Solution critical point

This vanishes at the critical-solution point as does (d p/d k) at the one-component fluid critical point. Thus... 

The system FLO - C02> H20 - ELS and H20 - (C HjOoO can be described by assuming cross-associationf The particular temperature dependence of the solubility for diethyl ether was reproduced by the calculation without making it the object of a fitting process. This suggests that the method might be able to describe systems with both an upper and lower critical solution point. 

S substrate P product Cat. catalyst CST critical solution point organic phase... 

Before the reaction, at temperatures below the critical solution point, the catalyst is insoluble in the organic solvent. When heated to temperatures above the critical solution point, the catalyst is soluble in the organic solvent and a homogeneous system is formed in which the catalyzed reaction takes place. After reaction, on cooling to temperatures below the critical solution point, the catalyst precipitates from the organic phase which contains the product. Thus, the catalyst can be easily separated from the product by decantation or filtration and reused. 

Note 1 An alternative definition of critical solution point refers strictly to liquid-vapor equilibria [3]. 

CRITICAL POINT. (I) A point where two phases, which are continually approximating each other, become identical and form but one phase. With a liquid in equilibrium with its vapor. Ihe critical point is such a combination of temperature and pressure lhal Ihe specific volumes of the liquid and its vapor arc identical, and there is no distinction between the two states. (2) The critical solution point is such a combination of temperature and pressure lhal two otherwise partially miscible liquids become consolule. 

Kubota, K. Abbey, K. M. Chu, B., "Static and Dynamical Properties of a Polymer Solution with Upper and Lower Critical Solution Points. NBS 705 Polystyrene in Methyl Acetate," Macromolecules, 16, 137 (1983). 

Myrat, C. D. Rowlinson, J. S., "The Separation and Fractionation of Polystyrene at a Lower Critical Solution Point," Polymer, 6, 645 (1965). 

Figure 5.13 Predicted phase diagrams for physical gels made from low-molecular-weight molecules with junctions of unrestricted functionality 4> is the total volume fraction of polymer, and Tr is here the reduced distance from the theta temperature, Tr = — Q/T. The parameter Aq controls the equilibrium constant among aggregates of various sizes. The outer solid lines are binodals, the inner solid lines are spinodals, and the dashed lines are gelation transitions. CP is a critical solution point, CEP is a critical end point, and TCP is a tricriti-cal point. (Reprinted with permission from Tanaka and Stockmayer, Macromolecules 27 3943. Copyright 1994 American Chemical Society.)...

In the next chapter we shall show that at the critical solution point of a binary system... 

At the point C the two liquid layers become identical, and this is called the critical solution point or con-solute point. If the total applied pressure is varied, both the critical temperature and composition of the critical mixture alter and we obtain a critical solution line. As an example of this we give in table 16. If the dependence of the critical solution temperature on pressure for the system cyclohexane -f aniline. An increase of pressure raises the critical solution temperature, and the mutual solubility of the two substances is decreased. We saw earlier that the applied pressure had only a small effect on the thermodynamic properties of condensed phases, and we notice in this case that an increase of pressure of 250 atm. alters the critical temperature by only 1.6 °C. 

The two branches of the coexistence curve meet in the point K, and the tangent at this point is the limit to which the tie lines tend as K is approached. Beyond K there are no tie lines and the system exists as a single stable phase. K is the critical solution point at the temperature and pressure under consideration. It also lies on the spinodal curve since it must of necessity lie on the boundary between stable and unstable states. 

The phases are therefore identical and the solution cannot have a critical solution point. 

In the final row of the table, we have listed values for the Crispation nuonber, Cr - na/ad. This number arises in stability analyses of interfacial transport when deflection of the interface under normal stresses is permitted (15., 16). Its importance was demonstrated by Scriven and Stemling who showed that the effect is always destabilizing a nondeflecting interface has Cr - 0 or infinite tension. Since we deal with vanishingly small interfacial tensions in the neighborhood of a critical solution point we were curious to see whether Cr was unusually high in our experiments. 

Oleinikova, A., and Bonetti, M. Electrical conductivity of highly concentrated electrolytes near the critical solute point A study of tetra-n-butylammonium picrate in alcohols of moderate dielectric constant. J. Chem. Phys., 2001, 115, p. 9871-82. 

Figure 3.1. Upper and lower critical solution points.

Because the correlation length increases as the critical solution point is approached, enhanced adsorption occurs in the pore space specifically in the near-critical region of the phase diagram. In the two-phase region the pore walls are wet, either partially or completely, by that phase in which the... 

From the above table it is clear that the lower critical solution temperature is raised, and the upper critical solution temperature is lowered, by increase of pressure. Under j>res,sure of 830 kgm. per sq. cm. the two critical solution points coincide. Under pressures higher than this, complete miscibility exists at all temperatures. A similar behaviour is found in the case of water and methylethylketone. 

G (KI -I- two liquid phases) H (critical solution point). K (KI + two liquid phases)... 

A third kind of phase diagram in a two-component system (as shown in figure A2.5.5(c) is one showing liquid-liquid phase separation below a critical-solution point, again at a fixed pressure. (On a T, x diagram, the critical point is always an extremum of the two-phase coexistence curve, but not always a maximum. 

A determination of the critical exponent 8 has been made for the liquid-liquid system, n-decane-fifi dichloroethyl ether (chlorex). Utilizing schlieren photographs of the system in an ultracentrifuge at a temperature slightly below the critical solution point, the density gradient was obtained as a function of radius. These gradients, used in conjunction with sedimentation theory, provided a means for calculating values for the exponent 8. The values thus obtained are consistent with accepted values for the exponents / and y in two-fluid systems. They are, however, smaller than those found for pure fluids. 

A pycnometer of approximately 50 mL was cleaned with hot cleaning solution for use in preparing the mixtures. The rubber cap, syringes, and needles were rinsed with research-grade acetone. Weighings of the pycnometer with and without the samples were performed in a temperature- and humidity-controlled room using an analytical balance with a precision of 0.0002 g. The sample used was one at 0.3952 dt 0.0001 mol fraction n-decane, the reported composition at the critical solution point (10). The phase separation temperature was 26.9°C. 

LIQUID-LIQUID CURVE AND CRITICAL SOLUTION POINT. In the now classical theory of regular solutions developed by Scatchard (10) and Hildebrand (5) with the nonideal entropy correction given by Flory and Huggins (5), the activities of the components of a binary system are given by... 

Ross-type foaming (340) A weak solvent-solute interaction may cause surface activity. This activity, and therefore the foaminess of the solution, increases with the tendency for separation of the solution into two liquid phases. As solute concentration increases toward the critical solution point, or the plait point, foaminess increases. Once this point is reached and two phases are formed, one phase may act as a foam inhibitor and destroy the foam. 

Fig. 14.2 Behavior of (average) chemical potential (xb) in a mixture of two liquid components depending upon temperature (top) and the corresponding phase diagram at constant pressure with an upper critical solution point (bottom).

Fig. 14.3 Applying the lever rule using the example of a phase diagram with an upper critical solution point.

Some systems exhibit a lower critical solution point (Fig. 14.4). At higher temperatures (and depending upon the composition), two phases can be present. At lower temperatures, the two substances are totally miscible. An example of this... 

Fig. 14.4 Phase diagram of a system with a lower critical solution point.

Some systems have both an upper and a lower critical solution point (Fig. 14.5). These kinds of systems are mostly found at higher pressures. It is therefore plausible to assume that aU systems having a lower critical solution point will also exhibit an upper critical solution point if the temperature and pressure are high... 

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