Homogenous systems

A further classification is based on the number of phases in the system homogeneous (1 phase) and heterogeneous (more than 1 phase) catalysis. 

In this chapter and in Chapters 10-12, we will review and validate some methods for asymmetric (transfer) hydrogenation of carbon-oxygen and carbon-carbon double bonds catalysed by non-metallic systems, homogeneous transition metal catalysts and biocatalysts. Reduction of carbon-nitrogen double bond systems will be reported in another volume of this series. 

This is a teaching book thus, simple ideas are treated first, and are then extended to the more complex. Also, emphasis is placed throughout on the development of a common design strategy for all systems, homogeneous and heterogeneous. 

Scheme 3.1-1. Proposed structure of the overall system Homogeneous Catalysis ...

The kinetic equation for S for calculating system homogeneous with respect to the translational degree of freedom and subject to no external field, the result is [4,117]... 

Gassy systems are untempered. This means that the operation of the relief system cannot control the rate of the runaway reaction, but simply acts to remove material from the reactor. For untempered systems, homogeneous flow in the reactor (see... 

In contrast to heterogeneous systems, homogeneous systems contain only one phase, which in water and waste water applications is the liquid phase. Ozone is either absorbed from the... 

It is clear that O-alkylation is favoured over C-alkylation with the heterogeneous system. Homogeneous BF3 reactions generally favour C-alkylation due to the rearrangement of the ether. The selectivity of the heterogeneous system towards ether formation is further illustrated by the reaction of phenol with... 

The production of species i (number of moles per unit volume and time) is the velocity of reaction,. In the same sense, one understands the molar flux, jh of particles / per unit cross section and unit time. In a linear theory, the rate and the deviation from equilibrium are proportional to each other. The factors of proportionality are called reaction rate constants and transport coefficients respectively. They are state properties and thus depend only on the (local) thermodynamic state variables and not on their derivatives. They can be rationalized by crystal dynamics and atomic kinetics with the help of statistical theories. Irreversible thermodynamics is the theory of the rates of chemical processes in both spatially homogeneous systems (homogeneous reactions) and inhomogeneous systems (transport processes). If transport processes occur in multiphase systems, one is dealing with heterogeneous reactions. Heterogeneous systems stop reacting once one or more of the reactants are consumed and the systems became nonvariant. 

At t - co, we have b(c(t)) —> vmb(cr ) voul and this result is independent of the smallness of um and uout. It is only necessary that they will be constant and the system homogeneous. In the case where ain and eout are sufficiently... 

Renyi (78) generalized the concept of information entropy to measure different aspects of system homogeneity, and Alemanskin et al. (79), and Alemanskin and Manas-Zloczower (80) adopted the Renyi entropy for measuring mixing. Considering only statistically independent partition, Renyi determined that the information entropy can be replaced with the following single-variable function... 

Tabelle 2. Systeme homogener, katalytischer Hvdrierung, welche quantitativ untersucht warden... 

Table 9.1 Classification of bioreactors according to system homogeneity ...

Secondly, the treatment of inhomogeneous system and clusters is straightforward. So far, the formulation does not assume the system homogeneity and the thermodynamic limit. The application to inhomogeneous and/or finite systems is then possible without modification. The binding of a molecule to such nanoscale structures as protein, micelle, and membrane can be viewed as a solvation in an inhomogeneous and finite, mixed solvent [57], The method of energy representation can thus be a... 

In addition to the heterogeneous systems, homogeneous systems have also become known in laboratory experiments. Table II gives various metals which heterogeneously and homogeneously catalyze the conversion of CO/Hj to methanol. 

The radicals and molecules that escaped from the track recombination can diffuse in the bulk by making the chemical system homogeneous where the slowest reactions can take place. At the... 

Other words and expressions system, homogeneous, heterogeneous, phase, precipitate, filtrate, residue, supernatant liquid, centrifuge, supercentriiuge, emulsion, separatory funnel, still, condenser, receiver, distillate, gaseous solution, liquid solution, crystalline solution (solid solution), alloy, components. 

Homogeneous vs. heterogeneous systems. Homogeneous systems are uniform in properties over their entire volume. Otherwise such systems are heterogeneous. 

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