Chemical equilibrium point

Helgeson (1967) constructed an activity diagram depicting chemical equilibrium points (albite-sericite-K-feldspar and albite-sericite-Na-montmorillonite) of NazO-K20-Si02-Al203-H20 system at elevated temperatures. At these points,... 

The general relationships involved for a single chemical reaction in a closed system are shown schematically in Figure 1, where the degree of advancement at point e corresponds to chemical equilibrium. Point t represents a state of the system corresponding to spontaneous chemical reaction. While the invariant condition of the closed system considered is the equilibrium state, e, this generally is not the case for a thermodynamic system open to its environment. For such a system, the time-... 

Note that when water is added to CaSO f Os, the latter dissolves until its rate of dissolution is equal to its rate of precipitation. This is, by definition, the chemical equilibrium point. If, at this point, a certain amount of NaCl (a very water-soluble salt) is added, it suppresses the single-ion activity coefficient of Ca2+ and SO2". Hence, the... 

The influence of Damkohler number on the trajectory of the residue curves is evident. For Da=0 the residue curve lines will end in the highest boihng stable node (i.e. pure component or nonreactive azeotrope), whereas for high Da the lines will also end in a stable node, corresponding to a pure component, chemical equilibrium point or a reactive azeotrope. 

Note that conditional averages appear in AEc, but not in A S- We shall now reinterpret this observation from a chemical equilibrium point of view i.e., the quantity Ep g - (Ep)o will be related to the shift in the chemical equilibrium L H induced by the adsorption of G. To do that we adopt a mixture-model point of view of the same system. This approach will be generalized in Chapter 5 to treat any liquid and in particular aqueous solutions. In our model we have two states of the adsorbent molecules. The mixture-model approach follows from the classification of molecules in state L as L-molecule, and likewise molecules in state H as an //-molecule. This is the same procedure we have discussed in section 2.4. We now assign partial molecular quantities to the species L and H, viewing Ml and Mh as independent variables. Theoretically these are defined as partial derivatives of the corresponding thermodynamic functions (see below). From the physical point of view, these can be defined only if we have a means of varying Ml and Mh independently, e.g., by placing an inhibitor that prevents the conversion between... 

Some chemical reactions are reversible and, no matter how fast a reaction takes place, it cannot proceed beyond the point of chemical equilibrium in the reaction mixture at the specified temperature and pressure. Thus, for any given conditions, the principle of chemical equilibrium expressed as the equilibrium constant, K, determines how far the reaction can proceed if adequate time is allowed for equilibrium to be attained. Alternatively, the principle of chemical kinetics determines at what rate the reaction will proceed towards attaining the maximum. If the equilibrium constant K is very large, for all practical purposes the reaction is irreversible. In the case where a reaction is irreversible, it is unnecessary to calculate the equilibrium constant and check the position of equilibrium when high conversions are needed. 

Equation (5.59) is the starting point for deriving the condition for chemical equilibrium. We have written a generalized chemical reaction as... 

One difficulty Haber faced is that the reactions used to produce compounds from nitrogen do not go to completion, but appear to stop after only some of the reactants have been used up. At this point the mixture of reactants and products has reached chemical equilibrium, the stage in a chemical reaction when there is no further tendency for the composition of the reaction mixture—the concentrations or partial pressures of the reactants and products—to change. To achieve the greatest conversion of nitrogen into its compounds, Haber had to understand how a reaction approaches and eventually reaches equilibrium and then use that... 

Fig. 9-3 Conceptual model to describe the interaction between chemical weathering of bedrock and down-slope transport of solid erosion products. It is assumed that chemical weathering is required to generate loose solid erosion products of the bedrock. Solid curve portrays a hypothetical relationship between soil thickness and rate of chemical weathering of bedrock. Dotted lines correspond to different potential transport capacities. Low potential transport capacity is expected on a flat terrain, whereas high transport is expected on steep terrain. For moderate capacity, C and F are equilibrium points. (Modified with permission from R. F. Stallard, River chemistry, geology, geomorphology, and soils in the Amazon and Orinoco basins. In J. I. Drever, ed. (1985), "The Chemistry of Weathering," D. Reidel Publishing Co., Dordrecht, The Netherlands.)...

More concretely, the aim of our investigation is to examine, from a theoretical point of view, the relation between the non-rigidity of pentacoordinate molecules and the characteristics of the temporal evolution of systems of such molecules towards chemical equilibrium. We also want to indicate the type of experimental information needed concerning the time evolution of these systems, in order to sharpen our ideas on the feasibility of the internal movements. We here give an account of the main aspects of our attempt and try to present it in a unified and synthesizing fashion. 

