Thermodynamic condition

Chain growth can only occur under suitable thermodynamic conditions. For the chains to have required properties, some chemical conditions must also be fulfilled. The possibility of the technical control of propagation depends on the rates of the respective reactions, i. e. on the kinetics of the process. 

As any other process, propagation can spontaneously proceed only when accompanied a decrease in the Gibbs energy (free enthalpy) of the system AG = AH - T AS (1) 

There must therefore exist some conditions where the rate of propagation is just equal to the rate of depropagation, i. e. where AG = 0. The temperature at which the rates of reaction (2) are equal in both directions is of special importance for polymerizations. 

Economy and technical possibilities determine and limit to some extent the extraction pressure, but for industrial plants a trend to higher pressures can be recognized in recent years. 

For already known systems, modifications based on the old semiempirical equation of state from Van der Waals have been developed, a successful one from Redlich and Kwong or the one from Soave. A variation specifically describing the properties in the critical and supercritical area is given by the equation of Peng and Robinson [18]. Derivations from the association laws for unknown solute properties are used to describe experimental results, the one from Chrastil [19] is the most popular one and usefid for the calculation of equilibrium distribution. 

Modeling supercritical extraction of solid material is based on the mass balances that are relevant for the internal diffusive transport of the extract within the solid matter and the external convective transport of the extract from the solid surface to the solvent fluid. 

The most important parameters in mass transfer modeling are the effective diffusion coefficient Defrand the mass transfer rate dXp/dt, which is linked to the mass transfer coefficient k in the balance equation for external transport. As for the calculation of effective diffusion coefficients, simple equations have been proposed in literature [10]. 

Us is the specific surface aria (m /m ) e is the porosity of solid bed k is the mass transfer coefficient (m/s) 

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It may be desirable to predict which crystal structure is most stable in order to predict the products formed under thermodynamic conditions. This is a very difficult task. As of yet, no completely automated way to try all possible crystal structures formed from a particular collection of elements (analogous to a molecular conformation search) has been devised. Even if such an effort were attempted, the amount of computer power necessary would be enormous. Such studies usually test a collection of likely structures, which is by no means infal-... 

The experimentally measured dependence of the rates of chemical reactions on thermodynamic conditions is accounted for by assigning temperature and pressure dependence to rate constants. The temperature variation is well described by the Arrhenius equation. 

Adadurov, G.A. and Gol danskii, V.I., Transformations of Condensed Substances Under Shock-Wave Compression in Controlled Thermodynamic Conditions, Russian Chem. Rev. 50 (10), 848-957 (1981). 

The molecular and liquid properties of water have been subjects of intensive research in the field of molecular science. Most theoretical approaches, including molecular simulation and integral equation methods, have relied on the effective potential, which was determined empirically or semiempirically with the aid of ab initio MO calculations for isolated molecules. The potential parameters so determined from the ab initio MO in vacuum should have been readjusted so as to reproduce experimental observables in solutions. An obvious problem in such a way of determining molecular parameters is that it requires the reevaluation of the parameters whenever the thermodynamic conditions such as temperature and pressure are changed, because the effective potentials are state properties. 

To facilitate the use of methanol synthesis in examples, the UCKRON and VEKRON test problems (Berty et al 1989, Arva and Szeifert 1989) will be applied. In the development of the test problem, methanol synthesis served as an example. The physical properties, thermodynamic conditions, technology and average rate of reaction were taken from the literature of methanol synthesis. For the kinetics, however, an artificial mechanism was created that had a known and rigorous mathematical solution. It was fundamentally important to create a fixed basis of comparison with various approximate mathematical models for kinetics. These were derived by simulated experiments from the test problems with added random error. See Appendix A and B, Berty et al, 1989. 

Scheme 7.1. Composition of Ketone-Enoiate Mixtures Formed under Kinetic and Thermodynamic Conditions"...

When the aldol reaction is carried Wt under thermodynamic conditions, the product selectivity is often not as high as under kinetic conditions. All the regioisomeric and stereoisomeric enolates may participate as nucleophiles. The adducts can return to reactants, and so the difference in stability of the stereoisomeric anti and syn products will determine the product composition. 

