Molecular physics of equilibrium gases : a handbook for engineers /

Includes bibliographical references and index.

Nonequilibrium expansions of air with coupled chemical reactions

Caption title.

Equilibrium diagrams for minerals at low temperature and pressure.

Mode of access: Internet.

Ultracentrifugal studies of the effect of molecular crowding by trimethylamine N-oxide on the self-association of muscle glycogen phosphorylase b

The suitability of sedimentation equilibrium for characterizing the self-association of muscle glycogen phosphorylase b has been reappraised. Whereas sedimentation equilibrium distributions for phosphorylase b in 40 mM Hepes buffer (pH 6.8) supplemented with 1 mM AMP signify a lack of chemical equilibrium attainment, those in buffer supplemented additionally with potassium sulfate conform with the requirements of a dimerizing system in chemical as we:ll as sedimentation equilibrium. Because the rate of attainment of chemical equilibrium under the former conditions is sufficiently slow to allow resolution of the dimeric and tetrameric enzyme species by sedimentation velocity, this procedure has been used to examine the effects of thermodynamic nonideality arising from molecular crowding try trimethylamine N-oxide on the self-association behaviour of phosphorylase b. In those terms the marginally enhanced extent of phosphorylase b self-association observed in the presence of high concentrations of the cosolute is taken to imply that the effects of thermodynamic nonideality on the dimer-tetramer equilibrium are being countered by those displacing the T reversible arrow R isomerization equilibrium for dimer towards the smaller, nonassociating T state. Because the R state is the enzymically active form, an inhibitory effect is the predicted consequence of molecular crowding by high concentrations of unrelated solutes. Thermodynamic nonideality thus provides an alternative explanation for the inhibitory effects of high concentrations of glycerol, sucrose and ethylene glycol on phosphorylase b activity, phenomena that have been attributed to extremely weak interaction of these cryoprotectants with the T state of the enzyme.

Mineral chemistry, whole-rock compositions, and petrogenesis of leg 176 gabbros: Data and discussion

We report mineral chemistry, whole-rock major element compositions, and trace element analyses on Hole 735B samples drilled and selected during Leg 176. We discuss these data, together with Leg 176 shipboard data and Leg 118 sample data from the literature, in terms of primary igneous petrogenesis. Despite mineral compositional variation in a given sample, major constituent minerals in Hole 735B gabbroic rocks display good chemical equilibrium as shown by significant correlations among Mg# (= Mg/[Mg+Fe2+]) of olivine, clinopyroxene, and orthopyroxene and An (=Ca/[Ca+Na]) of plagioclase. This indicates that the mineral assemblages olivine + plagioclase in troctolite, plagioclase + clinopyroxene in gabbro, plagioclases + clinopyroxene + olivine in olivine gabbro, and plagioclase + clinopyroxene + olivine + orthopyroxene in gabbronorite, and so on, have all coprecipitated from their respective parental melts. Fe-Ti oxides (ilmenite and titanomagnetite), which are ubiquitous in most of these rocks, are not in chemical equilibrium with olivine, clinopyroxene, and plagioclase, but precipitated later at lower temperatures. Disseminated oxides in some samples may have precipitated from trapped Fe-Ti–rich melts. Oxides that concentrate along shear bands/zones may mark zones of melt coalescence/transport expelled from the cumulate sequence as a result of compaction or filter pressing. Bulk Hole 735B is of cumulate composition. The most primitive olivine, with Fo = 0.842, in Hole 735B suggests that the most primitive melt parental to Hole 735B lithologies must have Mg# ≤ 0.637, which is significantly less than Mg# = 0.714 of bulk Hole 735B.

