Equilibrium/equilibria concept

Horie and his coworkers [90K01] have developed a simplified mathematical model that is useful for study of the heterogeneous nature of powder mixtures. The model considers a heterogeneous mixture of voids, inert species, and reactant species in pressure equilibrium, but not in thermal equilibrium. The concept of the Horie VIR model is shown in Fig. 6.3. As shown in the figure, the temperatures in the inert and reactive species are permitted to be different and heat flow can occur from the reactive (usually hot) species to the inert species. When chemical reaction occurs the inert species acts to ther-... 

Garrels, R. M. and Mackenzie, F. T. (1967). Origin of the chemical compositions of some springs and lakes. In "Equilibrium Concepts in Natural Water Systems" (W. Stumm, ed.). Advances in Chemistry Series 67, pp. 222-274. American Chemical Society, Washington. 

First, the simple thermodynamic description of pe (or Eh) and pH are both most directly applicable to the liquid aqueous phase. Redox reactions can and do occur in the gas phase, but the rates of such processes are described by chemical kinetics and not by equilibrium concepts of thermodynamics. For example, the acid-base reaction... 

A fiirther test of the equilibrium concept, introduced in Example 8.3, involves introducing the influence of the breaking probability into the equilibrium process. In this case repeat the process of Example 8.2, but with the change of Pb(AB) to 0.5. Do you expect an effect What do you observe What is Kgq for this case ... 

Mandelkern L (2002) Crystallization of polymers,vol 1, 2nd edn. Equilibrium concepts. Cambridge University Press, Cambridge, p 42... 

Catalytic activity of solid acids in hydrocarbon conversions is often correlated with their acidity. Problems arise from the difficulty to bridge the gap between the equilibrium thermodynamic concept of acidity and the composite kinetic concept of catalytic activity [1], The correlation is meaningful if connected parameters are related to each other, namely, intrinsic activities are correlated with intrinsic acidities or relationship is established between corresponding apparent parameters. 

Is the assumed nature of equilibrium appropriate The modeler defines an equilibrium system that forms the core of a geochemical model, using one of the equilibrium concepts already described. The modeler needs to ask whether the reactions considered in an equilibrium system actually approach equilibrium. If not, it may be necessary to decouple redox reactions, suppress miner-... 

Parks, G. A. (1967), "Aqueous Surface Chemistry of Oxides and Complex Oxide Minerals Isoelectric Point and Zero Point of Charge," in Equilibrium Concepts in Natural Water Systems, Advances in Chemistry Series, No. 67, American Chemical Society, Washington, DC. 

Garrels, R.M. Mackenzie, F.T. In "Equilibrium Concepts in Natural Water Systems" Stumm, W., Ed. ADVANCES IN CHEMISTRY SERIES No. 67, American Chemical Society Washington, D.C., 1967 pp. 222-42. 

In this chapter, you learned about the Haber process for manufacturing ammonia. You used this process to help you understand various concepts related to equilibrium. As you can see in Figure 7.11, ammonia is a valuable industrial chemical. Its annual global production is well over 100 million tonnes. The vast majority of ammonia, roughly 80%, is used to make fertilizers. You will now examine how the equilibrium concepts you have been studying work together to provide society with a reliable, cost-effective supply of ammonia. 

In this chapter, you will continue your study of acid-base reactions. You will find out how ions in aqueous solution can act as acids or bases. Then, by applying equilibrium concepts to ions in solution, you will be able to predict the solubility of ionic compounds in water and the formation of a precipitate. 

Introduction What is Equilibrium Concepts of frustrated Equilibrium... 

