Activity 311 liquid mixtures

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

If we vary the composition of a liquid mixture over all possible composition values at constant temperature, the equilibrium pressure does not remain constant. Therefore, if integrated forms of the Gibbs-Duhem equation [Equation (16)] are used to correlate isothermal activity coefficient data, it is necessary that all activity coefficients be evaluated at the same pressure. Unfortunately, however, experimentally obtained isothermal activity coefficients are not all at the same pressure and therefore they must be corrected from the experimental total pressure P to the same (arbitrary) reference pressure designated P. This may be done by the rigorous thermodynamic relation at constant temperature and composition ... 

The discussion so far has been confined to systems in which the solute species are dilute, so that adsorption was not accompanied by any significant change in the activity of the solvent. In the case of adsorption from binary liquid mixtures, where the complete range of concentration, from pure liquid A to pure liquid B, is available, a more elaborate analysis is needed. The terms solute and solvent are no longer meaningful, but it is nonetheless convenient to cast the equations around one of the components, arbitrarily designated here as component 2. 

In order to broaden the field of biocatalysis in ionic liquids, other enzyme classes have also been screened. Of special interest are oxidoreductases for the enan-tioselective reduction of prochiral ketones [40]. Formate dehydrogenase from Candida boidinii was found to be stable and active in mixtures of [MMIM][MeS04] with buffer (Entry 12) [41]. So far, however, we have not been able to find an alcohol dehydrogenase that is active in the presence of ionic liquids in order to make use of another advantage of ionic liquids that they increase the solubility of hydrophobic compounds in aqueous systems. On addition of 40 % v/v of [MMIM][MeS04] to water, for example, the solubility of acetophenone is increased from 20 mmol to 200 mmol L ... 

For liquid mixtures at low pressures, it is not important to specify with care the pressure of the standard state because at low pressures the thermodynamic properties of liquids, pure or mixed, are not sensitive to the pressure. However, at high pressures, liquid-phase properties are strong functions of pressure, and we cannot be careless about the pressure dependence of either the activity coefficient or the standard-state fugacity. 

In Section HI, we discussed the relation between fugacities and activity coefficients in liquid mixtures, and we emphasized that we have a fundamental choice regarding the way we wish to relate the fugacity of a component to the pressure and composition. This choice follows from the freedom we have in choosing a convention for the normalization of activity coefficients. 

In addition to deciding on the method of normalization of activity coefficients, it is necessary to undertake two additional tasks first, a method is required for estimating partial molar volumes in the liquid phase, and second, a model must be chosen for the liquid mixture in order to relate y to x. Partial molar volumes were discussed in Section IV. This section gives brief attention to two models which give the effect of composition on liquid-phase thermodynamic properties. 

Since Raoult s law activities become mole fractions in ideal solutions, a simple substitution of.Y, — a, into equation (6.161) yields an equation that can be applied to (solid + liquid) equilibrium where the liquid mixtures are ideal. The result is... 

As the components in a liquid mixture become more chemically dissimilar, their mutual solubility decreases. This is characterized by an increase in their activity coefficients (for positive deviation from Raoult s Law). If the chemical dissimilarity, and the corresponding increase in activity coefficients, become large enough, the solution can separate into two-liquid phases. 

Temperature Two modes of temperature parametric-pumping cycles have been defined—direct and recuperative. In direct mode, an adsorbent column is heated and cooled while the fluid feed is pumped forward and backward through the bed from reservoirs at each end. When the feed is a binary fluid, one component will concentrate in one reservoir and one in the other. In recuperative mode, the heating and cooling takes place outside the adsorbent column. Parametric pumping, thermal and pH modes, have been widely studied for separation of liquid mixtures. However, the primary success for separating gas mixtures in thermal mode has been the separation of propane/ethane on activated carbon [Jencziewski and Myers, Ind. Eng. Chem. Fundam., 9, 216-221 (1970)] and of air/S02 on silica gel... 

The term Supported Ionic Liquid Phase (SILP) catalysis has recently been introduced into the literature to describe the heterogenisation of a homogeneous catalyst system by confining an ionic liquid solution of catalytically active complexes on a solid support [68], In comparison to the conventional liquid-liquid biphasic catalysis in organic-ionic liquid mixtures, the concept of SILP-catalysis offers very efficient use of the ionic liquid. Figure 7.10 exemplifies the concept for the Rh-catalysed hydroformylation. 

Fredenslund, A., Jones, R. L., Prausnitz, J. M. (1975) Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AIChEJ. 21, 1086-1099. 

The activity of a mixture of liquids. It is rarely a good idea to suggest that the activity of a liquid in a mixture is equal to its mole fraction x because of complications borne of intermolecular interactions (e.g. see Chapter 2 and Section 5.6 concerning Raoult s law). Thankfully, it is generally rare that an electrochemist wants to study liquid mixtures of this sort (except amalgams diluted to a maximum mole fraction of about 1 per cent metal in Hg), so we will not consider such a situation any further. 

Composition of the membrane PVA/PAcr.Ac Composition of liquid mixture ethanol-water Permeation rate / / (g m 2 h"1) T/ °C Separation factor Permeate activation energy Ea/ (kJ mol"1)... 

Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures", AIChE Journal, 21(6), 1975... 

In solutions and liquid mixtures, activities are defined in various ways and somewhat different conventions are adopted for standard states. For a detailed discussion, the reader is referred to Denbigh [3] and Bett et al. [4]. Tabulated values of activities in many solutions are available [14, 15] and these can be used to calculate equilibrium constants using eqn. (26). 

When seeking a tool which could be used to determine the biological activity of mixture components in a more precise way, researchers directed their attention towards high-performance liquid chromatography (HPLC). Its advantage over TLC is its higher resolution, which helps to avoid false results caused by the co-elution of different compounds. 

In order to calculate the aqueous concentration of compound / at equilibrium, one needs to know its mole fraction, jcimix, in the mixture (or its molar concentration, Cimix, and the molar volume, Vmix, of the mixture), as well as its activity coefficients in the organic (ymix) and the aqueous (yiw) phases. Very often, when dealing with complex mixtures, V is not known and has to be estimated. At a first approximation, this can be done from the density, pmix, of the liquid mixture, and by assuming an average molar mass, M, of the mixture components ... 

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