Guggenheim Equation Research Articles

Application of hard convex body and hard sphere equations of state to the critical properties of binary mixtures

The critical properties of hydrocarbon mixtures, perfluorocarbon + hydrocarbon, perfluoromethylcyclohexane + siloxane, acetone + hydrocarbon and polydimethyl siloxane mixtures have been calculated from an equation of state for hard convex bodies and from Guggenheim's equation of state for hard spheres. In general, the results of both equations agree well with experimental data. It appears, however, that taking shape factors into account (by using the hard convex body equation) does not lead to a significant improvement in the agreement between theory and experiment for the critical properties.

Critical properties of ternary mixtures: Siloxane and perfluoromethylcyclohexane mixtures

The critical temperatures of some ternary siloxane mixtures are reported. The critical temperatures of binary perfluoromethylcyclohexane and siloxane mixtures were also measured. The results are compared to values calculated by solving the critical conditions from conformal solution theory using the one-fluid model, the ideal mixing equation and the Guggenheim equation of state. The agreement is good for mixtures of similar sized molecules whereas the agreement for dissimilar sized molecules is somewhat inadequate.

Surface tension and density measurements of the molten YCl 3-KCl binary system

The surface tension and the density of the YCl 3-KCl system were determined as a function of temperature (1073–1248 K) by the maximum bubble pressure technique. These results are represented by linear empirical equations as functions of temperature. At a constant temperature, the surface tensions of YCl 3-KCl melts show a negative deviation from Guggenheim's equation for ideal solutions.

Surface tension and density of the molten LaCl3–NaCl binary system

The surface tension and density of the LaCl3–NaCl system were determined as a function of temperature by the maximum bubble pressure technique. The surface tension and density were found to vary linearly with temperature (1123 < T < 1248 K). At constant temperature, the surface tensions of LaCl3–NaCl melts showed a small negative deviation from Guggenheim's Equation.

Determination of activity coefficients in aqueous solutions of trichloroacetic acid from emf measurements at 25°C

Activity coefficients were obtained for the hydrogen ion in aqueous solutions of HTCA at 25°C from the measurement of the emf of the cell: glass |HTCA ( m)|KCl (3 M), AgCl|Ag in which m varied between 0.006 and 0.1 mol kg −1. In order to eliminate the asymmetry potential of the glass electrode and to be able to neglect the liquid junction potential, this cell was combined with an auxiliary reference one. The equivalent cell resulting from this coupling is: ▪; which presents a small liquid junction potential, Δ E j= E j1 – E j2. Therefore, the values obtained here are apparent values, γ′ +, which will, in every case, lie between those of γ + and γ −, approaching the mean ionic value, γ ±. The concentration of the acid, m R, was constantly kept equal to 0.09549 mol kg −1. The Guggenheim equation was used to calculate γ′ + with C′ = −0.26 7. The very negative value found for this constant indicates the presence of a strong ionic association of the acid, as reported previously by other authors.

Activity coefficients in mixed-electrolyte solutions

The limitations of Guggenheim's equations for the activity coefficients of mixed electrolytes are well known. Some examples of these limitations are given. Modern theories of mixed-electrolyte solutions may be regarded as building on the Guggenheim treatment by adding terms for binary interactions of ions of the same sign and also ternary interactions involving two ions of one sign and one of opposite sign. The Scatchard treatment probably includes other short-range interactions as well and is very complicated. A simple physical interpretation of the interaction parameters appears to be lacking. The Pitzer treatment offers a more compact and convenient formalism with fewer parameters. These two approaches are outlined and some of the problems associated with their applications are discussed.

The derivatives along the critical line in a binary mixture near the critical points of pure components in one-fluid theory

Abstract Analytic expressions are obtained for all the first derivatives along the critical line in a binary mixture, near the critical points of pure components, in terms of the one-fluid Van der Waals theory. The conditions for the existence of the gas-gas equilibria of the first kind are shown and discussed for the reference substance represented by the accurate NBS equation of state of argon and by the Van der Waals and Guggenheim equations of state.

Standard potential of the mercury + mercury(I) picrate electrode from 288.15 to 303.15 K

Electromotive force measurements of cells of the type: Pt| Q· QH 2| HPc( m)| Hg 2 Pc 2| Hg| Pt, at four temperatures between 288.15 and 303.15 K have been used to derive the standard potential of the mercury + mercury(I) picrate electrode: E°/ V = 0.55678 − 0.48639 x 10 −3( T/ K) − 0.94022 x 10 −6( T/ K) 2. The solubility product of mercury(I) picrate was calculated at 298.15 K: K sp = (6.12 ± 0.05) x l0 −11 mol 3 kg −3. The molality m of the acid ranged from 0.011 to 0.045 mol kg −1. The standard potentials were determined by an extrapolation method utilizing a modified Guggenheim equation for the activity coefficients.

