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Equilibrium modeling

Although this experiment is written as a dry-lab, it can be adapted to the laboratory. Details are given for the determination of the equilibrium constant for the binding of the Lewis base 1-methylimidazole to the Lewis acid cobalt(II)4-trifluoromethyl-o-phenylene-4,6-methoxysalicylideniminate in toluene. The equilibrium constant is found by a linear regression analysis of the absorbance data to a theoretical equilibrium model. [Pg.447]

If the puncture occurs on a pipe which is at least 0.5 m from a vessel, it is justifiable to use a homogeneou.s equilibrium model (HEM) for which an analytical solution is available. The discharge rate pre-... [Pg.2346]

FIG. 26-69 Ratio of mass flux for inclined pipe flow to that for orifice discharge for flashing liquids by the homogeneous equilibrium model. Leung, J. of Loss Prev. Process Ind. 3 pp. 27-32, with kind peimission of Elsevier Science, Ltd, The Boulevard, Langford Lane, Kidlington, 0X5 IGB U.K., 1990.)... [Pg.2352]

For two-phase flow through pipes, an overall dimensionless dis-eharge eoeffieient, /, is applied. Equation 12-11 is referred to as the equilibrium rate model (ERM) for low-quality ehoked flow. Leung [28] indieated that Equation 12-11 be multiplied by a faetor of 0.9 to bring the value in line with the elassie homogeneous equilibrium model (HEM). Equation 12-11 then beeomes... [Pg.957]

To predict die capability of a flame arrester to cool hot combnstion gases, the U.S. Bnrean of Mines has developed an equilibrium model and one- and diree-dimensional transient diermal models of a flame arrester, which are nsed to predict die heat losses from die arrester and the maximum temperatures developed (Edwards 1991). [Pg.113]

The agonist receptor occupancy according to the hemi-equilibrium model of orthosteric antagonism (see Section 6.5) is given by Equation 6.2. The response species is... [Pg.221]

Bowers and Mudawar (1994a) performed an experimental smdy of boiling flow within mini-channel (2.54 mm) and micro-channel d = 510 pm) heat sink and demonstrated that high values of heat flux can be achieved. Bowers and Mudawar (1994b) also modeled the pressure drop in the micro-channels and minichannels, using the Collier (1981) and Wallis (1969) homogenous equilibrium model, which assumes the liquid and vapor phases form a homogenous mixture with equal and uniform velocity, and properties were assumed to be uniform within each phase. [Pg.350]

Table 10-10 Equilibrium model effect of complex formation on distribution of metals (all concentrations are given as — log(M)). pH = 8.0, T = 25°C. Ligands pS04 1.95 pHCOa 2.76 pCOs 4.86 pCl 0.25. Table 10-10 Equilibrium model effect of complex formation on distribution of metals (all concentrations are given as — log(M)). pH = 8.0, T = 25°C. Ligands pS04 1.95 pHCOa 2.76 pCOs 4.86 pCl 0.25.
The framework for constructing such multi-component equilibrium models is the Gibbs phase rule. This rule is valid for a system that has reached equilibrium and it states that... [Pg.264]

MacKenzie and Garrels equilibrium models. Most marine clays appear to be detrital and derived from the continents by river or atmospheric transport. Authigenic phases (formed in place) are found in marine sediments (e.g. Michalopoulos and Aller, 1995), however, they are nowhere near abundant enough to satisfy the requirements of the river balance. For example, Kastner (1974) calculated that less than 1% of the Na and 2% of the K transported by rivers is taken up by authigenic feldspars. [Pg.268]

While these calculations provide information about the ultimate equilibrium conditions, redox reactions are often slow on human time scales, and sometimes even on geological time scales. Furthermore, the reactions in natural systems are complex and may be catalyzed or inhibited by the solids or trace constituents present. There is a dearth of information on the kinetics of redox reactions in such systems, but it is clear that many chemical species commonly found in environmental samples would not be present if equilibrium were attained. Furthermore, the conditions at equilibrium depend on the concentration of other species in the system, many of which are difficult or impossible to determine analytically. Morgan and Stone (1985) reviewed the kinetics of many environmentally important reactions and pointed out that determination of whether an equilibrium model is appropriate in a given situation depends on the relative time constants of the chemical reactions of interest and the physical processes governing the movement of material through the system. This point is discussed in some detail in Section 15.3.8. In the absence of detailed information with which to evaluate these time constants, chemical analysis for metals in each of their oxidation states, rather than equilibrium calculations, must be conducted to evaluate the current state of a system and the biological or geochemical importance of the metals it contains. [Pg.383]

