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Thermodynamics Equilibrium/equilibria

Relaxation time is the statistical time lag value (a nonnegative constant) needed to establish steady-state heat flow conditions in a small elemental volume of material when a temperature gradient is suddenly imposed on the boundary. Chandrasekharaiah (1986) has reported relaxation time for different types of materials. The relaxation time for gases is in the range of 10 s, and the relaxation time for metals is in the range of 10 " s. Relaxation time, is associated with local thermodynamic equilibrium. Equilibrium is achieved in 5-20 collisions, Note A system may have different momentum (t ) and energy... [Pg.307]

If an appreciable current flows between the electrode and the solution, thus disturbing the reversible thermodynamic equilibrium conditions, the electrode is said to be polarized and the system is then operating under irreversible conditions. [Pg.150]

In the preceding derivation, the repulsion between overlapping double layers has been described by an increase in the osmotic pressure between the two planes. A closely related but more general concept of the disjoining pressure was introduced by Deijaguin [30]. This is defined as the difference between the thermodynamic equilibrium state pressure applied to surfaces separated by a film and the pressure in the bulk phase with which the film is equilibrated (see section VI-5). [Pg.181]

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. [Pg.172]

The true thermodynamic equilibrium constant, Ksp, for the solubility of AglOa, therefore, is... [Pg.173]

Several features of equation 6.50 deserve mention. First, as the ionic strength approaches zero, the activity coefficient approaches a value of one. Thus, in a solution where the ionic strength is zero, an ion s activity and concentration are identical. We can take advantage of this fact to determine a reaction s thermodynamic equilibrium constant. The equilibrium constant based on concentrations is measured for several increasingly smaller ionic strengths and the results extrapolated... [Pg.173]

A quantitative solution to an equilibrium problem may give an answer that does not agree with the value measured experimentally. This result occurs when the equilibrium constant based on concentrations is matrix-dependent. The true, thermodynamic equilibrium constant is based on the activities, a, of the reactants and products. A species activity is related to its molar concentration by an activity coefficient, where a = Yi[ ] Activity coefficients often can be calculated, making possible a more rigorous treatment of equilibria. [Pg.176]

In this experiment the equilibrium constant for the dissociation of bromocresol green is measured at several ionic strengths. Results are extrapolated to zero ionic strength to find the thermodynamic equilibrium constant. Equilibrium Constants for Calcium lodate Solubility and Iodic Acid Dissociation. In J. A. Bell, ed. Chemical Principles in Practice. Addison-Wesley Reading, MA, 1967. [Pg.176]

Gordus, A. A. Ghemical Equilibrium 1. The Thermodynamic Equilibrium Goncept, /. Chem. Educ. 1991, 68, 138-140. [Pg.178]

The amide formation reaction (highlighted by the circle) leads to the production of a hydrogen-bonded dimer (ZZ) of the reaction product Z with the template Z. The dimer is in thermodynamic equilibrium with free template in the reaction medium. [Pg.211]

Basic Thermodynamics. Equilibrium-phase behavior of mixtures is governed by the free energy of mixing and how this quantity, consisting of enthalpic... [Pg.408]

From a general point of view, the tautomeric studies can be divided into 12 areas (Figure 20) depending on the migrating entity (proton or other groups, alkyl, acyl, metals. ..), the physical state of the study (solid, solution or gas phase) and the thermodynamic (equilibrium constants) or the kinetic (isomerization rates) approach. [Pg.211]

Mass-Transfer Principles Dilute Systems When material is transferred from one phase to another across an interface that separates the two, the resistance to mass transfer in each phase causes a concentration gradient in each, as shown in Fig. 5-26 for a gas-hquid interface. The concentrations of the diffusing material in the two phases immediately adjacent to the interface generally are unequal, even if expressed in the same units, but usually are assumed to be related to each other by the laws of thermodynamic equihbrium. Thus, it is assumed that the thermodynamic equilibrium is reached at the gas-liquid interface almost immediately when a gas and a hquid are brought into contact. [Pg.600]

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. [Pg.1450]

Eroducts of reaction, the membrane reaclor can make conversion eyond thermodynamic equilibrium in the absence of separation. [Pg.2098]

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... [Pg.47]

The anticipated content of impurities in the refined metal may be calculated a priori by assuming thermodynamic equilibrium at both metal/gas interfaces, and using the relevant stabilities of tire gaseous iodides. Adequate thermodynamic data could provide the activities of the impurities widr that of zirconium close to unity, but tire calculation of tire impurity transport obviously requires a knowledge of activity coefficients in the original impure material, which are not sufficiently well known. [Pg.92]

