Variation Of Activity Coefficients Research Articles

Thermodynamic behaviours of manganese and phosphorus between CaO-MgOsat-SiO2 -Al2 O3 -Fet O-MnO-P2 O5 ladle slag and liquid iron

The thermodynamic equilibria of manganese and phosphorus between liquid iron and CaO-MgOSat-SiO2-FetO-MnO-P2O5-Al2O3 (0–33%) ladle slag have been investigated at 1873 K from the viewpoint of Mn and P yields for the production of high-strength steels. The equilibrium distribution ratios of Mn and P were found to increase with increasing FetO content; however, these ratios vary with basicity, but they do this the other way round. The addition of alumina into slag at a fixed basicity and FetO content decreases both the equilibrium manganese and phosphorus distributions. The equilibrium distribution ratios were discussed in terms of the variation of activity coefficients of FetO, MnO and PO2.5, according to the slag basicity and Al2O3 content. The quantitative contributions of basicity and (%FetO + %MnO) on LMn and LP were empirically determined and their usefulness was discussed with the aid of plant data: To improve Mn and P yields in the practical RH operation, it is strongly recommended that Fe-Mn and Fe-P alloys be added after Al deoxidation treatment inducing relatively high Al2O3 in slag and maintaining low FetO content. In addition, a ladle slag composition for the targeted Mn and P contents in liquid iron was substantially estimated using the empirical relationships. Das thermodynamische Gleichgewicht von Mangan und Phosphor zwischen Eisenschmelzen und CaO-MgOsat-SiO2-FetO-MnO-P2O5-Al2O3-(0–33%)-Pfannenschlacken wurde bei 1873 K untersucht. Dies geschah aus der Perspektive von Mn- und P-Ausbeute für die Herstellung von hochfesten Stählen. Es zeigte sich, daß die Gleichgewichtsverteilungsverhältnisse von Mangan und Phosphor mit zunehmendem FetO-Gehalt ansteigen; allerdings verändern sich diese Verhältnisse gegenläufig zur Basizität. Die Zugabe von Tonerde zur Schlacke bei bestimmter Basizität und FetO-Gehalt verursacht eine Absenkung sowohl der Phosphor- als auch der Mangan-Gleichgewichtsverteilung. Entsprechend der Schlackenbasizität und dem Al2O3-Gehalt werden die Gleichgewichtsverteilungsverhältnisse anhand der Variation der Aktivitätskoeffizienten von FetO, MnO und PO2.5 diskutiert. Die quantitative Beschreibung von Basizität und (%FetO + %MnO) auf LMn und LP wurde empirisch bestimmt und mit Anlagendaten überprüft: Zur Verbesserung der Mn- und P-Ausbeute im realen Betrieb einer RH-Anlage ist es unbedingt erforderlich, daß Fe-Mn- und Fe-P-Legierungen erst dann zugegeben werden, wenn die Desoxidationsbehandlung mit Aluminium, infolge der relativ hohe Al2O3-Gehalte in der Schlacke auftreten und niedrige FetO-Gehalte beibehalten werden, abgeschlossen ist. Mit den empirischen Beziehungen läßt sich zusätzlich eine Zusammensetzung für eine Pfannenschlacke angeben, mit der die zu erzielenden Mn- und P-Gehalte in Eisenschmelzen einzustellen sind.

Effects of aluminum on Cr dimerization in silicate melts and implications for Cr partitioning and redox equilibria

