Liquid sorption equilibrium

Figure 10 shows basal spacing (dn) for the liquid sorption equilibrium systems descri-... 

Figure 23 shows the degree of swelling for the liquid sorption equilibrium systems ethanol (l)-toluene (2)/hexadecylammonium vermiculite as a function... 

The sorption-exchange process taking place at the solid-liquid interface may be described in thermodynamically exact terms when the activities of the interfacial layer and of the bulk phase are known. In accordance with the exchange equilibrium at the solid-liquid interface, the liquid sorption equilibrium constant is given by the following formulas [1-5] ... 

Sorption isotherm curves are graphical relationships showing the partitioning between solid and liquid form where mass adsorbed per unit mass of dry solids (S) is plotted against the concentration (C) of the constituent in solution. K is the sorption equilibrium constant N is a constant describing the intensity of sorption. The linear sorption isotherm can be expressed as follows ... 

Most of these aspects of water-sorption equilibrium correspond to the equality of chemical potentials of water in the medium and in the polymer. The consequences of this principle are illustrated by the experiment of Fig. 14.2, where an interface is created between water and a nonmiscible liquid (oil, hydrocarbon, etc.), and a polymer sample is immersed into the organic liquid. It can be observed that, despite the hydrophobic character of the surrounding medium, the sample reaches the same level of water saturation as in direct water immersion or in a saturated atmosphere. What controls the water concentration in the polymer is the ratio C/Cs of water concentrations in the organic phase, where Cs is the equilibrium concentration, which can be very low but not zero. In other words, hydrophobic surface treatments can delay the time to reach sorption equilibrium but they cannot avoid the water absorption by the substrate. 

In a typical IINS experiment, a catalyst is characterized in a sealed reaction vessel or bypass can under vacuum, ambient conditions, equilibrium partial pressures of reactants, or higher gas pressures. The sample is quenched to liquid nitrogen temperature as fast as possible to maintain the conditions of a frozen sorption equilibrium as well as possible. Then the sample is loaded into a cryostat and cooled to a temperature below 30 K, and the spectrum is measured. 

Vapor pressure Partitioning between phases solubility of a gas in a liquid sorption of a solute in a fluid onto a sorbent Chemical reaction equilibrium Electric charge Phase change solid/liquid liquid/gas Diffusivity Ionic mobility Molecular size and shape... 

Deviation from sorption equilibrium in the stationary phase in chromatography on a liquid sorbent applied on a macroporous support (Cg,) ... 

A similar example of a promising application of solar heat for intensified process systems is pervaporation. In pervaporation, a selective membrane is used as barrier between two phases, the liquid feed and the vapour permeate. The process depends on the sorption equilibrium and the mobility of the components through the membrane and is rather independent of the vapour liquid equilibrium. The desired component, which is in liquid form in the feed, permeates through the membrane and evaporates while passing the membrane, because the partial pressure of the permeating component is kept lower than the equilibrium vapour pressure [21]. Permeabilities depend on the solubility and diffusion rates through the membrane. 

Both adsorption from a supercritical fluid to an adsorbent and desorption from an adsorbent find applications in supercritical fluid processing. The extrapolation of classical sorption theory to supercritical conditions has merits. The supercritical conditions are believed to necessitate monolayer coverage and density dependent isotherms. Considerable success has been observed by the authors in working with an equation of state based upon the Toth isoterm. It is also important to note that the retrograde behavior observed for vapor-liquid phase equilibrium is experimentally observed and predicted for sorptive systems. 

Figure 15.3 (Brown et al, 1992) shows the equilibrium isotherms for the sorption of copper and cadmium ions onto peat at 20°C. The figure shows the amount of metal ion sorbed /umol/g) at the liquid phase equilibrium metal ion concentration (C mmol/dm ). The maximum saturation capacities for copper and cadmium ions on peat are 270 and 180 /umol/g respectively. These results indicate the considerable potential for peat in metal ion removal.

Polymers are often polydisperse with respect to molecular weight. Whereas this is of minor importance for the solvent sorption in polymers (vapor-hquid equilibrium), this fact usually remarkably influences the polymer solubility (liquid-hquid equilibrium). Therefore, polydispersity needs to be accounted for in interpretation and modeling of experimental data. This can be done by applying continuous thermodynamics as well as by choosing a representative set of pseudocomponents. It was shown that a meaningful estimation of the phase boundary is possible when using only two or three pseudocomponents as soon as they reflect the important moments (Mn, Mw, Mz) of the molecular weight distribution. 

Figure 8.3b shows that the initial polymerization rate (Rpo) is not linearly dependent on the monomer concentration (here, the initii polymerization rates were estimated by extrapolating the polymerization rate data to t = 0). The initial rate levels off for the initial monomer concentration larger than about 2.0mol/l, possibly because of a rapid buildup of polymer around the silica-supported catalyst particles. The initial polymerization rate profile can be fitted experimentally using the following Langmuir-type equation where it is assumed that the monomer sorption equilibrium is established between the solid phase and the liquid phase ... 

Spherical particles 15 nm in diameter and of density 2290 kg/m3 are pressed together to form a pellet. The following equilibrium data were obtained for the sorption of nitrogen at 77 K. Obtain estimates of the surface area of the pellet from the adsorption isotherm and compare the estimates with the geometric surface. The density of liquid nitrogen at 77 K is 808 kg/m3. 

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