Ternary solution concentration

Ternary-phase equilibrium data can be tabulated as in Table 15-1 and then worked into an electronic spreadsheet as in Table 15-2 to be presented as a right-triangular diagram as shown in Fig. 15-7. The weight-fraction solute is on the horizontal axis and the weight-fraciion extraciion-solvent is on the veriical axis. The tie-lines connect the points that are in equilibrium. For low-solute concentrations the horizontal scale can be expanded. The water-acetic acid-methylisobutylketone ternary is a Type I system where only one of the binary pairs, water-MIBK, is immiscible. In a Type II system two of the binary pairs are immiscible, i.e. the solute is not totally miscible in one of the liquids. 

Activity coefficients in concentrated solutions are often described using Harned s rule (l ). This rule states that for a ternary solution at constant total molality the logarithm of the activity coefficient of each electrolyte is proportional to the molality of the other electrolyte. The expressions for the activity coefficients are written ... 

The success of Harned s rule for ternary solutions is largely fortuitous, and the rule has no theoretical basis to expect that it would be useful for solutions containing more than two electrolytes. Furthermore, for high concentrations of several electrolytes, activity coefficients such as Y3(g are hypothetical. There are, unfortunately, few experimental data available to test Harned s rule for concentrated solutions of three or more electrolytes. 

Equations 11 and 12 are not written for constant molality, and can not be easily used with the Gibbs-Duhem equation to obtain an analytical expression for the activity of water in the ternary solution. However, it is possible to propose a separate equation for the activity coefficient of water that is consistent with the proposed model of concentrated solutions. 

Figure 12.22 shows the composition in terms of the weight percent HNO, and H2S04 as a function of temperature as solid SAT is cooled from 194 K under conditions corresponding to a pressure of 50 rnbar in an atmosphere containing 5 ppm HzO and an HNO, concentration of 10 ppb (Koop and Carslaw, 1996). Under these particular conditions, as the temperature falls below 192 K, the SAT is in equilibrium with a liquid film on the particle containing both HN03 and H20. The particular temperature at which SAT deliquesces is a function of the water vapor and gaseous nitric acid concentrations as shown in Fig. 12.23. As the temperature falls further and more HNO, and HzO are taken up into the liquid, the solid SAT dissolves completely, forming a ternary solution of the two acids and water. This solution can then act again to nucleate PSCs.

The kinetics of these reactions in liquid solutions characteristic of the stratosphere, such as concentrated H2S04-H20 or ternary solutions with HN03, depend on temperature as expected and in some cases at least, on acidity as well. For example, Donaldson et al. (1997) have shown that the second-order rate constant for the... 

Arce et al. also investigated the effect of anion fluorination in [CjCjIm] ILs on fhe exfracfion of efhanol from ETBE [36]. For this purpose, two anions, methanesulfonate and trifluoromethanesulfonate, were selected. The corresponding phase diagrams were plotted for both ternary ETBE + ethanol + IL systems. The solute distribution ratios for the IL with the nonfluorinated anion were higher, especially at low concentrations. As for the selectivities, better results were obtained for mefhanesulfonate IL at low solute concentrations, while at higher solute concentrations the selectivity was better for the fluorinated analog. 

Abe et al. pointed out that the experimental S of PBLG [93] and PYPt [33] solutions at the phase boundary concentration cA largely departed from the prediction of Khokhlov and Semenov s second virial approximation theory [7,44]. Similar deviations of the scaled particle theory from experiment are seen in Fig. 12a,c, where the left ends of the theoretical curves and the experimental data points at the lowest c correspond to cA. Sato et al. [17] showed theoretically that ternary solutions containing two polymer species with different... 

Knowledge of the expressions for the chemical potentials of each of the components allows theoretical prediction of the critical concentration boundaries of the phase diagram for ternary solutions of biopolymeri + biopolymer2 + solvent. According to Prigogine and Defay (1954), a sufficient condition for material stability of this multicomponent system in relation to phase separation at constant temperature and pressure is the following set of inequalities for all the components of the system ... 

At small solute concentrations the second virial coefficient is the main contributor to the value of n, and so in practice the general equation (5.16) is usually restricted to just the term containing the second virial coefficient. At this level of approximation, the osmotic pressure of a ternary solution (biopolymer, + biopolymer, + solvent) may be expressed in the following simple form using the molal scale (Edmond and Ogston, 1968) ... 

The first PGSE investigation of a rubber-based ternary solution was described by Ferguson and von Meerwall31), who measured diffusion of C6F6(19F NMR) and n-paraffin (n-dodecane or n-hexatriacontane 1H NMR) in a commercial polybutadiene as function of both concentrations. They showed that both concentration dependences in the ternary region can be derived from the measured diffusivity of each diluent i = 1, 2 in binary solution in the rubber. To do this it was necessary to extend the Fujita-Doolittle expression, as follows ... 

In order to obtain microcapsules with the high solid content, a ternary solution with high concentration of the shell polymer and the core material should be chosen. 

In the ternary solution KCI-H2O-PEG-2OO, the quantity A, which can be considered a type of excess function, is positive except in the range of higher nonelectrolyte concentration, where it becomes negative. Its contribution to the binary data is 5-10%. 

