Chemical equilibrium abundances

Chemical equilibrium abundances for many C-, N-, and 0-bearing gases for T = 500-2500K and P = 10" -1000 bars for a solar composition gas can be found in 54). Although these calculations were applied to brown dwarfs and giant planet atmospheres, the pressure conditions also include those appropriate for O-rich photospheres and their inner CSEs (10" - 10" bars). 

Steady state The absence of change over time in the abundance of a chemical caused by equal rates of its production and removal. Chemical equilibrium is a special case of a steady state in which the processes producing and removing the chemicals are reversible. 

Two different approaches have been taken by researchers to determine the secondary mineralogy of CCBs (1) direct observation, which is accomplished via analysis of weathered ash materials, and (2) prediction, based on chemical equilibrium solubility calculations for ash pore-waters and/or experimental ash leachate or extractant solutions. Because the secondary phases are typically present in very low abundance, their characterization by direct analysis is difficult. On the other hand, predictions based on chemical equilibrium modelling or laboratory leaching experiments may not be reliable indicators of element leachability or accurately indicate the secondary phases that will form under field conditions (Eighmy et al. 1994 Janssen-Jurkovicova et al. 1994). 

All calculations presented in the following chapters are restricted to dust formation in C-stars and are performed under the assumption of chemical equilibrium for the molecular reactions among the various chemical elements. The element abundances have to be specified as additional external parameters. For dust driven winds the amount of condensed material determines the velocity field and in particular the terminal velocity of the wind. For this reason, the abundances of the dust forming elements and the terminal velocity of the wind are coupled very closely. For the case of M-stars similar calculations have been performed by Kozasa et al. (1984) considering formation of MgSi03 grains. 

A rational deduction of elemental abundance from solar and stellar spectra had to be based on quantum theory, and the necessary foundation was laid with the Indian physicist Meghnad Saha s theory of 1920. Saha, who as part of his postdoctoral work had stayed with Nernst in Berlin, combined Bohr s quantum theory of atoms with statistical thermodynamics and chemical equilibrium theory. Making an analogy between the thermal dissociation of molecules and the ionization of atoms, he carried the van t Hoff-Nernst theory of reaction-isochores over from the laboratory to the stars. Although his work clearly belonged to astrophysics, and not chemistry, it relied heavily on theoretical methods introduced by and associated with physical chemistry. This influence from physical chemistry, and probably from his stay with Nernst, is clear from his 1920 paper where he described ionization as a sort of chemical reaction, in which we have to substitute ionization for chemical decomposition. [81] The influence was even more evident in a second paper of 1922 where he extended his analysis. [82]... 

We will not mention effects on molecular formation due to shocks and shock fronts in dense molecular clouds, nor will we discuss the chemistry of the cir-cumstellar environment, where an abundance of molecular species has been detected during the past several years. In the warm, dense envelopes of stars the abundances can be matched by chemical-equilibrium calculations, in contrast to the chemical reactions which can take place in the cold interstellar molecular clouds. For example theoretical calculations based on chemical equilibrium have been performed for the expanding molecular envelope of the cool carbon star IRC H-10216 by McCabe et al. (1980), in agreement with the observed molecular column-densities. 

Smith J. T. and Ehrenberg S. N. (1989) Correlation of carbon dioxide abundance with temperature in clastic hydrocarbon reservoirs relationship to inorganic chemical equilibrium. Mar. Petrol. Geol. 6, 129-135. 

The influence of chemical equilibrium and/or kinetics on the progress of chemical reactions often determines the abundance, distribution, and fate of substances in the environment. An understanding of the basic concepts of chemical equilibrium and chemical kinetics, therefore, may help us to explain and predict the environmental concentrations of inorganic and organic species in aqueous systems, whether these species are present naturally or have been introduced by humans. In this chapter we will examine chemical equilibrium. The following chapter considers chemical kinetics or the study of rates of chemical reactions. 

As the hydrogen-burning reaction chains suggest, a complex web of nuclear reactions will occur at the same time. Yields are determined by the branching ratios and rates of individual reactions. The chemical composition of this thermonuclear soup can be obtained, at least for steady-state burning, by setting up a system of simultaneous equations that model the entire reaction network and solving for the equilibrium abundances of each chemical species. 