Trifluoromethyl alkyl ketones also undergo directed aldol condensations under thermodynamic conditions in the presence of piperidine and acetic acid [2, d] Under these reaction conditions, the product suffers a facile dehydration to form the unsaturated trifluoromethyl ketones (equations 2 and 3)... 

In a monetaiy bank, money is added and withdrawn, but if ill the end the bank is in exactly the same state, the net amount of money in the bank has not changed. Similarly, a gas may expand or be compressed and Its temperature may undergo changes, but if at the end it is in exactly the same thermodynamic condition, the internal energy has not changed. 

In practice, thermal cycling rather than isothermal conditions more frequently occurs, leading to a deviation from steady state thermodynamic conditions and introducing kinetic modifications. Lattice expansion and contraction, the development of stresses and the production of voids at the alloy-oxide interface, as well as temperature-induced compositional changes, can all give rise to further complications. The resulting loss of scale adhesion and spalling may lead to breakaway oxidation " in which linear oxidation replaces parabolic oxidation (see Section 1.10). 

Part of the gas can escape from the solution at a specific concentration and a fixed temperature, as the pressure level falls to under P < Pg. This takes place in two phases appearance of nuclei, and growth of bubbles of the free gas phase. Thermodynamic conditions for stable nucleation are formulated in [1], They are analogous to the conditions for starting the boiling of low-molecular liquids. The following changes take... 

The hydride phase may be present in a catalyst as a result of the method of its preparation (e.g. hydrogen pretreatment), or it may be formed during the course of a given reaction, when a metal catalyst is absorbing hydrogen (substrate—e.g. in H atom recombination product—e.g. in HCOOH decomposition). The spontaneous in situ transformation of a metal catalyst (at least in its superficial layer) into a hydride phase is to be expected particularly when the thermodynamic conditions are favorable. 

We calculated the melting temperature of a system characterized by predetermined values of parameters fi, y and N from the thermodynamic condition... 

Although liquid Hg would never be used as a reference (model) surface in surface physics because its liquid state and high vapor pressure do not allow appropriate UHV conditions, this metal turns out to be a reference surface in electrochemistry for precisely the same reasons reproducibility of the surface state, easy cleaning of its surface, and the possibility of measuring the surface tension (surface thermodynamic conditions). In particular, the establishment of a UHV scale for potentials is at present based on data obtained for Hg. 

Passivation is defined as the state where even though a metal electrode fulfills the thermodynamic condition for dissolution (solution composition, electrode potential, etc.), a corrosive reaction scarcely proceeds. 

The products of the dimerization of l,6-dihydroxy-2-hexanone118 are the simplest models for the dihexulose dianhydrides. Under thermodynamic conditions, the isomer (20) was the sole product. Under kinetic conditions, compounds 20 and 21 are formed as a 1 1 mixture. Whereas 20 has the conformation illus-... 

Variations in the proportions of the different components of product mixtures are observed in reactions that involve anhydrous HF31-80-82-84-85 and in pyridinium poly(hydrogen fluoride).86 These variations can also be explained in terms of kinetic and thermodynamic control. Thus, less stable, but more rapidly formed, dianhydrides isomerize under thermodynamic conditions to give more-stable products. It has also been noted that the starting isomeric forms of the ketose influence the kinetic outcome of the reaction.119... 

The last chapter in this introductory part covers the basic physical chemistry that is required for using the rest of the book. The main ideas of this chapter relate to basic thermodynamics and kinetics. The thermodynamic conditions determine whether a reaction will occur spontaneously, and if so whether the reaction releases energy and how much of the products are produced compared to the amount of reactants once the system reaches thermodynamic equilibrium. Kinetics, on the other hand, determine how fast a reaction occurs if it is thermodynamically favorable. In the natural environment, we have systems for which reactions would be thermodynamically favorable, but the kinetics are so slow that the system remains in a state of perpetual disequilibrium. A good example of one such system is our atmosphere, as is also covered later in Chapter 7. As part of the presentation of thermodynamics, a section on oxidation-reduction (redox) is included in this chapter. This is meant primarily as preparation for Chapter 16, but it is important to keep this material in mind for the rest of the book as well, since redox reactions are responsible for many of the elemental transitions in biogeochemical cycles. 

