Homogenous phase

All the theory developed up to this point has been limited in the sense that translational motion (the continuum degree of freedom) has been restricted to one dimension. In this section we discuss the generalization of this to three dimensions for collision processes where space is isotropic (i.e., collisions in homogeneous phases, such as in a... 

The more efficient system of genera ting OH radicals in the homogeneous phase is H2O2/uv, where the quantum yield, < >254 0.50 (20,21). There... 

Early ia the development of chemical reaction engineering, reactants and products were treated as existing ia single homogeneous phases or several discrete phases. The technology has evolved iato viewing reactants and products as residing ia interdependent environments, a most important factor for multiphase reactors which are the most common types encountered. 

An example of heterogeneous-azeotrope formation is shown in Fig. 13-13 for the water-normal butanol system at 101.3 kPa. At liquid compositions between 0 and 3 mole percent butanol and between 40 and 100 mole percent butanol, the liquid phase is homogeneous. Phase sphtting into two separate liquid phases (one with 3 mole percent butanol and the other with 40 mole percent butanol) occurs for any overall hquid composition between 3 and 40 mole percent butanol. A miuimum-boihug heterogeneous azeotrope occurs at 92°C (198°F) when the vapor composition and the over l composition of the two liquid phases are 75 mole percent butanol. 

DEF. When the constitution point lies in a single-phase region, the alloy consists of a single, homogeneous, phase. Its composition must (obviously) be that of the alloy. The phase composition and the alloy composition coincide in single-phase fields. 

Consider a single homogeneous phase of one eomponent of unehang-ing eomposition. If it undergoes an isothermal reversible ehange and does work, then from the first law of thermodynamies ... 

Now eonsider a homogeneous phase eontaining different substanees or eomponents. Its phase eontains ... 

After the rates have been determined at a series of reactant concentrations, the differential method of testing rate equations is applied. Smith [3] and Carberry [4] have adequately reviewed the designs of heterogeneous catalytic reactors. The following examples review design problems in a plug flow reactor with a homogeneous phase. 

Now, assume that the adsorbed layer is not a homogeneous phase but exhibits two-phase eoexistenee between the low density phase (1) and the high density phase (2) and that these two phases eontain Ni and N2 mole-eules, respeetively, and oeeupy the areas A j and A2. Of eourse, the total area of the sample is + 2 the total number of adsorbed partieles is... 

When water-miscible ionic liquids are used as solvents, and when the products are partly or totally soluble in these ionic liquids, the addition of polar solvents, such as water, in a separation step after the reaction can make the ionic liquid more hydrophilic and facilitate the separation of the products from the ionic liquid/water mixture (Table 5.3-2, case e). This concept has been developed by Union Carbide for the hydroformylation of higher alkenes catalyzed by Rh-sulfonated phosphine ligand in the N-methylpyrrolidone (NMP)/water system. Thanks to the presence of NMP, the reaction is performed in one homogeneous phase. After the reaction. 

Different polymers that are incompatible with each other do not form a stable homogeneous phase. In the block... 

Because flashing steam-condensate lines represent two-phase flow, with the quantity of liquid phase depending on die system conditions, these can be designed following the previously described two-phase flow methods. An alternate by Ruskin [28] uses the concept but assumes a single homogeneous phase of fine liquid droplets dispersed in the flashed vapor. Pressure drop was calculated by the Darcy equation ... 

All gas mixtures are homogeneous hence all gas mixtures are solutions. Air is an example. There is only one phase—the gas phase—and all the molecules, regardless of the source, behave as gas molecules. The molecules themselves may have come from gaseous substances, liquid substances, or solid substances. Whatever the source of the constituents, this gaseous solution, air, is a single, homogeneous phase. As with other solutions, the constituents of air are separated by phase changes. 

From a theoretical point of view the study of the kinetics of coupled catalytic reactions makes it possible to investigate mutual influencing of single reactions and the occurrence of some phenomena unknown in the kinetics of complex reactions in the homogeneous phase. This approach can yield additional information about interactions between the reactants and the surface of the solid catalyst. 

Thus, from (3), (4) and (5) we have, as the condition for stable equilibrium of a homogeneous phase ... 

Inequalities (6) and (7) show that the surface is, at every point which corresponds with a homogeneous phase in stable equilibrium, convex downwards in every direction. 

If a homogeneous phase is formed from two or more components it is called a solution it may be gaseous, liquid, or solid. 

When two homogeneous phases are placed in contact, it is often found that, although no chemical action results, a more or less marked alteration of concentration occurs at the interface. Thus, gases are absorbed by porous charcoal, and with such tenacity is this layer of gas held that the removal of the minute amount of gas remaining in a space exhausted by a mercury pump is best effected by means of cocoa-nut charcoal cooled in liquid air... 

For a system composed of any number of condensed chemically homogeneous phases and a homogeneous gas phase we have the symbol ... 

Since the free energy of a molecule in the liquid phase is not markedly different from that of the same species volatilized, the variation in the intrinsic reactivity associated with the controlling step in a solid—liquid process is not expected to be very different from that of the solid—gas reaction. Interpretation of kinetic data for solid—liquid reactions must, however, always consider the possibility that mass transfer in the homogeneous phase of reactants to or products from, the reaction interface is rate-limiting [108,109], Kinetic aspects of solid—liquid reactions have been discussed by Taplin [110]. 

If at high temperatures (> 600 K) the volatilized NH3 and HC104 are prevented from leaving the heated zone by the presence of an inert gas, decomposition in the homogeneous phase follows. This is the high temperature (gas phase) reaction in which there is complete conversion of the reactant to volatile products and no residue remains. 

The reactions of some aromatic metal carboxylates are on the borderline of classification as solid-state processes. While there is no evidence of liquefaction, rates of decomposition in the poorly crystallized or vitreous reactant obey kinetic expressions more characteristic of reactions proceeding in a homogeneous phase. 

In THF the reaction system became turbid and gelled as the polymerization proceeded. In DMSO it proceeded in a homogeneous phase. It is also worth noting that 61 is able to polymerize in these solvents even in the absence of activator 65. 

In addition to the insoluble polymers described above, soluble polymers, such as non-cross-linked PS and PEG have proven useful for synthetic applications. However, since synthesis on soluble supports is more difficult to automate, these polymers are not used as extensively as insoluble beads. Soluble polymers offer most of the advantages of both homogeneous-phase chemistry (lack of diffusion phenomena and easy monitoring) and solid-phase techniques (use of excess reagents and ease of isolation and purification of products). Separation of the functionalized matrix is achieved by either precipitation (solvent or heat), membrane filtration, or size-exclusion chromatography [98,99]. 

Just as, in Group VB, niobium, so, in this Group, molybdenum provides most of the examples of the chalcogenide halides. The occurrence and preparation of such compounds are described in numerous publications. In most cases, they have been obtained as powders, with the composition based on chemical analyses only. The presence of defined, homogeneous phases is, therefore, in many cases doubtful. In addition, some published results are contradictory. A decision is possible where a complete structure analysis has been made. As will be shown later, the formation of metal-metal bonds (so-called clusters), as in the case of niobium, is the most characteristic building-principle. Such clusters... 

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