To this point, we have emphasized that the cycle of mobilization, transport, and redeposition involves changes in the physical state and chemical form of the elements, and that the ultimate distribution of an element among different chemical species can be described by thermochemical equilibrium data. Equilibrium calculations describe the potential for change between two end states, and only in certain cases can they provide information about rates (Hoffman, 1981). In analyzing and modeling a geochemical system, a decision must be made as to whether an equilibrium or non-equilibrium model is appropriate. The choice depends on the time scales involved, and specifically on the ratio of the rate of the relevant chemical transition to the rate of the dominant physical process within the physical-chemical system. [Pg.401]

Hoffman, M. R. (1981). Thermodynamic, kinetic and extra-thermodynamic considerations in the development of equilibrium models for aquatic systems. Environ. Sci. Technol. 15,345-353. [Pg.417]

Meylan S, Odzak N, Behra R, Sigg L (2004) Speciation of copper and zinc in natural freshwater comparison of voltammetric measurements, diffusive gradients in thin Aims (DGT) and chemical equilibrium models. An Chim Acta 510 91... [Pg.53]

It is important to realize that the assumption of a rate-determining step limits the scope of our description. As with the steady state approximation, it is not possible to describe transients in the quasi-equilibrium model. In addition, the rate-determining step in the mechanism might shift to a different step if the reaction conditions change, e.g. if the partial pressure of a gas changes markedly. For a surface science study of the reaction A -i- B in an ultrahigh vacuum chamber with a single crystal as the catalyst, the partial pressures of A and B may be so small that the rates of adsorption become smaller than the rate of the surface reaction. [Pg.61]

The basic relationships between solubility and pH can be derived for any given equilibrium model. The model refers to a set of equilibrium equations and the associated equilibrium quotients. In a saturated solution, three additional equations need to be considered, along with the ionization Eqs. (2a)-(2d), which describe the equilibria between the dissolved acid, base or ampholyte in solutions containing a suspension of the (usually crystaUine) solid form of the compounds ... [Pg.68]

Avdeef, A. STBLTY methods for construction and refinement of equilibrium models. In Computational Methods for the Determination of Formation Constants, Leggett, D. J. (eds.). Plenum, New York, 1985, pp. 355 73. [Pg.80]

Several workers have intended to estimate the chemical compositions of Kuroko ore fluids based on the chemical equilibrium model (Sato, 1973 Kajiwara, 1973 Ichikuni, 1975 Shikazono, 1976 Ohmoto et al., 1983) and computer simulation of the changes in mineralogy and chemical composition of hydrothermal solution during seawater-rock interaction. Although the calculated results (Tables 1.5 and 1.6) are different, they all show that the Kuroko ore fluids have the chemical features (1 )-(4) mentioned above. [Pg.50]

The behavior of silica and barite precipitation from the hydrothermal solution which mixes with cold seawater above and below the seafloor based on the thermochemical equilibrium model and coupled fluid flow-precipitation kinetics model is described below. [Pg.67]

There is another explanation for the variations in values of sulfide sulfur. It was cited that oxidation state (/02) od pH of ore fluids are important factor controlling values of ore fluids (e.g., Kajiwara, 1971). According to the sulfur isotopic equilibrium model (Kajiwara, 1971 Ohmoto, 1972), of sulfides in predominance... [Pg.150]

D. R. Parker, R. L. Chaney, and W. A. Norvell. Chemical equilibrium models applications to plant nutrition research. Chemiccd Equilbrium and Reaction Models (R. H. Loeppert, ed.), Madison, WI, Soil Science Society of America Special Publication, 42 163 (1995). [Pg.254]

