Phase equilibria simple

Figure A2.5.15. The molar Gibbs free energy of mixing versus mole fraetionxfor a simple mixture at several temperatures. Beeause of the synuuetry of equation (A2.5.15) the tangent lines indieating two-phase equilibrium are horizontal. The dashed and dotted eiirves have the same signifieanee as in previous figures.

Concentration-time curves. Much of Sections 3.1 and 3.2 was devoted to mathematical techniques for describing or simulating concentration as a function of time. Experimental concentration-time curves for reactants, intermediates, and products can be compared with computed curves for reasonable kinetic schemes. Absolute concentrations are most useful, but even instrument responses (such as absorbances) are very helpful. One hopes to identify characteristic features such as the formation and decay of intermediates, approach to an equilibrium state, induction periods, an autocatalytic growth phase, or simple kinetic behavior of certain phases of the reaction. Recall, for example, that for a series first-order reaction scheme, the loss of the initial reactant is simple first-order. Approximations to simple behavior may suggest justifiable mathematical assumptions that can simplify the quantitative description. 

Equilibrium data must be obtained for material balance showing raffinate and extracted phases. A simple separation funnel for single-stage extraction using amyl acetate as organic solvent is shown in Figure 7.13. 

This is usually thought of as a phase equilibrium problem. Earlier, we indicated that a phase equilibrium is nothing more than a simple chemical equilibrium. This problem is one such example. 

Simple phase equilibrium calculations, like the one illustrated here, can be readily implemented in spreadsheet software and automated. In practice, the calculations will most often be carried out in commercial physical property packages, allowing more elaborate methods for calculating the equilibrium K-values to be used. 

The proposed correlation is, however, a simple technique for phase-equilibrium calculations in concentrated solutions. 

Whereas liquid separation method selection is clearly biased toward simple distillation, no such dominant method exists for gas separation. Several methods can often compete favorably. Moreover, the appropriateness of a given method depends to a large extent on specific process requirements, such as the quantity and extent of the desired separation. The situation contrasts markedly with liquid mixtures in which the applicability of the predominant distillation-based separation methods is relatively insensitive to scale or purity requirements. The lack of convenient problem representation techniques is another complication. Many of the gas—vapor separation methods are kinetically controlled and do not lend themselves to graphical-phase equilibrium representations. In addition, many of these methods require the use of some type of mass separation agent and performance varies widely depending on the particular MSA chosen. 

Identification of crystals under the microscope. Of the characteristics which are most useful for identification purposes the most readily determined are shape and refractive indices, The determinative method which has proved most valuable for microscopic crystals (such as those in the average experimental or industrial product) is to measure the principal refractive indices (up to three in number, depending on the symmetry of the crystal) and, if possible, to find the orientation of the principal opticafdirections with respect to the geometrical form of the crystal. This information, which can all be obtained by simple and rapid microscopio methods, is usually sufficient to identify any crystalline substances whose properties have previously been recorded. Mixtures of two or more crystalline substances can be identified by the same method in phase equilibrium studies and in industrial research it is not uncommon to encounter mixtures of three or four constituents, all of which can be identified in this way. 

The defining features of phase diagrams are the phase boundaries that delineate phase domains and mark the conditions of coexistence with adjacent phases. Theoretical description of a phase diagram is therefore tantamount to finding the equations of coexistence that describe these phase boundaries. For a simple phase equilibrium between phases a and /3, as shown below, the a + /3 coexistence curve is described by an equation of the form P = P(T), whose form we now wish to determine ... 

The calculation of the equilibrium conversion of heterogeneous reactions is in most cases much more complicated then in the case of homogeneous reactions, because the calculations involve in general the solution of the conditions for chemical equilibrium and the conditions for phase equilibrium. In the following a relatively simple example is given. 

Table 4.10 shows the literature values for hydrate numbers, all obtained using de Forcrand s method of enthalpy differences around the ice point. However, Handa s values for the enthalpy differences were determined calorimetrically, while the other values listed were determined using phase equilibrium data and the Clausius-Clapeyron equation. The agreement appears to be very good for simple hydrates. Note also that hydrate filling is strongly dependent on... 

