Macroscopic particles, liquid phase chemical

Alternative Approach in the Absence of Liquid-Phase Chemical Reaction. The previous scaling law for the dissolution of spherical solid particles in a surrounding quiescent liquid can be addressed by performing an unsteady-state macroscopic mass balance on the liquid solution, with volume Viiquid- The accumulation of species A is balanced by the rate of interphase mass transfer (MT) when no chemical reaction occurs. Hence,... 

Production of phenol and acetone is based on liquid-phase oxidation of isopropylbenzene. Synthetic fatty acids and fatty alcohols for producing surfactants, terephthalic, adipic, and acetic acids used in producing synthetic and artificial fibers, a variety of solvents for the petroleum and coatings industries—these and other important products are obtained by liquid-phase oxidation of organic compounds. Oxidation processes comprise many parallel and sequential macroscopic and unit (or very simple) stages. The active centers in oxidative chain reactions are various free radicals, differing in structure and in reactivity, so that the nomenclature of these labile particles is constantly changing as oxidation processes are clarified by the appearance in the reaction zone of products which are also involved in the complex mechanism of these chemical conversions. 

Now, it is instructive to re-analyze the unsteady-state macroscopic mass balance on an isolated solid pellet of pure A with no chemical reaction. The rate of output due to interphase mass transfer from the solid particle to the liquid solution is expressed as the product of a liquid-phase mass transfer coefficient c, liquids a Concentration driving force (Ca, — Ca), and the surface area of one spherical pellet, 4nR. The unsteady-state mass balance on the solid yields an ordinary differential equation for the time dependence of the radius of the peUet. For example,... 

Electrons residing in molecular clusters can be viewed as microscopic probes of both the local liquid structure and the molecular dynamics of liquids, and as such their transitory existence becomes a theoretical and experimental metaphor for one of the major fundamental and contemporary problems in chemical and molecular physics, that is, how to describe the transition between the microscopic and macroscopic realms of physical laws in the condensed phase. Since this chapter was completed in the Spring of 1979, several new and important observations have been made on the dynamics and structure of e, which, as a fundamental particle interacting with atoms and molecules in a fundamental way, serves to assist that transformation for electronic states in disordered systems. In a sense, disorder has become order on the subpicosecond time-scale, as we study events whose time duration is shorter than, or comparable to, the period during which the atoms or molecules retain some memory of the initial quantum state, or of the velocity or phase space correlations of the microscopic system. This approach anticipated the new wave of theoretical and experimental interest in developing microscopic theories of... 

When we observe chemical reactions macroscopically, we encounter three common forms, or phases, of matter solids, liquids, and gases. At the macroscopic level, solids are hard and do not change their shapes easily. When a solid is placed in a container, it retains its own shape rather than assuming that of the container. Even a powdered solid demonstrates this trait because the individual particles still retain their shape, even though the collection of them may take on the shape of the container. 

Phases in thermodynamic systems are then macroscopic homogeneous parts with distinct physical properties. For example, densities of extensive thermodynamical variables, such as particle number N of the fth species, enthalpy U, volume V, entropy S, and possible order parameters, such as the nematic order parameter for a liquid crystalline polymer etc, differ in such coexisting phases. In equilibrium, intensive thermodynamic variables, namely T,p, and the chemical potentials pi have to be the same in all phases. Coexisting phases are separated by well-defined interfaces (the width and internal structure of such interfaces play an important role in the kinetics of the phase transformation (1) and in other... 

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