Thermodynamic equilibrium, gaseous

The anticipated content of impurities in the refined metal may be calculated a priori by assuming thermodynamic equilibrium at both metal/gas interfaces, and using the relevant stabilities of tire gaseous iodides. Adequate thermodynamic data could provide the activities of the impurities widr that of zirconium close to unity, but tire calculation of tire impurity transport obviously requires a knowledge of activity coefficients in the original impure material, which are not sufficiently well known. 

It follows that the position of thermodynamic equilibrium will change along the reactor for those reactions in which a change of tire number of gaseous molecules occurs, and therefore that the degree of completion and heat production or absorption of the reaction will also vaty. This is why the external control of the independent container temperature and the particle size of the catalyst are important factors in reactor design. 

Thermodynamic equilibrium is found by balancing chemical potentials, where the chemical potentials of condensed species are functions of only pressure and temperature, whereas the potentials of gaseous species also depend on concentrations. To solve for the chemical potentials, it is necessary to know the pressure-volume relations for species that are important products in detonation. It is also necessary to know these relations at the high pressures and temperatures that typically characterize the C-J state. Thus, there is a need for improved high-pressure equations of state for fluids, particularly for molecular fluid mixtures. 

Lasers and plasma provide means for investigating the rapid carbonization of coal at high temperatures. Owing to the short residence time of coal particles in a plasma jet, it is unlikely that thermodynamic equilibrium or even thermal equilibrium will be attained. Moreover the gaseous products will be heavily diluted by the carrier gas. Nevertheless the thermodynamics presented here provide a useful guide to the type of products which may be expected at various temperatures and their relative yields. 

A further proof of the great speed of the equilibration of the gaseous components was given by running experiments with H2 + D2 mixtures in the gas phase in the same vessel and over the same catalyst sample. Only at the lowest temperature (77° K.) and shortest contact time (15 min.) was the resulting mixture observed to deviate from thermodynamic equilibrium. 

There are cases, however, including the very common one of an air-water surface, where no ions can possibly pass the boundary thermodynamical equilibrium cannot therefore be set up between the water and air, and adsorption potentials (the surface potentials of Chapters II and III) are permanent. The usual method for measuring surface potentials with a radioactive air-electrode does not appreciably disturb the adsorption potentials the gaseous ions are very few and are attracted into the water by image forces so that no double layer, compensating the double layer in the water due to the dipoles of the molecules in the surface film, can build up in the air. 

The selectivity and activity of these preparations in the dehydrogenation and dehydration of n-butyl alcohol were determined. The reactions were conducted at atmospheric pressure with temperatures between 400° and 460°C., and an hourly space velocity of 1.3 which precluded thermodynamic equilibrium. The activities were expressed in milliliters (STP) of gaseous product formed by each of the reactions per milliliter of alcohol... 

Simple molecules may occur in three states, the solid, the liquid and the gaseous state. The transitions between these phases are sharp and associated with a thermodynamic equilibrium. Under these conditions, phase changes are typical first-order transitions, in which a primary thermodynamic function, such as volume or enthalpy, shows a sudden jump. 

This mechanism allows the alkylidene groups to change partners back and forth with the catalytic metal until a thermodynamic equilibrium is reached. As we saw earlier, good yields of products result if there is an effective driving force (such as formation of a gaseous by-product or release of ring strain) to push the equilibrium toward the desired products. 

In order to simulate the pressure increase and pressure build-up time in the storage system, we shall first assume a closed system in thermodynamic equilibrium with a constant heat input Q, see Figure 1.11. We assume that the pressure and temperature of the boiling liquid hydrogen and the gaseous saturated hydrogen vapor are the same throughout the whole system. 

CVD normally involves a multi-component and a multi-phase system. There are various ways to calculate thermodynamic equilibrium in multicomponent systems. The following is a brief discussion of the optimization method where the minimization of Gibbs free energy can be achieved. The free energy G of a system consisting of m gaseous species and s solid phases can be described by. 

The energy transfer from an irradiated sohd towards the gaseous phase, which can result in a modification of the thermodynamical equilibrium of the considered system, clearly distinguishes this aspect of the radiation catalysis from the activation process. This transfer phenomenon is related... 

In two-phase systems in which the catalytic reaction takes place in the liquid phase between a liquid reactant and gaseous reactants, the latter have to be transferred over the gas/liquid boundary layer into the liquid phase. In this situation the reaction engineering prediction described above can be performed in an analogous way as long as the rate of transfer of the gaseous reactants into the liquid phase is fast compared with the intrinsic catalytic reaction. Under these circumstances it can usually be assumed that the liquid-phase concentrations of the gaseous reactants correspond to gas/liquid thermodynamic equilibrium. 

The convention we follow in this book is to describe chemical equilibrium in terms of the thermodynamic equilibrium constant K, even when analyzing reactions empirically. Consequently, for gaseous reactions we will state values of K without dimensions, and we will express all pressures in atmospheres. The Pref factors will not be explicitly included because their value is unity with these choices of pressure unit and reference pressure. Following this convention, we write the mass action law for a general reaction involving ideal gases as... 

Just as with gaseous reactions, the convention we follow in this book is to describe solution equilibria in terms of the thermodynamic equilibrium constant K rather than the empirical Kq. Thus, we express solution concentrations in units of mol with the reference state as c ef = 1 M, and we state values of K as dimensionless quantities. For these conditions the mass action law for solution reactions becomes... 

Thermodynamics views a chemical reaction as a process in which atoms flow from reactants to products. If the reaction is spontaneous and is carried out at constant T and P, thermodynamics requires that AG < 0 for the process (see Section 13.7). Consequently, G always decreases during a spontaneous chemical reaction. When a chemical reaction has reached equilibrium, AG = 0 that is, there is no further tendency for the reaction to occur in either the forward or the reverse direction. We will use the condition AG = 0 in the following three subsections to develop the mass action law and the thermodynamic equilibrium constant for gaseous, solution, and heterogeneous reactions. 

Thermodynamic equilibrium constants are dimensionless because they are expressed in terms of activities rather than partial pressure or concentration. The convention in chemical kinetics is to use concentrations rather than activities, even for gaseous species. Therefore, the equilibrium constants Ki, K2, and introduced here are the empirical equilibrium constants described briefly in Section 14.2. These constants are not dimensionless and must be multiplied by the concentration of the reference state, = l T/Pref, raised to the appropriate power to be made equal to the thermodynamic equilibrium constant. Nevertheless, to maintain consistency with the conventions of chemical kinetics, such constants as Ki, K2, and are referred to as equilibrium constants in this section and are written without the subscript c. 

At the gas-liquid interface, the liquid and gas concentrations of the gaseous reactant are assumed to be at thermodynamic equilibrium. 

This approach is based on classical thermodynamics and statistical mechanics the latter makes the link to the microscopic picture of the adsorption processes. From the point of view of thermodynamics, adsorption can be treated like a chemical reaction. It will be shown that adsorption can proceed with or without a change of the number of gaseous molecules, so that the thermodynamic equilibrium constant expressed in partial pressures may or may not equal the constant expressed in concentrations. Notice that the standard values of some quantities accepted here when deriving formulae for the adsorption characteristics are not the standard states commonly used in chemical thermodynamics. In particular, it concerns the concentrations. 

Chemical equilibrium in homogeneous systems, from the thermodynamic standpoint—Gaseous systems—Deduction of the law of mass action—The van t Hoff isotherm—Principle of mobile equilibrium (Le Chateher and Braun)— Variation of the equilibrium constant with temperature—A special form of the equilibrium constant and its variation with pressure... 

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