Melt topology and chemistry during partial melting in contact aureoles : an experimental study and field example

This study was initiated to investigate partial melting within the high-grade metamorphic rocks beneath the Little Cottonwood contact aureole (Utah, USA), in order to understand the melt generation, melt migration, and geometry of initial melt distribution on grain scale during crustal anatexis. The emplacement of the Little Cottonwood stock produced a contact aureole in the pelitic host rocks of the Big Cottonwood formation (BC). Metamorphic isogrades in pelitic rocks range form biotite to 2nd sillimanite grade as a function of distance from the contact. Migmatites are restricted to the highest grade and resulted form partial melting of the BC formation rocks. First melt was produced by a combined muscovite/biotite dehydration reaction in the sillimanite + k-feldspar stability field. Melt extraction from the pelites resulted in restites (magnetite + cordierite + alumosilicate ± biotite) surrounded by feldspar enriched quartzite zones. This texture is the result of gradual infiltration of partial melts into the quartzite. Larger, discrete melt accumulation occurred in extensional or transpressional domains such as boudin necks, veins, and ductile shear zones. Melt composition are Si02- rich, crystallized as pegmatites, and apparently were very mobile. They were able to infiltrate the quartzite pervaisivly. These melts are similar in composition to first melts produced in the hydrothermal partial melt experiments at 2kbar between 700 - 800°C on fine grained high metamorphic rocks (andalusite-cordierited-biotite-zone) of the BC formation. The experimental melts are water rich and in disequilibrium with the melting rock. Initial melt composition is heterogeneous for short run duration, reflective a lack of chemical equilibrium between individual melt pools. Rock core scale heterogeneity decreased with time indicating partial homogenization of melt compositions. A simultaneous shift of melt composition to higher silica content with time was observed. The silica content of the melt increased due to local melt/mineral reactions. Melt textures indicate that reactive melt transport is most efficient along grain boundaries rimmed by dissimilar grains. Melt heterogeneity resulted in chemical potential gradients which are major driving forces for initial melt migration and govern melt distribution during initial melting. An additional subject of the thesis is the crystal size distributions of opaque minerals in a fine-grained, high-grade meta-pelite of the Big Cottonwood which were obtained from 3D X-ray tomography (uCT) and 2D thin section analysis. µCT delivers accurate size distributions within a restricted range (~ a factor of 20 in size in a single 3D image), while the absolute number of crystals is difficult to obtain from these sparsely distributed, small crystals on the basis of 2D images. Crystal size distributions obtained from both methods are otherwise similar. - Ce travail de recherche a été entrepris dans le but d'étudier les processus de fusion partielle dans les roches fortement métamorphiques de l'auréole de contact de Little Cottonwood (Utah, USA) et ceci afin de comprendre la génération de liquide de fusion, la migration de ces liquides et la géométrie de la distribution initiale des liquides de fusion à l'échelle du grain durant l'anatexie de la croûte. L'emplacement du petit massif intrusif de Little Cottonwood a produit une auréole de contact dans les roches pélitiques encaissantes appartenant à la Foimation du Big Cottonwood (BC). Les isogrades métamorphiques dans les roches pélitiques varient de l'isograde de la biotite à la deuxième isograde de la sillimanite en fonction de la distance par rapport au massif intrusif. Les migmatites sont restreintes aux zones montrant le plus haut degré métamorphique et résultent de la fusion partielle des roches de la Formation de BC. Le premier liquide de fusion a été produit par la réaction de déshydratation combinée de la muscovite et de la biotite dans le champ de stabilité du feldspath potassique Pt de la sillimanite. L'extraction du liquide de fusion des pélites forme des restites (magnétites + cordiérite + aluminosilicate ± biotite) entourées par des zones de quartzites enrichies en feldspath. Cette texture est le résultat de l'infiltration graduelle du liquide de fusion partielle dans les quartzites. Des accumulations distinctes et plus larges de liquide de fusion ont lieu dans