Composition Dependence Of Activity Coefficients Research Articles

Application of NEAT for determining the composition dependence of activity coefficients in poorly specified mixtures

Poorly specified mixtures, of which the composition is only partially known, are important in many fields. In a recent work of our group, the method NEAT for estimating activity coefficients of target components in such mixtures was introduced. In the present work, it is shown that based on a single NMR analysis of a poorly specified mixture not only the activity coefficient of the target component in that mixture but also its composition dependence can be predicted with NEAT. Hence, based on a single NMR analysis, the activity coefficient of the target component in many mixtures can be predicted with NEAT. This is possible, if the unknown part of the mixture remains unchanged, which is the case e.g. when the target component is selectively removed or when a known solvent is added or removed. The approach is successfully tested using several aqueous test mixtures.

Activities and volatilities of trace components in silicate melts: a novel use of metal–silicate partitioning data

Ian Carmichael spent 45 years thinking about and working on the activities of components in silicate melts and their use to estimate physicochemical conditions at eruption and in the source regions of igneous rocks. These interests, principally in major components such as SiO2, led us to think about possible ways of determining the complementary activity coefficients of trace components in silicate melts. While investigating the conditions of accretion and differentiation of the Earth, a number of authors have determined the partitioning of trace elements such as Co, Ni, Mo and W between liquid Fe metal and liquid silicate. These data have the potential to provide activity information for a large number of trace components in silicate melts. In order to turn the partitioning measurements into activities, however, we need to know the activity coefficient of FeO, γFeO in the silicate. We obtained γFeO as a function of melt composition by fitting a simple model to 83 experimental data for which the authors had measured the FeO content of the silicate melt in equilibrium with metal (Fe-bearing alloy) at known fO2. The compositional dependence of γFeO is weak, but, when calculated in the system Diopside–Anorthite–Forsterite, it decreases towards the Forsterite apex. A similar approach for Ni, for which twice as many data are available, leads to similar composition dependence of activity coefficient and confirms the suggestion that γNiO/γFeO is almost constant over a wide range of silicate melt composition. The activity coefficients for FeO were used in conjunction with measured Mo and W partitioning between Fe-rich metal and silicate melt to estimate activity coefficients for trace MoO2 and WO3 dissolved in silicate melt. When combined with data on Mo- and W-saturated silicate melts a strong dependence of activity coefficient is observed. Calculated in the system Diopside–Anorthite–Forsterite, both MoO2 and WO3 exhibit similar behaviour to FeO and NiO in that activity coefficients decrease as Forsterite content increases. The effect is much larger for Mo and W, however, γMoO2 and γWO3 varying by factors of 20 and nearly 100, respectively, in this system. In order to illustrate the potential applications of the metal–silicate partitioning approach to determine the activity coefficients of volatile elements, we used it to determine activity coefficients of PbO, CuO0.5 and InO1.5 in a silica-saturated melt at 1,650 °C. We find values of 0.22, 3.5 and 0.02, respectively, indicating a strong dependence on cation charge. The value for CuO0.5 is in excellent agreement with experimental data of Holzheid and Lodders (Geochim Cosmochim Acta 65:1933–1951, 2001), which shows that the method is viable. When combined with thermodynamic data on the gas species, we find that Pb is the most volatile of the 3 elements under ‘normal’ terrestrial conditions of oxygen fugacity but that In should become the most volatile under strongly reducing conditions such as those of the solar nebula. The oxygen fugacity dependence of volatility has implications for the high relative abundance of In in silicate Earth. We conclude that metal–silicate partitioning experiments are a viable means for determining activities of trace components in silicate melts and are particularly useful if the metal of the element is unstable or volatile at igneous temperatures.

Incremental Gravimetry: A Method for Two-Parameter Model Building of Binary Gas Co-Adsorption Equilibria

This paper presents and develops a novel methodology to determine thermodynamic parameters of binary gas co-adsorption equilibria at given total pressure, based exclusively on binary gravimetric measurements at this same total pressure, together with single component isotherms. By “Incremental Gravimetry”, we designate a procedure in which the adsorbent sample is submitted to increments of composition of a flowing binary gas, and the corresponding increments of weight of the sample at equilibrium are measured. The experimental example is the co-adsorption of methane and carbon dioxide on Norit activated carbon near ambient temperature and pressure. The approach relies on the thermodynamics of non-ideal adsorbed solutions. The experimental methodology is described, the underlying theory is then presented. Compact analytical expressions are established that relate the measured limiting slopes of the incremental gravimetric curves (at infinite dilution of one component in the other) to quantities that derive only from the pure component isotherms, and to the infinite dilution activity coefficients. The latter are then uniquely determined. Classical two-parameter models for the composition dependence of activity coefficients are then implemented to reconstruct the complete binary isotherms and the incremental gravimetric curves. The comparison of the latter with the measured curves permits to test the different models.

