Phase equilibrium table

Under the condition of constant temperature, there is no freedom at equilibrium, which means that both the pressure (P02) and the compositions of the coexisting solid phases are definitely determined. This is the reason why the composition versus the oxygen pressure curves in the two phase region shows a straight line parallel to the abscissa as shown in Fig. 1.2. The result of Fig. 1.3 can be explained in a similar way. Thus, eqn (1.46) is very important in understanding the phase equilibrium. Table 1.1 summarizes the relationship between the composition, the pressure (Pof), and the temperature for the binary M-O and ternary O systems for the case of the... 

D. Two-box sediment/water model combined with three-phase equilibrium (Table 23.7) ... 

The phase rule is important for thermal separation processes as, if certain process parameters are choosen, it establishes which state variables are cogently fixed at an arbitrarily adjusted phase equilibrium (Table 1-5). 

Ternary-phase equilibrium data can be tabulated as in Table 15-1 and then worked into an electronic spreadsheet as in Table 15-2 to be presented as a right-triangular diagram as shown in Fig. 15-7. The weight-fraction solute is on the horizontal axis and the weight-fraciion extraciion-solvent is on the veriical axis. The tie-lines connect the points that are in equilibrium. For low-solute concentrations the horizontal scale can be expanded. The water-acetic acid-methylisobutylketone ternary is a Type I system where only one of the binary pairs, water-MIBK, is immiscible. In a Type II system two of the binary pairs are immiscible, i.e. the solute is not totally miscible in one of the liquids. 

Let us first consider the three-phase equilibrium ( -clathrate-gas, for which the values of P and x = 3/( +3) were determined at 25°C. When the temperature is raised the argon content in the clathrate diminishes according to Eq. 27, while the pressure can be calculated from Eq. 38 by taking yA values following from Eq. 27 and the same force constants as used in the calculation of Table III. It is seen that the experimental results at 60°C and 120°C fall on the line so calculated. At a certain temperature and pressure, solid Qa will also be able to coexist with a solution of argon in liquid hydroquinone at this point (R) the three-phase line -clathrate-gas is intersected by the three-phase line -liquid-gas. At the quadruple point R solid a-hydroquinone (Qa), a hydroquinone-rich liquid (L), the clathrate (C), and a gas phase are in equilibrium the composition of the latter lies outside the part of the F-x projection drawn in Fig. 3. The slope of the three-phase line AR must be very steep, because of the low solubility of argon in liquid hydroquinone. 

Values of p can be determined, in principle, from any phase equilibrium data. A small table of p 2 values is available in reference (2). However, one of the most straightforward ways of determining pf values is to fit phase equilibrium data for solvent sorption in concentrated polymer solutions. To do this, equations (2) and (13) are combined to solve for p utilizing experimental partial pressure data. 

Depicted in Fig. 2, microemulsion-based liquid liquid extraction (LLE) of biomolecules consists of the contacting of a biomolecule-containing aqueous solution with a surfactant-containing lipophilic phase. Upon contact, some of the water and biomolecules will transfer to the organic phase, depending on the phase equilibrium position, resulting in a biphasic Winsor II system (w/o-ME phase in equilibrium with an excess aqueous phase). Besides serving as a means to solubilize biomolecules in w/o-MEs, LLE has been frequently used to isolate and separate amino acids, peptides and proteins [4, and references therein]. In addition, LLE has recently been employed to isolate vitamins, antibiotics, and nucleotides [6,19,40,77-79]. Industrially relevant applications of LLE are listed in Table 2 [14,15,20,80-90]. 

For the purpose of deciding which phase equilibrium method to use, it is convenient to classify components into the classes shown in Table 8.10. 

Equilibrium constants calculated from the composition of saturated solutions are dependent on the accuracy of the thermodynamic model for the aqueous solution. The thermodynamics of single salt solutions of KC1 or KBr are very well known and have been modeled using the virial approach of Pitzer (13-15). The thermodynamics of aqueous mixtures of KC1 and KBr have also been well studied (16-17) and may be reliably modeled using the Pitzer equations. The Pitzer equations used here to calculate the solid phase equilibrium constants from the compositions of saturated aqueous solutions are given elsewhere (13-15, 18, 19). The Pitzer model parameters applicable to KCl-KBr-l O solutions are summarized in Table II. 

The formulae given in Table 4.1 for the molecular partition functions enable us to write the partition function ratio qheavy/qiight or q2/qi where, by the usual convention, the subscript 2 refers to the heavy isotopomer and 1 refers to the light isotopomer if heavy and light are appropriate designations. Then, a ratio of such partition function ratios enables one to evaluate the isotope effect on a gas phase equilibrium constant, as pointed out above. Before continuing, it is appropriate to... 

