Liquid mixture excess volumes

Klein, A. Svejda, P. Isothermal vapor-liquid equihbriaand excess volumes of binary mixtures of benzene + gamma.-butyrolactone,. gamma.-valerolactone,. delta.-valerolactone, or. epsilon.-caprolactone at 293.15 and 313.15 K ELDATA Int. Electron. J. Phys.-Chem. Data 1995,1, 87-94... 

FIG. 4-1 Excess volumes at 25°C for liquid mixtures of cyclobexane(l) with some other Cg hydrocarbous. 

Bjola, B.S., Siddiqi, M.A., and Svejda, P. Excess enthalpies of binary liquid mixtures of y-butyrolactone + benzene. + toluene, -t ethylbenzene, and -t carbon tetrachloride, and excess volume of the y-butyrolactone + carbon tetrachloride liquid mixture, / Chem. Eng. Data, 46(5) 1167-1171, 2001. 

An iron deficiency could be accommodated by a defect structure in two ways either iron vacancies, giving the formula Fe] /D, or alternatively, there could be an excess of oxygen in interstitial positions, with the formula FeOi+ f. A comparison of the theoretical and measured densities of the crystal distinguishes between the alternatives. The easiest method of measuring the density of a crystal is the flotation method. Liquids of differing densities which dissolve in each other, are mixed together until a mixture is found that will just suspend the crystal so that it neither floats nor sinks. The density of that liquid mixture must then be the same as that of the crystal, and it can be found by weighing an accurately measured volume. 

At 2S°C and atmospheric pressure the excess volumes of binary liquid mixtures of sp and 2 are given by the equation... 

Sample Preparation Weigh about 0.5 g of sample and reflux with 20 mL of ethanolic 1 N potassium hydroxide solution for 2 h. Reduce the volume of ethanol by evaporation at 45° to 50° in a stream of nitrogen. Add 10 mL of water, and acidify with concentrated hydrochloric acid. Extract the fatty acids from the aqueous phase with successive 20-mL volumes of hexane. Wash the hexane extracts with 20 mL of water, and combine the wash with the aqueous phase. Adjust the aqueous polyol solution to pH 7.0 with aqueous potassium hydroxide solution with the aid of a pH meter. Evaporate to 2 to 3 mL under reduced pressure, and extract three times with 30 mL of boiling ethanol. Filter off any residue, and evaporate the ethanol under reduced pressure to yield a viscous liquid mixture of polyols. Transfer and dissolve 0.1 g of the mixture into a 10-mL capped vial containing 0.5 mL of warm pyridine previously dried over potassium hydroxide. Add 0.2 mL of hexamethyldisilazane, shake, add 2 mL of trimethylchloro-silate, and shake again. Place the vial on a warm plate at about 80° for 3 to 5 min. Check that white fumes are present, indicating an excess of reagent. 

The study of molecular interactions in liquid mixtures is of considerable importance in the elucidation of the structural properties of molecules. Interactions between molecules influence the structural arrangement and shape of molecules. Dielectric relaxation of polar molecules in non-polar solvents using microwave absorption has been widely employed to study molecular structures and molecular interactions in liquid mixtures [81]. Ever since Lagemann and Dunbar developed a US velocity approach for the qualitative determination of the degree of association in liquids [82], a number of scientists have used ultrasonic waves of low amplitude to investigate the nature of molecular interactions and the physico-chemical behaviour of pure liquids and binary, ternary and quaternary liquid mixtures, and found complex formation to occur if the observed values of excess parameters (e.g. excess adiabatic compressibility, intermolecular free length or volume) are negative. These parameters can be calculated from those for ultrasonic velocity (c) and density (p). Thus,... 

All calculations were carried out at T = 313.15 K. The vapor-liquid equilibrium (VLB) data for the ternary mixture and the corresponding binaries were taken from [32]. The excess volume data for the ternary mixture A,A-dimethylformamide-methanol-water and binary mixtures A, A-dimethylformamide-methanol and methanol-water were taken from [33], and the excess volume data for the binary mixture A,A-dimethylformamide-water from [34]. There are no isothermal compressibility data for the ternary mixture, but the contribution of compressibility to the binary KBls is almost negligible far from the critical point [6]. For this reason, the compressibilities in binary and ternary mixtures were taken to be equal to the ideal compressibilities, and were calculated from the isothermal compressibilities of the pure components as follows ... 

The present paper is devoted to the local composition of liquid mixtures calculated in the framework of the Kirkwood—Buff theory of solutions. A new method is suggested to calculate the excess (or deficit) number of various molecules around a selected (central) molecule in binary and multicomponent liquid mixtures in terms of measurable macroscopic thermodynamic quantities, such as the derivatives of the chemical potentials with respect to concentrations, the isothermal compressibility, and the partial molar volumes. This method accounts for an inaccessible volume due to the presence of a central molecule and is applied to binary and ternary mixtures. For the ideal binary mixture it is shown that because of the difference in the volumes of the pure components there is an excess (or deficit) number of different molecules around a central molecule. The excess (or deficit) becomes zero when the components of the ideal binary mixture have the same volume. The new method is also applied to methanol + water and 2-propanol -I- water mixtures. In the case of the 2-propanol + water mixture, the new method, in contrast to the other ones, indicates that clusters dominated by 2-propanol disappear at high alcohol mole fractions, in agreement with experimental observations. Finally, it is shown that the application of the new procedure to the ternary mixture water/protein/cosolvent at infinite dilution of the protein led to almost the same results as the methods involving a reference state. 

