Reaction between pure phases

We now know how to determine in which direction any chemical reaction will proceed at a given temperature and pressure, at least when all the products and reactants are pure phases. When even one of the products or reactants is a solute, that is, part of a solution, we would be stuck because although we have had a brief look at how calorimetry can be used with liquids and liquid solutions, we haven t yet seen how to use the data obtained. We will start considering this problem in the next chapter. Before going on, however, we should explore some relationships using the concepts we have defined so far, so as to make sure we fully understand them. Naturally, we will only be able to consider some simple properties of pure phases, and reactions between pure phases. 

Consideration of the condition of equilibrium applied to reactions between pure condensed phases, liquid or solid only, leads to some interesting... 

A tank reactor and separator (Fig. 12-6) are used to study the heterogeneous reaction between pure liquid A (phase 1) and reactant B dissolved in phase 2 (also liquid). The solvent in phase 2, reactant B, and the products of reactior are all insoluble in liquid A. No reaction occurs in the separator. The reactor operates isothermally at 25°C, and at this temperature A has a limited solubility in phase 2, the value being 2.7 x 10 g mole/liter. Phase 2 is dispersed aj bubbles in continuous phase 1, which is recycled. There is excellent stirring in the reactor, but the fluid motion within the bubbles of phase 2 is insufficien to prevent some mass-transfer resistance. From independent measurements it is estimated that at average conditions the reaction resistance within the bubbles is 75% of the total resistance (mass-transfer plus reaction resistance) (n) Derive a relationship between the concentration of reactant B entering the reactor in phase 2 and the concentration leaving the separator. 

In the case of reactions between pure condensed phases,... 

Historically, the third law of thermodynamics emerges from the heat theorem, by Nernst which states A chemical reaction between pure crystalline phases that occurs at absolute zero produces no entropy change. This means that adiabatic and isothermal processes approach each other at very low temperatures. The importance of Nernst s theorem is that it gives a solid base for the calculation of thermodynamic equilibria. 

Indifferent Substances The chemical potential of homogeneous mixtures can be applied so that reactions between mixed phases can be treated exactly like reactions between pure substances. As an example the chemical drive Amix for the mixing process of two substances that are indifferent to each other should be determined. Because the conversion numbers va and vb coincide with the mole fractions Xa and Xb, the conversion formula simplifies to... 

The determination of equilibrium constants for heterogeneous isotope-exchange reactions involving isotope-exchange between pure phases and solution phases yields partition-function ratios for the isotopic, solution-phase species. In favorable cases a comparison of calculated values for the solute partition-function ratio with the experimental value allows one to distinguish between possible solute models. 

Phase diagrams can be used to predict the reactions between refractories and various soHd, Hquid, and gaseous reactants. These diagrams are derived from phase equiHbria of relatively simple pure compounds. Real systems, however, are highly complex and may contain a large number of minor impurities that significantly affect equiHbria. Moreover, equiHbrium between the reacting phases in real refractory systems may not be reached in actual service conditions. In fact, the successful performance of a refractory may rely on the existence of nonequilibrium conditions, eg, environment (15—19). 

In a system of this sort, the rate of the reaction depends upon the amount of interface between the phases, or, in other words, the area of contact between them. For example, a log burns in air at a relatively slow rate. If the amount of exposed surface of the wood is increased by reducing the log to splinters, the burning is much more rapid. If, further, the wood is reduced to fine sawdust and the latter is suspended in a current of air, the combustion takes place explosively. Where one of the reactants is a gas, such as in the above example, the concentration of the gas is also a factor. A piece of wood bums much more rapidly in pure oxygen than it does in ordinary air, in which the oxygen makes up only about 20% of the mixture. 

Figure 2 shows the conversions obtained with the three series studied, as a function of the mechanical mixtures composition, one hour after the beginning of the reaction and at the steady-state. Each series presents a maximum of activity, but at a different composition. SA6 series has a maximum between R , values of 50 and 75, whereas SA12 series has a maximum around = 50, and SA60 series near R , = 75. The dashed lines on the figures represent the sum of the individual contributions of the pure phases, calculated according to Equation 3. A very important synergetic effect is observed in all series, i.e., the activity of the mixtures is... 

Early workers, and some later ones, ignored the fact that aluminium is always found in the orthophosphoric acid liquid of the practical cement its presence profoundly affects the course of the cement-forming reaction. It affects crystallinity and phase composition, and renders deductions based on phase diagrams inappropriate. Nevertheless we first describe the simple reaction between zinc oxide and pure orthophosphoric acid solution, which was the system studied by the earliest workers. 