The inhalational anesthetics have distinctly different solubility (affinity) characteristics in blood as well as in other tissues. These solubility differences are usually expressed as coefficients and indicate the number of volumes of a particular agent distributed in one phase, as compared with another, when the partial pressure is at equilibrium (Table 25.3). For example, isoflurane has a blood-to-gas partition coefficient (often referred to as the Ostwald solubility coefficient) of approximately 1.4. Thus, when the partial pressure has reached equilibrium, blood will contain 1.4 times as much isoflurane as an equal volume of alveolar air. The volume of the various anesthetics required to saturate blood is similar to that needed to saturate other body tissues (Table 25.3) that is, the blood-tissue partition coefficient is usually not more than 4 (that of adipose tissue is higher). 

The thermodynamics experiments are subdivided into experiments on calorimetry and heat capacity, Table XVI phase transitions, Table XVII properties of gases, liquids, solids, solutions and mixtures, Table XVIII and finally equilibrium and miscellaneous thermodynamic topics , Table XIX. 

Owing to the strength of the B—F bond, die BF3 complexes are of widespread use as model compounds, for investigating Lewis acid-base interactions and the nature of the donor-acceptor bond. BF3 is frequently employed as a standard Lewis acid, for the quantitative characterization of the Lewis basicity of donor mojecules.62,63 The gas-phase equilibrium constants for some BF3 complexes are shown in Table 5. 

The next step is to determine whether or not the water as a result of the pH change has become saturated with respect to any of the solid phases considered (Table VII). For this, ion activity products are computed for each phase and compared with the equilibrium value (Table VIII). The calculation for calcite is given to illustrate the procedure. The ion activity product is... 

Similar comparisons between the thermodynamic /J-silyl stabilization measured in the gas phase20,21 and the kinetic -silicon effect81,83 found in protonation experiments in solution are possible for the acetylenes 186 and 188 and for the alkene 190. The data for both solution study and gas phase equilibrium measurements are summarized in Table 5. 

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... 

Second, since the entire enterprise is constmcted so as to locate points (of phase equilibrium) at which the free-energy difference vanishes, in NIRM one is inevitably faced with the task of determining some very small number by taking the difference between two relatively large numbers. This point is made more explicitly by the hard-sphere data in Table I. One sees that the difference between the values of the free energy [37] of the two crystalline phases is some four orders of magnitude smaller than the separate results for the two phases, determined by ESM. Of course one can see this as a testimony to the remarkable care with which the most recent recent ESM studies have been carried out [34]. Alternatively, one may see it as a strong indicator that another approach is called for. 

The process, kinetic, and phase-equilibrium parameters are given in Table 2.5. There is a single feedstream F0 (m3/s) with concentrations of the reactants Cao and Cbo (kmol/m3). A slight excess of reactant B is fed to the reactor, so the conversion is specified in terms of this reactant ... 

It is important to note, that the interaction parameters between the components (two per binary) were estimated solely from binary phase equilibrium data, including low-pressure VLE data for the binary acetone - water no ternary data were used in the fitting. The values of the interaction parameters obtained are shown in Table III. 

The gas-phase acidity of some of the simplest organogermanes and of trimethylstannane have been determined by a combination of gas-phase equilibrium measurements and proton-transfer bracketing experiments using FTMS185 190. The experimental values of A//°cjd are shown in Table 6 and refer to the enthalpy change associated with reaction 29. 

Mujtaba (1989) simulated the same example for the first product cut using a reflux ratio profile very close to that used by Nad and Spiegel in their own simulation and a nonideal phase equilibrium model (SRK). The purpose of this was to show that a better model (model type IV) and better integration method achieves even a better fit to their experimental data. Also the problem was simulated using an ideal phase equilibrium model (Antoine s equation) and the computational details were presented. The input data to the problem are given in Table 4.7. 

Vapour phase enthalpies were calculated using ideal gas heat capacity values and the liquid phase enthalpies were calculated by subtracting heat of vaporisation from the vapour enthalpies. The input data required to evaluate these thermodynamic properties were taken from Reid et al. (1977). Initialisation of the plate and condenser compositions (differential variables) was done using the fresh feed composition according to the policy described in section 4.1.1.(a). The simulation results are presented in Table 4.8. It shows that the product composition obtained by both ideal and nonideal phase equilibrium models are very close those obtained experimentally. However, the computation times for the two cases are considerably different. As can be seen from Table 4.8 about 67% time saving (compared to nonideal case) is possible when ideal equilibrium is used. 

Mujtaba (1989) and Mujtaba and Macchietto (1992) considered a ternary separation using Butane-Pentane-Hexane mixture. Only the optimal operation for the first main-cut and the first off-cut was considered. Table 8.7 lists a variety of separation specification (on CUT 1) and column configurations in each case. A fresh feed of 6 kmol at a composition of <0.15, 0.35, 0.50> (mole fraction) is used in all cases. Also in each case a constant condenser vapour load of 3 kmol/hr is used. For convenience Type IV-CMH model was used with ideal phase equilibrium. 

Table 7.7 Phase equilibrium of the reactor-outlet mixture at 135 °C and 15 bar.

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