It follows that the position of thermodynamic equilibrium will change along the reactor for those reactions in which a change of tire number of gaseous molecules occurs, and therefore that the degree of completion and heat production or absorption of the reaction will also vaty. This is why the external control of the independent container temperature and the particle size of the catalyst are important factors in reactor design. [Pg.144]

A number of metals, such as copper, cobalt and h on, form a number of oxide layers during oxidation in air. Providing that interfacial thermodynamic equilibrium exists at the boundaries between the various oxide layers, the relative thicknesses of the oxides will depend on die relative diffusion coefficients of the mobile species as well as the oxygen potential gradients across each oxide layer. The flux of ions and electrons is given by Einstein s mobility equation for each diffusing species in each layer... [Pg.253]

Constitutive relation An equation that relates the initial state to the final state of a material undergoing shock compression. This equation is a property of the material and distinguishes one material from another. In general it can be rate-dependent. It is combined with the jump conditions to yield the Hugoniot curve which is also material-dependent. The equation of state of a material is a constitutive equation for which the initial and final states are in thermodynamic equilibrium, and there are no rate-dependent variables. [Pg.40]

In the original announcement of the workshop the participants were told that everything was to be taken from methanol synthesis except the kinetics. Some may have interpreted this to mean that the known thermodynamic equilibrium information of the methanol synthesis is not valid when taken together with the kinetics. This was not intended, but... [Pg.138]

It is essential, however, to follow a r rous experimental protocol for such applications. To maintain the quantitadve character of NMR spectroscopy, the reped-tion rate of signal averaging experiments has to be at least five times the longest spin-latdce relaxadon dme present in the sample. This waiting period is necessary to ensure that the magnetizadon is probed in a reproducible state, corresponding to thermodynamic equilibrium. [Pg.470]

Local Thermodynamic Equilibrium (LTE). This LTE model is of historical importance only. The idea was that under ion bombardment a near-surface plasma is generated, in which the sputtered atoms are ionized [3.48]. The plasma should be under local equilibrium, so that the Saha-Eggert equation for determination of the ionization probability can be used. The important condition was the plasma temperature, and this could be determined from a knowledge of the concentration of one of the elements present. The theoretical background of the model is not applicable. The reason why it gives semi-quantitative results is that the exponential term of the Saha-Eggert equation also fits quantum-mechanical expressions. [Pg.108]


See other pages where Thermodynamics Equilibrium/equilibria is mentioned: [Pg.5]    [Pg.14]    [Pg.111]    [Pg.373]    [Pg.136]    [Pg.136]    [Pg.174]    [Pg.248]    [Pg.248]    [Pg.211]    [Pg.255]    [Pg.35]    [Pg.346]    [Pg.1126]    [Pg.1505]    [Pg.2315]    [Pg.19]    [Pg.46]    [Pg.59]    [Pg.102]    [Pg.325]    [Pg.337]    [Pg.3]    [Pg.593]    [Pg.376]   


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A Statistical Thermodynamic Approach to Hydrate Phase Equilibria

A mosaic in non-equilibrium thermodynamics (MNET)

Acid-base equilibria thermodynamics

Activity thermodynamic, equilibrium

Adsorption thermodynamic equilibrium

Ammonia atmospheric thermodynamic equilibrium

Analytical Criteria for Thermodynamic Equilibrium

Applications equilibrium thermodynamics

Applied Non-Equilibrium Thermodynamics

BASIC PRINCIPLES OF NON-EQUILIBRIUM THERMODYNAMICS

Basic Thermodynamics of Phase Equilibrium

Binding equilibrium thermodynamics

Boltzmann equilibrium distribution thermodynamics

Carbocations thermodynamic equilibria

Chemical equilibria thermodynamics Nernst equation

Chemical equilibria thermodynamics Pourbaix

Chemical equilibria thermodynamics electrochemical equilibrium

Chemical equilibria thermodynamics hydrogen electrode

Chemical equilibria thermodynamics internal

Chemical equilibria thermodynamics metals

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Chemical equilibria thermodynamics reference electrodes

Chemical equilibria thermodynamics standard

Chemical equilibria thermodynamics standard potential/Gibbs free energy

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Chemical equilibrium statistical thermodynamics

Chemical equilibrium thermodynamic

Chemical equilibrium thermodynamic approach

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Chemical equilibrium thermodynamic criterion

