do not represent significant improvements of the simple theory. The molar enthalpies of mixing of triethylamine+CH3CCl, and diethyl ether+ CH3CCl3 have been measured at 288.15 and 298.15 K.

Phase diagrams of ascending and minimum type in terms of concentration fluctuations in binary liquid and solid solutions

Abstract The thermodynamics of binary alloy phase diagrams of ascending and minimum types is shown to lead to a rather direct relation between the ratio of the slopes of the liquidus and the solidus curves, at a given temperature T, and the ratio <(δc)2 1(δc)2 s of the concentration fluctuations in the liquid and the solid solutions. The latent heats of the two pure components also enter in a direct manner, as could have been anticipated from the results of ideal solution theory

Thermodynamic Properties of Associated Solutions II. Mixtures of the Type A + B + ABj

AbstractThe theory of ideal associated solutions of the type A + B + ABj is investigated. Equations describing the chemical equilibrium, number average molecular weight, activity coefficients and excess thermodynamic functions are given. For the type of association considered, GE is always negative, HE has the same sign as the standard enthalpy of the association reaction, ΔH°, and SE can have positive or negative values. The excess entropy of mixing as a function of composition has a fairly complicated shape, especially in the region where the enthalpy and the free energy term compensate for each other. The extremum properties of the thermodynamic functions are at the stoichiometric mole fraction × = 1/(1 + j), and the functions have an asymmetric parabola‐like form.

Effect of the sixth period elements on the melting and transformation temperatures of praseodymium: Part II. Thermodynamic analysis

A thermodynamic analysis of the praseodymium-rich alloys containing Os, Ir, Pt, Au, Hg, Tl, Pb, and Bi indicated that most of the solutes dissolved in praseodymium follow ideal solution theory over a limited range of temperatures up to 40° to 135°C below the melting point of praseodymium (or concentrations out to 3 to 8 at. pct solute). The activity coefficients, activities, and excess partial free energies were calculated for liquid praseodymium at its melting point and for β-Pr at its α to β transformation temperature. The so-calledQ parameter has also been determined for these praseodymium systems, and it was found to exhibit the usual periodic dependence on the solute metal. As a result of these analyses a method has been developed which makes it possible to calculate phase boundaries for undetermined systems. This technique is shown to be especially valuable in calculating unknown phase boundaries for lanthanide-rich alloys, but for other metal solvents this method will probably be of a lesser utility.

Thermodynamic Calculations on Phase Equilibria Involving Fused Salts; Part 2, Solid Solutions and Application to the Olivines

A theory is developed for ideal solutions of ionic salts giving Roozeboom Type I phase diagrams, based on the assumption that the mole fraction of an ion in a phase is equal to the number of specified ions present divided by the total number of ions of all species in the phase. When applied to solid solutions of fayalite and forsterite the theory predicts for the components heats of fusion, 25,200 and 29,300 cal mole (super -1) respectively, which differ considerably from the value, 14,000 cal mole (super -1) for each component, calculated by Bowen and Schairer, who assumed ideal behavior for the undissociated molecules. Orr found a calorimetric heat of fusion of 22,000 cal mole (super -1) for fayalite. When applied to solid solutions of Mg 2 SiO 4 and Mg 2 GeO 4 , where there is a common cation, the theory predicts that ideal solution theory for undissociated molecules may be used. The data of Ringwood for this system show, however, practically no separation between liquidus and solidus, and do not admit of the calculation of heats of fusion. The behavior of the system Mg 2 GeO 4 +Fe 2 SiO 4 with no common ion is predicted. Mg 2 SiO 4 and Mn 2 SiO 4 , with a common anion, behave like forsterite and fayalite.

Thermodynamic calculations on phase equilibria involving fused salts; Part 2, Solid solutions and application to the olivines

A theory is developed for ideal solutions of ionic salts giving Roozeboom Type I phase diagrams, based on the assumption that the mole fraction of an ion in a phase is equal to the number of specified ions present divided by the total number of ions of all species in the phase. When applied to solid solutions of fayalite and forsterite the theory predicts for the components heats of fusion, 25,200 and 29,300 cal mole (super -1) respectively, which differ considerably from the value, 14,000 cal mole (super -1) for each component, calculated by Bowen and Schairer, who assumed ideal behavior for the undissociated molecules. Orr found a calorimetric heat of fusion of 22,000 cal mole (super -1) for fayalite. When applied to solid solutions of Mg 2 SiO 4 and Mg 2 GeO 4 , where there is a common cation, the theory predicts that ideal solution theory for undissociated molecules may be used. The data of Ringwood for this system show, however, practically no separation between liquidus and solidus, and do not admit of the calculation of heats of fusion. The behavior of the system Mg 2 GeO 4 +Fe 2 SiO 4 with no common ion is predicted. Mg 2 SiO 4 and Mn 2 SiO 4 , with a common anion, behave like forsterite and fayalite.