des domaines d'extension ou de transpression tels que les boudins, les veines, et les zones de cisaillement ductile. La composition des liquides de fusion est similaire à celle des liquides pegmatoïdes, et ces liquides sont apparemment très mobiles et capables d'infiltrer les quartzites. Ces liquides de fusion ont la même composition que les premiers liquides produits dans les expériences hydrotheunales de fusion partielle à 2kbar et entre 700-800° C sur les roches finement grenues et hautement métamorphiques (andalousite-cordiérite-biotite zone) de la Formation de BC. Les liquides de fusion obtenus expérimentalement sont riches en eau et sont en déséquilibre avec la roche en fusion. La composition initiale des liquides de fusion est hétérogène pour les expériences de courte durée et reflète l'absence d'équilibre chimique entre les différentes zones d'accumulation des liquides de fusion. L'hétérogénéité à l'échelle du noyau s'estompe avec le temps et témoigne de l'homogénéisation de la composition des liquides de fusion. Par ailleurs, on observe parallèlement un décalage de la composition des liquides vers des compositions plus riches en silice au cours du temps. Le contenu en silice des liquides de fusion évolue vers un liquide pegmatitique en raison des réactions liquides/minéraux. Les textures des liquides de fusion indiquent que le transport des liquides est plus efficace le long des bordures de grains bordés par des grains différents. Aucun changement apparent du volume total n'est visible. L'hétérogénéité des liquides s'accompagne d'un gradient de potentiel chimique qui sert de moteur principal à la migration des liquides et à la distribution des liquides durant la fusion. Un sujet complémentaire de ce travail de thèse réside dans l'étude de la distribution de la taille des cristaux opaques dans les pélites finement grenues et fortement métamorphiques de la Formation de Big Cottonwood. Les distributions de taille ont été obtenues suite à l'analyse d'images 3D acquise par tomographie ainsi que par analyse de lames minces. La microtomographie par rayon X fournit une distribution de taille précise sur une marge restreinte (- un facteur de taille 20 dans une seule image 3D), alors que le nombre absolu de cristaux est difficile à obtenir sur la base d'image 2D en raison de la petite taille et de la faible abondance de ces cristaux. Les distributions de taille obtenues par les deux méthodes sont sinon similaire. Abstact: Chemical differentiation of the primitive Earth was due to melting and separation of melts. Today, melt generation and emplacement is still the dominant process for the growth of the crust. Most granite formation is due to partial melting of the lower crust, followed by transport of magma through the crust to the shallow crust where it is emplaced. Partial melting and melt segregation are essential steps before such a granitic magma can ascent through the crust. The chemistry and physics of partial melting and segregation is complex. Hence detailed studies, in which field observations yield critical information that can be compared to experimental observations, are crucial to the understanding of these fundamental processes that lead and are leading to the chemical stratification of the Earth. The research presented in this thesis is a combined field and experimental study of partial melting of high-grade meta-pelitic rocks of the Little Cottonwood contact aureole (Utah, USA). Contact metamorphic rocks are ideal for textural studies of melt generation, since the relatively short times of the metamorphic event prevents much of the recrystallization which plagues textural studies of lower crustal rocks. The purpose of the study is to characterize melt generation, identify melting reactions, and to constrain melt formation, segregation and migration mechanisms. In parallel an experimental study was undertaken to investigate melt in the high grade meta pelitic rocks, to confirm melt composition, and to compare textures of the partial molten rock cores in the absence of deformation. Results show that a pegmatoidal melt is produced by partial melting of the pelitic rocks. This melt is highly mobile. It is capable of pervasive infiltration of the adjacent quartzite. Infiltration results in rounded quartz grains bordered by a thin feldspar rim. Using computed micro X-ray tomography these melt networks can be imaged. The infiltrated melt leads to rheological weakening and to a decompaction of the solid quartzite. Such decompaction can