Chemical equilibrium thermodynamic studies

Classical equilibrium thermodynamics

Conditions for thermodynamic equilibrium

Configuration space, equilibrium phase thermodynamics

Corrosion thermodynamics, chemical equilibria

Criteria for thermodynamical equilibrium

Crystallization thermodynamic equilibria

Determination of thermodynamic equilibrium constants

Differentiability equilibrium thermodynamic state

Dissipative macroscopic systems equilibrium thermodynamic modeling

Electrochemical-potential thermodynamic equilibrium

Enantiomers thermodynamic equilibria

Entropy Balance Near the Reversible-Thermodynamic Equilibrium

Entropy generation equilibrium thermodynamics

Equation, thermodynamic activity equilibrium constant

Equilibria and Thermodynamic Functions

Equilibria statistical thermodynamics

Equilibrium Aspects Thermodynamics of Micellisation

Equilibrium Aspects Thermodynamics of Micellization

Equilibrium Thermodynamic Properties

Equilibrium Thermodynamics and Electrochemistry

Equilibrium Thermodynamics of Reacting Multiphase Mixtures

Equilibrium cells Thermodynamic measurements and potentiometric sensors

Equilibrium compositions, thermodynamic

Equilibrium constant Thermodynamic data)

Equilibrium constant and thermodynamics

Equilibrium constants biochemical thermodynamics

Equilibrium in thermodynamics

Equilibrium process, thermodynamic concentration

Equilibrium process, thermodynamic concentration governing

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Equilibrium statistical mechanics canonical thermodynamic functions

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Equilibrium thermodynamical

Equilibrium thermodynamics

Equilibrium thermodynamics

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Equilibrium thermodynamics of electronic defects

Equilibrium thermodynamics of point defect formation

Equilibrium thermodynamics of the perfect solid

Equilibrium thermodynamics, Prigogine

Equilibrium values, thermodynamic

Equilibrium, chemical conditions, thermodynamic

Equilibrium-hydrogen thermodynamic diagrams

Examples of equilibrium thermodynamics

Fluid phase equilibrium excess thermodynamic properties

Folding equilibrium data, thermodynamic

Free-radical polymerization thermodynamic equilibria

Freezing thermodynamic equilibrium

General principles of equilibrium surface thermodynamics

Geometrical Representation of Equilibrium Thermodynamics

Glucose thermodynamic equilibrium

Interfacial thermodynamics and local mechanical equilibria

Irreversible processes, equilibrium nonequilibrium thermodynamics

Irreversible processes, equilibrium thermodynamic modeling

Kinetics, thermodynamic equilibrium

Kinetics, thermodynamic equilibrium models

Limitations of Equilibrium Thermodynamics

Liouville equation thermodynamic equilibrium

Local thermodynamic equilibrium

Local thermodynamic equilibrium plasma

Mesoscope Non-Equilibrium Thermodynamics

Mesoscopic Non-Equilibrium Thermodynamics of Activated Processes

Mesoscopic equilibrium thermodynamics

Methanation thermodynamic equilibrium

Modeling thermodynamic equilibrium model

Monte Carlo equilibrium simulations of ligand-protein thermodynamics

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

Multiscale equilibrium thermodynamics

Multiscale equilibrium thermodynamics systems

Non-Equilibrium Meso-Thermodynamics of Fluid Phase Separation

Non-Equilibrium Surface Thermodynamics

Non-Equilibrium Thermodynamics for Industry

Non-equilibrium Thermodynamics of Polymer Crystallization

Non-equilibrium thermodynamics of electro-osmotic phenomena

Nonequilibrium thermodynamics local equilibrium assumption

Observed Deviations from Local Thermodynamical Equilibrium

Oxide surface/oxygen thermodynamic equilibrium

Oxygen pressure - thermodynamic equilibrium

PDC in a Reversible-Thermodynamic Equilibrium

Phase Equilibrium and Thermodynamic Properties - Summary

Phase equilibria thermodynamic framework for

Phase equilibrium thermodynamics, polymer

Porous media equilibrium thermodynamics

Racemic compounds thermodynamic equilibria

Reaction thermodynamic equilibrium limited

Reactions and Thermodynamic Equilibrium

Recap on calculating the equilibrium constants using statistical thermodynamics

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Separation mechanisms thermodynamic equilibrium

Some Basic Relations of Equilibrium Thermodynamics

Spontaneous Processes and Thermodynamic Equilibrium

Subject thermodynamic equilibrium

Synthesis near thermodynamic equilibrium

Systems at Equilibrium Thermodynamics

THERMODYNAMIC RELATIONSHIPS INVOLVING THE EQUILIBRIUM CONSTANT

THERMODYNAMICS, COMBUSTION CHAMBER EQUILIBRIA AND FLAME TEMPERATURE

THERMODYNAMICS, SEPARATIONS, AND EQUILIBRIUM

The Equilibrium Thermodynamic Functions

The Fundamental Thermodynamic Criterion of Phase and Chemical Equilibrium

The Mesoscopic Non-Equilibrium Thermodynamics Approach to Polymer Crystallization