The electrochemical measurements reported here provide insight into the activities and structure of individual Cr and Sn species in the melt. This represents an improvement over activity coefficients averaged over multiple species such as can be derived from simple melt/mineral equilibrium experiments. Knowledge of the presence and activities of individual species of Cr in a melt can lead to better understanding and prediction of the complex variations in partitioning of Cr between minerals and melt, which have thus far defied accurate description. Electrochemical experiments in four different silicate melts indicate that, under important magmatic conditions, Cr can be present in the melt as any of three species: Cr2+, Cr3+, and some polymeric form which we represent in this paper as the dimer Cr26+. The presence of two trivalent Cr species, and the oxidation state change between Cr2+ and Cr3+, makes it easy to understand why the partitioning behavior of Cr is complex. The presence of two species (a dimer and a monomer), each containing Cr3+, means that the activity coefficient for a single composite Cr3+ component will vary in a complex way with melt composition, temperature, fO2, and Cr concentration even when mixing in the melt is ideal. For example, if a fixed Cr3+ component is used to model the melt, its activity coefficient will vary by an order of magnitude over the region in which the Cr3+ goes from being present as mostly monomer to mostly dimer. This occurs even if there were no nonideal mixing. Trivalent Cr dimers are particularly sensitive to Al concentration in the melt, consistent with the interpretation that dimers exist as spinel-like structures in the melt. The preceding discussion bears on melts with ideal mixing. But the experiments reported here indicate that mixing in the compositions studied is not ideal. Activity coefficients for the Cr3+ dimer vary by over a factor of 3 as a function of composition for the silicate melts reported here. In addition, we report variations of a factor of 3 in the activity coefficient for divalent Cr as a function of melt composition, meaning that Cr partition coefficients will be significantly sensitive to melt composition even where little trivalent Cr is present. Thus, the effects of nonideal mixing will be added to the effects of the presence of a dimer. The transition from mostly dimer to mostly monomer occurs at concentrations of Cr and Al typical of natural systems, with the dimer becoming less important as Cr3+ concentration decreases. At concentrations of Al of about 8 wt.%, the dimer is an important component down to about 0.25 wt.% Cr3+. At Al concentrations of 11–12 wt.%, the dimer was important to the limit of our experimental resolution, about 0.1 wt.% Cr3+. This means that in the range of natural melts, not only is the Cr not present as a single species, but the proportion that each of the species comprises of the total Cr3+ is not fixed. Because the trivalent Cr exists as more than a single species in the melt, and the proportion of those species is not fixed, use of a single species model to predict variations in activity will work only poorly and require complex variations in activity coefficients. Trivalent Cr activity coefficients, relative to typically-used fixed component models, can be expected to vary as a function not only of melt composition, but of fO2 and total Cr concentration as well. Based on the results presented here, variations in activity of trivalent Cr of more than 100% can be expected over natural ranges of conditions. These results have broader implications for how we view thermodynamic components in magmatic systems. In a thermodynamic treatment of the behavior of an element in a melt, any form of that element can serve as the species of description. However, choosing the principle form of the element actually present in the melt usually minimizes variations of the activity coefficient and improves intuitive understanding of the behavior of the element in the system. What’s more, if an element exists in multiple species, no single species will provide a simple or intuitive model for the variation of activity of the element as a whole. Use of a simple ionic model for melts, although successful in some general applications, is not correct in detail as shown by the dimerization of Cr in silicate melts. Other elements may exhibit similar speciation in melts. We demonstrate in this report that Sn also exists as a dimer in silicate melts. At all concentrations of Sn which we studied, the Sn dimer (which we represent as Sn24+) dominated over any monomer present. However, the concentrations we studied were far above natural Sn concentrations, and Sn may exhibit similar behavior to Cr at more natural concentrations of Sn where monomerization would be more likely to occur.

Partitioning of trace elements between clinopyroxene and garnet: data from mantle eclogites

