Homogeneous Equilibria Research Articles

Temperature and concentration dependence of homogeneous chemical equilibria

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTTemperature and concentration dependence of homogeneous chemical equilibriaC. Brent Smith Cite this: J. Chem. Educ. 1988, 65, 11, 965Publication Date (Print):November 1, 1988Publication History Received3 August 2009Published online1 November 1988Published inissue 1 November 1988https://doi.org/10.1021/ed065p965RIGHTS & PERMISSIONSArticle Views95Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (2 MB) Get e-Alerts Get e-Alerts

Physical and chemical controls (fO2,T,pH) of the opposite behaviour of U and Sn-W as examplified by hydrothermal deposits in France and Great-Britain, and solubility data

The aim of this paper is to determine the physical and chemical parameters which control the opposite behaviour of uranium and tin-tungsten between 300° and 500 °C. In uranium deposits, fO2 and fS2 of mineralizing fluids are higher than values fixed by the pyrite-hematite-magnetite triple point, as shown by uraninite-hematite and/or pyrite mineral association. The stability of quartz-K feldspar-muscovite paragenesis in the wall-rocks of hydrothermal U deposits indicates weakly acid pH. By contrast, in the Sn-W occurrences from the French Southern Massif Central, the fO2 of mineralizing fluids is between Ni-NiO and Q-F-M buffers as shown by CO2-CH4-H2O-NaCl bearing fluid inclusions. The pH of these fluids is weakly acid to weakly basic as shown by the stability of muscovite in presence or absence of quartz and/or feldspar. Sn-W mineralizing fluids from Cornwall are by contrast purely aqueous and acid, as indicated by the mineral assemblage muscovite-quartz which is typical of greisens. Experimental data on UO2, SnO2, FeWO4, CaWO4 solubility and metal species in fluids show that fO2 > H-M are required for uranium transport whereas fO2 ≤ Ni-NiO favours Sn transport. The fluid oxidation state has no direct influence on the transport and deposition of tungsten. The fO2 control on the hydrothermal transport properties of these three metals is related on the one hand to the fluid and rock composition, and on the other hand to the minimal 320 °C temperature required for homogeneous equilibria in the C-O-H system to control the oxidation state at low values. At high temperatures, Sn, Fe and Ca chloride complexes are more stable than carbonate and phosphate uranium complexes ; this is attributable to their structure and to the dielectric content of the fluid. The presence of dissolved gases at high concentration, which are produced by devolatilization reactions at high temperatures, is emphasized since they lower the dielectric constant of the fluid which enhances the stability of chloride complexes. All these results show that temperature and fO2 account for the opposite behaviour of uranium and tin-tungsten in hydrothermal systems between 300° to 500 °C.

Oxidation-reduction relations in basic magma: a case for homogeneous equilibria

Published analyses of Fe 2O 3 and FeO in basaltic glassy lavas allow their equilibrium oxygen fugacities to be calculated. These values are plotted relative to NNO (nickel-nickel oxide oxygen buffer) at the same temperature (1200°C), so that the relative f O 2 , ΔNNO, becomes essentially independent of temperature. For 61 submarine tholeiitic lavas from the Pacific, ΔNNO lies between FMQ (fayalite-magnetite-quartz oxygen buffer) and NNO, whereas 95 glassy lavas from the Atlantic show a greater range, and can be more oxidised than NNO; in both oceans, alkali types have higher ΔNNO. In contrast, subaerial glassy lavas, dominated by those of Kilauea, are more reduced than the Pacific submarine lavas, and cluster between FMQ and W-Mt (wüstite-magnetite oxygen buffer). This subaerial reduction, first recognised by Anderson and Wright [1], is caused by SO 2 degassing. The iron redox state of Kilauea subaerial and submarine glassy lavas can vary considerably, but as found in other submarine lavas, their sulphur redox state varies more. We conclude that the iron and sulphur redox systems of tholeiitic liquids, in combination, could act as a self-regulating internal oxygen reservoir, constraining a cooling liquid to the constant relative oxygen fugacity observed in well characterised liquid lines of descent. A second experimentally verifiable hypothesis is offered, namely that Fe 2O 3 in natural silicate liquids is very compressible. Thus magmas equilibrating at great depth (∼30–50 kbar) with a solid mantle assemblage of low relative f O 2 (intrinsic measurements) would have a higher iron redox state than those equilibrating with shallow mantle sources at the same relative f O s . The redox states of basic magmas, ascending isochemically and involving Fe and S, could therefore be a depth indicator to their source regions.

Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems

A time-space continuum model for transport of hydrothermal fluids in porous media is presented which provides for simultaneous, reversible and irreversible chemical reactions involving liquids, gases and minerals. Homogeneous and heterogeneous reactions are incorporated in the model in a similar fashion through source/sink terms added to the continuity equation. The model provides for moving reaction fronts through surfaces of discontinuity across which occur jump discontinuities in the various field variables satisfying generalized Rankine-Hugoniot relations. Reversible reactions including aqueous complexing, oxidation-reduction reactions, mineral precipitation and dissolution reactions and adsorption are explicitly accounted for by imposing chemical equilibrium constraints in the form of mass action equations on the transport equations. This is facilitated by partitioning the reacting species into primary and secondary species corresponding to a particular representation of the stoichiometric reaction matrix referred to as the canonical representation. The transport equations for the primary species combined with homogeneous and heterogeneous equilibria result in a system of coupled, nonlinear algebraic/partial differential equations which completely describe the evolution of the system in time. Spatially separated phase assemblages are accommodated in the model by altering the set of independent variables across surfaces of discontinuity. Constitutive relations for the fluid flux corresponding to primary species are obtained describing transport of both neutral and charged species by advection, dispersion and diffusion. Numerical implementation of the transport equations is considered and both explicit and implicit finite difference algorithms are discussed. Analytical expressions for the change in porosity and permeability with time are obtained for an assemblage of minerals reacting reversibly with a hydrothermal fluid under quasi-steady state conditions. Fluid flow is described by Darcy's law employing a phenomenological expression relating permeability and porosity. Finally an expression for the local retardation factor of solute species is derived for the case of advective transport in a single spatial dimension which accounts for the effects of homogeneous and heterogeneous equilibria including adsorption on the rate of advance of a reaction front. The condition for the formation of shock waves is given.

ジメチルスルホキシド中におけるビス（β‐ジケトナト）コバルト（ＩＩ）錯体の溶液内平衡と電気化学的挙動

Homogeneous chemical equilibria and electrochemical behaviors of three bis(β-diketonato)cobalt(II) complexes, viz., [Co(hfac)2], [Co(tfac)2] and [Co(acac)2], in di methyl sulfoxide (DNISO) were studied by means of the conductivity flicl electronic spectral measur ements, poktrography, and cyclic voltaminctry with a platinum electrode; where hfac tfac- and acacrepresent the enolate anions of hexafluoroacetylacetone, trifluoroacetylacetone and acetylacetone, respectively. Tetrabutylammonium Perchlorate (TBAP) of 0.05 mol⋅dm-3 in the concentration was used as the supporting electrolyte fur voltammetric measurements. It was found that these complexes were involved in the following chemical equilibria in the solution:In DC polarography, the first wave of [Co(hfac)2] was presumed to be due to the two-electron reduction of CO2+, [Co(hfac)]+ and [Co(hfac)2], and the wave of [Co(acac)2] to that of monomeric and polymeric bis-comlexes. Furthermore, two waves of [Co(tfac)2] corresponded to the two-electron reduction of [Co(tfac)]+ and [Co(tfac)2], respectively; where the first wave included the kinetic current due to the preceding reaction.

Vapour growth mechanism of silicon layers by dichlorosilane decomposition

This work aims to calculate the growth rates of epitaxial and polycrystalline Si from the SiH 2Cl 2-H 2 system by using a simple kinetic model for the heterogeneous reaction. The growth process assumes reaction sequences which differ according to the high, low or intermediate value of the substrate temperature. The kinetic analysis is carried out by including the homogeneous and heterogeneous equilibria established in the system and by using the steady-state approximation. According to the rate equations found, which are in good agreement with the experimental data, the Si growth rate is proportional to the SiH 2Cl 2 concentration in the gas phase, irrespective of temperature, and depends on P -1/2 H 2 or P -1 H 2 for different pressuress of the system. In the homogeneous mechanism, the Si growth rate depends only on the SiH 2Cl 2 concentration.