Rotation Ebulliometer, Part 2. Thermodynamic Investigation on Dilute Solutions of Diphenyl and Benzil in Benzene

AbstractA new pressure controlled twin‐ebulliometer without Cottrell‐pump is described. The boiling temperature can be chosen by setting the pressure by means of a pressure regulator in the range of 100 – 760 Torr. Measurements of polystyrene and other polymers show that in this rotation ebulliometer foaming is no more effective. This fact and the agreement of the experimental ideal ebullioscopic constant with those calculated mean that thermodynamic equilibrium between vapour and liquid may be established in the rotation ebulliometer. ‐ The systems diphenyl + benzene and benzil + benzene were investigated in a solute mole fraction between 0.01 and 0.04 at various temperatures (30–80 °C). The activity coefficients of benzene in the diphenyl + benzene system at 65 °C were compared with those obtained from vapour pressure measurements in more concentrated solutions. The experimental data can all be fitted by the Guggenheim's equation with r = 2, z = 6, and zw/k = 76°. The data in the benzil + benzene system at 65°C can be represented by the same equation with zw/k = 200°, which agrees with the value obtained by calorimetric determinations of the heats of dilution.

Excess Volumes of Mixtures of Acetone, Chloroform, Carbon tetrachloride, 1,4-Dioxane and Tetrahydrofuran with o-Dichlorobenzene

Abstract Excess volumes of mixtures of o-dichlorobenzene with acetone, chloroform, carbon tetrachloride, 1,4-dioxane, and tetrahydrofuran have been measured at 293.15 K as a function of composition. The excess volume data have been used to check the one-fluid theory of mixtures with van der Waals's and Guggenheim's equations of state.

A quasi lattice-local composition model for the excess Gibbs free energy of liquid mixtures

Two new expressions for the excess Gibbs energy of liquid mixtures are derived from Guggenheim's quasi-lattice model and Wilson's local composition concept. These are called the Local Surface Guggenheim equation (LSG) and the Local Composition Guggenheim equation (LCG). The LSG equation is similar, but not identical to UNIQUAC. The new equations require only two adjustable parameters per binary, and no higher-order parameters for extension to multicomponent systems. A critical discussion is given of Guggenheim's quasi-lattice expression for the excess Gibbs energy of athermal mixtures. This expression gives the combinatorial contribution to the new equations. A new method is proposed in the evaluation of the pure component structural parameters, independent of particular assumptions about the lattice parameters. The application of the LSG and the LCG equations to practical problems of phase-equilibria is considered in detail.

Theoretical prediction of phase behaviour at high temperatures and pressures for non-polar mixtures. Part 2.—Gas–gas immiscibility

An attempt has been made to predict gas–gas immiscibility using the Guggenheim and van der Walls equations of state. The stability conditions have been solved, using a digital computer, for the van der Waals one fluid model. The computational aspects have been discussed in previous papers in this series.The Guggenheim equation of state successfully predicts gas–gas immiscibility of the correct kind for most of the systems which have been studied experimentally. In contrast the van der Waals equation of state predicts the correct kind of gas–gas immiscibility in only a very few cases.The applicability of the model is briefly discussed.

Theoretical prediction of phase behaviour at high temperatures and pressures for non-polar mixtures. Part 3.—Comparison with upper critical solution temperatures for perfluoromethylcyclohexane + hydrocarbons

The upper critical solution temperatures of perfluoromethylcyclohexane + n-alkanes (C5 to C15) have been measured. The results have been compared with the van der Waals one fluid model using the Guggenheim equation of state and employing the technique for solving the criticality conditions described previously. The energy parameter, ξ, defined by the equation ξ=Tc12/(Tc11Tc22)½(where Tcij is the energy reducing parameter characterising interactions between molecules of species i and j) needed to fit the experimental UCST data have been calculated. The value of ξ is always less than unity and decreases with an increase in the chain length of the n-alkane. Similar trends have been previously observed for values of ξ obtained from gas–liquid critical points of mixtures of hexafluorobenzene + n-alkanes and perfluoron-heptane + n-alkanes. Possible explanations of such trends are suggested.

