Binary Mixtures—High Pressure

Self-Diffusivity Self-diffusivity is a property that has little intrinsic value, e.g., for solving separation problems. Despite that, it reveals quite a lot about the inherent nature of molecular transport, because the effects of discrepancies of other physical properties are eliminated, except for those that constitute isotopic differences, which are necessary to ascertain composition differences. Self-diffusivity has been studied extensively under high pressures, e.g., greater than 70 atm. There are few accurate estimation methods for mutual diffu-sivities at such high pressures, because composition measurements are difficult. 

The general observation for gas-phase diffusion Dab P — constant, which holds at low pressure, is not valid at high pressure. Rather, DAb P decreases as pressure increases. In addition, composition effects, which frequently are negligible at low pressure, are very significant at high pressure. 

Liu and Ruckenstein [Ind. Eng. Chem. Res. 36, 3937 (1997)] studied self-diffusion for both liquids and gases. They proposed a semiem-pirical equation, based on hard-sphere theory, to estimate self-diffusivities. They extended it to Lennard-Jones fluids. The necessary energy parameter is estimated from viscosity data, but the molecular collision diameter is estimated from diffusion data. They compared their estimates to 26 pairs, with a total of 1822 data points, and achieved a relative deviation of 7.3 percent. 

Zielinski and Hanley [AlChE J. 45,1 (1999)] developed a model to predict multicomponent diffusivities from self-diffusion coefficients and thermodynamic information. Their model was tested by estimated experimental diffusivity values for ternary systems, predicting drying behavior of ternary systems, and reconciling ternary selfdiffusion data measured by pulsed-field gradient NMR. 

Mathur and Thodos [18] showed that for reduced densities less than unity, the product DAAp is approximately constant at a given temperature. Thus, by knowing the value of the product at low pressure, it is possible to estimate its value at a higher pressure. They found at higher pressures the density increases, but the product DaaP decreases rapidly. In their correlation, p = MA2Pc /Tc- 

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The previous seetion showed how the van der Waals equation was extended to binary mixtures. However, imieh of the early theoretieal treatment of binary mixtures ignored equation-of-state eflfeets (i.e. the eontributions of the expansion beyond the volume of a elose-paeked liquid) and implieitly avoided the distinetion between eonstant pressure and eonstant volume by putting the moleeules, assumed to be equal in size, into a kind of pseudo-lattiee. Figure A2.5.14 shows sohematieally an equimolar mixture of A and B, at a high temperature where the distribution is essentially random, and at a low temperature where the mixture has separated mto two virtually one-eomponent phases. 

A result different from that of Nakafuku et al. [144-147] was obtained by us from the study of a binary mixture of PE-ethyl cellulose liquid crystal under high pressure. We have reported [104,117] that addition of 1% ethyl cellulose by weight facilitates the formation of ECC of PE and moderates the conditions for the formation of ECC, that is, the pressure limit is lowered from 440 MPa to 150-200 MPa, and the temperature limit lowered from 200-245°C to 170°C. The DSC melting curves at atmospheric pressure for pure PE (Mt, = 1.06 x 10, p = 0.9556 g/cm ) and PE-ethyl cellulose mixture crystallized at various pressures are shown in Figs. 20 and... 

Chueh s method for calculating partial molar volumes is readily generalized to liquid mixtures containing more than two components. Required parameters are and flb (see Table II), the acentric factor, the critical temperature and critical pressure for each component, and a characteristic binary constant ktj (see Table I) for each possible unlike pair in the mixture. At present, this method is restricted to saturated liquid solutions for very precise work in high-pressure thermodynamics, it is also necessary to know how partial molar volumes vary with pressure at constant temperature and composition. An extension of Chueh s treatment may eventually provide estimates of partial compressibilities, but in view of the many uncertainties in our present knowledge of high-pressure phase equilibria, such an extension is not likely to be of major importance for some time. 

The difficulties encountered in the Chao-Seader correlation can, at least in part, be overcome by the somewhat different formulation recently developed by Chueh (C2, C3). In Chueh s equations, the partial molar volumes in the liquid phase are functions of composition and temperature, as indicated in Section IV further, the unsymmetric convention is used for the normalization of activity coefficients, thereby avoiding all arbitrary extrapolations to find the properties of hypothetical states finally, a flexible two-parameter model is used for describing the effect of composition and temperature on liquid-phase activity coefficients. The flexibility of the model necessarily requires some binary data over a range of composition and temperature to obtain the desired accuracy, especially in the critical region, more binary data are required for Chueh s method than for that of Chao and Seader (Cl). Fortunately, reliable data for high-pressure equilibria are now available for a variety of binary mixtures of nonpolar fluids, mostly hydrocarbons. Chueh s method, therefore, is primarily applicable to equilibrium problems encountered in the petroleum, natural-gas, and related industries. 

