Pure-fluid critical point

The critical isotherm (T = 304.2 K in Figure 8.4) separates those fluids that are always one phase from those that can split in two. The critical isotherm does not contain any unstable points (points having positive slopes), but it does pass through one point of zero slope. This is a point of inflection and identifies the critical point, any pure-fluid critical point has... 

Since this condition is also satisfied by the critical point, a pure-fluid critical point must lie on the spinodal. For a pure substance that obeys the Redlich-Kwong equation of state, the spinodal temperatures and volumes are related by... 

These conditions identify both vapor-liquid and liquid-liquid critical points. For vapor-liquid equilibria, they are satisfied when the spinodal coincides with the vapor-liquid saturation curve. However, that point need not occur either at the maximum in the saturation envelope or at the maximum in the spinodal see Figure 8.12. Along a spinodal the one-phase metastable system is balanced on the brink of an instability at a critical point that balance coincides with a two-phase situation and the resulting fluctuations cause critical opalescence, just as they do at pure-fluid critical points. 

Eig. 1. Schematic pressure—temperature diagram for a pure material showing the supercritical fluid region, where is the pure component critical point... 

The mole fraction of acetone in the liquid phase is not a strong function of intermolecular interactions for pressures less than approximately 80 bar. For the immiscible systems, the shape of the mole fraction versus pressure curve is characteristic of solubility curves of solids in supercritical solvents Q4), with a minimum around the pure solvent critical point. The effect of changing the intermolecular interactions is in the expected direction the solubility of acetone in the fluid phase is lower (by a factor of 5) for the system with - 0.70 relative to the one with - 0.80. Again, a few percent change in the magnitude of the unlike-pair interactions has a greatly amplified effect on the solubility. 

Figure 9. Critical lines for a binary mixture of components with several critical points. Solid lines (A, B, C) indicate binary mixture critical lines dashed lines are phase existence curve of pure components Cn rn are the m critical point ( w > i) for the pure component (n = 1,2% m = 1 identifies the vapor-liquid critical point m > 1 corresponds to the fluid-fluid critical points.

In principle the stability of pure solid phases can be judged using the thermal and mechanical stability criteria derived in 8.1.2, but those criteria are not useful for solids when they are implemented via volumetric equations of state. To use an equation of state to test for solid-phase stability, the equation would have to extend an isotherm from a fluid phase into a solid region of the phase diagram. But any analytically continuous, differentiable function that provides such an extension also predicts a solid-fluid critical point—a point that does not actually exist. 

Class C. These binaries have both a UCST and an LCST at temperatures removed from the critical temperatures of the pure components. The locus of UCSTs intersects the VLLE line at a UCEP, while that for LCSTs intersects the VLLE line at an LCEP. The loci of UCSTs and LCSTs may or may not form a continuous line of fluid-fluid critical points. Few binaries have both UCSTs and LCSTs, so few fall into class C. 

First, recall the close analogies that exist between pure-component critical points and those of binary-mixtures. Unlike simple phase changes, which represent transitions between stable and metastable behavior, all critical points represent transitions between stable and unstable behavior. For pure components, the transition is driven by mechanical instabilities, and at vapor-liquid critical points pure fluids have... 

Figure 1 shows second virial coefficients for four pure fluids as a function of temperature. Second virial coefficients for typical fluids are negative and increasingly so as the temperature falls only at the Boyle point, when the temperature is about 2.5 times the critical, does the second virial coefficient become positive. At a given temperature below the Boyle point, the magnitude of the second virial coefficient increases with... 

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

A third exponent y, usually called the susceptibility exponent from its application to the magnetic susceptibility x in magnetic systems, governs what m pure-fluid systems is the isothennal compressibility k, and what in mixtures is the osmotic compressibility, and detennines how fast these quantities diverge as the critical point is approached (i.e. as > 1). 