Theoretical prediction of phase behaviour at high temperatures and pressures for non-polar mixtures. Part 4.—Comparison with experimental results for carbon dioxide + n-alkane mixtures

The phase diagrams for carbon dioxide + n-alkanes (C1-C20) have been constructed for the one fluid model using both the van der Waals and Guggenheim equations of state by the techniques described in a previous paper. Various combining rules for calculating the volume and energy parameters characterising interactions between unlike molecules have been used. Comparison between theory and experiment suggest that the interaction parameter ξ is slightly greater than that calculated from the Hudson and McCoubrey combining rule. This is consistent with conclusions reached from an analysis of other thermodynamic properties.

溶融MgCl<SUB>2</SUB>-KClおよびKNO<SUB>3</SUB>-NaNO<SUB>3</SUB> 2成分系の表面張力

Surface tensions of MgCl2-KCl and KNO3-NaNO3 binary melts have been measured by means of the maximum bubble pressure method over the temperature ranges of 650∼875°C and 270∼405°C respectively.The variation of the constituent ionic species with composition for the MgCl2-KCl binary system has been estimated by comparing the results obtained with those determined for the KNO3-NaNO3 binary system having relatively strong ionic characters. The results obtained are summarized as follows:(1) For both systems, the surface tension shows an approximately linear decrement with increasing temperature at each composition. The surface tension and its temperature coefficient of molten MgCl2 are considerably low as compared with those of other chlorides but these are markedly increased by the addition of KCl. These trends are considered to be indicating the associating property as in the case of molten ZnCl2 previously studied by the authors.(2) The variation of the surface tension at the melting point with composition is well corresponding to the phase diagram for the KNO3-NaNO3 system, but not for the MgCl2-KCl system, particularly on the MgCl2-rich side. The temperature coefficient of surface tension corresponding to the surface entropy per unit area and the surface enthalpy per unit area vary monotonously with composition in the KNO3-NaNO3 system, but show notable inflections at about 30 and 80 mol%KCl in the MgCl2-KCl system. The surface heat of mixing per unit area for the MgCl2-KCl system shows a maximum and a minimum at about 30 and 90 mol%KCl.(3) The surface tensions calculated from a modified Guggenheim equation agreed very well with the experimental values for KNO3-NaNO3 binary melts, indicating that this system can be treated as a nearly ideal solution.(4) It is also found that the variations of the surface properties with composition are well corresponding to the changes of the other physicochemical properties in the MgCl2-KCl system.

A Generalized Correlation for Predicting Saturated Liquid Densities of Mixtures

AbstractA generalized correlation for saturated liquid densities of pure compounds, based on the Guggenheim equation, has been extended for applications to mixtures. The method employs a mole‐average acentric factor and scaling volume, and a weighted average critical temperature for the mixture. The method was tested on twenty‐four binary and two ternary systems comprising hydrocarbons and non‐hydrocarbons. Overall average absolute deviation in predicted densities is less than two percent for a total of 1,096 data points.

Generalized correlation of saturated liquid densities

Numerous methods have been proposed in the literature for correlating and predicting density data for pure liquids at saturation states. The Guggenheim equation is used to represent saturated liquid densities of 23 nonpolar and slightly polar compounds in the reduced temperature range from 0.2 to 1.0. This investigation develops a generalized but simpler correlation over the same reduced temperature range. Tabular data provide the following information: (1) acentric factors, critical temperatures, critical densities, scaling densities, and values of alpha and beta for 23 compounds; (2) deviations of calculated saturated liquid densities from literature values; and (3) plot of deviations between calculated densities and literature values for 9 compounds as the function of reduced temperature. The average deviation of the calculated densities and literature values for a total of 595 data points tested is 0.27%. (22 refs.)

Thermodynamic excess functions of mixtures of molecules of different sizes

Van der Waals's equation of state, with his original rules for relating his a and b to the composition of the mixture, is shown to lead to values of the thermodynamic excess functions for mixtures of spherical (or nearly spherical) molecules, which agree nearly as well with experiment as those obtained even with Leland, Rowlinson and Sather's greatly improved version of the more elaborate “pure-fluid based” theories of Prigogine, Kirkwood, Scott, Brown and others. Guggenheim's equation of state is shown to lead to excess functions which agree more closely with experiment than any previously published version of the more elaborate theories.

Surface tensions of simple liquids

The variation of surface tension with temperature has been determined for several cryogenic fluids. Differential capillary rise measurements have been performed on nitrogen, argon, carbon monoxide and methane. From these as well as previous measurements, parameters of the Ferguson and Guggenheim equations have been calculated from experimental data on nine cryogenic fluids. The surface tensions of simple liquids are considered with reference to the theory of corresponding states.

The Neglected Term in the Guggenheim Equation for Calculation of Dipole Moment from Solution Data

The Neglected Term in the Guggenheim Equation for Calculation of Dipole Moment from Solution Data