Chemical equilibria calculating

Selective extractions, chemical equilibria calculations, and crystallization measurements presented here imply that the hydrous iron oxides, even in the carbonate dominated Genesee River, play a major part in inorganic phosphorus transport by sediments in the fluvial system. Saturation levels of inorganic phosphate and calcium carbonate minerals in the Genesee River... 

The Nernst equation is applicable only if the redox reaction is reversible. Not all reactions are completely reversible in natural systems activities of reacting components may be too low or equilibrium may be reached very slowly. In a sediment, the biotic microenvironment may create a redox potential that is different from the surrounding macroenvironment. For this reason, measurements of Eh in natural systems must be cautiously evaluated and not used strictly for calculations of chemical equilibria. Calculations of redox equilibria are in some cases valuable, in the sense that they will give information about the direction of chemical reactions. 

Perform chemical equilibria calculations for ideal and nonideal fluids in gas phase. 

We are now prepared to use thermodynamics to make chemical equilibrium calculations. The following examples demonstrate some of the possibilities. 

Advances continue in the treatment of detonation mixtures that include explicit polar and ionic contributions. The new formalism places on a solid footing the modeling of polar species, opens the possibility of realistic multiple fluid phase chemical equilibrium calculations (polar—nonpolar phase segregation), extends the validity domain of the EXP6 library,40 and opens the possibility of applications in a wider regime of pressures and temperatures. 

Predictions of high explosive detonation based on the new approach yield excellent results. A similar theory for ionic species model43 compares very well with MD simulations. Nevertheless, high explosive chemical equilibrium calculations that include ionization are beyond the current abilities of the Cheetah code, because of the presence of multiple minima in the free energy surface. Such calculations will require additional algorithmic developments. In addition, the possibility of partial ionization, suggested by first principles simulations of water discussed below, also needs to be added to the Cheetah code framework. 

STANJAN The Element Potential Method for Chemical Equilibrium Analysis Implementation in the Interactive Program STANJAN, W.C. Reynolds, Thermosciences Division, Department of Mechanical Engineering, Stanford University, Stanford, CA, 1986. A computer program for IBM PC and compatibles for making chemical equilibrium calculations in an interactive environment. The equilibrium calculations use a version of the method of element potentials in which exact equations for the gas-phase mole fractions are derived in terms of Lagrange multipliers associated with the atomic constraints. The Lagrange multipliers (the element potentials ) and the total number of moles are adjusted to meet the constraints and to render the sum of mole fractions unity. If condensed phases are present, their populations also are adjusted to achieve phase equilibrium. However, the condensed-phase species need not be present in the gas-phase, and this enables the method to deal with problems in which the gas-phase mole fraction of a condensed-phase species is extremely low, as with the formation of carbon particulates. 

Figure 24.9 illustrates measured CO and CO2 mole fractions as a function of equivalence ratio. The solid lines represent chemical equilibrium calculations of CO and CO2 mole fractions at measured temperatures. The vertical bars represent the uncertainty in measured CO and CO2 mole fractions due to line... 

The concepts of physical equilibria (Sections 8.1-8.3) and free energy of reaction (Section 7.12). Chemical equilibrium calculations depend on a thorough knowledge of reaction stoichiometry (Section L). 

R. A. Alberty and I. Oppenheim, Use of semigrand ensembles in chemical equilibrium calculations on complex organic systems. J. Chem. Phys. 91, 1824-1828 (1989). 

From Eqn. (14) it follows that with an exothermic reaction - and this is the case for most reactions in reactive absorption processes - decreases with increasing temperature. The electrolyte solution chemistry involves a variety of chemical reactions in the liquid phase, for example, complete dissociation of strong electrolytes, partial dissociation of weak electrolytes, reactions among ionic species, and complex ion formation. These reactions occur very rapidly, and hence, chemical equilibrium conditions are often assumed. Therefore, for electrolyte systems, chemical equilibrium calculations are of special importance. Concentration or activity-based reaction equilibrium constants as functions of temperature can be found in the literature [50]. 

V. N. Maikova, V. D. Ryzhkov, and V. I. Belevantsev, Study of Chemical Equilibriums (Calculation Methods, Algorithms, and Programs), Nauka, Sib. Otd., Novosibirsk,... 

VL(L) E measurements for binaries involving water with alcohol and acid have been done, as described elsewhere [2]. Figure 8.6 presents experimental vapor pressure data for 2-ethylhexyl laurate. The normal boiling point (nbp) is 607.6 K, close to the prediction by Gani s method. On the other hand, the prediction of the whole saturation curve by Riedel s method (noted estimation in Figure 8.6) is in large error at lower pressures. This fact can affect the accuracy of chemical equilibrium calculation, but fortunately the errors compensate each other [2]. 

From the selective extraction analysis of sediment, chemical equilibrium calculations, and seeded crystallization measurements, several conclusions can be reached concerning the behavior of phosphate in alkaline surface waters. 

