Solution ternary

The steel will be considered to be an ideal ternary solution, and therefore at all temperatures a, = 0-18, Ani = 0-08 and flpc = 0-74. Owing to the Y-phase stabilisation of iron by the nickel addition it will be assumed that the steel, at equilibrium, is austenitic at all temperatures, and the thermodynamics of dilute solutions of carbon in y iron only are considered. 

The Diels-Alder reaction of methyl methacrylate with cyclopentadiene was studied [72] with solutions from three different regions of the pseudophase diagram for toluene, water and 2-propanol, in the absence and in the presence of surfactant [sodium dodecyl sulfate (SDS) and hexadecyltrimethylammonium bromide (HTAB)]. The composition of the three solutions (Table 6.11) corresponds to a W/O-fiE (A), a solution of small aggregates (B) and a normal ternary solution (C). The diastereoselectivity was practically constant in the absence and in the presence of surfactant a slight increase of endo adduct was observed in the C medium in the presence of surfactant. This suggests that the reaction probably occurs in the interphase and that the transition state has a similar environment in all three media. 

Table 6.11 Diastereoselectivity of Diels-Alder reaction of methyl methacrylate with cyclopentadiene performed in ternary solutions...

If the partially labelled star/solvent system is considered as an incompressible ternary solution, the double differential cross section 02ct/0 20E can be written as... 

Tonon RV, Baroni AF and Hubinger MD. 2007. Osmotic dehydration of tomato in ternary solutions influence of process variables on mass transfer kinetics and an evaluation of the retention of carotenoids. J Food Eng 82 509-817. 

Many reactions encountered in extractive metallurgy involve dilute solutions of one or a number of impurities in the metal, and sometimes the slag phase. Dilute solutions of less than a few atomic per cent content of the impurity usually conform to Henry s law, according to which the activity coefficient of the solute can be taken as constant. However in the complex solutions which usually occur in these reactions, the interactions of the solutes with one another and with the solvent metal change the values of the solute activity coefficients. There are some approximate procedures to make the interaction coefficients in multicomponent liquids calculable using data drawn from binary data. The simplest form of this procedure is the use of the equation deduced by Darken (1950), as a solution of the ternary Gibbs-Duhem equation for a regular ternary solution, A-B-S, where A-B is the binary solvent... 

Tables and correlating equations for density, vapor pressure, thermal conductivity and viscosity of binary and ternary solutions...

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. 

For the ternary solution, the Gibbs-Duhem equation can be easily integrated to calculate the activity coefficient of water when the expressions for the activity coefficients of the electrolytes are written at constant molality. For Harned s rule, integration of the Gibbs-Duhem equation gives the activity of water as ... 

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. 

The activity coefficient of water in the ternary solution f> 3)> ls estimated by ... 

Many different types of phase behaviour are encountered in ternary systems that consist of water and two solid solutes. For example, the system KNO3—NaNC>3— H20 which does not form hydrates or combine chemically at 323 K is shown in Figure 15.6, which is taken from Mullin 3 . Point A represents the solubility of KNO3 in water at 323 K (46.2 kg/100 kg solution), C the solubility of NaN(>3 (53.2 kg/100 kg solution), AB is the composition of saturated ternary solutions in equilibrium with solid KNO3 and BC... 

Hillert M. (1980). Empirical methods of predicting and representing thermodynamic properties of ternary solution phases. CALPHAD, 4 1-12. 

Statistical thermodynamic descriptions of these transitions in substitutional alloys have been developed for the cases of both binary and ternary alloys , using a simple nearest neighbor bond model of the surface segregation phenomenon (including strain energy effects). Results of the model have been evaluated here using model parameters appropriate for a Pb-5at%Bi-0.04at%Ni alloy for which experimental results will be provided below. However, the model can be applied in principle to the computation of equilibrium surface composition of any ternary solution. 

There are many different types of surfaces available for reactions in the atmosphere. In the stratosphere, these include ice crystals, some containing nitric acid, liquid sulfuric acid-water mixtures, and ternary solutions of nitric and sulfuric acids and water. In the troposphere, liquid particles containing sulfate, nitrate, organics, trace metals, and carbon are common. Sea... 