explain the recent discovery of abundant xenocrysts in many magmas, since it favors the isolation of mineral grains. Pervasive infiltration is apparently strongly influenced by melt viscosity and melt-crystal wetting behavior, both of which depend on the water content of melt and the temperature. In all experiments the first melt is produced on grain boundaries, dominantly by the local minerals. Grain scale heterogeneity of a melting rock leads thus to chemical concentration gradients in the melt, which are the driving force for initial melt migration. Pervasive melt films along grain boundaries leading to an interconnected network are immediately established. The initial chemical heterogeneities in the melt diminish with time. Résumé large public: La différenciation chimique de la Terre primitive est la conséquence de la fusion des roches et de la séparation des liquides qui en résultent. Aujourd'hui, la production de liquide magmatique est toujours le mécanisme dominant pour la croissance de la croûte terrestre. Ainsi la formation de la plupart des granites est un processus qui implique la production de magma par fusion partielle de la croûte inférieure, la migration de ces magmas à travers la croûte et finalement son emplacement dans les niveaux superficielle de la croûte terrestre. Au cours de cette évolution, les processus de fusion partielle et de ségrégation sont des étapes indispensables à l'ascension des granites à travers la croûte. Les conditions physico-chimiques nécessaires à la fusion partielle et à l'extraction de ces liquides sont complexes. C'est pourquoi des études détaillées des processus de fusion partielle sont cruciales pour la compréhension de ces mécanismes fondamentaux responsables de la stratification chimique de la Terre. Parmi ces études, les observations de terrain apportent notamment des informations déterminantes qui peuvent être comparées aux données expérimentales. Le travail de recherche présenté dans ce mémoire de thèse associe études de terrain et données expérimentales sur la fusion partielle des roches pélitiques de haut degré métamorphiques provenant de l'auréole de contact de Little Cottonwood (Utah, USA). Les roches du métamorphisme de contact sont idéales pour l'étude de la folination de liquide de fusion. En effet, la durée relativement courte de ce type d'événement métamorphique prévient en grande partie la recristallisation qui perturbe les études de texture des roches dans la croûte inférieure. Le but de cette étude est de caractériser la génération des liquides de fusion, d'identifier les réactions responsables de la fusion de ces roches et de contraindre la formation de ces liquides et leur mécanisme de ségrégation et de migration. Parallèlement, des travaux expérimentaux ont été entrepris pour reproduire la fusion partielle de ces roches en laboratoire. Cette étude a été effectuée dans le but de confirmer la composition chimique des liquides, et de comparer les textures obtenues en l'absence de déformation. Les résultats montrent qu'un liquide de fusion pegmatoïde est produit par fusion partielle des roches pélitiques. La grande mobilité de ce liquide permet une infiltration pénétrative dans les quarzites. Ces infiltrations se manifestent par des grains de quartz arrondis entourés par une fine bordure de feldspath. L'utilisation de la tomography à rayons X a permis d'obtenir des images de ce réseau de liquide de fusion. L'infiltration de liquide de fusion entraîne un affaiblissement de la rhéologie de la roche ainsi qu'une décompaction des quartzites massifs. Une telle décompaction peut expliquer la découverte récente d'abondants xénocristaux dans beaucoup de magmas, puisque elle favorise l'isolation des minéraux. L'infiltration pénétrative est apparemment fortement influencée par la viscosité du fluide de fusion et le comportement de la tension superficielle entre les cristaux et le liquide, les deux étant dépendant du contenu en eau dans le liquide de fusion et de la température. Dans toutes les expériences, le premier liquide est produit sur les bordures de grains, principalement par les minéraux locaux. L'hétérogénéité à l'échelle des grains d'une roche en fusion conduit donc à un gradient de concentration chimique dans le liquide, qui sert de moteur à l'initiation de la migration du liquide. Des fines couches de liquide de fusion le long de bordures de grains formant un réseau enchevêtré s'établit immédiatement. Les hétérogénéités chimiques initiales dans le liquide s'estompent avec le temps.