Mechanism of the chemical vapour deposition of Si 3N 4 films prepared from SiH 2Cl 2 and NH 3 under kinetically controlled conditions

The deposition rate of Si 3N 4 films prepared from an SiH 2Cl 2-NH 3-N 2 system is calculated using a kinetic model of the heterogeneous reaction. The deposition process takes place by three different reaction sequences, depending on whether the substrate temperature is high, low or intermediate. The kinetic analysis is carried out by including the homogeneous and heterogeneous equilibria established in the system and using the steady state approximation.

Compilation and Evaluation of Solubility Data in the Mercury (I) Chloride‐Water System

The more than one dozen papers dealing with the solubility of mercury (1) chloride in water or in aqueous chloride solutions have been compiled in the format set by the IUPAC Solubility Data Project, and have been evaluated. Mercury (I) chloride dissolves in water, forming the following species: He(OH)2, HgCl2, HgOH+, HgOH+, HgCl+, Hg2+2, and Hg2OH− in addition to H+ and Cl−. In excess chloride solutions it dissolves to give, mainly, HgCl−3 and HgCl2−4. Thus, many homogeneous equilibria have to be considered beside the two heterogeneous ones; Hg2Cl2(s)=Hg2+2(aq)+2Cl−(aq) and Hg2+2(aq)=Hg2+(aq)+ Hg(l), of which K°s0 and (K°r)−1, respectively, are the equilibrium constants. The papers in which the total solubility (sum of all the mercury containing aqueous species) and the solubility product (derived from e.m.f. data) are reported do not give as accurate and reliable quantities as are obtained from the appropriate standard electrode potentials. The following values are recommended as valid at 298.15 K: log ...

Energy anisotropy instabilities in high-beta plasmas: A comparison of various kinetic and fluid descriptions

The Vlasov-fluid model is employed to study linear perturbations of a particular class of magnetized, infinite, homogeneous equilibria. The dispersion properties of waves and anisotropy driven instabilities with frequencies at or below the ion cyclotron frequency are used to compare and contrast the Vlasov-fluid model with other well-known models of a high-beta plasma. Although the various models differ widely in physical content and in the manner in which the dispersion equation is derived, the results obtained from any one of them agree with appropriate limits of all the others. The results illuminate the nature of the anisotropy driven fluid-like instabilities and illustrate their connection to kinetic descriptions that include dispersion due to finite gyroradius effects. For the simple equilibria that have been considered, no reason has been found not to regard the Vlasov-fluid model as an acceptable model of a high-beta plasma.

Gasförmige Komplexe zwischen Kobaltchlorid und Indiumchlorid

Gaseous Complexes between Cobaltchloride and IndiumchlorideThe equilibria (1) and (2): were investigated by optical spectroscopy and by vapour pressure measurements using the transpiration method: Together with thermodynamic data from the literature the results obtained allow a complete description of all heterogeneous solid/gas as well as the homogeneous equilibria in the gas phase of the system CoCl2/InCl3 in the temperature range 500–800°.

The configurational entropies of Ca2MgSi2O7-Ca2SiAl2O7 melilites and related minerals

Equations for the configurational entropy and homogeneous equilibria in Ca2MgSi2O7-Ca2SiAl2O7 melilites are derived for a site constraint that does not permit Mg on the smaller T2 tetrahedral sites. This constraint leads to one ordering parameter and one composition parameter. The maximum configurational entropy for perfectly ordered crystalline solutions is 3.795 cal K−1 mol−1, corresponding to the structural formula Ca2(Mg0.33Al0.67) (Si0.67Al0.33)2O7 and not the equimolar composition Ca2(Mg0.5Al0.5)(Si0.75Al0.25)2O7. Similarly, the configuration Ca2(Si0.33Al0.67)(Si0.33Al0.67)2O7 has the maximum entropy for the gehlenite end-member composition. The tabulated entropy of end-member gehlenite at 298.15 K must be corrected by at least 2Rln2, which corresponds to a substantial correction to its Gibbs energy at high temperature. The same corrections are applicable to other minerals having two crystallographically distinct sites in a 2∶1 ratio and where the same configurational entropy equation applies: MgFe2O4 (magnesioferrite), NiFe2O4 (trevorite), TiFe2O4 (ulvospinel), TiMg2O4, TiZn2O4, CuFe2O4, and TiFe2O5 (pseudobrookite) inasmuch as these substances prefer the same inverse ordered state as gehlenite at low temperatures. The effects of the ideal enthalpy and entropy on temperatures of homogeneous equilibria in gehlenite and MgTi2O5 are evaluated. Geological-thermometer phase diagrams of the long-range ordering parameter plotted against temperature have a sigmoidal shape for these minerals owing to the fact that this type of disordering is non-convergent.

