Binary isotherms examples

The equilibrium amounts adsorbed of component i from a binary gas mixture (n ) are generally described as functions of gas phase mole fractions (y ) at a constant system temperature (T) and total gas pressure (P). An example is given in Fig. 4 for adsorption of binary N2-O2 mixtures on Na-mordenite at various temperatures where the total gas pressure was 1.0 atm. These binary isotherm shapes are typical for Type I adsorption systems on microporous adsorbents. 

Examples of single-component and binary isotherms showing good agreement between the experimental isotherms determined by chromatographic and static methods are shown in Figure 8.8. It should be noted that this method is restricted to binary systems and cannot be easily extended to ternary or multicomponent mixtures. 

The IAS model is practical for predicting binary isotherms from singlecomponent isotherm data. As an example, isotherms of propane and butane on activated carbon are shown in Fig. 3.20. The assumption of ideal adsorbed solution may need careful consideration in some cases where a combination of two components forms an azeotropic mixture in the adsorbed phase as reported by Glessner and Meyers (1969). 

Despite the obviously tedious calculations involved, the VSM has been very successful in predicting binary isotherms from single component data. Figure 3.12 shows how closely the model conforms to experimentally determined data for four pairs of gases adsorbed on an activated carbon. Because interaction between adsorbed species and between adsorbates and adsorbent is taken into account in the VSM, the model is capable of predicting azeotrope formation. Figure 3.13 is an example where azeotrope formation is predicted for the adsorption of a mixture of i - CtHio and C2H4 on zeolite 13X. 

Despite the occurrence of binary AIB2 borides (see also Fig. 2), no ternary representatives are known (Mn, Mo)B2 found from isothermal sections is a stabilized high-T phase by conversion to lower T by a statistical ( ) metal-metal substitution. Both MnB2 and M0B2 are high-T compounds stable above 1075°C and 1517°C respectively WB2 is claimed but is either metastable or impurity stabilized. Similar examples are observed with (W, Pd>2B5 (M02B5 type) as well as (Mo, Rh),, (B3 and (W, Ni), B3 (Mo,., 83 type). The phase relations in the B-rich section of the Mo(W)-B binaries, however, are not known precisely. 

A simple example of a real ternary diagram is shown in Fig. 2.26, where the isothermal section, determined at 200°C, of the Al-Bi-Sb system is shown together with the relevant binary diagrams Al-Bi showing a miscibility gap in the liquid state and complete insolubility in the solid state, Bi-Sb with complete mutual... 

Figure 2.27. Isothermal section at 307°C of the Al-Zn-Si diagram. The boundary binary systems are shown. The isothermal section at 307°C is marked on the binary Al-Zn diagram. The corresponding single-phase (thick segment) and two-phase regions are indicated in the base edge of the triangle. By additions of Si (immiscible in the solid state in the other two elements) two- and three-phase fields are formed. ( ) = three-phase region. In the two-phase region on the left examples of tie-lines are presented.

The Al-Zn-Si is another example of simple ternary system its isothermal section at 307°C is shown in Fig. 2.27 together with its boundary binaries. Si, in the solid state, is practically insoluble in A1 or in Zn and in their binary solutions. In the... 

The system is sketched in Fig. 3.1 and is a simple extension of the CSTR considered in Example 2.3. Product B is produced and reactant A is consumed in each of the three perfectly mixed reactors by a first-order reaction occurring in the liquid. For the moment let us assume that the temperatures and holdups (volumes) of the three tanks can be different, but both temperatures and the liquid volumes are assumed to be constant (isothermal and constant holdup). Density is assumed constant throughout the system, which is a binary mixture of A and B. 

Transition Region Considerations. The conductance of a binary system can be approached from the values of conductivity of the pure electrolyte one follows the variation of conductance as one adds water or other second component to the pure electrolyte. The same approach is useful for other electrochemical properties as well the e.m. f. and the anodic behaviour of light, active metals, for instance. The structure of water in this "transition region" (TR), and therefore its reactions, can be expected to be quite different from its structure and reactions, in dilute aqueous solutions. (The same is true in relation to other non-conducting solvents.) The molecular structure of any liquid can be assumed to be close to that of the crystals from which it is derived. The narrower is the temperature gap between the liquid and the solidus curve, the closer are the structures of liquid and solid. In the composition regions between the pure water and a eutectic point the structure of the liquid is basically like that of water between eutectic and the pure salt or its hydrates the structure is basically that of these compounds. At the eutectic point, the conductance-isotherm runs through a maximum and the viscosity-isotherm breaks. Examples are shown in (125). 

EXAMPLE 9.4 Kinetic-Theory-Based Description of Binary Adsorption. Assume that two gases A and B individually follow the Langmuir isotherm in their adsorption on a particular solid. Use the logic that results in Equation (46) to derive an expression for the fraction of surface sites covered by one of the species when a mixture of the two gases is allowed to come to adsorption equilibrium with that solid. 