The plan of this chapter is the following. Section II gives a summary of the phenomenology of irreversible processes and set up the stage for the results of nonequilibrium statistical mechanics to follow. In Section III, it is explained that time asymmetry is compatible with microreversibility. In Section IV, the concept of Pollicott-Ruelle resonance is presented and shown to break the time-reversal symmetry in the statistical description of the time evolution of nonequilibrium relaxation toward the state of thermodynamic equilibrium. This concept is applied in Section V to the construction of the hydrodynamic modes of diffusion at the microscopic level of description in the phase space of Newton s equations. This framework allows us to derive ab initio entropy production as shown in Section VI. In Section VII, the concept of Pollicott-Ruelle resonance is also used to obtain the different transport coefficients, as well as the rates of various kinetic processes in the framework of the escape-rate theory. The time asymmetry in the dynamical randomness of nonequilibrium systems and the fluctuation theorem for the currents are presented in Section VIII. Conclusions and perspectives in biology are discussed in Section IX. 

Before leaving this section we consider a slightly different optimization problem that may also be expensive to solve. In flowsheet optimization, the process simulator is based almost entirely on equilibrium concepts. Separation units are described by equilibrium stage models, and reactors are frequently represented by fixed conversion or equilibrium models. More complex reactor models usually need to be developed and added to the simulator by the engineer. Here the modular nature of the simulator requires the reactor model to be solved for every flowsheet pass, a potentially expensive calculation. For simulation, if the reactor is relatively insensitive to the flowsheet, a simpler model can often be substituted. For process optimization, a simpler, insensitive model will necessarily lead to suboptimal (or even infeasible) results. The reactor and flowsheet models must therefore be considered simultaneously in the optimization. 

In Goulded RF, Equilibrium concepts in natural water systems. Adv Chem Ser 67 161-172 Stumm W, Furrer G, Wieland E, Zinder B (1985) The effects of complex-forming ligands on the dissolution of oxides and aluminosilicates In Drever JI (ed) The chemistry of weathering. Reidel, Dordrecht, pp 55-74... 

THE RAPID-EQUILIBRIUM TREATMENT. The first rate equation for an enzyme-catalyzed reaction was derived by Henri and by Michaelis and Menten, based on the rapid-equilibrium concept. With this treatment it is assumed that there is a slow catalytic conversion step and the combination and dissociation of enzyme and substrate are relatively fast, such that they reach a state of quasi-equilibrium or rapid equilibrium. 

In the course of attempts to quantitatively and a priori describe separation of macromolecules by SEC, a theory was formulated, which considered the effect of porous structure of the column packing on the diffusion rate of separated macromolecules. The resulting theory of restricted diffusion by Ackers [56], however, rather contradicts the equilibrium conception of SEC. 

If this is the case, the interest in the phenomenology of /—r) in terms of the Butler Volmer equation (no diffusion control, all electron transfer at the interface) is lessened. It will be acceptable to use equilibrium concepts at the interface for many purposes, and concentrate on the rate-determining transport process outside the interfacial region. 

Finally, it should be pointed out that Part III will add a new important element that we need to describe organic compounds in natural systems, that is, time. So far, we have dealt only with equilibrium concepts (e.g., with the partitioning of organic compounds between different phases), but we have not addressed the question of how fast such equilibria are reached. Thus, in Chapter 12 we will introduce the time axis, that is, we will describe the temporal evolution of a compound concentration due to the influence from various transformation and transport processes. In Part IV we will go one step further and also add space into our considerations. 

In order to extend the above theory, we have to make use of the equilibrium partition concepts described in Part II. Here we generally define the equilibrium partition function between any phase B and A by ... 

This equilibrium-stage concept based on a transfer unit has been proposed for such continuous-contacting devices as, for example, packed towers. 

Schlenk equilibrium concept sot forth above, the magnesium halide component of tertiary alkyl Grignard reagents causes halohydria formation faster than the diaJkylmagnesium component can add. Spocial conditions have, howover. been found, which permit addition of (erf-butylmagnesium chloride to ethylene oxide (Eq. 818), giving a modest yield of the desired primary alcohol.1484 1101... 

Thermodynamics and Equilibrium Second We present chemical equilibrium from the viewpoint of thermodynamics. We believe that the quantitative formulation of equilibrium should rest on an understanding of free energy and entropy. To this end, we introduce the laws of thermodynamics before equilibrium, and we formulate equilibrium concepts in terms of standard free energies. This approach allows us to present a unified treatment of a wide range of chemical processes. 

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