Statistical thermodynamics of collisionless plasma. II. Stability theory of inhomogeneous systems

For pt. I see ibid., vol. 14, no. 5, 427. The statistical model developed in Part I is applied to the discussion of the stability of inhomogeneous Vlasov equilibria. The existence of instability is expressed by the general condition integral I(x)( theta (x)- phi 0)dV>0 provided a certain class of variations compatible with the physical constraints imposed on the system does exist. In this criterion I(x) is the information variable depending on the physical system under consideration, phi (x) the corresponding potential, and phi 0 its spatial average. When I(x) is the charge density the criterion can be applied in order to show the instability of the Bernstein, Greene and Kruskal solutions. It is also shown, by means of the entropy principle, that the isolated inhomogeneous collisionless systems evolve towards more homogeneous equilibria, associated with a higher entropy, by transforming their collective energy into the energy of the random individual fluctuations. Moreover, nearly homogeneous but electrostatically unstable collisionless plasmas prove to evolve towards the marginal state of the stable equilibrium (which is a state of maximum entropy for the collisionless systems), while an electrostatic quasi-static marginally unstable mode with long wavelength appears in the system.

Diagenesis, Chemical Sediments, and the Mixing of Natural Waters

ABSTRACT Mixing of aqueous solutions is an important procedure in chemical laboratories. The chemical effects of mixing in the laboratory include changes in the concentration and electrical properties of a solution, shifts in homogeneous equilibria, and precipitation or dissolution of a solid phase. Similar chemical effects can be expected to occur in nature as a result of the mixing of natural waters, and in some instances these may result in diagenesis. A simple classification yields 14 distinct categories of natural waters with 91 possible combinations of mixing of pairs of such waters. Examples are known of the precipitation of hydroxides and carbonates as a result of the mixing of chemically dissimilar surface waters. Documented examples of subsurface mixing and diagenesis are few. However, because of the great variety of chemically dissimilar subsurface waters, plus the existence of several types of potential fields which cause the movement of subsurface waters, mixing and diagenesis in the subsurface may be a common and significant geologic process. The solubility of rock forming minerals is a non-linear function of such independent variables as salinity, partial pressure of gases, temperature, and so on. The dissolution of calcium carbonate as a result of Mischungskorrosion can be viewed in the light of the non-linearity of the solubility curve. Experimental data on the solubility of calcium carbonate and calcium sulfate as a function of added salts indicate that mixing of solutions which differ only in their content of dissolved electrolytes may cause either the precipitation or dissolution of the rock-forming minerals. Other common rock-forming minerals, with the exception of quartz at low temperatures, should exhibit similar behavior.

Keto-enol tautomerism of ethyl acetoacetate: Experiment in homogeneous equilibrium

The tautomerism of ethyl acetoacetate provides the basis for a satisfactory experiment illustrating homogeneous equilibria in liquid solution.

Activity Coefficients of Gases... Application to Calculation of Effect of Pressure on Homogeneous Chemical Equilibria and to Calculation of Integral Joule-Thomson Effects

Activity Coefficients of Gases... Application to Calculation of Effect of Pressure on Homogeneous Chemical Equilibria and to Calculation of Integral Joule-Thomson Effects

On the graphical representation of homogeneous chemical equilibria. I. Systems with three kinds of molecules

On the graphical representation of homogeneous chemical equilibria. I. Systems with three kinds of molecules

Homogeneous equilibria in magmatic melts and their bearing on the processes of igneous rock-formation

Homogeneous equilibria in magmatic melts and their bearing on the processes of igneous rock-formation