These sulfuric acid particles become less concentrated as the temperature decreases or the water vapour increases. Under very cold stratospheric conditions, these liquid aerosols may take up water and HNO, forming ternary solutions H,S0/HN0,/H,0, which eventually freeze [19,24,26], Below 192 K, HNO, becomes the dominant condensed acid, and H,S04 drops to below 3 wt %. The thermodynamics and freezing nucleation of ice and H,S04 or HNO, hydrates from such solutions are however not well understood [27,28]. Other types of solid particles, such as the less stable nitric acid dihydrate (NAD, HN0,.2H,0) [29], sulfriric acid tetrahydrate (SAT, H S04.4H,0) [18,30], sulphuric acid hemihexahydrate (SAH, H2S04.6.5H20) [18], nitric acid penta-hydrate (NAP, HN03.5H,0) [31] and more complex sulfuric acid/nitric acid mixed hydrates [32] may also be a key to understanding Type IPSC nucleation and evolution [28],... 

For mass transfer in a simple ternary system without chemical reaction, the solute concentration profiles near the interface are as shown in Fig. 3. The concentration in the bulk of each phase is uniform because of convective mixing effects, but very near the interface the rate of mass transfer depends increasingly on molecular diffusion. 

Ternary solutions of immiscible polymers in a low-molecular solvent display wide miscibility gaps. Consequently, they invariably involve demixing above a critical concentration of total polymer by spinodal decomposition and subsequent coarsening processes. When solvent evaporation progresses the enhanced viscosity will slow down the rate of phase separation to a level at which no further phase changes can be observed. 

Qualitatively, the same effect has been observed in ternary solutions of p- PODZ, PA-6 and sulfuric acid [104]. At room temperature the quiescent system displays phase separation above 14% of total polymer concentration. Above the critical concentration shearing of initially biphasic solutions led to transparent one-phase systems. After cessation of the shear stress the biphasic morphologies recovered. 

Coprecipitate complex from ternary solution Working with concentrated polyelectrolytes (10% vs. 1%) possible pure compact product Product not necessarily stoichiometric solvent handling and disposal can be difficult, expensive solvents 438... 

The presence of the PMMA or PET lowers the criticd concentration of the CTA. For example, a 19.6/1.2/70.2 (w/w/w) ternary solution of CTA, PMMA and TFA-CH2CI2 (6 4 v/v) and an 18.6/1.2/80.2 ternary solution of CTA, PET and TFA-CH2Q2 (6 4 v/v) were biphasic when viewed under crossed polars. Each solution appeared to be one ph but a small isotrq>ic phase may have been present, a required an extremely long time to separate due to the high viscosity of the anisotropic matrix. 

For the cases in which only the solute concentration is small, the derivation of an expression for the fugacity coefficient 02 (see Eq. (2)) is still critical for the prediction of the solubility x . Let us consider those compositions of the ternary mixture which are located on the line between the points (xf" = 0,... 

The usefulness of inverse gas chromatography for determining polymer-small molecule interactions is well established (1,2). This method provides a fast and convenient way of obtaining thermodynamic data for concentrated polymer systems. However, this technique can also be used to measure polymer-polymer interaction parameters via a ternary solution approach Q). Measurements of specific retention volumes of two binary (volatile probe-polymer) and one ternary (volatile probe-polymer blend) system are sufficient to calculate xp3 > the Flory-Huggins interaction parameter, which is a measure of the thermodynamic... 

For the determination of component concentration in equilibrium solution the columns packed by adsorbent with some stationary phase is used for the complete separation of component. The adsorption of volatile compounds on hydroxylated silica from ternary solutions was investigated by gas chromatography [3 - 5].For alt components the heats of adsorption on silica were known and it was possible to find the correlation between the heats of adsorption and the shape of isotherm of component adsorption. 

It is imperative to know the S-L-V equilibrium compositions for the ternary (C02-solvent-solid) system, for these give the concentrations at the interface, which are needed for calculating the two-way mass transfer rates of CO2 and solvent in the antisolvent crystallization processes and for the selection of operating conditions for the desired crystallization pathways. Three kinds of data are usually generated for ternary (solute-solvent-antisolvent) systems (a) the liquid phase compositions for S-L equilibrium at a fixed... 

Ternary Systems.—Wq pass over the binary system FeClg—HgO, which has already been discussed (p. 187), and the similar system HCl—HgO (see Fig. 132), and turn to the discussion of some of the ternary systems represented by points on the surface of the model between the planes XOT and YOT. As in the case of carnallite, a plane represents the conditions of concentration of solution and temperature under which a ternary solution can be in equilibrium with a single solid phase (bivariant systems), a line represents the conditions for the co-existence of a solution with two solid phases (univariant systems), and a point the conditions for equilibrium with three solid phases (invariant systems). 

Figure 8. Concentration dependence of components of a ternary solution on temperature (top plot) anthracene, (center plot) 2-methylanthra-cene, (bottom plot) benzanthracene.

The treatment of diffusion given in this section is valid only for the analysis of solutions in the limit of inifinite dilution. We return to the question of diffusion in several sections of this book. In Section 9.2 a simple theory of diffusion in electrolyte solutions is discussed. In Section 10.6 the coupling between diffusion and heat conduction is treated in some detail. In section 11.6 a microscopic description of diffusion is given. Finally in Sections 13.5 and 13.6 a detailed treatment of diffusion in binary and ternary solutions of nonelectrolytes and electrolytes is presented. The concentration-dependence of the diffusion coefficient is considered in Section 13.5. These sections are based on the theory of nonequilibrium thermodynamics and are thus relegated to the chapter on this subject. Particular attention should be given to these sections by any reader interested in the analysis of diffusion. 

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