Fick's law adapted to cationic diffusion in a semi-infinite solid: application to spinel megacrystals

In alkaline lavas, the chemical zoning of megacrystals of spinel is due to the cationic exchange between the latter and the host lava. The application of Fick's law to cationic diffusion profiles allows to calculate the time these crystals have stayed in the lava. Those which are in a chemical equilibrium were in contact with the lava during 20 to 30 days, whereas megacrystals lacking this equilibrium were in contact only for 3 or 4 days. The duration of the rise of an ultrabasic nodule in the volcanic chimney was calculated by applying Stokes' law.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Surface Complexation Modeling in Variable Charge Soils: Charge Characterization by Potentiometric Titration

ABSTRACT Intrinsic equilibrium constants of 17 representative Brazilian Oxisols were estimated from potentiometric titration measuring the adsorption of H+ and OH− on amphoteric surfaces in suspensions of varying ionic strength. Equilibrium constants were fitted to two surface complexation models: diffuse layer and constant capacitance. The former was fitted by calculating total site concentration from curve fitting estimates and pH-extrapolation of the intrinsic equilibrium constants to the PZNPC (hand calculation), considering one and two reactive sites, and by the FITEQL software. The latter was fitted only by FITEQL, with one reactive site. Soil chemical and physical properties were correlated to the intrinsic equilibrium constants. Both surface complexation models satisfactorily fit our experimental data, but for results at low ionic strength, optimization did not converge in FITEQL. Data were incorporated in Visual MINTEQ and they provide a modeling system that can predict protonation-dissociation reactions in the soil surface under changing environmental conditions.

Surface Complexation Modeling in Variable Charge Soils: Prediction of Cadmium Adsorption

ABSTRACT Intrinsic equilibrium constants for 22 representative Brazilian Oxisols were estimated from a cadmium adsorption experiment. Equilibrium constants were fitted to two surface complexation models: diffuse layer and constant capacitance. Intrinsic equilibrium constants were optimized by FITEQL and by hand calculation using Visual MINTEQ in sweep mode, and Excel spreadsheets. Data from both models were incorporated into Visual MINTEQ. Constants estimated by FITEQL and incorporated in Visual MINTEQ software failed to predict observed data accurately. However, FITEQL raw output data rendered good results when predicted values were directly compared with observed values, instead of incorporating the estimated constants into Visual MINTEQ. Intrinsic equilibrium constants optimized by hand calculation and incorporated in Visual MINTEQ reliably predicted Cd adsorption reactions on soil surfaces under changing environmental conditions.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Algunes reflexions al voltant del tractament de l'equilibri químic en el batxillerat

En aquest escrit es recorda el tractament que rebia l"equilibri químic en el batxillerat que va estudiar l"autor de l"article i es compara amb el què es dóna en el batxillerat actual. Es palesa que en el batxillerat d"avui dia, l"equilibri químic rep un tractament força més extens i amb una major càrrega conceptual que el d"aquells anys. Aquest fet pot portar, si la matèria no es tracta amb el temps requerit, a que els estudiants d"avui dia no acabin d"entendre massa bé el significat i la utilitat de les magnituds i constants fisicoquímiques introduïdes i, a la vegada, es dificulti que puguin assolir completament d"altres objectius més elementals. D"altra banda, a partir de la revisió d"alguns dels textos de química més usats en els centres de batxillerat, es proposa reconsiderar el tractament que reben alguns aspectes concrets de l"equilibri químic i, en aquest sentit, es discuteixen algunes de les inconveniències observades i es plantegen alternatives per a tractar d"una manera més adient.

Fluid geochemistry of the Acqui Terme-Visone geothermal area (Piemonte, Italy)

The main geothermal reservoir of Acqui Terme-Visone hosts Na-Cl waters, which are in chemical equilibrium at 120-130 degrees C with typical hydrothermal minerals including quartz, albite, K-feldspar, illite, chlorite (or smectite), anhydrite, calcite and an unspecified Ca-Al-silicate. In the Acqui Terme-Visone area, these geothermal waters ascend along zones of high vertical permeability and discharge at the surface almost undiluted or mixed with cold, shallow waters. To the SW of Acqui Terme, other ascending geothermal waters, either undiluted or mixed with low-salinity waters, enter relatively shallow secondary reservoirs, where they reequilibrate at 65-70 degrees C. Both chemical and isotopic data indicate that bacterial SO4 reduction affects all these waters, especially those discharged by the secondary reservoirs. Therefore, geothermal waters must get in contact with oil, acquiring the relatively oxidized organic substances needed by SO4-reducing bacteria. This oil-water interaction process deserves further investigations, for potential economic implications. (C) 2000 Elsevier Science Ltd. All rights reserved.