A distinction between solid/fluid and solid/solid boundaries is irrelevant from the point of view of transport theory. Solid/fluid boundaries in reacting systems are, for example, (A,B)/A, B, X (aq) or (A,B)/X2(g). More important is the distinction according to the number of components. In isothermal binary systems, the boundary is invariant if local equilibrium prevails. In higher than binary systems, the state of the a/fi interface is, in principle, variable and will be determined by the reaction kinetics, including the diffusion in the adjacent bulk phases. 

The nature of HSDSC instruments allows experiments to be run incorporating both isothermal and scanning steps. This enables rapid screens for excipient compatibility. An example is provided by the study of aspirin with two excipients using HSDSC (41). Figure 10 shows the HSDSC trace obtained for a binary mixture of acetylsalicylic acid (aspirin) with lactose and Figure 11... 

Figure 11.6 shows an example of the phase diagram for a reactive system, in which a compound C is formed from components A and B. An isothermal cut and the polythermal projection are also shown. Such a phase diagram can be obtained via a reaction invariant projection of a higher-dimensional simple eutectic phase diagram. AS and BS are binary nonreactive eutectics, since their presence is not affected by the reaction, while ACSb and BCSa are ternary reactive eutectics. Similar... 

Example 6.7 Binary and ternary isothermal gas mixtures For a binary mixture of gases under isothermal and isobaric conditions and without shear forces, from Eq. (6.213) we have... 

Several experimental techniques have been developed for the investigation of the mass transport in porous catalysts. Most of them have been employed to determine the effective diffusivities in binary gas mixtures and at isothermal conditions. In some investigations, the experimental data are treated with the more refined dusty gas model (DGM) and its modifications. The diffusion cell and gas chromatographic methods are the most widely used when investigating mass transport in porous catalysts and for the measurement of the effective diffusivities. These methods, with examples of their application in simple situations, are briefly outlined in the following discussion. A review on the methods for experimental evaluation of the effective diffusivity by Haynes [1] and a comprehensive description of the diffusion cell method by Park and Do [2] contain many useful details and additional information. 

In a number of cases, when the heterogeneity is such that groups of sites may be considered as independent subsystems, statistical approaches may also be helpful. This may be so for surfaces with periodical structures like binary crystals or copolymers. Consider, by way of a simple example, a surface where pairs of sites (say A and B) form independent subsystems, and assume that molecules can adsorb on A and/or on B (site partition functions nd q. respectively) and that there is a lateral Interaction energy w if the two sites are both occupied. This leads to Isotherm (1.5.411. 

The examples discussed in the previous sections Illustrate models for deriving Isotherms for binary systems. A variety of variants (e.g. mobile adsorbates), alternatives (e.g. models based on computer simulations) and extensions (e.g. multimolecular adsorption. Inclusion of surface heterogeneity, can be, and have been, proposed. The extensions usually require more parameters so that agreement with experiment is more readily obtained, but as long as various models are not compared against the evidence, discrimination is impossible. As there are numerous theoretical (e.g. distinction between molecules in the first and second layer) and experimental (presence of minor admixtures, tenaciously adsorbing on part of the surface) variables one tends to enter a domain of diminishing returns. On the other hand, there are detailed models for certain specific, well-defined situations. Here we shall review some approaches for the sake of illustration. 

To Judge by the number of papers published annually on adsorption from dilute solution, this subject is more important than adsorption from binary solutions. However, the basic issues can be better illustrated from the latter so we have emphasized them in the previous sections. Now we shall review some important features of adsorption from dilute solutions. The examples to be given are merely meant to illustrate certain points and do not claim to be a selection based on a "quality test" among the. say. 10 isotherms published in the literature. 

Fig.4 and Fig.5 show adsorption isotherms for single component systems, obtained from fixed bed experiments and molecular simulation, respectively. Adosorption equilibria were simulated well. Except EtOH system, quantitative order of amount adsorbed was good agreement with experimental data. As for BEN and TOL systems, the amount of adsorbed for simulations were lower than experimental data. So it is necessary to examined van der Waals parameter for benzene ring. Fig.6 and Fig.7 show adsorption equilibria For binary component systems, obtained from fixed>bed experiments and molecular simulation, respectively. These are examples, which show azeotropic adsorption. Especially, IPA-TCE, BEN-EtOH systems show two azeotropic points. Result of simulation shows only one azeotropic point. More investigative is necessary. 

The P-V Diagram for a Multicomponent System. For a relatively volatile multicomponent system, a gasoline for example, an isotherm on the P-V diagram is similar to its counterpart for a binary system (Figure 23). However, it is commonly found that at the dew point the break in the P-V isotherm is not very pronounced in multi-component systems. Consequently, for systems of this type, it may be very difficult to fix the dew point in this manner. This experimental difficulty can be overcome by using a windowed cell and observing the pressure and volume when traces of liquid appear in the system. 

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