The non-steady-state optical analysis introduced by Ding et al. also featured deviations from the Butler-Volmer behavior under identical conditions [43]. In this case, the large potential range accessible with these techniques allows measurements of the rate constant in the vicinity of the potential of zero charge (k j). The potential dependence of the ET rate constant normalized by as obtained from the optical analysis of the TCNQ reduction by ferrocyanide is displayed in Fig. 10(a) [43]. This dependence was analyzed in terms of the preencounter equilibrium model associated with a mixed-solvent layer type of interfacial structure [see Eqs. (14) and (16)]. The experimental results were compared to the theoretical curve obtained from Eq. (14) assuming that the potential drop between the reaction planes (A 0) is zero. The potential drop in the aqueous side was estimated by the Gouy-Chapman model. The theoretical curve underestimates the experimental trend, and the difference can be associated with the third term in Eq. (14). [Pg.209]

One possibility for increasing the minimum porosity needed to generate disequilibria involves control of element extraction by solid-state diffusion (diffusion control models). If solid diffusion slows the rate that an incompatible element is transported to the melt-mineral interface, then the element will behave as if it has a higher partition coefficient than its equilibrium partition coefficient. This in turn would allow higher melt porosities to achieve the same amount of disequilibria as in pure equilibrium models. Iwamori (1992, 1993) presented a model of this process applicable to all elements that suggested that diffusion control would be important for all elements having diffusivities less than... [Pg.198]

The discussion above of enzyme reactions treated the formation of the initial ES complex as an isolated equilibrium that is followed by slower chemical steps of catalysis. This rapid equilibrium model was first proposed by Henri (1903) and independently by Michaelis and Menten (1913). However, in most laboratory studies of enzyme reactions the rapid equilibrium model does not hold instead, enzyme... [Pg.34]


See other pages where Equilibrium modeling is mentioned: [Pg.830]    [Pg.833]    [Pg.655]    [Pg.1493]    [Pg.1504]    [Pg.2350]    [Pg.330]    [Pg.348]    [Pg.210]    [Pg.499]    [Pg.53]    [Pg.380]    [Pg.406]    [Pg.264]    [Pg.428]    [Pg.249]    [Pg.264]    [Pg.386]    [Pg.324]    [Pg.500]    [Pg.151]    [Pg.229]    [Pg.261]    [Pg.36]   
See also in sourсe #XX -- [ Pg.79 ]

See also in sourсe #XX -- [ Pg.741 , Pg.755 ]

See also in sourсe #XX -- [ Pg.79 ]




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Activity coefficient-models equilibrium

Activity, Speciation, and Equilibrium Models

Adoption of Central Field Model at Equilibrium

An Equilibrium-Based Model for Predicting Potential Ammonia Volatilization from Soil

