Equilibrium, chemical homogeneous

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

Guldberg and Waage (1867) clearly stated the Law of Mass Action (sometimes termed the Law of Chemical Equilibrium) in the form The velocity of a chemical reaction is proportional to the product of the active masses of the reacting substances . Active mass was interpreted as concentration and expressed in moles per litre. By applying the law to homogeneous systems, that is to systems in which all the reactants are present in one phase, for example in solution, we can arrive at a mathematical expression for the condition of equilibrium in a reversible reaction. 

In its simplest form a partitioning model evaluates the distribution of a chemical between environmental compartments based on the thermodynamics of the system. The chemical will interact with its environment and tend to reach an equilibrium state among compartments. Hamaker(l) first used such an approach in attempting to calculate the percent of a chemical in the soil air in an air, water, solids soil system. The relationships between compartments were chemical equilibrium constants between the water and soil (soil partition coefficient) and between the water and air (Henry s Law constant). This model, as is true with all models of this type, assumes that all compartments are well mixed, at equilibrium, and are homogeneous. At this level the rates of movement between compartments and degradation rates within compartments are not considered. 

The analysis of Ref. [42] as well as the NJL-type model investigation of Ref. [43] are based on a comparison of homogeneous phases. The neutrality conditions can, however, also be fulfilled giving up the requirement of separately neutral phases and to consider mixed phases in chemical equilibrium which are only neutral in total. This procedure has been pushed forward by Glendenning in the context of the quark-hadron phase transition in neutron stars where a similar problem related to electrical neutrality occurs [44], For the case of electrically and color neutral quark matter the phase boundaries are... 

FIA is a fixed-time analytical methodology, since neither physical equilibrium (homogenization of a portion of the flow) nor chemical equilibrium (reaction completeness) has been attained by the time the signal is detected. The operational timing must be highly reproducible, because the measurements are made under non-steady-state conditions, so that small changes may give rise to serious errors in the results obtained. 

Ion-exchange equilibrium can be considered to be analogous to chemical equilibrium. From that point of view, the mass-action law can be used to express the state of equilibrium despite the fact that this law is defined exclusively for homogeneous systems. Derived this way, the so-called pseudo-equilibrium constant Ke is not really a constant, since it depends on the total concentration ... 

A chemical equilibrium system may generally consist of p distinct homogeneous sub-regions ( phases ) in coexistence. For such a composite equilibrium system, the total internal energy is additive in each subregion ... 

The calculation of the equilibrium conversion of heterogeneous reactions is in most cases much more complicated then in the case of homogeneous reactions, because the calculations involve in general the solution of the conditions for chemical equilibrium and the conditions for phase equilibrium. In the following a relatively simple example is given. 

Diffusion is the transport of a chemical by random motion due to a state of disequilibrium. For example, diffusion causes the movement of a chemical within a phase (e.g., water) from a location of relatively high concentration to a place of lower concentration until the chemical is homogeneously distributed throughout the phase. Likewise diffusive transport will drive a chemical between media (e.g., water and air) until their equilibrium concentrations are reached and thus the chemical potentials or fugacities are equal in each phase. 

Sometimes the oxidized species can exist in two forms in chemical equilibrium, with one of them electro-inactive in the potential range where the electrochemical process occurs. This type of reaction pathway is known as a CE mechanism because a homogeneous chemical reaction (C) precedes the heterogeneous electrochemical process (E). If the chemical step is of first or pseudo-first order, the process can be expressed by the reaction scheme ... 

Homogeneous equilibrium refers to a chemical equilibrium among reactants and products that are all in the same phase of matter. Heterogeneous equilibrium takes place between two or more chemicals in different phases. 

Heidemann (12) observes that "the chemical reaction equilibrium problem in a homogeneous phase is knoym to have an unique solution except when the thermodynamic model of the phase can exhibit diffusional instability." Hence, for chemical equilibrium in a single phase, local minima in Gibbs free energy do not occur and the search is simplified. 

This equation is valid for a homogeneous state of equilibrium. For slow reactions, it is reasonable to assume that the chemical process is proceeding through states that are in thermomechanical equilibrium at all times, although chemical equilibrium is not established. This assumption is supported by the fact that, for example, for a gaseous mixture, collisions not causing reactions are far more frequent than collisions that cause reactions. At a specified... 

The framework within which condensed phases are studied is provided by the phase rule, which gives the number of independent thermodynamic variables required to determine completely the state of the system. This number, called the number of degrees of freedom or the variance of the system, will be denoted by F. The number of phases present (that is, the number of homogeneous, physically distinct parts) will be denoted by P, and the number of independently variable chemical constituents will be called C. By independently variable constituents, we mean those whose concentrations are not determined by the concentrations of other constituents through chemical-equilibrium equations or other subsidiary conditions. The phase rule states that... 

In this section, we discuss the general problem of chemical equilibrium under the assumption that the system considered is guaranteed to exist in a one-phase (homogeneous) condition at all possible compositions. We initially follow the logical approach discussed in Chapter 3 of Astarita (1989a), and we are therefore very concise in the first subsection, referring the reader to that work for details. 

Equilibrium in gases. Applications. In dealing with applications, we come now to the methods by which we may determine the quantity of each substance present in a gaseous mixture in the state of chemical equilibrium, or more generally in any homogeneous mixture. Two ways are open. 

Chemical Equilibrium in Homogeneous Condensed Ideal Solutions... 

CHEMICAL EQUILIBRIUM IN HOMOGENEOUS CONDENSED IDEAL SOLUTIONS... 

The subsequent discussion is based on the theorem that all reactions in a homogeneous system come to a stop when a certain definite chemical equilibrium has been established between the substances which take part in the reaction. In other words, that such reactions never proceed so far that the substances entering into the reaction have disappeared entirely. All the... 

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