Determination of the solid-liquid equilibrium diagram for the nitrogen-methane system

The equilibrium between the solid and liquid phases of the nitrogen-methane system has been studied. The liquids and solidus curves together with the three phase line of the system are determined using a combined method comprising measurements of the total vapour pressure, the heat capacity and thermal analysis of mixtures of various concentrations. Methane and nitrogen are found to be partially miscible in the solid state, the melting diagram is of an eutectic type. The eutectic concentration is 23.8% methane. Liquid nitrogen containing methane up to the eutectic concentration solidifies and melts nearly at the same temperature of 62.6°K. The liquidus and solidus curves are very close to each other in this concentration range where the temperature difference does not exceed 0.5°K. The total amount of nitrogen which is soluble in the methane lattice is less than 45%. A three dimensional space model of the phase-equilibrium diagrams of this system is constructed, and the discussion of previous work and the various experimental methods is presented. The ideal solution theory does not adequately describe the melting diagram. A better agreement with the results is obtained by considering the behaviour of the system as a regular liquid solution in equilibrium with a regular solid solution.

Application of a Theory of Nonideal Solutions to Results of Ultrasonic Absorption Measurements

It is shown that results of ultrasonic absorption measurements on solutions can sometimes be explained by application of a theory of nonideal solutions when the corresponding ideal-solution theory is inadequate. The results of ultrasonic absorption in tertiary butanol solutions in cyclohexane reported recently by R. Musa and M. Eisner are studied using a theory of nonideal solutions. This differs from the corresponding ideal-solution theory by the appearance of terms proportional to the derivatives of the ratio (k/l) of the relevant rate constants with respect to the concentration of the solute. In ideal solutions, these derivatives are zero. It is assumed that monomers and dimers are the only complexes present and it is concluded that a perturbation of the monomer-dimer equilibrium is responsible for the measured ``excess absorption.'' The nonideality of the solutions is discussed, and a ``nonideality coefficient'' is introduced. A comparison with the imperfect gas theory of Tabuchi is made.

Analysis of the glyceride structure of cocoa butter by thermal gradient crystallization

AbstractCocoa butter was separated into 43 fractions by crystallization in a thermal gradient. Similar fractions were pooled and converted into methyl esters which were analyzed by gas‐liquid chromatography. The amount of cocoa butter separated into a pure glyceride type was 85%. No significant difference was found in the ratio of palmitic to stearic acid in the GSU2 and GS2U. In the GS2U, ternary and binary eutectic mixtures are predicted by the ideal solution theory. When the eutectics are taken into consideration, the individual glyceride composition of cocoa butter agrees well with the composition predicted by restricted random distribution. To test the ability of thermal gradient crystallization to separate GU3 and GS2U a sample of cocoa butter plus 10% triolein was analyzed. The apparent composition of the cocoa butter and triolein indieated that the GU3 and the GS2U separation was incomplete.

Equilibrium distribution of molecular weights in noncyclic polymerizations

AbstractThe equilibrium molecular weight distribution in noncyclic condensation polymers depends upon the free energies of the various species in solution as well as upon the multiplicity of ways the polymerizable groups can be combined. It is shown that, although both the ideal solution theory and the Flory‐Huggins formula for the free energy of the solution lead to the well‐known molecular weight distribution obtained originally by Flory and by Stockmayer, only a restrictive group of deviations from ideality will lead to this distribution. Distributions were calculated using Guggenheim's expression for the free energy of mixing of the polymeric species, together with two alternative expressions for the free energy of the pure, separate, polymers, and in one case the distribution deviates markedly from the ideal solution result. It is concluded that reasonable deviations from ideality may significantly affect the equilibrium molecular weight distribution.

L. On the kinetic theory of the ideal dilute solution

L. On the kinetic theory of the ideal dilute solution