Concentrations of REE, Ba, Sr, Y and Zr have been measured by ion microprobe (SIMS) for garnet and clinopyroxene in a suite of eclogite xenoliths from the Roberts Victor kimberlite pipe in South Africa. The xenoliths have a restricted set of temperatures of formation estimated at 1100 ± 100°C at 5 GPa, but span a wide range of compositions; garnet Ca/(R 2+) ratios range from 0.08 to 0.50, whilst the associated clinopyroxenes also show increasing jadeite solid solution as their Ca/(R 2+) ratios increase. The cpx/grt partition coefficients ( D i ) for REE, Sr and Y decrease progressively as Ca/(R 2+ in the minerals increase; in the LREE this change amounts to approximately three orders of magnitude. Evidence for such large changes in partition coefficients as a function of Ca content is also seen in other data for mantle eclogites from South Africa and Siberia. Cpx and grit with low Ca/(R 2+ ratios have ( D i ) for HREE which are similar to those implied by mineral/liquid data for basic-ultrabasic melts. Poor correlations of Ba, La and Lu partition coefficients with cpx-grt Ca contents in the present dataset, are the result of late-stage partial alteration and relatively large errors of measurement associated with low concentrations. Zr partition coefficients show only a weak correlation with mineral Ca/(R 2+). Strong correlations are demonstrated between cpx/grt D i (calculated on a ppm or molar basis) and molar cpx/grt D Ca for most REE, Sr and Y. These may be expressed in the form: In D i ∗ cpx grt =A ln D Ca ∗ cpx grt + B B (Eq. (1)), where A and B are empirical constants for each element and vary with ionic radius in the REE. The partitioning of a given trace element progressively favours garnet rather than pyroxene as increasing amounts of Ca are more strongly partitioned into garnet than clinopyroxene; and the magnitude of this effect increases with ionic radius in the REE. The empirical linear calibrations (Eq. (1)) given for REE, Y and Sr allow calculation of the ( D i ) of a cpx-grt pair from their Ca contents (for 1100 ± 100°C, ∼ 5 GPa). Using the well-documented R 3+ Al [4] Ca −1Si −1 (YAG-type) substitution relationship for REE and Y in garnets as the basis of an exchange reaction, it is suggested that the A term in empirical Eq. (1) may be related to variations in activity coefficients as the major element (Ca) composition changes, whilst term B is largely dependent on the standard state free energy.

Diffusion and activity of NiO in CaO-MgO-Al2O3-SiO2 melts considering effects of aO2− and γNi2+

Variations in activity coefficients for oxides in silicate melts are complex functions of silicate melt composition. For example, the activity coefficient (y) for NiO shows a minimum when plotted against a parameter reflecting the degree of polymerization (or basicity or fraction of bridging oxygens) (e.g., Pretorius and Muan, 1992). In this paper, we propose that this complexity occurs in part because NiO is not an actual species in silicate melts. Variations in y can be better understood and predicted if the activity of NiO is treated as the product of activities of Ni2+ and 02− ions. Using voltammetric methods, we have measured independent activity coefficients for Ni2+ and O- for compositions between diopsidic and anorthitic melt and have found that variations in these values are more easily understood in terms of the melt composition and structure and permit qualitative variations in γNiOo (activity coefficient of NiO relative to the free energy of formation reported in Robie and Waldbaum, 1968) to be predicted in compositions other than those studied. We suggest that a similar consideration of ionic behavior might improve our understanding of activity coefficients for other oxides in silicate melts as well. In addition, we report diffusion rates for Ni and free energies for the reaction Ni2+ + 02- ⇌ Ni0 + 1202, for melt compositions along the compositional joins CaMgSi206-CaAl2Si208 and CaMgSi206-MgAl2Si 2O8.

Diffusion and activity of NiO in CaO-Mg0-Al 20 3-Si0 2 melts considering effects of αo 2− and γNi 2+

Variations in activity coefficients for oxides in silicate melts are complex functions of silicate melt composition. For example, the activity coefficient (y) for NiO shows a minimum when plotted against a parameter reflecting the degree of polymerization (or basicity or fraction of bridging oxygens) (e.g., Pretorius and Muan, 1992). In this paper, we propose that this complexity occurs in part because NiO is not an actual species in silicate melts. Variations in y can be better understood and predicted if the activity of NiO is treated as the product of activities of Ni 2+ and 0 2− ions. Using voltammetric methods, we have measured independent activity coefficients for Ni 2+ and O - for compositions between diopsidic and anorthitic melt and have found that variations in these values are more easily understood in terms of the melt composition and structure and permit qualitative variations in γ NiO o (activity coefficient of NiO relative to the free energy of formation reported in Robie and Waldbaum, 1968) to be predicted in compositions other than those studied. We suggest that a similar consideration of ionic behavior might improve our understanding of activity coefficients for other oxides in silicate melts as well. In addition, we report diffusion rates for Ni and free energies for the reaction Ni 2+ + 0 2- ⇌ Ni 0 + 1 2 0 2 , for melt compositions along the compositional joins CaMgSi 20 6-CaAl 2Si 20 8 and CaMgSi 20 6-MgAl 2Si 2O 8.