Sulfuric acid tetrahydrate (SAT) also ultimately freezes out of these ternary solutions (Molina et al., 1993 Iraci et al., 1995). At higher temperatures found at higher altitudes in the middle and low latitudes, sulfuric acid monohydrate (SAM) may also be stable (Zhang et al., 1995). 

Some field measurements of HN03 suggest that the formation of liquid or solid Type I PSCs depends on the initial background sulfate aerosols on which the PSCs form. If they are liquid, then liquid ternary solution PSCs tend to form first as the temperature drops below 192 K, whereas if the sulfate particles are initially solids, solid Type lc PSCs may be generated (Santee et al., 1998). 

Toon and Tolbert (1995) suggest that if Type I PSCs are primarily ternary solutions rather than crystalline NAT, the higher vapor pressure of HN03 over the solution would in effect distill nitric acid from Type I to Type II PSCs, assisting in denitrification of the stratosphere. This overcomes the problem that if Type II PSCs have nitric acid only by virtue of the initial core onto which the water vapor condenses, the amount of HN03 they could remove may not be very large. The supercooled H20-HN03 liquid layer observed by Zondlo et al. (1998) clearly may also play an important role in terms of the amount of HNO, that can exist on the surface of these PSCs. 

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.

HC1 is efficiently absorbed into H2S04-H20 and into HN03-H2S04-H20 solutions, which as discussed earlier, are found in the stratosphere in the form of aerosol particles and Type I PSCs under some conditions (Wolff and Mulvaney, 1991). The solubility of HC1 in these liquid solutions can be expressed in terms of the usual Henry s law constant (Elrod et al., 1995 Abbatt, 1995 Luo et al., 1995 Hanson, 1998). Table 12.4 shows some typical measurements of the Henry s law constants for HC1 in several typical binary and ternary solutions, respectively. Hanson (1998) has shown that the solubility data for HC1 in binary mixtures of H2S04 and water in these and other studies can be fit by the form... 

The reactions tend to be fast on ice as well as on liquid solutions characteristic of the stratosphere. This indicates that they should occur on Type II PSCs as well as on H2S04-H20 mixtures characteristic of SSA and on HN03-H2S04-H20 ternary solutions which... 

CIO and decrease in HCI as the temperature fell, even though PSCs were not present (although it is possible that they were present at some earlier time). These observations were shown to be consistent with heterogeneous reactions on liquid binary and ternary solutions, with the temperature dependence reflecting the increased reaction probability for HCI + C10N02 due to increased solubility of HCI at the lower temperatures. 

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... 

Beyerle, G., B. Luo, R. Neuber, T. Peter, and I. S. McDermid, Temperature Dependence of Ternary Solution Particle Volumes As Observed by Lidar in the Arctic Stratosphere during Winter 1992/1993, J. Geophys. Res., 102, 3603-3609 (1997). 

A ternary system consisting of two polymer species of the same kind having different molecular weights and a solvent is the simplest case of polydisperse polymer solutions. Therefore, it is a prototype for investigating polydispersity effects on polymer solution properties. In 1978, Abe and Flory [74] studied theoretically the phase behavior in ternary solutions of rodlike polymers using the Flory lattice theory [3], Subsequently, ternary phase diagrams have been measured for several stiff-chain polymer solution systems, and work [6,17] has been done to improve the Abe-Flory theory. 

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... 

The solid curves in the figure represent the molecular weight dependence of r)0 for quasi-binary system consisting of a fractionated xanthan sample and 0.1 mol/1 aqueous NaCl. The circles for quasi-ternary solutions almost follow them at the same c, except at small 2. Thus, to a first approximation, r)o of stiff polymer solutions is independent of molecular weight distribution, and may be treated as a function of Mw or Mv and c. 

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) ... 

In data analysis, it is conventional to plot TVC versus C for the binary solution (biopolymer + solvent) or Yl/im, + m]) versus (mi + mj) for the ternary solution (biopolymer + biopolymer + solvent). The initial slope of the curve can then be used to determine the second virial coefficient... 

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 ... 

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