Critical pressure ration

Solutions in hand for the reference pairs, it is useful to write out empirical smoothing expressions for the rectilinear densities, reduced density differences, and reduced vapor pressures as functions of Tr and a, following which prediction of reduced liquid densities and vapor pressures is straightforward for systems where Tex and a (equivalently co) are known. If, in addition, the critical property IE s, ln(Tc /Tc), ln(PcVPc), and ln(pcVPc), are available from experiment, theory, or empirical correlation, one can calculate the molar density and vapor pressure IE s for 0.5 < Tr < 1, provided, for VPIE, that Aa/a is known or can be estimated. Thus to calculate liquid density IE s one uses the observed IE on Tc, ln(Tc /Tc), to find (Tr /Tr) at any temperature of interest, and employs the smoothing relations (or numerically solves Equation 13.1) to obtain (pR /pR). Since (MpIE)R = ln(pR /pR) = ln[(p /pc )/(p/pc)] it follows that ln(p7p)(MpIE)R- -ln(pcVpc). For VPIE s one proceeds similarly, substituting reduced temperatures, critical pressures and Aa/a into the smoothing equations to find ln(P /P)RED and thence ln(P /P), since ln(P /P) = I n( Pr /Pr) + In (Pc /Pc)- The approach outlined for molar density IE cannot be used to rationalize the vapor pressure IE without the introduction of isotope dependent system parameters Aa/a. 

While the foregoing concepts have been utilized to rationalize the product distribution obtained on hydrogenation of a number of monocyclic olefins, it should be noted that the effect of pressure on the stereochemistry of hydrogenation of steroidal double bonds has not been critically evaluated. 

FIGURE 11.20. Variation of (a) critical purge-feed ration. b) fractional recovery of high-pressure product, and (c) enrichment of low-pressure product. Parameter (modified separation factor). [Reprinted with permission from Chem. Eng. Sci. 36, after Chan, Hill, and Wong (ref. 27). Copyright 1981, Pergamon Press, Ltd.]... 

The last point which can be evoked here is conceptually linked to the hot-spot theory. If the limit liquid layers around a bubble are in direct contact with the heated and pressurized bubble content, far above the critical point of the liquid, these layers should be in a supercritical state. 23 This attractive hypothesis (see p. 61) was used by Hoffmann et al to rationalize the sonolysis of nitrophenyl derivatives. Supercritical fluids are characterized by a very high flexibility of important parameters (density, dielectric constant, solubilizing power) as a function of pressure. Experts in the field distinguish gas-like and liquid-like media, in which the kinetics of a reaction can vary over a broad range. For instance, the conjugate addition of piperidine to methyl propiolate was studied in supercritical ethane or fluoroform (Fig. 5). ... 

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