Therefore, it is important to have a theoretical tool which allows one to examine (or even predict) the thickness of the LC region and the value of the LC on the basis of more easily available experimental information regarding liquid mixtures. A powerful and most promising method for this purpose is the fluctuation theory of Kirkwood and Buff (KB). " The KB theory of solutions allows one to extract information about the excess (or deficit) number of molecules, of the same or different kind, around a given molecule, from macroscopic thermodynamic properties, such as the composition dependence of the activity coefficients, molar volume, partial molar volumes and isothermal compressibilities. This theory was developed for both binary and multicomponent solutions and is applicable to any conditions including the critical and supercritical mixtures. 

A new expression (8) for the excess (or deficit) around any central molecule in a liquid mixture, which was derived by us in a recent paper, is employed to examine various binary mixtures. Eqn (8) involves a KBI as well as a volume F due to the presence of the central molecule, which is inaccessible to the considered component of the mixture. In our previous paper, it was suggested to equate with (Vj-RoTkT), where Vj is the partial molar volume of component j. In this paper, additional options are suggested for F, namely the molar volume of the pure components j (Vj) (eqn (14)), or the van der Waals volumes (eqn (15)). The excesses (or deficits) have been calculated for the isopropanol-water mixture using all three eqns (13)-(15). Fig. 2 shows that eqns (13)-(15) lead to comparable results for the excesses (or deficits) for the isopropanol-water mixture. 

The excess volume for liquid mixtures is usually small, and in accord with Eq. (4-249) the pressure dependence of is usually ignored. Thus, engineering efforts to model G center on representing its composition and temperature dependence. Eor binary systems at constant T, C becomes a function of just Xi, and the quantity most conveniently represented by an equation is G /xpc RT. The simplest procedure is to express this quantity as a power series in Xi ... 

In 2003, Hanke and Lynden-Bell carried out MD simulations of IL-water mixtures [96], The behavior of [Cjmim][Cl] and the hydrophobic C,mim PI ILs was compared. Differences in the signs of both the excess volumes and the enthalpies of mixing were found. In both liquids, water molecules tended to be isolated from each other in mixtures with more ions than water molecules. When the molar proportion of water molecules reached 75%, a percolating network of waters was found as well as some isolated molecules and small clusters. In all cases, molecular motion became faster as the proportion of water increased [96],... 

It is well known that volume changes on mixing are likely to occur in polymer-solvent systems, and both theoretical and experimental studies have been devoted to this subject (26,27,28). When the volumes of the components are not strictly additive, both theoretical and phenomenological approaches include an excess volume term in the thermodynamic equations for the system. These treatments, however, concern polymeric solutions in equilibrium, i.e. the mixture is liquid or rubbery, not glassy. For solutions in the glassy state, no theoretical descriptions of the excess volume of mixing seems to be available up to date. 

Calculation of Compressed Liquid Excess Volumes and Isothermal Compressibilities for Mixtures of Simple Species... 

Figure 5.1 Excess volumes (relative to Lewis-RandaU ideal solutions) for binary liquid mixtures of benzene plus an alcohol, aU at 25°C. MeOH = methanol, EtOH = ethanol, 1-PrOH = n-propanol, 1-BuOH = n-butanol, and 2-PrOH = isopropanol. Adapted from Battino [4].

For a certain binary liquid mixture the excess volume and excess enthalpy obey... 

This chapter deals with experimental methods for determining the thermodynamic excess functions of binary liquid mixtures of non-electrolytes. Most of it is concerned with techniques suitable for measurements in the temperature range 250 to 400 K and the pressure range 0 to 100 kPa. Techniques suitable for lower temperatures will be briefly reviewed. Techniques for measuring the molar excess Gibbs function G, the molar excess enthalpy and the molar excess volume will be discussed. The molar excess entropy can only be determined indirectly from either measurements of (7 and at a specific temperature = (If — C /T], or from the temperature dependence of G m [ S m = The molar excess functions have been defined by... 

Experimental excess functions of liquid mixtures are useful in that they provide data to test theories of liquid mixtures and provide a guide for the formulation of new theories. The data are also useful in the chemical and petroleum industries. This chapter does not contain a summary of experimental data since Chapter 9 of this volume consists of a bibliography of excess function and related measurements on binary mixtures of non-electrolytes. 

The majority of excess volumes for liquid mixtures reported in the literature have been calculated from the measurement of the density at known composition. For most mixtures is usually no greater than 0.3 per cent of the total volume of the mixture. To achieve a reasonable accuracy in K , density measurements... 

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