Ionic metallic solutions

The variation of activity coefficients at low concentrations is examined to determine if one can demonstrate charge transfer and formation of ionic solutions for mixtures of some metals.

SXLSQA, A Computer Program for Including Both Complex Formation and Activity Effects in the Interpretation of Solvent Extraction Data

Abstract A previously reported computer program for the interpretation of solvent extraction data in systems that can include two extractants, one acidic and one neutral, has been extended to treat the effects of: (1) variation of activity coefficients of solute species and of water activity in the aqueous phase, calculated by the Pitzer treatment; (2) variation of activity coefficients of solute species in the organic phase, calculated by the Hildebrand-Scott treatment; and (3) product species formed in the aqueous phase. The interaction parameters of the Pitzer treatment and the solubility parameters of the Hildebrand-Scott treatment can be refined along with the formation constants of various assumed product species to fit the data. Like its predecessor, the program is capable of fitting simultaneously a variety of data, including the distribution of an extractable cation, anion, or water, as well as spectra, vapor pressure, or heats of mixing for the organic phase. Use of the program is illustrated by...

An ion interaction model for the volumetric properties of natural waters: Density of the solution and partial molal volumes of electrolytes to high concentrations at 25°C

Literature density data for binary and common ion ternary solutions in the Na-K-Ca-Mg-Cl-SO 4-HCO 3-CO3-H 2O system at 25°C have been analysed with Pitzer's ion interaction model, which provides an adequate representation of the experimental data for binary and common ion ternary solutions up to high concentration. This analysis yields Pitzer's interaction parameters for the apparent and partial molal volumes, which are the first derivatives with respect to pressure of the interaction parameters for the free energy. From this information, densities of natural waters as well as partial molal volumes of their solutes can be predicted with good accuracy, as shown by several comparisons of calculated and measured values. It is shown that V ̄ MX - V ̄ 0 mx , the excess partial molal volume of the salt MX, depends more on the type of salt than on the electrolyte itself and that it increases with the charges of the salt components. The influence of concentration and composition on the variation of activity coefficients with pressure and on the partial molal volumes of the salts is discussed, using as an example the partial molal volume of CaSO 4(aq) in solutions of various compositions. The increase of V ̄ CaSO 4 , with ionic strength is very large but is not very different for a NaCl-dominated natural water like the Red Sea lower brine than for a simple NaCl solution. Although the variation of activity coefficients with pressure is usually ignored for moderate pressures, like those found in hydrothermal environments, the present example shows that it can be as large as 30% for a 2-2 salt for a pressure increase from 1 to 500 bars at high ionic strength.

Thermodynamics of methylenebromide + aromatic hydrocarbon mixtures: Molar excess Gibbs free energy of mixing

Vapour—liquid equilibrium data have been taken at 308.15 K for methylenebromide (A) + benzene, toluene or o-xylene (B) mixtures and have been used to compute the excess Gibbs free energy of mixing G E. The G E data of these mixtures suggest that all these (A + B) mixtures are characterized by electron donor—acceptor interactions between the π electron cloud of B and the bromine atoms of A. G E data of these mixtures have also been analysed in terms of a graph-theoretical approach (using previously reported molar excess enthalpy H E ( T, X A = 0.5 and 0.4) data alone), and it has been observed that while this approach correctly predicts the H E data, it fails to predict correctly the variation in activity coefficient γ i ( i = A or B) with composition x i . The present study highlights the roles of (a) steric repulsions and (b) intermolecular A—B interactions in the thermodynamics of binary mixtures of non-electrolytes.

Calculation of the thermodynamic driving force in crystallization from solution

The dependence of the thermodynamic driving force for crystallization on the degree of supercooling δ T is given by the differential heat (partial molar enthalpy increment) of solution divided by RT 2 . For sparingly soluble nonelectrolytes the differential heat of solution may be obtained directly from the slope of a logarithmic plot of solubility versus 1/ T, but for more soluble substances the variation of activity coefficient with concentration should be taken into account. For nonelectrolytes this dependence may be estimated from the thermodynamic properties of pure solute, using a series expansion for the activity coefficient. Highly soluble electrolytes require a more precise treatment, but adequate activity or heat of solution data are found in the literature for most systems of interest. Examples of calculations with different degrees of approximation are presented.

