Thermodynamic feasibility

We say the solution is saturated if solute is partitioned between a liquid-phase solution and undissolved, solid material (Figure 5.16). In other words, the solution contains as much solute as is feasible, thermodynamically, while the remainder remains as solid. The best way to tell whether a solution is saturated, therefore, is to look for undissolved solid. If -Repartition) is small then we say that not much of the solute resides in solution, so most of the salt remains as solid - we say the salt is not very soluble. Conversely, most, if not all, of the salt enters solution if K(partition) is large. 

Table 1(b) on the formation or removal in vacua of carbon monoxide by reaction of surface oxides with carbon in the metal shows the results of these calculations. The reactions are feasible thermodynamically in vacua of the order of 10-10 atm. at temperatures of 600°C. or higher for the metals tungsten, chromium, and iron. Thus, carbon monoxide will be formed by the diffusion of carbon to the surface and subsequent reaction with the surface oxides. This reaction has been discussed for the case of steels by Holm (11). The effect of carbon content on the reaction is not shown in the table. However, the effect can be seen from the expression for the equilibrium constant K for the reaction of ferrous oxide with carbon in the iron ... 

Before digging further into the mathematical details, the reader may wish to try sketching alternative flux direction patterns. Doing so, one will find that no other pattern agrees with the transport flux directions and has a feasible thermodynamic potential. For example consider the direction patterns illustrated in Figure 9.8. 

Using Equation (9.19), the thermodynamic constraint that there must exist a feasible thermodynamic driving force for any flux pattern can be expressed as follows ... 

A catalyst is a substance that speeds up a chemical reaction but is not itself consumed. Catalysts do not alter the thermodynamics of a reaction or the position of equilibrium, but act by providing an alternative pathway of lower activation energy. A high proportion of industrial chemical processes, inorganic and organic, use catalysts. They allow many reactions to be performed at lower temperatures than without a catalyst, and also provide selectivity in producing a specific product in reactions where several products are feasible thermodynamically. Enzymes (which often contain metallic elements see Topic J3) are uniquely selective biological catalysts. 

There are two major approaches for the synthesis of crystallization-based separation. In one approach, the phase equilibrium diagram is used for the identification of separation schemes (For example Cisternas and Rudd, 1993 Berry et al., 1997). While these procedures are easy to understand, they are relatively simple to implement only for simple cases. For more complex systems, such as multicomponent systems and multiple temperatures of operation, the procedure is difficult to implement because the graphical representation is complex and because there are many alternatives to study. The second strategy is based on simultaneous optimization using mathematical programming based on a network flow model between feasible thermodynamic states (Cisternas and Swaney, 1998 Cisternas, 1999 Cisternas et al. 2001 Cisternas et al. 2003). 

Oxamidinium salts are very common by-products when tetra-aminoethylenes (even of the aralkyl type) are treated with acids, Bronsted or Lewis. With Bronsted acids, reduction to molecular hydrogen is feasible thermodynamically, but it has been ruled out in at least one instance The oxidizing agent is air in some reactions of this type (section III.B.5), but care has been taken to exclude it in others, for example the reaction of bi(imidazolidine) (5) with boron trifluoride in methylene chloride . Much remains to be learned about the mechanisms of these processes. 

In general, the normal DA reaction mechanism is a domino process that is initialized by the polar reaction between the diene and the dienophile to give the primary cicloadduct. These DA reactions have a two-step non-intermediate mechanism characterized by the nucleophilic attack on the non-substituted methylene of the diene to the electrophilically activated position of the dienophile. The subsequent ring-closure affords the primary cicloadduct. This behavior makes the reaction to be regioselective. The latter concerted elimination of the nitrous acid from the primary cicloadduct yields the precursor of the final aromatic product. Spite of the large activation free energy associated with the DA reaction and the endergonic character of formation of the primary cicloadduct, the irreversible extrusion of the nitrous acid make feasible thermodynamically the domino reaction. 

GCMC simulations have also been used to explore the favorable thermodynamic conditions for exchanging carbon dioxide and methane in the S-I clathrate hydrates. Of practical interest is the need to find a feasible thermodynamic pathway in the phase diagram consisting of methane, carbon... 

The first step in designing a reaction system is to establish the thermodynamic equilibrium relationship between the reactants and products and to calculate the heat effects of the reaction. This step is vital because the equilibrium constants and heat effects, which may be readily calculated [88, 89], will immediately tell us whether the reaction is in fact feasible thermodynamically and whether some special precautions are needed to remove the products and... 

Unfortunately, this is not a feasible approach for calculating thermodynamic properties di to the large number of configurations that have extremely small (effectively zero) Boltzmar... 

Although the number of ring atoms is the structural feature upon which we focus attention, we shall use the criteria of thermodynamics and kinetics to assess the feasibility of the reactions listed above. 

Electrolysis. Electrowinning of zirconium has long been considered as an alternative to the KroU process, and at one time zirconium was produced electrolyticaHy in a prototype production cell (70). Electrolysis of an aH-chloride molten-salt system is inefficient because of the stabiUty of lower chlorides in these melts. The presence of fluoride salts in the melt increases the stabiUty of in solution, decreasing the concentration of lower valence zirconium ions, and results in much higher current efficiencies. The chloride—electrolyte systems and electrolysis approaches are reviewed in References 71 and 72. The recovery of zirconium metal by electrolysis of aqueous solutions in not thermodynamically feasible, although efforts in this direction persist. 