T, 0.1 MPa) condition to be calculated, t is then known for any P and T corresponding to an ambient pressure value of TV. This method is quite powerful because it allows determination of relaxation times for any thermodynamic condition T, P, or V) provided only that the same value of T had been measured at ambient pressure. 

The third law of thermodynamics establishes a starting point for entropies. At 0 K, any pure perfect crystal is completely constrained and has S = 0 J / K. At any higher temperature, the substance has a positive entropy that depends on the conditions. The molar entropies of many pure substances have been measured at standard thermodynamic conditions, P ° = 1 bar. The same thermodynamic tables that list standard enthalpies of formation usually also list standard molar entropies, designated S °, fbr T — 298 K. Table 14-2 lists representative values of S to give you an idea of the magnitudes of absolute entropies. Appendix D contains a more extensive list. 

Electrochemical cells can be constructed using an almost limitless combination of electrodes and solutions, and each combination generates a specific potential. Keeping track of the electrical potentials of all cells under all possible situations would be extremely tedious without a set of standard reference conditions. By definition, the standard electrical potential is the potential developed by a cell In which all chemical species are present under standard thermodynamic conditions. Recall that standard conditions for thermodynamic properties include concentrations of 1 M for solutes in solution and pressures of 1 bar for gases. Chemists use the same standard conditions for electrochemical properties. As in thermodynamics, standard conditions are designated with a superscript °. A standard electrical potential is designated E °. 

However, making an even small step to qualitative assessment of availability of active particles on the surface under regular thermodynamic conditions is difficult. This is especially difficult if we are faced with the problem of quantitative evaluation of particles origin and role in specific heterogeneous processes. 

Up to date, several experimental techniques have been developed which are capable of detecting some of these particles under ordinary thermodynamic conditions. One can use these methods to keep track of transformations of the particles. For instance, it is relevant to mention here the method of electron paramagnetic resonance (EPR) with sensitivity of about 10 particles per cm [IJ. However, the above sensitivity is not sufficient to study physical and chemical processes developing in gaseous and liquid media (especially at the interface with solids). Moreover, this approach is not suitable if one is faced with detection of particles possessing the highest chemical activity, namely, free radicals and atoms. As for the detection of excited molecular or atom particles... 

The acidifying effect of an adjacent phenyl group outweighs steric effects in the case of l-phenyl-2-propanone, and as a result the conjugated enolate is favored by both kinetic and thermodynamic conditions (Entry 5). 

Under other reaction conditions, the product can result from thermodynamic control. Aldol reactions can be effected for many compounds using less than a stoichiometric amount of base. In these circumstances, the aldol reaction is reversible and the product ratio is determined by the relative stability of the various possible products. Thermodynamic conditions also permit equilibration among the enolates of the nucleophile. The conditions that lead to equilibration include higher reaction temperatures, protic or polar dissociating solvents, and the use of weakly coordinating cations. Thermodynamic conditions can be used to enrich the composition in the most stable of the isomeric products. 

Triethyl orthoformate or chloroform can react with arene nucleophiles to give triphenylmethanes with three identical aryl groups.5,52,67 In addition, dialkylarylamines, when treated with dialkoxycarbenium tetrafluoro-borates under thermodynamic conditions or with triethyl orthoformate/zinc chloride in ether under anhydrous conditions, give triarylmethanes.68 For example, 4-methoxycarbazole and triethyl orthoformate in the presence of acid catalyst give 44 in 66% yield69 (Scheme 7). In general, phenolic or... 

A great many electrolytes have only limited solubility, which can be very low. If a solid electrolyte is added to a pure solvent in an amount greater than corresponds to its solubility, a heterogeneous system is formed in which equilibrium is established between the electrolyte ions in solution and in the solid phase. At constant temperature, this equilibrium can be described by the thermodynamic condition for equality of the chemical potentials of ions in the liquid and solid phases (under these conditions, cations and anions enter and leave the solid phase simultaneously, fulfilling the electroneutrality condition). In the liquid phase, the chemical potential of the ion is a function of its activity, while it is constant in the solid phase. If the formula unit of the electrolyte considered consists of v+ cations and v anions, then... 

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