We now briefly discuss how thermodynamics can work for us or, better, how thermodynamics functions to solve a problem where it can help to provide the answer. We wish to illustrate this for a relatively simple problem how much work is required to compress a unit of gas per unit time (Figure 2.4) from a low to a high pressure. Figure 2.5 schematically gives the path to the answer and the structure of the solution. In fact, the same steps will have to be taken to apply thermodynamics to problems such as the calculation of the heat released from or required for a process, of the position of the chemical or phase equilibrium, or of the thermodynamic efficiency of a process. 

Treybal, in his book Liquid Extraction [1], works equilibrium material balances with triangular coordinates. The most unique and simple way to show three-phase equilibrium is a triangular diagram (Fig. 7.1), which is used for extraction unit operation in cumene synthesis plants [2], In this process benzene liquid is used as the solvent to extract acetic acid (the solute) from the liquid water phase (the feed-raffinate). The curve D,S,P,F,M is the equilibrium curve. Note that every point inside the triangle has some amount of each of the three components. Points A,... 

The wave and pulse patterns of nonreactive separation processes, as well as the integrated reaction separation processes illustrated above, can be easily predicted with some simple graphical procedures derived from Eqs. (4) and (5). The behavior crucially depends on the equilibrium function y(x) in the nonreactive case, and on the transformed equilibrium function Y(X) in the reactive case. In addition to phase equilibrium, the latter also includes chemical equilibrium. An explicit calculation of the transformed equilibrium function and its derivatives is only possible in special cases. However, in Ref. [13] a numerical calculation procedure is given, which applies to any number of components, any number of reactions, and any type of phase and reaction equilibrium. 

Hence it is possible to compute the ternary phase equilibrium data with a equation of state. The effort to transfer these results to a multi-Figure 4 Correlation between the partition coefficient for component system is tedious, the pseudo components versus the molecular weight of the Therefore a simple empirical... 

Related Calculations. This illustration outlines the procedure for obtaining coefficients of a liquid-phase activity-coefficient model from mutual solubility data of partially miscible systems. Use of such models to calculate activity coefficients and to make phase-equilibrium calculations is discussed in Section 3. This leads to estimates of phase compositions in liquid-liquid systems from limited experimental data. At ordinary temperature and pressure, it is simple to obtain experimentally the composition of two coexisting phases, and the technical literature is rich in experimental results for a large variety of binary and ternary systems near 25°C (77°F) and atmospheric pressure. Example 1.21 shows how to apply the same procedure with vapor-liquid equilibrium data. 

For a cell membrane in a living animal, a very slight pressure difference will activate transport processes in the membrane, which will effectively eliminate the pressure difference. Introducing this change, there is no longer a state of equilibrium across the membrane, and other transport processes will take place. Such transport often is supported by chemical pumps, which move sodium ions from the protein phase to the aqueous phase. The simple estimation above illustrates that relatively small changes in the concentration are necessary to eliminate the osmotic pressure. In order to force PB — PA = 0, c(Na) in phase B must be reduced by 11 mmol/L, or by less than 10% of the previously determined concentration of 128 mmol/L (Gaiby and Larsen, 1995). 

These led to matrix studies of the structure of ion pairs and triple ions, such as the thorough studies by Devlin and coworkers on matrix isolated alkali nitrate (21), chlorate (22) and perchlorate ion pairs (23 ). For relatively simple salts, such as the alkali halides, investigations were conducted into the structure of the dimeric salt species (6, 7, ), which is present in a gas phase equilibrium with the monomeric salt species. These dimers have been found to be very strongly bound in a cyclic structure. 

The models in the R D stage can first be simple, and then become more detailed as work proceeds. At this stage, attention has to be focused on the phenomena of phase equilibrium, on the physical properties of the materials, on chemical kinetics as well as on the kinetics of mass and heat transfer. As previously shown (see Figs 1.2 and 1.3), the decomposition ofthe process into different elementary units is one of the first activities. This action requires careful attention especially because, at this life-cycle stage, the process could be nothing but an idea. The work starts with the physical properties, as they act as an input to all other components. The guidelines to choose physical properties, phase equilibrium data, characteristic state equations etc. can be found in the usual literature. For each studied... 

Relationships governing the distribution of a substance between gas and liquid phases are the subject matter of phase-equilibrium thermodynamics and, for the most part, fall beyond the scope of this text. However, we will cover several simple approximate relationships that provide reasonably accurate results over a wide range of conditions. Such relationships form the bases of more precise methods that must be used when system conditions require them. 

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