Applications of the Equilibrium-Dispersive Model

Aquatic equilibrium models

Basic models phase equilibrium

Buoyancy force equilibrium model

Calcite equilibrium model

Chemical equilibrium model

Chemical equilibrium model simulation

Chemical equilibrium models, computer-based

Chemical reactors equilibrium model

Chemistry /chemical equilibrium models

Chromatography equilibrium model

Columns equilibrium stage model

Computable general equilibrium model

Computable general equilibrium model PACE

Coulombic term, chemical equilibrium models

Crystal field model equilibria

Debye equilibrium model

Design According To Leungs Equilibrium Model

Dispersion equilibrium-dispersive model

Dissipative macroscopic systems equilibrium thermodynamic modeling

Drag force equilibrium model

Drop model equilibrium concentration

Electrochemical (Equilibrium) Modeling

Electron models equilibrium state equations

Enzyme reactions equilibrium model

Equilibrium Flux Models

Equilibrium Geometry Model

Equilibrium Models of Seawater

Equilibrium and Quasiequilibrium Solutions to the LG Model

Equilibrium and reaction modelling

Equilibrium behavior, model

Equilibrium criteria model

Equilibrium ensembles and Landau-Ginzburg model

Equilibrium flux models, membranes

Equilibrium ideal Langmuir model

Equilibrium model

Equilibrium model assumptions

Equilibrium model for organic materials

Equilibrium model, dehydrogenation

Equilibrium model, ideal

Equilibrium model, reactions

Equilibrium model, reactions charged interfaces

Equilibrium models for

Equilibrium models of natural waters

Equilibrium models, assessments

Equilibrium models, assessments environment

Equilibrium parameters Langmuir kinetic model

Equilibrium parameters complex kinetic models

Equilibrium parameters film resistance model

Equilibrium partition model

Equilibrium partitioning model

Equilibrium sorption models

Equilibrium stage model

Equilibrium stage model MESH equations

Equilibrium state parameters, electron models

Equilibrium transport dispersive model

Equilibrium, environmental fate models

Equilibrium, quasi-species model

Equilibrium-Constant Models

Equilibrium-dispersive model

Equilibrium-dispersive model applications

Equilibrium-dispersive model displacement chromatography

Equilibrium-dispersive model finite difference methods

Equilibrium-dispersive model multicomponent systems

Equilibrium-dispersive model numerical solution

Equilibrium-dispersive model single components

Equilibrium-dispersive model system peaks

Equilibrium-orbit Models the Model of Barth

Extraction equilibria modeling

Flow regime equilibrium model

Fluid phase equilibrium activity coefficient models

Frontal Analysis, Displacement and the Equilibrium-Dispersive Model

Fundamental Basis of the Equilibrium Dispersive Model

General-equilibrium model

Hard-sphere model solid-fluid equilibrium

Homogeneous equilibrium model (HEM)

Hydrolysis equilibrium models

Ideal kinetic model equilibrium approximations

Interest rate modeling equilibrium

Intrinsic equilibrium constants triple layer model

Irreversible processes, equilibrium thermodynamic modeling

Kinetic models equilibrium rate

Kinetics, thermodynamic equilibrium models

Liquid-vapor equilibrium modeling

Local equilibrium sorption model

Local equilibrium sorption transport model

Micellization phase equilibrium model

Microbial degradation equilibrium models

Mixed equilibrium-dynamic modeling

Model Experiment on Dynamic Equilibrium

Model for equilibrium calculations

Modeling Polymer Dynamics Beyond Equilibrium

Modeling chemical equilibria

Modeling equilibrium constant

Modeling thermodynamic equilibrium model

Models closed equilibrium

Models homogeneous equilibrium

Models liquid-vapor equilibrium

Models local equilibrium

Models metal-silicate equilibria

Models of Adsorption Isotherms in Liquid-Solid Equilibria

Molecular Modelling Equilibrium Geometries

Multi-equilibrium model

Multiple equilibrium model

Multiscale Modeling and Coarse Graining of Polymer Dynamics Simulations Guided by Statistical Beyond-Equilibrium Thermodynamics

Non-equilibrium Stage Modeling

Non-equilibrium models

Non-equilibrium models for scalar dissipation

Numerical Analysis of the Equilibrium-Dispersive Model

Numerical Solutions of the Equilibrium-Dispersive Model

Phase Equilibrium Modelling

Phase equilibrium model

Phase-equilibrium modeling

Protein adsorption equilibrium model development

Proteins, protonation equilibria modeling

Quantum Mechanical Modelling - Equilibrium Structures of Isolated Metal Complexes

Quasi-equilibrium adsorption model

Quasi-equilibrium model

RANS models equilibrium model

Radiative equilibrium model

Rapid equilibrium, enzyme kinetic modeling

Real versus Model Equilibrium

Results Obtained with the Equilibrium Dispersive Model

Scalar dissipation rate equilibrium model

Seawater equilibrium models

Sediments equilibrium model

Separable equilibrium solvation model

Sillen equilibrium model

Simplified equilibrium rate model (ERM)

Single-Component Profiles with the Equilibrium Dispersive Model

Solid-fluid equilibrium molecular models

Some Aspects of a Fluid Phase Equilibria and UNIFAC Model

Sorption equilibria, isotherm models

Stoichiometric equilibrium model

System Peaks with the Equilibrium-Dispersive Model

The Equilibrium Stage Model

The Equilibrium-Dispersive Model

The Langmuir model of chemisorption equilibrium

The equilibrium or algebraic Eulerian model

Thermal equilibrium models

Thermodynamic Equilibrium Models and Kinetics

Thermodynamic equilibrium constants constant capacitance model

Thermodynamic equilibrium models

Three equilibrium model

Two-Component Band Profiles with the Equilibrium-Dispersive Model

Vapor-Liquid Equilibrium Based on Activity Coefficient Models

Vapor-Liquid Equilibrium Modeling with Two-Parameter Cubic Equations of State and the van der Waals Mixing Rules

Vapor-Liquid Phase Equilibrium Calculations with the PVDW Model

Vapor-liquid equilibrium activity coefficient models

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