Ion-exchange resins as stationary phase in reactive chromatography

Dynamic behavior of bothisothermal and non-isothermal single-column chromatographic reactors with an ion-exchange resin as the stationary phase was investigated. The reactor performance was interpreted by using results obtained when studying the effect of the resin properties on the equilibrium and kinetic phenomena occurring simultaneously in the reactor. Mathematical models were derived for each phenomenon and combined to simulate the chromatographic reactor. The phenomena studied includes phase equilibria in multicomponent liquid mixture¿ion-exchange resin systems, chemicalequilibrium in the presence of a resin catalyst, diffusion of liquids in gel-type and macroporous resins, and chemical reaction kinetics. Above all, attention was paid to the swelling behavior of the resins and how it affects the kinetic phenomena. Several poly(styrene-co-divinylbenzene) resins with different cross-link densities and internal porosities were used. Esterification of acetic acid with ethanol to produce ethyl acetate and water was used as a model reaction system. Choosing an ion-exchange resin with a low cross-link density is beneficial inthe case of the present reaction system: the amount of ethyl acetate as well the ethyl acetate to water mole ratio in the effluent stream increase with decreasing cross-link density. The enhanced performance of the reactor is mainly attributed to increasing reaction rate, which in turn originates from the phase equilibrium behavior of the system. Also mass transfer considerations favor the use ofresins with low cross-link density. The diffusion coefficients of liquids in the gel-type ion-exchange resins were found to fall rapidly when the extent of swelling became low. Glass transition of the polymer was not found to significantlyretard the diffusion in sulfonated PS¿DVB ion-exchange resins. It was also shown that non-isothermal operation of a chromatographic reactor could be used to significantly enhance the reactor performance. In the case of the exothermic modelreaction system and a near-adiabatic column, a positive thermal wave (higher temperature than in the initial state) was found to travel together with the reactive front. This further increased the conversion of the reactants. Diffusion-induced volume changes of the ion-exchange resins were studied in a flow-through cell. It was shown that describing the swelling and shrinking kinetics of the particles calls for a mass transfer model that explicitly includes the limited expansibility of the polymer network. A good description of the process was obtained by combining the generalized Maxwell-Stefan approach and an activity model that was derived from the thermodynamics of polymer solutions and gels. The swelling pressure in the resin phase was evaluated by using a non-Gaussian expression forthe polymer chain length distribution. Dimensional changes of the resin particles necessitate the use of non-standard mathematical tools for dynamic simulations. A transformed coordinate system, where the mass of the polymer was used as a spatial variable, was applied when simulating the chromatographic reactor columns as well as the swelling and shrinking kinetics of the resin particles. Shrinking of the particles in a column leads to formation of dead volume on top of the resin bed. In ordinary Eulerian coordinates, this results in a moving discontinuity that in turn causes numerical difficulties in the solution of the PDE system. The motion of the discontinuity was eliminated by spanning two calculation grids in the column that overlapped at the top of the resin bed. The reactive and non-reactive phase equilibrium data were correlated with a model derived from thethermodynamics of polymer solution and gels. The thermodynamic approach used inthis work is best suited at high degrees of swelling because the polymer matrixmay be in the glassy state when the extent of swelling is low.

Simulação do equilíbrio: o método de Monte Carlo

We make several simulations using the Monte Carlo method in order to obtain the chemical equilibrium for several first-order reactions and one second-order reaction. We study several direct, reverse and consecutive reactions. These simulations show the fluctuations and relaxation time and help to understand the solution of the corresponding differential equations of chemical kinetics. This work was done in an undergraduate physical chemistry course at UNIFIEO.