Separation thermodynamics

Many, but not all, reactor configurations are discussed. Process design, catalyst manufacture, thermodynamics, design of experiments (qv), and process economics, as well as separations, the technologies of which often are appHcable to reactor technology, are discussed elsewhere in the Eniyclopedia (see Catalysis Separation Thermodynamics). 

Imagine we want to convert 1 mol of water starting at a room temperature of, say, 25 °C to steam. In fact we must consider two separate thermodynamic processes we first consider the heat needed to warm the water from 25 °C to its boiling temperature of 100 °C. The water remains liquid during this heating process. Next, we convert 1 mol of the liquid water at 100°C to gaseous water (i.e. we boil it), but without altering the temperature. 

For a problem involving surface chemistry, the next step is to execute the Surface Chemkin Interpreter, which reads the user s symbolic description of the surface-reaction mechanism. Required thermodynamic data can come from the same Thermodynamic Database used by Chemkin or from a separate Thermodynamic Database compiled for surface species. Both Interpreters provide the capability to add to or override the data in the database by user input in the reaction description. The Surface Chemkin Interpreter extracts all needed information about gas-phase species from the Chemkin Linking File. (Thus the Chemkin Interpreter must be executed before the Surface Chemkin Interpreter.) Like the Chemkin Interpreter, the Surface Chemkin Interpreter also provides a printed output and a Linking File. Again, the Surface Linking File is read by an initialization subroutine in the Surface Subroutine Library that makes the surface-reaction mechanism information available to all other subroutines in the Library. 

There are various methods for the prediction of stereoselectivities, both in racemate separation (thermodynamics, usually computed by force field methods) and enantioselective catalysis (reactivity, usually computed by quantum mechanics)18. Promising recent developments, primarily based on force field and statistical methods, but also involving QM modeling, are based on stereocartography, the computation of the chirality content and the evaluation of chirophores.151 154... 

Mixing Rules for the Penq-Robinson Equation of State. In order to separate thermodynamic variables from constants of the Peng-Robinson equation of state, we will insert Equations 8 and 9 in Equation 7 and we will write it in the following form ... 

The spontaneous mixing of the two polymers will transpire at a rate which reflects the degree of miscibility of the system. As X approaches the critical value for phase separation, "thermodynamic slowing down" of the interdiffusion will occur [12]. The rate of increase of the scattering contrast reflects the proximity of the system to criticality, as well as the strong composition dependence of the glass transition temperature of the blend. Extraction of a value for either the self diffusion constants [13,14] or the interaction parameter is not feasible from the presently available data. 

The adsorbate forms a separate thermodynamic phase in its own right, characterized by a volume Vs, an entropy Ss, mole numbers for each species, and a corresponding chemical potential ps It is assumed that at equilibrium the temperature T and pressure P for the adsorbate matches that of the gas phase. To handle... 

As Bunnett has noted (4), the kinetic barrier to nucleophilic attack is affected by the thermodynamics of the reaction. If this thermodynamic contribution could be removed, then intrinsic nucleophilicities for substitution reactions could be obtained that would be independent of the leaving group. Pioneering work by Albery and Kreevoy (7), Pellerite and Brauman (8), and Lewis et al. (9) has shown that Marcus theory can be applied to methyl-transfer reactions to separate thermodynamic and kinetic contributions and provide intrinsic barriers to nucleophilic attack. One expression of Marcus theory is given in equation 1, where AE is the activation energy, AE° is the heat of reaction, and AE0 is the intrinsic activation energy or the barrier to reaction in the absence of any thermodynamic driving force. 

Ping-Pong mechanisms have separate thermodynamic and kinetic Haldanes for each half-reaction, and the overall Haldanes are the product of those for each half-reaction. Since one can combine two thermodynamic or two kinetic Haldanes, or one of each, there are four possible Haldanes for a Ping-Pong mechanism with two half-reactions, although only two of these will have V i/V 2 to the first power (the other two have this ratio to the second or zero power). 

The conventional method of correlating vapor-liquid equilibrium data is to separate deviations from ideality into deviations occurring in the vapor phase and deviations occurring in the liquid phase, and then to fit these deviations with separate thermodynamically consistent correlation expressions. By this method deviations from ideality occurring in the vapor are usually calculated from an equation of state and deviations from ideality occurring in the liquid are calculated with reference to the pure liquid component. This method has proved very useful, even at pressures approaching the critical pressure of a mixture and at temperatures above the critical temperature of a component... 

There are several contributions of thermodynamics to the field of reactive separations. Thermodynamics provides the basic relations, such as energy balances of equilibrium conditions, used in the process models, which again are the key to reactive separation design. Furthermore, thermodynamics provides models and experimental methods for the investigations of the properties of the reacting fluid that have to be known for any successful process design. We will focus on equilibrium thermodynamics here but discuss relations to kinetic models. 

There are two basic approaches to modeling the thermodynamics of micelle formation. The mass action model views the micelles as reversible complexes of the monomer that are aggregating and predicts the sharp change in tendency of incremental surfactant to form micelles instead of monomer at the CMC this sharp transition is a consequence of the relatively large number of molecules forming the aggregate. The mass action model predicts that micelles are present below the CMC but at very low concentrations. The ocher major model used to describe micelle formation is the pseudophase separation model, which views micelles as a separate thermodynamic phase in equilibrium with monomer. Because micelle formation is a second-order phase transition, micelles are not a true thermodynamic phase, and this model is an approximation. However, the assumption that there are no mi-celies present below the CMC, and that the surfactant activity becomes constant above the CMC. is close to reality. and the mathematical simplicity of the pseudophase... 

For a two-component system, for example, Pb/PbCl2, 5max = F that is, in the presence of the individual metal phase, the LVl cannot form a separate thermodynamically stable phase. For a three-component system, e.g., Si/K2SiF6-KF, coexistence of solid Si and one solid phase of an intermediate is possible if Si02 is added to the melt, then two stable solid intermediate phases are thermodynamically possible, etc. 

Equilibrium versus conservation. The notion of static equilibrium is to proscribe, if one is interested in better understanding the notion of reversibility and related concepts, such as the role of time, the distinction between dynamic and static, the separation thermodynamics—thermodynamics of irreversible processes, etc. In replacing this notion of static equilibrium by a rule of conservation, one has access to a more interesting conceptual level. 

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