Solvent Strength of Pure Fluids. The density of a pure fluid is extremely sensitive to pressure and temperature near the critical point, where the reduced pressure, P, equals the reduced temperature, =1. This is shown for pure carbon dioxide in Figure 2. Consider the simple case of the solubihty of a soHd in this fluid. At ambient conditions, the density of the fluid is 0.002 g/cm. Thus the solubiUty of a soHd in the gas is low and is given by the vapor pressure over the total pressure. The solubiUties of Hquids are similar. At the critical point, the density of CO2 is 0.47 g/cm. This value is nearly comparable to that of organic Hquids. The solubiHty of a soHd can be 3—10 orders of magnitude higher in this more Hquid-like CO2. 

Fig. 3. PF diagram for a pure fluid (not to scale) point c is the gas—liquid critical state, is the constant pressure at which phase transition occurs at...

A. de Keizer, T. Michalski, G. H. Findenegg. Fluids in pores experimental and computer simulation studies of multilayer adsorption, pore condensation and critical point shifts. Pure Appl Chem (55 1495-1502, 1991. 

Potoff, J. J. Panagiotopoulos, A. Z., Critical point and phase behavior of the pure fluid and a Lennard-Jones mixture, J. Chem. Phys. 1998,109,10914—10920... 

Application of this technique to measurements of the spectral distribution of tight scattered from a pure SF fluid at its critical point was present by Ford and Benedek The scattering is produced by entropy fluctuations which decay very slowly in the critical region. Therefore the spectrum of the scattered light is extremely narrow (10 - lO cps) and can only be observed by this light beating technique 240a)... 

Type V fluid phase behaviour shows at temperatures close to 7C-A a three-phase curve hhg which ends at low temperature in a LCEP (h=h)+g and at high temperature in a UCEP (h+h) g The critical curve shows two branches. The branch h=g runs from the critical point of pure component A to the UCEP. The second branch starts in the LCEP and ends in the critical point of pure component B. This branch of the critical curve is at low temperature h=h in nature and at high temperature its character is changed into h=g- The h=h curve is a critical curve which represents lower critical solution temperatures. In Figure 2.2-7 four isothermal P c-sections are shown. 

To consider in detail the critical point as defined in (I), examine Fig. I, which shows the family of isotherms of a pure substance in Ihe fluid range lliquid or gas) such for example as shown in the figure for carbon dioxide. 

Figure 14.10 The five types of (fluid + fluid) phase diagrams according to the Scott and van Konynenburg classification. The circles represent the critical points of pure components, while the triangles represent an upper critical solution temperature (u) or a lower critical solution temperature (1). The solid lines represent the (vapor + liquid) equilibrium lines for the pure substances. The dashed lines represent different types of critical loci. (l) [Ar + CH4], (2) [C02 + N20], (3) [C3H8 + H2S],...

A gaseous pure component can be defined as supercritical when its state is determined by values of temperature T and pressure P that are above its critical parameters (Tc and Pc). In the proximity of its critical point, a pure supercritical fluid (or a dense gas as it is alternatively known) has a very high isothermal compressibility, and this makes possible to change significantly the density of the fluid with relatively limited modifications of T and P. On the other hand, it has been shown that the thermodynamic and transport properties of supercritical fluids can be tuned simply by changing the density of the medium. This is particularly interesting for... 

For any pure chemical species, there exists a critical temperature (Tc) and pressure (Pc) immediately below which an equilibrium exists between the liquid and vapor phases (1). Above these critical points a two-phase system coalesces into a single phase referred to as a supercritical fluid. Supercritical fluids have received a great deal of attention in a number of important scientific fields. Interest is primarily a result of the ease with which the chemical potential of a supercritical fluid can be varied simply by adjustment of the system pressure. That is, one can cover an enormous range of, for example, diffusivities, viscosities, and dielectric constants while maintaining simultaneously the inherent chemical structure of the solvent (1-6). As a consequence of their unique solvating character, supercritical fluids have been used extensively for extractions, chromatographic separations, chemical reaction processes, and enhanced oil recovery (2-6). 

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