Phase equilibrium liquid

Here Klx a (kmol/m s) is the overall mass transfer coefficient for the liquid phase, based on mole fraction in the L-phase, x is the equilibrium liquid phase mole fraction, and Ac is the cross-sectional area of the column (m ). Hence... 

Kinetics and equilibrium analysis To use Patterson s model (eq. (4.52)), we first need the parameter w, and thus the equilibrium liquid-phase concentration Ce. The maximum loading of the zeolite particles for the specific initial concentration can be calculated by means of the equilibrium relationship (eq. (4.5)) ... 

Then, a trial-and-error procedure is needed for estimating the equilibrium liquid-phase dimensionless concentration. In this way, we get X = 0.1 and thus... 

Then, the equilibrium liquid-phase dimensionless concentration is estimated following a trial-and-eiTor procedure, and it is easy to find that X = 0.032. Thus,... 

Adsorption equilibria for the systems phenol-p-toluene sulfonate, phenol-p-bromophenol and phenol-dodecyl benzene sulfonate are shown in Figures 5, 6 and 7. In these figures, the ratio of the observed equilibrium values and computed values from equation (14) are plotted against the equilibrium liquid phase concentration of the solute in the mixture. It is seen that most of the data points are well within a deviation of 20%. The results for these diverse solute systems indicate that equation (14) is suitable for correlating binary equilibrium data for use in multicomponent rate models. 

The equilibrium liquid phase concentration of A is given by Henry s law for both small and large bubbles. Thus,... 

Nonlinear optimization techniques have been applied to determine isotherm parameters. It is well known (Ncibi, 2008) that the use of linear expressions, obtained by transformation of nonlinear one, distorts the experimental error by creating an inherent error estimation problem. In fact, the linear analysis method assumes that (i) the scatter of points follows a Gaussian distribution and (ii) the error distribution is the same at every value of the equilibrium liquid-phase concentration. Such behavior is not exhibited by equilibrium isotherm models since they have nonlinear shape for this reason the error distribution gets altered after transforming the data... 

A procedure is presented which is based upon Barkers method (2) for calculating vapor compositions from the known temperature dependence of the vapor pressure of the pure constituents, with suitable modification for the presence of salt, and from the dependence of the boiling point of the mixture with composition of the equilibrium liquid phase. 

Tf - ratio of key components in the equilibrium liquid phase of feed. 

To determine y, it is necessary to know the equilibrium liquid-phase mole fraction, x, at the bubble point corresponding to the accumulated relieving pressure. 

Complex coacervation is a phenomenon by which an aqueous solution of oppositely charged polyelectrolytes separates into two distinct phases. The more dense phase is called the complex coacervate or coacervate. It is a relatively concentrated polyelectrolyte solution. The second phase, a relatively dilute polyelectrolyte solution, is called the equiibrium liquid. The difference in concentration of the coacervate and equilibrium liquid phases is determined by the intensity of the coacervation interaction. The more intense this interaction is, the greater the concentration difference. ... 

The curve in figure 1 extends from pH 2.8 to 4.7, the pH range over which this mixture forms a complex coacervate. At lower or higher pH values, no coacervate forms and the system exists as a homogeneous solution. The solids content of the coacervate and equilibrium liquid phases converge as these pH limits are approached. Between the pH limits of coacervation, the total solids content of the coacervate phases passes through a maximum of 23 percent. This maximum coacervate solids content occurs between pH... 

Since we have the concentrations of the coexisting equilibrium liquid phase we can determine two binary parameters. Also, since we are interested in two different temperatures (LLE at 20°C and VLE at 73.4° C) we want an activity coefficient model with some built in temperature dependence (otherwise, we will get LLE with the same compositions at all temperatures.) Consequently, I will use the two constant Margules equation... 

Second, at pressures below about 4.8 kPa there is no equilibrium liquid phase (i.e., / = 0) 4.8 kPa is the dew point pressure of this reacting mixture at 25 C. Consequently, to solve for the equilibrium state of this system at pressures lower than 4.8 kPa, only vapor-phase chemical equilibrium needs to be considered without any phase equilibrium constraints. In this case, the mass balance equations are... 

Use this data, together with that of Problem 5.26, to predict by the van Laar equation the compositions and amounts of each of the two equilibrium liquid phases formed from 100, 100, and 50 kgmoles of isooctane, furfural, and benzene, respectively. 

Example 7.3. Cyclopentane is to be separated from cyclohexane by liquid-liquid extraction with methanol at 25°C. Calculate the bubble-point pressure using the equilibrium liquid-phase compositions given in Example 5.11. 

---