Chemical equilibrium calculations predict the distribution of each element between its gaseous, solid, and liquid compounds as a function of temperature, pressure, and bulk elemental composition. These calculations are often called condensation calculations because they show the stable phases that condense out of a cooling gas with solar system elemental abundances. However, chemical equilibrium calculations are path independent because the Gibbs energy is a state function, i.e., its differential dG is an exact (or perfect) differential. Thus, the results of chemical equilibrium calculations apply equally well to heating or cooling of a solar composition system. 

The inputs to the chemical equilibrium calculations are the temperature, pressure, bulk elemental composition, and thermodynamic data for all compounds included in the calculations. The temperatures and pressures used in the calculations depend on the system being studied, e.g., a protoplanetary accretion disk, the photospheric region of a cool star, the ejecta from a nova or supernova, a planetary atmosphere, and so on. The bulk elemental composition is the set of elemental abundances that are appropriate for the system... 

The chemical equilibrium calculations are done by sophisticated computer codes, such as the CONDOR code [2], This code simultaneously considers the dual constraints of mass balance and chemical equilibrium. The operation of the CONDOR code and the general principles of chemical equilibrium calculations are best illustrated using a simplified version of iron chemistry in solar composition material. We define the total elemental abundance of iron as A(Fe). This is the atomic abundance of Fe relative to 106 Si atoms and is 838,000 Fe atoms [5]. The mole fraction (X) of total iron (XFe) in all Fe-bearing compounds is... 

Several points are worth emphasizing. The first point is mass balance. The total amount of each element is conserved in the chemical equilibrium calculations. Thus the abundances of all gases and all condensed phases (solids and/or liquids) sum to the total elemental abundance - no less and no more. The second point is that chemical equilibrium is completely independent of the size, shape, and state of aggregation of condensed phases - a point demonstrated by Willard Gibbs over 130 years ago. Finally, the third point is that chemical equilibrium is path independent. Thus, the results of chemical equilibrium calculations are independent of any particular reaction. A particular chemical reaction does not need to be specified because all possible reactions give the same result at chemical equilibrium. This is completely different than chemical kinetic models where the results of the model are critically dependent on the reactions that are included. However, a chemical equilibrium calculation does not depend on kinetics, is independent of kinetics, and does not need a particular list of reactions. This point may seem obvious, but is often misunderstood. 

The most important of the atmophile elements is hydrogen, which is the most abundant element in solar composition material. Hydrogen s dominance controls the chemistry of solar composition material. With the exception of helium, which is non-reactive, hydrogen is about 1,000 times as abundant as all other elements combined. Thus, hydrogen-bearing gases (hydrides) are major or important gases at chemical equilibrium for many elements. A few examples are H2O, CH4 (at low temperatures), NH3 (at low temperatures), H2S, HF, HC1, and HBr. 

In this chapter, we reviewed the methods and results of chemical equilibrium calculations applied to solar composition material. These types of calculations are applicable to chemistry in a variety of astronomical environments including the atmospheres and circumstellar envelopes of cool stars, the solar nebula and protoplanetary accretion disks around other stars, planetary atmospheres, and the atmospheres of brown dwarfs. The results of chemical equilibrium calculations have guided studies of elemental abundances in meteorites and presolar grains and as a result have helped to refine nucleosynthetic models of element formation in stars. 

Nitric oxide is formed in combustion engines by the interaction of oxygen and nitrogen in air at the high temperatures reached during the combustion cycle. The percentages of NO found in the exhaust gas is close to that calculated from the chemical equilibrium N2+02 = 2N0 at peak temperatures near 2500 K. Once NO is formed, its abundance seems to be effectively frozen in. The mechanism of NO formation is not precisely known. Most authors have adopted the reaction chain first proposed by Zeldovich et al. (1947) ... 

A recurring theme in this work is the importance of the interaction of flow and transport between fractures and the adjoining porous matrix. We note here that large-scale chemical equilibrium cannot be maintained in a system where mineral precipitation and dissolution are taking place at different rates in fractures and matrix (which have different mineral assemblages and abundances), the advective transport in fractures is faster than diffusive transport in the matrix. 

Unfortunately, little experimental information is available on how the chemical equilibria and the kinetics of the reactions become altered on passing from the gas phase to the solution, since as commented previously, the techniques which enable this kind of analysis are relatively recent. It is true that diere is abundant experimental information, nevertheless, on how the chemical equilibrium and die velocity of the reaction are altered when one same process occurs in the midst of different solvents. 

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