As an indispensable source of fertilizer, the Haber process is one of the most important reactions in industrial chemistry. Nevertheless, even under optimal conditions the yield of the ammonia synthesis in industrial reactors is only about 13%. This Is because the Haber process does not go to completion the net rate of producing ammonia reaches zero when substantial amounts of N2 and H2 are still present. At balance, the concentrations no longer change even though some of each starting material is still present. This balance point represents dynamic chemical equilibrium. 

Here, the sign of equality (=) has been replaced by the double oppositely directed arrows (s=) called a sign of reversibility. Such a reaction is called a reversible reaction. The reversibility of reactions can be detected when both the forward and the reverse reactions occur to a noticeable extent. Generally, such reactions are described as reversible reactions. The most important criterion of a reaction of this type is that none of the reactants will become exhausted. When the reaction is allowed to take place in a closed system from where none of the substances involved in the reaction can escape, one obtains a mixture of the reactants and the products in the reaction vessel. Every reversible reaction, depending on its nature, will after some time reach a stage when the reactants and the products coexist in a state of balance, and their amounts will remain unaltered for unlimited time. Such a state of a chemical reaction is called chemical equilibrium, and the point of such an equilibrium varies only with temperature. 

A catalyst cannot change the ultimate equilibrium point set by thermodynamics, but it can affect the rate at which this point is approached. However, it can facilitate approach to equilibrium with respect to a desired reaction while not influencing the rates of other less desirable reactions. In optimizing yields of desired products, chemical engineers are very concerned with the selectivity or specificity of a catalyst. For commercial applications, selectivity is often more important than activity per se. 

In this point we disagree with Macosko, who deduced a rather large correction from a small sol fraction, assuming that the extract consists of molecules, which could in principle react, but did not do so, because the chemical equilibrium was attained, or because there was steric hindrance etc. (6, 7). ... 

Aqueous geochemists work daily with equations that describe the equilibrium points of chemical reactions among dissolved species, minerals, and gases. To study an individual reaction, a geochemist writes the familiar expression, known as the mass action equation, relating species activities to the reaction s equilibrium constant. In this chapter we carry this type of analysis a step farther by developing expressions that describe the conditions under which not just one but all of the possible reactions in a geochemical system are at equilibrium. 

The tools for calculating the equilibrium point of a chemical reaction arise from the definition of the chemical potential. If temperature and pressure are fixed, the equilibrium point of a reaction is the point at which the Gibbs free energy function G is at its minimum (Fig. 3.1). As with any convex-upward function, finding the minimum G is a matter of determining the point at which its derivative vanishes. 

Knowing the chemical potential function for each species in a reaction defines the reaction s equilibrium point. Consider a hypothetical reaction,... 

We can find the reaction s equilibrium point from Equation 3.3 as soon as we know the form of the function representing chemical potential. The theory of ideal solutions (e.g., Pitzer and Brewer, 1961 Denbigh, 1971) holds that the chemical potential of a species can be calculated from the potential pg of the species in its pure form at the temperature and pressure of interest. According to this result, a species chemical potential is related to its standard potential by... 

Several chemical geothermometers are in widespread use. The silica geothermometer (Fournier and Rowe, 1966) works because the solubilities of the various silica minerals (e.g., quartz and chalcedony, Si02) increase monotonically with temperature. The concentration of dissolved silica, therefore, defines a unique equilibrium temperature for each silica mineral. The Na-K (White, 1970) and Na-K-Ca (Fournier and Truesdell, 1973) geothermometers take advantage of the fact that the equilibrium points of cation exchange reactions among various minerals (principally, the feldspars) vary with temperature. 

The mixture we have just described, even with a chemical reaction, must obey thermodynamic relationships (except perhaps requirements of chemical equilibrium). Thermodynamic properties such as temperature (T), pressure (p) and density apply at each point in the system, even with gradients. Also, even at a point in the mixture we do not lose the macroscopic identity of a continuum so that the point retains the character of the mixture. However, at a point or infinitesimal mixture volume, each species has the same temperature according to thermal equilibrium. 

Fig. 3. Classification of human prion diseases. Sporadic the transformation from PrPc (circle) to PrPSc (square) occurs without apparent cause. Familial a point mutation ( ) is thought to facilitate the transformation. Infectious the transformation arises via PrPSc which acts as a template. The kinetic equations are defined by Eigen (1996). The infectious form includes kuru, iatrogenic CJD (iCJD), variant CJD (vCJD first reported in 1996), bovine spongiform encephalopathy (BSE first reported in 1985), and scrapie. In the nucleation-dependent model, monomeric PrPc and PrPSc are in chemical equilibrium.

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