Determination of alkalinities of estuarine waters by a two-point potentiometric titration

Gran plots of titrations of seawater with acid are straight lines after protonation of all weak acids when ion-pairing is taken into account. This property is used to calibrate the pH electrode and to determine the endpoint of what is essentially a two-point alkalinity titration of the sample. First the initial sample pH is measured; then a standard addition of acid is made giving a pH near 3.2 (pH 1); a further acid addition is made giving a pH near 2 (pH 2). The slope of the electrode response and the total alkalinity are calculated from pH 2 and pH 1. The advantages of this method are that no separate calibrations are necessary: no corrections for variations in activity coefficients are needed because pH values are obtained on the seawater pH scale; and the instruments used for the determinations are very simple. The standard deviation of the alkalinity determination of seawater by the proposed technique was − 0.10%.

Volatile solubilities in magmas: Transport of volatiles from mantles to planet surfaces

Experimental measurements of the solubility of CO2, CO, CH4, H2, and H2O in silicate melt were made at pressures from 10 to 20 Kb and temperatures of 1200°C. The C‐O‐H fluid phase was buffered by graphite, iron, and wüstite. Detailed measurements were made on melts of NaAlSi3O8 composition and the results confirmed for alkalic and tholeiitic basalt liquids. The melt volatiles have dramatically lower H2/H2O and higher CO/CO2 ratios than the fluid. The result is large differences between the C‐O‐H compositions of the melt and the fluid (fluids about 16 atm % C, 6% O, and 78% H; melts about 4% C, 32% O, and 64% H). The measured solubilities allow calculation of activity coefficients for volatile species in the melt. They are, roughly, CO = 0.1, H2O = 0.6, CO2 = 1, H2 = 3, and CH4 = 60. This two‐order‐of‐magnitude variation in activity coefficients causes the significant volatile fractionation observed between fluid and melt. We argue that the same fractionation will occur in the more usual case of fluid‐absent partial melting of planetary mantles. The fractionation is such that reducing mantles will form magmas that yield volcanic gases about 1.5 orders‐of‐magnitude more oxidizing than the mantle source, while oxidizing mantles will form magmas with more reduced volcanic gases. We conclude that a volcanic gas composition cannot be directly used to estimate either the oxygen fugacity or volatile composition of its magma source region. The results suggest that volcanic gases will normally lie in the “neutral” range of oxygen fugacity, near that of the quartz‐fayalite‐magnetite buffer. These gases are predominately H2O with minor CO2, CO, H2, and CH4.

Adsorption behaviour of dihydrogen phosphate ions on mercury from constant ionic strength solutions

The adsorption behaviour of H 2PO − 4 anions on mercury has previously been analysed from capacitance-potential relations at the interface of mercury with KH 2PO 4.It is not possible to determine unambiguously the adsorption characteristics of H 2PO − 4 ions from single salt solution experiments because of the possible existence of a layer of water molecules between the electrode and the adsorbed ions. In this work, the adsorption behaviour of H 2PO − 4 ions on mercury is analysed from experimental measurements of the capacitance as a function of potential at the interface of mercury with constant ionic strength solutions of compositions x M KH 2PO 4 + (1 − x) M KF. It is shown that the calculated amounts of adsorbed ions do not depend on the position of these ions relative to the solvent molecules. The double layer parameters were calculated taking into account the variations of activity coefficients of KH 2PO 4 and KF with solution composition. In constant ionic strength solutions, the plot of adsorbed charge vs electrode charge exhibits a maximum due to competition between the adsorbed H 2PO − 4 anions with the solvent or other ionic species. This result is shown to be important in determining the properties of the double layer characteristics in the presence of adsorbed H 2PO − 4 ions.

