Porter equation

Portable EDXRF instruments, 26 442 Portable scales, 26 244 Porter equation, 15 724 Portimicin, 20 137 Portland cement, 4 583... 

Correlations of viscosity with density and refractive index have been evaluated for various homologous series [7] and correlations between viscosity and boiling point and between viscosity and vapor pressure have been reported, for example, for n-alkyl /3-ethoxypropionates [8]. Viscosity correlations with vapor pressure are represented by the Porter equation [9] ... 

To estimate liquid viscosity using Porter equation (6.2.1)... 

Barkas proposed a generalized osmotic pressure theory for hygroscopic gels such as wood, based on the generalized Porter equation in the form... 

Here, g Is linear with mole fraction see the methyl acetate-1-hexene system in Fig. 1.4-1. Finally, if O,i = >, = 0 and <4,2 — A2I = A, then Eq. (1-4-8) reduces to the one-parameter Margeles equation, or Porter equation, Here,... 

The Porter equation is the simplest realistic expression for gE- It is appropriste for "symmetrical binary mixtures shewing small deviations from ideality, for example, the acetone-methanol system depicted in Fig. 1.4-1,... 

When Eq. (1.4-14) is substituted into Eqs. (1.5-32) and (1.5-33). we find that a two-component liquid mixture is unstable only if A > 2. In other words, a single liquid phase described by (he Porter equation splits into two liquid phases only if, 4 > 2, As Indicated also by Eq. (1.5-31). ]IA 2, the two components are completely miscible. 

FIGURE 1.5-3 Binary [[quid-liquid solubility diagrams implied by the Porter equation for gE. Tv and TL are upper and tower consolute temperatures the T depeodence of parameter A determines die shape of die solubility diagram. 

Figure 5.8 Substantial symmetry exists in the composition dependence of the excess Gibbs energy and activity coefficients for binary mixtures that obey the Porter equation (5.6.1).

For some mixtures, values of can be extracted from experiment and in those cases we have a convenient means for determining a value for the parameter A. Because the Porter equation (5.6.1) contains only one parameter, a high degree of symmetry exists among the values of g, In and In y2- For binary mixtures, the symmetry appears as in Figure 5.8. 

The Porter equation is the simplest expression we can write for nonideal solutions nevertheless, it can describe both positive (A > 0) and negative (A < 0) deviations from ideal-solution behavior. Some real mixtures obey the Porter equation fairly well, especially mixtures composed of molecules that are nonpolar and have similar sizes and shapes. Even some mixtures containing polar components may obey the Porter equation over limited ranges of temperatures. Values of A are given in Table E.l (Appendix E) for some representative mixtures. 

We caution that a binary mixture may obey the Porter equation (5.6.1) but still not be a quadratic mixture that is, may be parabolic in composition but and may not be. An example is the hexane-cydohexane mixture shown in Figure 5.2. Such behavior occurs because as)unmetries in and approximately cancel when they combine via the Legendre transform (5.2.18) to form g. Such cancellations are the norm rather than the exception. To say this another way, the Redlich-Kister expansion for (5.6.3) is usually dominated by the first term, which is symmetric in Xj and Xi-However, in the analogous expansions for and s, asymmetric terms are frequently important. 

So if we have experimental data for both Y Y2 / then (5.6.14) and (5.6.15) provide a straightforward way to obtain values for the Margules parameters. If a binary mixture happens to have Yi° = Y2 that A = A2, then the Margules equations collapse to the Porter equations. 

This F-term is the dominant contribution to h. With and determined, can be obtained from the Legendre transform (5.2.18). But we caution that, just as some mixtures may obey the Porter equation and yet not be quadratic mixtures, so too may some mixtures obey the Wilson equation (5.6.24) for and yet not obey (5.6.31) for h. Consequently, while we might obtain values for the parameters AA,y by fitting calorimetric data, the resulting values may or may not reliably predict g. ... 

Inspired by the simplicity of the Porter equation, Tabitha the Untutored claims that it is easy to contrive models for the composition dependence of activity coefficients. 

Evaluate the reversible work and the heat effect associated with the isothermal-isobaric conversion of an equimolar liquid solution of carbon tetrachloride + chloroform into an ideal gas at 298 K, 0.1 MPa. Assume the real mixture can be modeled by the Porter equation with parameter given in Table E.l. 

Figure 8.19 Stability of binary mixtures as given by the Porter equation (8.4.32) over a range of values for the parameter A. For A < 2, mixtures are stable in all proportions. For A > 2, mixtures can be stable, unstable, or metastable, depending on composition. Shaded regions are metastable. Curve separating stable from metastable states is the two-phase equilibrium curve, obtained by solving (8.4.35). A sample solution to (8.4.35) is shown for A = 3 filled circles give compositions of phases in equilibrium.

Since pressure and density are often unimportant to descriptions of liquids and solids, binary liquid-liquid and solid-solid phase diagrams are often limited to plots of temperature vs. composition. Figure 8.20 shows such a Txx diagram computed from the Porter equation with the temperature dependence of A given by... 

Figure 8.20 Txx diagram for liquid-liquid or solid-solid equilibria in binary mixtures that obey the Porter equation (8.4.32) with parameter A given by (8.4.38). Filled square is the critical point filled circles lie on the isotherm at 30°C. The inner envelope, with labels C and D, is the spinodal and satisfies (8.4.37). The outer envelope is the equilibrium curve, which satisfies the equilibrium conditions (8.4.35).

The excess Gibbs energy for a certain binary mixture obeys the Porter equation... 

Estimate the infinite-dilution distribution coefficient for naphthalene(l) distributed between immiscible phases of water(2) and benzene(3) at 300 K. Assume ACp = 0.6 AS and that the binaries with naphthalene are described by the Porter equation. The following data may help is the melting point and values of the solubilities are given here in gm/100 gm solvent at 300 K. 

The following tables provide values for parameters in models for the excess Gibbs energy of selected binary liquid mixtures. Table E.l contains values for the Porter equation ( 5.6.2), Table E.2 for the Margules equation ( 5.6.3), and Table E.3 for Wilson s equation ( 5.6.5). 

Equation (1.5-21) is a genera/relationship between Heniy s Law and Raoult s Law activity coefficients for a component in a binary mixture. Farticu/ar expressions for 7 are obtained from particular expressions for7 which require a model for for their determination see Sections 1.4-1-1.4-3. To illustrate, suppose that g is described by the Porter equation, Eq. (1.4-14). Then, by Eqs. (1.5-21), (1.4-I5a), and (1.4-19a), we find the one-parameter expression... 

The above discussion considers only die calculation of equilibrium compositions xf and xf at a single temperature. The temperature dqiendence of xf and xf, as represented by a liquid-liquid solubility diagram, is also of interest. This temperature dependence enters the equilibrium formulation through the temperature dqiendence of the parameters in the assumed oqnession fiw thermodynamically, it is determined by the behavior of the molar excess enthalpy If a binary liquid system is described by the Porter equation,... 

FIGURE 1.5-3 Binaiy liquid-liquid solubility db iams imidied by the Porter equation for Ty and 7 are upper and lower consolute tenqieratuies the T dependence of parameter A determines the sha of the sohit ty diagram. 

The so-called Porter equation is the simplest mathematical approach to describe the property change of mixing of a binary mixture as a function of the composition ... 

For the binary case the excess Gibbs energy g shows a value of 0 for Xi = 1 and X2 = 1. The simplest expression which obeys the boundary conditions is the Porter equation [9] ... 

Figure 5.70 Concentration dependence of the molar Gibbs energy for systems with different strong real behavior A = coefficient of the Porter equation (Eq. (5.19)).

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