Pure-component isotherms examples

The graphical interpretation of Eq. (16-197) is shown in Fig. 16-37 for the conditions of Example 12. An operating hne is drawn from the origin to the point of the pure displacer isotherm at = cf. For displacement to occur, the operating hne must cross the pure component isotherms of the feed solutes. The product concentrations in the iso-tachic train are found where the operating hne crosses the isotherms. When this condition is met, the feed concentrations do not affect the final product concentrations. 

The above conclusion for the Langmuir equation does not readily apply to other isotherms. For example, if the pure component isotherm is described by the Sips equation... 

A wide variety of physical properties are important in the evaluation of ionic liquids (ILs) for potential use in industrial processes. These include pure component properties such as density, isothermal compressibility, volume expansivity, viscosity, heat capacity, and thermal conductivity. However, a wide variety of mixture properties are also important, the most vital of these being the phase behavior of ionic liquids with other compounds. Knowledge of the phase behavior of ionic liquids with gases, liquids, and solids is necessary to assess the feasibility of their use for reactions, separations, and materials processing. Even from the limited data currently available, it is clear that the cation, the substituents on the cation, and the anion can be chosen to enhance or suppress the solubility of ionic liquids in other compounds and the solubility of other compounds in the ionic liquids. For instance, an increase in allcyl chain length decreases the mutual solubility with water, but some anions ([BFJ , for example) can increase mutual solubility with water (compared to [PFg] , for instance) [1-3]. While many mixture properties and many types of phase behavior are important, we focus here on the solubility of gases in room temperature IFs. 

As an example, Fig. 6.25a gives the results of the isotherm determination for Troger s base enantiomer on Chiralpak AD (dp = 20 xm) from perturbation measurements (Mihlbachler et al., 2001). Theoretical retention times for the pure components and racemic mixtures (lines) were fitted to the measured data (symbols) by means of Eq. 6.185 to determine the unknown parameter in Eq. 6.186. Total differentials for the mixture (Eq. 6.53) were evaluated using the coherence condition Eq. 6.54, resulting in the isotherm equation Eq. 6.186. Note that the Henry coefficients were independently determined by pulse experiments and were fixed during the fitting procedure. 

This example. serves to demonstrate tlie predictive mode of the program WS, which is selected with the preceding entry. This mode is used in the absence of VLE data, and therefore no data are entered to, or can be accessed from the disk in this mode. Instead, the user provides the critical temperature, critical presssure, acentric factor, and the PRSV kj parameter for each pure component, selects an excess free-energy model provides model parameters and a temperature. The program will return isothermal x-y-P predictions at the temperature entered, in the composition range X] = 0 to 1, at intervals of 0.1.)... 

When two or more solutes are dissolved in the solvent, it is sometimes possible to separate these into pure components or separate one and leave the other in solution. Whether or not this can be done depends upon the solubility and phase relations of the system under consideration. How to plot and use this data is explained by Fitch (1970), and Campbell and Smith (1951). It is helpful if one of the components has a much more rapid change in solubility with temperature than does the other. A typical example, which is practiced on a large scale, is the separation of KCI and NaCl from water solution. A simplified phase diagram for this system is shown in Figure 5.1. In this case, the solubility of NaCl is plotted on the Y-axis as parts per 100 parts of solvent, and the solubility of the KCI is plotted on the X-axis in the same units. The isotherms show a marked decrease in solubility for each component as the other component is increased. This example is typical for many inorganic salts. 

The situation can be analyzed more clearly on the enthalpy/pressure chart of pure component (Figure 11-2). The more volatile component (acetonitrile in the previous example) is a hypothetical liquid at the bubble temperature. It is shown by point H, located on the liquid portion of the isotherm at Tbubwe but extrapolated into the vapor-liquid region. Since isotherms in the compressed liquid region are almost vertical, the enthalpy of state is to a very good... 

In the last chapter, we discussed the description of pure component adsorption equilibrium from the fundamental point of view, for example Langmuir isotherm equation derived from the kinetic approach, and Volmer equation from the Gibbs thermodynamic equation. Practical solids, due to their complex pore and surface structure, rarely conform to the fundamental description, that is very often than not fundamental adsorption isotherm equations such as the classical Langmuir equation do not describe the data well because the basic assumptions made in the Langmuir theory are not readily satisfied. To this end, many semi-empirical approaches have been proposed and the resulting adsorption equations are used with success in describing equilibrium data. This chapter will particularly deal with these approaches. We first present a number of commonly used empirical equations, and will discuss some of these equations in more detail in Chapter 6. 

In Step 3, we need to evaluate the pure component pressure from the reduced spreading pressure. This is fine if the integral for the reduced spreading pressure (eq. 5.3-21) can be obtained analytically, for example when the single component isotherm takes the form of Langmuir equation ... 

The masses of these have to be approximately determined from pure adsorption isotherms of both components (1, 2) and calculations of coadsorption equilibria including only pure components parameters as for example the lAST-formalism [4.10,4.4,4.15,4.17]. 

Solution For a stable homogeneous phase, whether a pure component, a binary mixture, or a multicomponent system, the heat capacities Cp and Cy and the isothermal compressibility Ct should be positive. The derivations for a single-component system were presented in the text. Example 4.10 provides the derivation for C-p. The derivations for Cy and Cp are straightforward (see Problem 4.8),... 

Example 4.1.2 Markham and Benton (1931) studied experimentally the adsorption of pure O2, pure CO as well as CO-O2 mixtures on 19.6 g of silica at 0°C. The data obtained are provided in Table 4.1.8. The column for the mixtures under "isotherm" contains values obtained from pure component adsorption isotherms via interpolation. 

For example, let us assume the more reahstic case where the adsorption isotherm can be represented by the Langmuir equation (Equation 14.2). Then, by simple integration of Equation 14.11b using (14.2) (for single gas) and solving with respect to the pure component pressure we get ... 

In the first step, in which the molecules of the fluid come in contact with the adsorbent, an equihbrium is established between the adsorbed fluid and the fluid remaining in the fluid phase. Figures 25-7 through 25-9 show several experimental equihbrium adsorption isotherms for a number of components adsorbed on various adsorbents. Consider Fig. 25-7, in which the concentration of adsorbed gas on the solid is plotted against the equilibrium partial pressure p of the vapor or gas at constant temperature. At 40° C, for example, pure propane vapor at a pressure of 550 mm Hg is in equilibrium with an adsorbate concentration at point P of 0.04 lb adsorbed propane per pound of silica gel. Increasing the pressure of the propane will cause... 

---