Medium composition dependence of lead(II) complexation by chloride ion

Stepwise formation constants of PbCl (super +) , PbCl (super degrees ) 2 , and PbCl (super -) 3 in aqueous HCl-HClO 4 , NaCl-NaClO 4 , MgCl 2 , and CaCl 2 media exhibit systematic medium composition effects at constant ionic strength. Cationic composition of test media influences the affinity of chloride ions for trace metals in a quantitatively predictable manner. Medium composition effects for both Pb(II) and Cu(II) complexation can be described in terms of chloride activity coefficient variation at constant ionic strength. Lead chloride formation constant results at ionic strengths up to one molar are quantitatively examined in terms of chloride ion pairing.--Modified journal abstract.

Atmospheric equilibrium model of sulfate and nitrate aerosols

Given local rates of production of gas-phase sulfate and nitrate, ammonia concentration, relative humidity and temperature, a model is presented that enables calculation of the quantity of sulfate/nitrate/ammonium/water aerosol, its precise chemical composition and physical state. The model is based on a complete thermodynamic chemical and phase equilibrium calculation for the sulfate/nitrate/ammonium system. Detailed simulations of sulfate/nitrate/ammonium aerosol evolution are presented, and recent ambient data from Tanner are interpreted. Some new results on temperature variation of activity coefficients are presented in the Appendix.

ChemInform Abstract: SPECIFIC ADSORPTION OF SULFAMATE IONS AT THE MERCURY/SOLUTION INTERFACE

AbstractDie Adsorption von SO3NH;‐Ionen an Hg‐Elektroden wurde mit Lösungen der Zusammensetzung xM NH4 SO3 NH2 + (1‐x)M NH4 Fdurch Messung der Doppelschicht‐Kapazität untersucht (12 Lösungen konstanter Ionenstärke mit x von 0 bis 1).

Specific adsorption of sulfamate ions at the mercury/solution interface

The adsorption of sulfamate ions on mercury electrodes has been studied by measuring the double layer capacity in constant ionic strength solutions of composition xM NH4SO3NH2 + (1−x)M NH4F. It was found that sulfamate ions are weakly adsorbed on mercury, the amount adsorbed being significant only for x > 0.1 at positive charges on the electrode. Because of this, the properties of the inner layer were found to be strongly dependent on the adsorbed water molecules and the structure of the diffuse layer. It was determined that the adsorption of sulfamate ions can be described by an isotherm based on the electrostatic model of the double layer. The possible effects of the activity coefficient variation with solution composition are discussed.

Premiers résultats sur la solubilité de la silice amorphe dans les pores de petite taille. Variation du coefficient d'activité de la silice en fonction de l'activité de l'eau

In the small size pores, amorphous silica is less soluble than in the pores of larger size. Within the siliceous materials, the following relationships are observed : the larger the water extracting pressure, the smaller the size of the pores concerned, the smaller the water activity, the smaller the silica solubility. Variations of activity coefficients of aqueous silica are calculated as a function of water activity.

Factors affecting the retention of polycyclic aromatic hydrocarbons in gas chromatography

The retention index of a planar polynuclear aromatic hydrocarbon on the GC phases OV-101, SE-52, and OV-17 is strictly related only to the boiling point, and less closely to the relative molecular mass. The very approximates relation with connectivity index ins only a consequence of the latter. On a nematic lqiuid crystal phase, a variation of activity coefficient, expressed in terms of a shape factor, also influences the retention of PAH.

Isothermal binary and ternary diffusion in the system (C2H5)4 NBr–KBr–H2O

Isothermal free diffusion in the binary systems KBr–H2O, (C2H5)4NBr–H2O and in the ternary system (C2H5)4NBr–KBr–H2O has been studied at various compositions with a precision single-lens Gouy interferometer. For the binary systems, the observed diffusion coefficients have been compared with those of similar compounds and, in the case of (C2H5)4NBr, have been compared with theoretical values predicted from activity coefficient behaviour for which a parameter-fitting least-squares approach has been used to determine the activity coefficient variation with concentration. Ternary coefficients have been analysed qualitatively in terms of ionic attractions in the solution and have been compared with the binary coefficients at similar concentrations. The Onsager Reciprocal Relation has been verified for one composition of the ternary system, but the calculations differ from previous tests in that the more versatile Scatchard approach to multicomponent solutions has been used rather than Harned's rule.