Several chemical reactions, including calcium carbonate and hydroxyapatite precipitation, have been studied to determine their relationship to observed water column and sediment phosphorus contents in hard water regions of New York State. Three separate techniques have been used to Identify reactions important in the distribution of phosphorus between the water column and sediments 1) sediment sample analysis employing a variety of selective extraction procedures 2) chemical equilibrium calculations to determine ion activity products for mineral phases involved in phosphorus transport and 3) seeded calcium carbonate crystallization measurements in the presence and absence of phosphate ion. 

Chemical equilibrium calculations for the reaction between ZnO and (NH4)2S04 indicate that both ZnS04 and Zn0.2ZnS04 can form as the stable reaction products. A series of thermogravimetric/ differential thermal analyses/mass spectrometric (TG/DTA/MS) experiments has been carried out to determine the exact nature of all ZnO + (NH4)2S04 reaction products. Results obtained to date are presented and discussed. 

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. 

For complex chemistry, in many cases, a conserved scalar or a mixture fraction approach can be used, in which a single conserved scalar (mixture fraction) is solved instead of transport equations for individual species. The reacting system is treated using either chemical equilibrium calculations or by assuming infinitely fast reactions (mixed-is-reacted approach). The mixture fraction approach is applicable to non-premixed situations and is specifically developed to simulate turbulent diffusion flames containing one fuel and one oxidant. Such situations are illustrated in Fig. 5.6. The basis for the mixture fraction approach is that individual conservation equations for fuel and oxidant can be combined to eliminate reaction rate terms (see Toor, 1975 for more details). Such a combined equation can be simplified by defining a mixture... 

Because reactions among ionic species in solution are rapid, thermo-d5mamic calculations are used to constrain the activities of dissolved chemical species at equilibrium. Garrels and Thompson (1962) were the first to calculate the speciation of the major ions in seawater by determining the extent to which each species is involved in ion pairing with each counter-ion. This information is necessary to establish the percentages of free major ions available in chemical equilibrium calculations. This section presents an example of how such multiple equilibrium systems can be constrained. 

Each of the rate terms, k+ and k, in Eq. (9.16) is related to concentrations in a way that one would predict if the probability of reaction were dependent on the collision of randomly moving particles the rate is proportional to the product of the number of entities involved in the reaction. All other factors that determine the reaction rate (energy barriers, temperature dependence, the effect of other species in solution, catalysis, etc.) are represented in the rate constant, k, which has units necessary to balance the left- and right-hand sides of the rate expression. Because ion interaction effects that are accounted for by activity coefficients in chemical equilibrium calculations (Chapter 3) are all incorporated into the rate constant, concentrations and not activities are used on the right-hand side of the reaction rate equation. 

These spectral variations like disappearance of TiO, VO and other molecular features at later L subclasses are believed to be caused by formation of various types of condensates at the temperatures lower than 2600 K. Lodders [12] have made extensive chemical equilibrium calculations and the atmospheric composition changes as the material is removed from gas to solid phase. 

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. 

This section summarizes the results of chemical equilibrium calculations for naturally occurring elements. We review the cosmochemical behavior of the elements in order of increasing volatility, i.e., decreasing condensation temperature using the cosmochemical classification scheme. 

The results of the chemical equilibrium calculations for the refractory lithophiles are also confirmed by the mineralogy and chemistry of the Ca, Al-rich inclusions in Allende and other meteorites. The major minerals in CAIs are the same ones predicted by the calculations, namely melilite (a solid solution of gehlenite CaALSiOr and akermanite Ca2MgSi2C>7), spinel, corundum, grossite, hibonite, and perovskite. Chemical analyses of CAIs show that the refractory lithophiles are enriched by an average of 20 times solar elemental... 

Equation (19) gives the equilibrium constant from 298 - 2500 K for reaction (18). Chemical equilibrium calculations using this data and the solar elemental... 

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. 

Many concepts and techniques of cosmochemistry have a generic nature. The methods and results of chemical equilibrium calculations applied to solar composition are applicable to chemistry in a variety of astronomical... 

All titrations were performed at least in duplicate to confirm the results. For the ISE titrations, the lowest total Cu concentration for which reliable potential measurements could be made was 1 x 10 M. For the FQ titrations, there was no observable quenching below 1 x 10 M total Cu. The highest possible total Cu concentration for titrations performed at pH 7.0 and natural pH values (approximately 8.0) was approximately 1 x 10 M. At 10 M total Cu, the rate of change of the ISE potential with added Cu became less than 29 mV (log Cu ) (Nernstian value) and chemical equilibrium calculations indicated that the solutions became oversaturated with respect to Cu(OH)2. The lowest total Cu concentration used in CSV titrations was 1 x 10 M. The upper limit of Cu concentrations for CSV was approximately 2 x 10 M due to loss of hnearity of the calibration above that value. 

For all future chemical equilibrium calculations in single-phase, single-reaction systems, we will start from Eqs. 13.1-12 or 13 as appropriate, rather than starting at Eq. 

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