The Thermodynamic Basis of Chemical Equilibrium

The Thermodynamics of Phase Equilibria

The formalism of equilibrium thermodynamics

The thermodynamic criterion of equilibrium

The thermodynamics of protolytic equilibria

Thermodynamic Aspects Phase Equilibrium

Thermodynamic Description of the Equilibrium State

Thermodynamic Equilibrium Measurements

Thermodynamic Equilibrium Methods

Thermodynamic Equilibrium Models and Kinetics

Thermodynamic Equilibrium Studies

Thermodynamic Equilibrium and Kinetics

Thermodynamic Equilibrium in Large Scale Biochemistry

Thermodynamic Equilibrium of the Reaction

Thermodynamic Functions of Quasi-Equilibrium Thermal Plasma Systems

Thermodynamic Principles of Phase Equilibria

Thermodynamic Relations for the Calculation of Solid-Liquid Equilibria

Thermodynamic criteria of chemical equilibrium in general

Thermodynamic criteria of equilibrium

Thermodynamic description of equilibrium

Thermodynamic equations chemical equilibria pressure effects

Thermodynamic equilibria interface

Thermodynamic equilibria processes

Thermodynamic equilibria separation

Thermodynamic equilibria synthesis

Thermodynamic equilibria, dissolved

Thermodynamic equilibrium

Thermodynamic equilibrium calculations

Thermodynamic equilibrium closed system

Thermodynamic equilibrium condition

Thermodynamic equilibrium constant

Thermodynamic equilibrium constant The

Thermodynamic equilibrium constant definition

Thermodynamic equilibrium constant relating free-energy change

Thermodynamic equilibrium constant solubility product

Thermodynamic equilibrium constant, activity

Thermodynamic equilibrium constant-based

Thermodynamic equilibrium constants constant capacitance model

Thermodynamic equilibrium curve

Thermodynamic equilibrium diagram

Thermodynamic equilibrium force

Thermodynamic equilibrium force limitations

Thermodynamic equilibrium fundamental

Thermodynamic equilibrium half-cell

Thermodynamic equilibrium half-cell relation

Thermodynamic equilibrium heat-conducting

Thermodynamic equilibrium isolated system

Thermodynamic equilibrium limitations

Thermodynamic equilibrium melting temperature

Thermodynamic equilibrium melting temperature of polymer crystals

Thermodynamic equilibrium models

Thermodynamic equilibrium open system

Thermodynamic equilibrium permeable

Thermodynamic equilibrium porous media

Thermodynamic equilibrium potential

Thermodynamic equilibrium programs

Thermodynamic equilibrium selectivity factor

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Thermodynamic equilibrium universe

Thermodynamic equilibrium variable

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Thermodynamic functions activity equilibrium constant

Thermodynamic interactions, equilibrium

Thermodynamic noncanonical equilibrium

Thermodynamic parameters from phase equilibria

Thermodynamic phase-equilibrium

Thermodynamic phase-equilibrium binary mixture behavior

Thermodynamic phase-equilibrium ideal mixture behavior

Thermodynamic phase-equilibrium liquid mixture behavior

Thermodynamic phase-equilibrium mixing process

Thermodynamic phase-equilibrium solutions

Thermodynamic phase-equilibrium system

Thermodynamic, non-equilibrium

Thermodynamic-equilibrium yields

Thermodynamics - Equilibrium Potentials

Thermodynamics Equilibrium constant

Thermodynamics Process Control in Fluid-phase Equilibria

Thermodynamics Thermodynamic equilibrium

Thermodynamics affecting equilibrium

Thermodynamics and Biochemical Equilibria

Thermodynamics and Chemical Equilibrium

Thermodynamics and Fluid-Phase Equilibria

Thermodynamics and Phase Equilibria

Thermodynamics apparent equilibrium constant

Thermodynamics aqueous systems, chemical equilibrium

Thermodynamics basics thermodynamic equilibrium

Thermodynamics chemical equilibria

Thermodynamics chemical reaction equilibrium

Thermodynamics dynamic equilibrium

Thermodynamics equilibrium and

Thermodynamics equilibrium constants, determination

Thermodynamics equilibrium conversion from

Thermodynamics equilibrium criterion

Thermodynamics equilibrium parameters

Thermodynamics equilibrium, thermodynamic description

Thermodynamics heterogeneous chemical equilibria

Thermodynamics homogeneous chemical equilibria

Thermodynamics non-equilibrium

Thermodynamics of Addition-Elimination Equilibria

Thermodynamics of Chemical Reaction Equilibria

Thermodynamics of Protonation Equilibria

Thermodynamics of equilibria

Thermodynamics of equilibrium polymerization

Thermodynamics of phase equilibria

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Xylenes thermodynamic equilibrium composition

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