The increase in the rate of reactions catalysed by quaternary ammonium salts is often proportional to the concentration of the catalyst used. When I started to collect data for their use in organic synthesis, it rapidly became obvious that it was difficult to make a clear distinction between purely catalytic reactions and those using stoichiometric amounts of the ammonium salt this was because the practical techniques often varied (e.g., liquidiliquid two-phase reactions vs liquid solid two-phase reactions). Consequently, I have presented a general practical overview of the use quaternary ammonium salts, categorised according to specific bond formations or reaction types. I have tried to be as comprehensive as possible, but in order to keep the text concise, some abstruse experimental variations have been omitted, as has a complete citation of the patent literature. 

The chemical composihons of the zeolites such as Si/Al ratio and the type of cation can significantly affect the performance of the zeolite/polymer mixed-matrix membranes. MiUer and coworkers discovered that low silica-to-alumina molar ratio non-zeolitic smaU-pore molecular sieves could be properly dispersed within a continuous polymer phase to form a mixed-matrix membrane without defects. The resulting mixed-matrix membranes exhibited more than 10% increase in selectivity relative to the corresponding pure polymer membranes for CO2/CH4, O2/N2 and CO2/N2 separations [48]. Recently, Li and coworkers proposed a new ion exchange treatment approach to change the physical and chemical adsorption properties of the penetrants in the zeolites that are used as the dispersed phase in the mixed-matrix membranes [56]. It was demonstrated that mixed-matrix membranes prepared from the AgA or CuA zeolite and polyethersulfone showed increased CO2/CH4 selectivity compared to the neat polyethersulfone membrane. They proposed that the selectivity enhancement is due to the reversible reaction between CO2 and the noble metal ions in zeolite A and the formation of a 7i-bonded complex. 

VOCs), and to a decrease in production yields. Quantitation of these phenomena and determination of material balances and conversion yields remain the bases for process analysis and optimisation. Two kinds of parameters are required. The first is of thermodynamic nature, i.e. phase equilibrium, which requires the vapour pressure of each pure compound involved in the system, and its activity. The second is mass-transfer coefficients related to exchanges between all phases (gas and liquids) existing in the reaction process. 

Equation (1) may be applied to the equilibrium between vapor and liquid of a pure substance (X = vapor pressure) or to the equilibrium between an ideal dilute solution and the pure phase of a solute X = solubility) or to the equilibrium of a chemical reaction (X = equilibrium constant). 

It would lie far beyond the aim of this chapter to introduce the state-of-the art concepts that have been developed to quantify the influence of colloids on transport and reaction of chemicals in an aquifer. Instead, a few effects will be discussed on a purely qualitative level. In general, the presence of colloidal particles, like dissolved organic matter (DOM), enhances the transport of chemicals in groundwater. Figure 25.8 gives a conceptual view of the relevant interaction mechanisms of colloids in saturated porous media. A simple model consists of just three phases, the dissolved (aqueous) phase, the colloid (carrier) phase, and the solid matrix (stationary) phase. The distribution of a chemical between the phases can be, as first step, described by an equilibrium relation as introduced in Section 23.2 to discuss the effect of colloids on the fate of polychlorinated biphenyls (PCBs) in Lake Superior (see Table 23.5). 

In these types of laboratory reactor, the flow of the liquid is very carefully controlled so that, although the mass transfer step is coupled with the chemical reaction, the mass transfer characteristics can be disentangled from the reaction kinetics. For some reaction systems, absorption of the gas concerned may be studied as a purely physical mass transfer process in circumstances such that no reaction occurs. Thus, the rate of absorption of C02 in water, or in non-reactive electrolyte solutions, can be measured in the same laboratory contactor as that used when the absorption is accompanied by the reaction between C02 and OH ions from an NaOH solution. The experiments with purely physical absorption enable the diffusivity of the gas in the liquid phase DL to be calculated from the average rate of absorption per unit area of gas-liquid interface NA and the contact time te. As shown in Volume 1, Chapter 10, for the case where the incoming liquid contains none of the dissolved gas, the relationship is ... 

In the past, most solids were prepared on a large scale by standard ceramic techniques, in which accurate control of the composition, as well as uniform homogeneity of the product, were not readily achieved. Unfortunately, this has sometimes led to uncertainty in the interpretation of the physical measurements. In recent years more novel methods have been developed to facilitate the reaction between solids. This is particularly true for the preparation of polycrystalline samples, on which the most measurements have been made. It is of utmost importance to prepare pure single-phase compounds, and this may be very difficult to attain. Even for a well-established reaction, careful control of the exact conditions is essential to ensure reproducible results. For any particular experiment, it is essential to devise a set of analytical criteria to which each specimen must be subjected. It will be seen from the solid-state syntheses included in this volume that one or more of the following common tests of purity are used to characterize a product. 

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