Ternary systems temperature dependence

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

Due to the fact that K2TaF7 - KF is considered to be part of the TaF5 - KF binary system, while the K2TaF7 - KCI system is a component of the interconnected ternary system K+, Ta5+//F", Cl", the single-molecule conductivity and activation energy of the systems was calculated based on density and specific conductivity data [322, 324]. Molar conductivity (p) depends on the absolute temperature (T), according to the following exponential equation ... 

A considerable amount of experimental work has been carried out on the so-called gel emulsions of water/nonionic surfactant/oil systems [9-14, 80, 106, 107]. These form in either the water-rich or oil-rich regions of the ternary phase diagrams, depending on the surfactant and system temperature. The latter parameter is important as a result of the property of nonionic surfactants known as the HLB temperature, or phase inversion temperature (PIT). Below the PIT, nonionic surfactants are water-soluble (hydrophilic form o/w emulsions) whereas above the PIT they are oil-soluble (hydrophobic form w/o emulsions). The systems studied were all of very high phase volume fraction, and were stabilised by nonionic polyether surfactants. 

The thermodynamic quantity 0y is a reduced standard-state chemical potential difference and is a function only of T, P, and the choice of standard state. The principal temperature dependence of the liquidus and solidus surfaces is contained in 0 j. The term is the ratio of the deviation from ideal-solution behavior in the liquid phase to that in the solid phase. This term is consistent with the notion that only the difference between the values of the Gibbs energy for the solid and liquid phases determines which equilibrium phases are present. Expressions for the limits of the quaternary phase diagram are easily obtained (e.g., for a ternary AJB C system, y = 1 and xD = 0 for a pseudobinary section, y = 1, xD = 0, and xc = 1/2 and for a binary AC system, x = y = xAC = 1 and xB = xD = 0). 

In those cases in which V2/Vi is known, both gv° and g ° are given. For the rest of the systems, only gv° is given. Prediction of thermodynamic properties on ternary systems formed by a polymer and two solvents or two polymers and a solvent requires the knowledge of the parameter g°, characteristic of the interaction of the corresponding binary pairs [9], However, due to the variety of sources for the several systems studied, the data correspond to different polymer molecular weights, m, and to different temperatures. Since the variation of x with concentration may depend on M for low M s, it has selected data only for M > 2 x 109, where no M dependence is detected. 

Another ternary system is K2Ba4C60, which is synthesised by reaction of excess potassium with preformed Ba4C60 [68]. Figure 19 shows the temperature dependence of the magnetic susceptibility of Ba4C60, K3Ba3C60 and K2Ba4C60 (Tc=6.7 K,... 

At this temperature the X-phase shows its maximum solid solution towards the Cu-rich portion of the system which diminishes above. However, with still increasing temperature, the X-phase solid solution width extends towards the Mo—S side, in particular towards MoS2 or sulfur, respectively. Figure 19 shows a schematic ternary T-X block diagram. To simplify the perspective drawing only a few isotherms are indicated. The extension of the whole solid solution width of the X-phase is projected on the base. Thus, the variation and the shifting of the temperature-dependent... 

As a third liquid is added to the partially miscible binary liquid system, the ternary (three-component) system is dependent on the relative solubility of the third liquid in the two liquids. If the third substance is soluble only in one liquid of the original binary mixture or if the solubility of the third in the two liquids is considerably different, the solubility of one liquid in the others will be lowered. The upper consolute temperature should be raised or the lower consolute temperature should be lowered in order to obtain a homogeneous solution. On the other hand, if the third substance is soluble to the same extent in both liquids of the binary system, the complementary solubility of the two liquids is increased. This results in the lowering of an upper consolute temperature or the elevation of a lower consolute temperature. 

In the studies described here, we examine in more detail the properties of these surfactant aggregates solubilized in supercritical ethane and propane. We present the results of solubility measurements of AOT in pure ethane and propane and of conductance and density measurements of supercritical fluid reverse micelle solutions. The effect of temperature and pressure on phase behavior of ternary mixtures consisting of AOT/water/supercritical ethane or propane are also examined. We report that the phase behavior of these systems is dependent on fluid pressure in contrast to liquid systems where similar changes in pressure have little or no effect. We have focused our attention on the reverse micelle region where mixtures containing 80 to 100% by weight alkane were examined. The new evidence supports and extends our initial findings related to reverse micelle structures in supercritical fluids. We report properties of these systems which may be important in the field of enhanced oil recovery. 

Rather little is known about the chemical nature of fused salts. Because of the high temperatures required, such studies are usually inaccessible to NMR. The exceptionally low-melting ternary system AlCls-NaCl-KCl has recently been investigated by combined H, Na, Al, and C1 NMR. (151) Whereas the proton and sodium line-widths show no composition dependence, both the Al and C1 line-widths depend sensitively on the relative populations. The data permit the conclusion that the ALCl ion exists in rapid equilibrium with AICI4. 

The solid products in the reactions with S02 depended on the partial pressures of the reacting gases. A low-temperature study of the ternary system N2H4-NH3-H20 has revealed seven solid phases below -80°C anhydrous N2H4 is precipitated from solution.27 Since it is of importance in... 

The density of the melts of the molten system KF-K2M0O4-B2O3 was measured by Chrenkova et al. (1994). For the concentration dependence of the molar volume in the investigated ternary system at the temperature of 827°C, the following equation was obtained... 

The calculated coefficients of the concentration dependence of the excess molar Gibbs energy of mixing together with the standard deviations of the fit temperature in the ternary systems are given in Table 3.6. 

The calculation of the dependency of the surface tension of the ternary system KF(1)-KC1(2)-KBF4(3) on composition was performed according to Eq. (6.54). The regression coefficients were calculated using the multiple linear regression analysis excluding the statistically non-important terms on the 0.99 confidence level. The surface tension of this system at temperature of 823°C was described by the equation... 

However, based on the validity of the Arrhenius equation for temperature dependence of viscosity and on the additivity of activation energies of viscous flow due to the general validity of Hess s law, the additivity of logarithms of viscosity could be accepted as the ideal behavior, e.g. for a ternary system at constant temperature, it may be written as... 

Oppermann et al. studied the ternary system Bi-O-Se. Six crystalline phases were prepared by high temperature synthesis from Bi203(cr) and Se02(cr). The phases were characterised by X-ray powder diffraction and IR spectroscopy. The standard enthalpies of formation and entropies of the compounds were obtained from the temperature dependence of the equilibrium constants of the decomposition reactions. The standard enthalpies of formation were also found from solution calorimetric work in which the enthalpies of dissolution of the compounds, Bi203(cr), and Se02(cr) in 4 M HCI were measured. It should benoted that the results in the paper were obtained with a correct value of the enthalpy of formation of Se02(cr) and not the erroneous value in Table II of tha paper. 

---