Dynamic meteorological models, much like air pollution models, strive to describe the physics and thermodynamics of atmospheric motions as accurately as is feasible. Besides being used in conjunction with air quaHty models, they ate also used for weather forecasting. Like air quaHty models, dynamic meteorological models solve a set of partial differential equations (also called primitive equations). This set of equations, which ate fundamental to the fluid mechanics of the atmosphere, ate referred to as the Navier-Stokes equations, and describe the conservation of mass and momentum. They ate combined with equations describing energy conservation and thermodynamics in a moving fluid (72) ... 

Protein-DNA complexes present demanding challenges to computational biophysics The delicate balance of forces within and between the protein, DNA, and solvent has to be faithfully reproduced by the force field, and the systems are generally very large owing to the use of explicit solvation, which so far seems to be necessary for detailed simulations. Simulations of such systems, however, are feasible on a nanosecond time scale and yield structural, dynamic, and thermodynamic results that agree well with available experimen-... 

Estimation of the free-energy change associated with a reaction permits the calcula-aon of the equilibrium position for a reaction and indicates the feasibility of a given chemical process. A positive AG° imposes a limit on the extent to which a reaction can x cur. For example, as can be calculated using Eq. (4.2), a AG° of 1.0 kcal/mol limits conversion to product at equilibrium to 15%. An appreciably negative AG° indicates that e reaction is thermodynamically favorable. 

Whether AH for a projected reaction is based on bond-energy data, tabulated thermochemical data, or MO computations, there remain some fundamental problems which prevent reaching a final conclusion about a reaction s feasibility. In the first place, most reactions of interest occur in solution, and the enthalpy, entropy, and fiee energy associated with any reaction depend strongly on the solvent medium. There is only a limited amount of tabulated thermochemical data that are directly suitable for treatment of reactions in organic solvents. Thermodynamic data usually pertain to the pure compound. MO calculations usually refer to the isolated (gas phase) molecule. Estimates of solvation effects must be made in order to apply either experimental or computational data to reactions occurring in solution. 

Equation (3.5) can be used to establish a one-to-one correspondence among all composition scales for which mass exchange is feasible. Since most environmental applications involve dilute systems, one can assume that these systems behave ideally. Hence, the transfer of the pollutant is indifferent to the existence of other species in the waste stream. In other words, even if two waste streams contain species that are not identical, but share the same composition of a particular pollutant, the equilibrium composition of the pollutant in an MSA will be the same for both waste streams. Hence, a single composition scale, y, can be used to represent the concentration of the pollutant in any waste stream. Next, (3.5) can be employed to generate Ns scales for the MSAs. For a given set of corresponding composition scales y,x, X2,..., xj,..., it is thermodynamically and practically feasible to transfer the pollutant from any waste stream to any MSA. In addition, it is also feasible to transfer the pollutant from any waste stream of a composition y/ to any MSA which has a composition less than the xy obtained from (3.5b). 

Next, both composite streams are plotted on the same diagram (Fig. 3.7). On this diagram, thermodynamic feasibility of mass exchange is guaranteed when the lean composite stream is always above the waste composite stream. This is equivalent to ensuring that at any mass>exchange level (which comesponds to a horizontal line), the composition of the lean composite stream is located to the left of the waste composite stream, asserting thermodynamic feasibility. Therefore,... 

Interpreting results of the pinch diagram As can be seen from Fig. 3.12, the pinch is located at the corresponding mole fractions (y,Xi.jc ) - (0.(K)10, 0.0030, 0.0010). The excess capacity of the process MSAs is 1.4 x lO" kg mol benzene/s and cannot be used because of thermodynamic and practical-feasibility limitations. This excess can be eliminated by reducing the outlet compositions and/or flowrates of the process MSAs. Since the inlet composition of S2 corresponds to a mole fraction of 0.0015 on the y scale, the waste load immediately... 

Cost estimation and screening external MSAs To determine which external MSA should be used to remove this load, it is necessary to determine the supply and target compositions as well as unit cost data for each MSA. Towards this end, one ought to consider the various processes undergone by each MSA. For instance, activated carbon, S3, has an equilibrium relation (adsorption isotherm) for adsorbing phenol that is linear up to a lean-phase mass fraction of 0.11, after which activated carbon is quickly saturated and the adsorption isotherm levels off. Hence, JC3 is taken as 0.11. It is also necessary to check the thermodynamic feasibility of this composition. Equation (3.5a) can be used to calculate the corresponding... 

This value corresponds to a corresponding y-scale composition of 0.0012, which is less than the supply mass fmction of phenol in either waste stream as well as the pinch composition. Hence, it is thermodynamically feasible for Sf to recover phenol from R] and R2. In addition, miy amount of phenol removed by S5 does not overlap with the load handled by the process MSAs. Therefore, the operating cost of air needed to remove 1 kg of phenol can be evaluated as follows ... 

Since it is thermodynamically feasible for any of the three external MSAs to remove the remaining phenolic load (0.0124 kg phenol/s), one should select... 

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