NMR Studies of Binary Surfactant Mixture Thermodynamics: Molecular Size Model for Asymmetric Activity Coefficients

Pulsed-field-gradient NMR methods are used for determining the partitioning of surfactants between unimeric and micellar forms in mixed surfactant systems. The method allows determination of the composition dependence of activity coefficients in binary surfactant mixtures. Application of the regular solution approach to NMR data for several mixtures gives β parameters which are dependent on concentration and which differ systematically among the surfactants within the same binary mixtures. The β parameter summarizes interactions among different pairs of surfactants and, in principle, should not be composition dependent. The observed behavior is therefore not consistent with expectations from the regular solution model. Use of the van Laar expressions, on the other hand, accounts well for the composition dependence of the activity coefficients. The van Laar expressions also account for the often-observed composition dependence of regular solution β parameters determined from CMC measurements. Though simila...

Is the Reaction Equilibrium Composition in Non-ideal Mixtures Uniquely Determined by the Initial Composition?

Reaction equilibrium can be mathematically described by the equilibrium equation and the reaction equilibrium composition can be calculated by solving this equation. It can be proved by non-elementary thermodynamic arguments that for a generic system with given initial composition, temperature and pressure there is a unique stable equilibrium state corresponding to the global minimum of the Gibbs free energy function. However, when the concept of equilibrium is introduced in undergraduate chemistry and chemical engineering courses, such arguments are generally not accessible. When there is a single reaction equilibrium among mixture components and the components form an ideal mixture, it has been demonstrated by a simple, elegant mathematical argument that there is a unique composition satisfying the equilibrium equation. It has been also suggested that this particular argument extends to non-ideal mixtures by simply incorporating activity coefficients. We show that the argument extension to non-ideal systems is not generally valid. Increasing non-ideality can result in non-monotonicity of the function crucial for the simple uniqueness argument, and only later it leads to non-uniqueness and hence phase separation. The main feature responsible for this is a composition dependence of activity coefficients in non-ideal mixtures.

Vapour-liquid equilibrium in the binary system ethanoic acid (1)-cyclohexane (2) at 101.325 kPa

Malijevská, I., Chýlková, K. and Sýsová, M., 1991. Vapour-liquid equilibrium in the binary system ethanoic acid (l)-cyclohexane (2) at 101.325 kPa. Fluid Phase Equilibria, 68: 219-228. Isobaric ( P = 101.325 kPa) measurements were performed on the binary mixture ethanoic acid-cyclohexane by using a modification of the Dvořák-Boublík recirculation unit. This mixture forms a minimum boiling azeotrope which occurs at the mole fraction of acid equal to 0.222. This value, which differs significantly from previously reported values, was checked by the distillation method. The thermodynamic consistency of the data was checked by the Herington and the Counsell and Hicks tests. The Wilson, modified Wilson and Redlich-Kister equations were used to fit the composition dependence of activity coefficients.

Effects of thermodynamic nonideality on protein interactions. Equivalence of interpretations based on excluded volume and preferential solvation.

Published results on the stabilization of proteins by sucrose (J.C. Lee and S.N. Timasheff, J. Biol. Chem. 256 (1981) 7193) have been reexamined and interpreted in terms of thermodynamic nonideality. The composition dependence of activity coefficients may be accounted for on a statistical-mechanical basis using the concept of excluded volume. An expression is derived in which the effect of sucrose on determination of the partial specific volume of a protein, previously interpreted in terms of preferential protein solvation, is also seen to be attributable to excluded volume. Gel chromatographic studies of the reversible unfolding of alpha-chymotrypsin are presented which demonstrate temperature- and sucrose-mediated changes in the effective volume of the enzyme. These measurements support the quantitative interpretation of the stabilization in terms of thermodynamic nonideality arising from the difference between covolumes for sucrose and the two isomeric states of alpha-chymotrypsin. By establishing the equivalence of the two approaches that have been used to account for the effects of inert solutes on protein transitions, the present investigation eliminates the need for any distinction between such solutes on the basis of molecular size; and also enhances greatly the potential sensitivity of thermodynamic nonideality as a means of probing protein isomerizations, since greater displacement of the equilibrium position may be effected by small rather than by macromolecular solutes present at the same weight concentrations.

Infinite dilution fugacity coefficients and the general behavior of dilute binary systems

AbstractA universally valid formal expression for the composition dependence of solute and solvent fugacity coefficients in any dilute binary system far from criticality is derived in this paper. In the present context, dilution denotes the y1 → O limit, regardless of the mixture's molar density. The results are independent of the system under study and of the choice of equation of state. The solute fugacity coefficient is simply the product of a composition‐independent term (the infinite dilution fugacity coefficient) and an exponential decay composition correction. These two parameters have important thermodynamic implications: their temperature and pressure derivatives are related to the solute's partial molar enthalpy and volume, respectively. When applied to activity coefficients, the same theoretical analysis yields universal relationships for the composition dependence of activity coefficients which can be used as consistency checks for empirical correlations. The relationship between infinite dilution activity and fugacity coefficients can be used to estimate relative solubilities of a given solute in different solvents. Excellent agreement is found when the theoretical expressions are tested with three different binary systems involving a nonvolatile solid solute and a supercritical fluid.

Allowance for composition dependence of activity coefficients in the analysis of sedimentation equilibrium results obtained with heterogeneously associating systems

An iterative procedure is described that permits analysis of sedimentation equilibrium distributions obtained with heterogeneously associating systems, account being taken of the dependence of each activity coefficient on the composition of the solution, which varies with radial distance. The procedure is illustrated with treatment of distributions simulated for a system of the type A + B ⇌ C, and comment is made on its applicability to systems involving higher order complexes.