Thermodynamic consistency tests for binary vapor-liquid equilibria at low pressures have been described by many authors a good discussion is given in the monograph by Van Ness (VI). Extension of these methods to isothermal high-pressure equilibria presents two difficulties first, it is necessary to have experimental data for the density of the liquid mixture along the saturation line, and second, since the ideal gas law is not valid, it is necessary to calculate vapor-phase fugacity coefficients either from volumetric data for... 

In the previous sections, we indicated how, under certain conditions, pressure may be used to induce immiscibility in liquid and gaseous binary mixtures which at normal pressures are completely miscible. We now want to consider how the introduction of a third component can bring about immiscibility in a binary liquid that is completely miscible in the absence of the third component. Specifically, we are concerned with the case where the added component is a gas in this case, elevated pressures are required in order to dissolve an appreciable amount of the added component in the binary liquid solvent. For the situation to be discussed, it should be clear that phase instability is not a consequence of the effect of pressure on the chemical potentials, as was the case in the previous sections, but results instead from the presence of an additional component which affects the chemical potentials of the components to be separated. High pressure enters into our discussion only indirectly, because we want to use a highly volatile substance for the additional component. 

Kinetic studies of various systems have been carried out as follows the reaction of 2,2 -dichlorodiethyl sulfide and of 2-chloroethyl ethyl sulfide with diethylenetriamine and triethylamine in 2-methoxyethanol ° the catalysed reactions of substituted phenols with epichlorohydrin the reactions of para-substituted benzyl bromides with isoquinoline under high pressure the reactions of O-alkylisoureas with OH-acidic compounds [the actual system was N, N -dicyclohexyl-0-(l-methylheptyl)isourea with acetic acid] and tlie ring opening of isatin in aqueous binary mixtures of methanol and acetonitrile cosol vents. 

Yang, M. et al.. Solid-liquid phase equilibria in binary 1-octanol plus n-alkane mixtures under high pressure. Part 2 (1-Octanol + n-octane, n-dodecane) systems, Fluid Phase Equilib., 204, 55,2003. 

In this basic overview of the thermodynamic of fluid mixtures at high-pressure emphasis is given to the behaviour of binary mixtures in order to introduce the reader to the wide variety of phase transitions, which are not observed for pure fluids. As the number of component increases the phase behaviour is mainly determined by interactions between unlike molecules at the expenses of interactions between similar molecules, but fortunately, in most cases, it is only necessary to consider pair interactions and not three or more body interactions. References are given for a more detailed study of the different aspect considered. 

Electrolytic (coukxnetric) hygrometers The quantity of electricity required to carry out a chemical reaction is measured. The principle is based upon Faraday s law of electrolysis. Water is absorbed on to a thin film of dessicant (e.g. P2O5) and electrolysed. The current required for the electrolysis varies according to the amount of water vapour absorbed. The current depends also upon the flowrate. Capable of high precision. Used in the range 1000 to 3000 ppm of water by volume. Somewhat complicated procedure. Recombination of products to water is necessary after electrolysis. Density, pressure and flowrates have to be maintained precisely. Contamination can poison the cell. It is ideal for binary mixtures but is of limited range. Suitable for on-line operation. 

Under high pressure powdered PETN agglomerates to a mass which has the appearance of porcelain, but which, when broken up into grains, is a very powerful smokeless powder functioning satisfactorily with the primers which are commonly used in small arms ammunition. The powder is hot and unduly erosive, but cooler powders have been prepared by incorporating and compressing PETN in binary or in ternary mixtures with TNT,... 

Figure 14.7 Schematic representation of the different types of binary (liquid + liquid) phase equilibria, showing the effect of p, T, and x on the two-phase volume. Examples are known for all except figures (k), (o), and (s). Reproduced with permission from G. M. Schneider, High-pressure Phase Diagrams and Critical Properties of Fluid Mixtures , M. L. McGlashan, ed., Chapter 4 in Chemical Thermodynamics, Vol. 2, The Chemical Society, Burlington House, London, 1978.

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