Isobar plot

This is the criterion for material or diffusional stability for a binary mixture to be differentially stable, the mixture must have Q > 0, Kt- > 0, and (at fixed T and P) the chemical potential of component 1 must always increase in response to any increase in Nj. This means that if an isothermal-isobaric plot of the chemical potential (or fugacity) passes through an extremum with Xj, then the mixture is unstable for some Xj-values. The result (8.3.13) confirms (3.7.29) in which we claimed that the chemical potential of a pure component is always greater than its value in any mixture at the same T and P. 

Figure 8.16 Isothermal-isobaric plot of fugadty /j for a binary mixture exhibiting class IIIB stability behavior. The pure component-1 equation of state bifurcates, producing three branches in /j however, since the pure component-2 equation of state does not bifurcate, only one branch spans all Xj. Filled cirdes mark phases in equilibrium. Solid lines stable long dashes metastable short dashes unstable. AU curves computed from the Redlich-Kwong equation of state.

Figure 8.18 Isothermal-isobaric plot of fugacity for component 1 in a binary mixture. Portions of the curve above the broken horizontal line are not stable because of (8.4.9). The three mixtures a, P, and y have the same value for the fugacity, but only one of the three forms a stable single phase e.g., mixture at y violates (8.4.8) and so it is unstable even though it satisfies (8.4.9).

Sketch an isothermal-isobaric plot of the change of Gibbs energy on mixing g>" vs. mole fraction Xj for a binary mixture in three-phase vapor-liquid-liquid equilibrium. Include the tie lines on your plot and indicate the compositions of the... 

These mean that an isothermal-isobaric plot of /j vs. x passes through a point of inflection at the critical point, as was illustrated in Figure 8.13. Points that satisfy only (9.3.23) locate the spinodal, and when the spinodal coincides with the vapor-liquid saturation curve, then both (9.3.23) and (9.3.24) are satisfied and a vapor-liquid critical point occurs. 

In total there are seven isobars plotted on the graph two of these pass through the two-phase dome (10 and 50 bar), the third is the critical isobar (73.773 bar), and finally five supercritical isobars (100,200,400,600, and 1000 bar). 

As can be seen from a typical isothermal-isobaric plot of X vs 9 (Fig. IS), the quality of fit between the experimental data and the theoretkal curve constructed according to the SSA technique with the set of parameters listed in Table 4... 

Alternatively, data may be plotted as n versus T at constant pressure or as P versus T at constant n. One thus has adsorption isobars and isosteres (note Problem XVII-2). 

Read off points from Fig. XVII-1 and plot a set of corresponding isosteres and isobars. 

Remick and Geankoplis made flux measurements for both species in the isobaric diffusion of nitrogen and helium through their tube bundle. Pressures spanned the interval from 0.444 nim, Hg to 300,2 ram Hg, which should cover the whole range between the limits of Knudsen streaming and bulk diffusion control. Then, since K and K, are known in this case, the form of the proposed flux relations could be tested immediately by plotting the left hand side of equation (10.15) against... 

Diagrams of isobaric heat capacity (C and thermal conductivity for carbon dioxide covering pressures from 0 to 13,800 kPa (0—2,000 psi) and 311 to 1088 K have been prepared. Viscosities at pressures of 100—10,000 kPa (1—100 atm) and temperatures from 311 to 1088 K have been plotted (9). 

For apphcation to distiUation (a nearly isobaric process), as shown in Figs. 13-8 to 13-13, binary-mixture data are frequently plotted, for a fixed pressure, as y versus x, with a line of 45° slope included for reference, and as T versus y and x. In most binary systems, one of the components is more volatile than the other over the entire composition range. This is the case in Figs. 13-8 and 13-9 for the benzene-toluene system at pressures of both 101.3 and 202.6 kPa (1 and 2 atm), where benzene is more volatile than toluene. 

An attempt to construct one equation for both high and low pressme data fails because of a discontinuity, which is too smaU to be shown by plotting of isobars, but is strikingly exhibited when the pressure variations of the parameters of the isobars are examined. A similar discontinuity exists between the given data at 30 atmospheres and Haber s data at the same pressure. Both discontinuities are believed to be the result, not of experimental error, but of variation in the composition of the gas mixture. 

The linearity of van t Hoff plots, such as Figure 3.14, depends on the degree to which the isobaric heat capacity of the system (Cp) remains constant between the... 

At a given temperature and pressure eqs. (4.7) and (4.8) must be solved simultaneously to determine the compositions of the two phases a and P that correspond to coexistence. At isobaric conditions, a plot of the composition of the two phases in equilibrium versus temperature yields a part of the equilibrium T, x-phase diagram. 

Figure 13. Changes in 6 Fe values of HPS Fe standard as a function of contaminate elements Al, Mg, or La (12.5 to 75 ppb). All solutions were 400 2 ppb Fe. The Fe isotope compositions of the solutions are shifted from those in the pure Fe standard (6 Fe = +0.49 0.05%o) as a function of the impurity concentration. The magnitude of the this shift with impurity concentration is variable, as shown by data collected during three analytical sessions (parts A, B, and C). These impurity matrix elements do not produce molecular isobars, as evidenced by the fact that 5 Fe and 5 Fe values plot along a mass-dependent array (part D). Note that an important conclusion of these tests is that accuracy of Fe isotope measurements cannot be demonstrated by preservation of mass-dependent trends in Fe/ Fe and Fe/ Fe. Data were collected using the Univ. of Wisconsin-Madison Micromass IsoProbe.

Fig. 3.14. Exact masses of isobaric ions of nominal mass 310 u. The Am scale is plotted in mmu relative to the saturated hydrocarbon, C22H46, at 310.3599 u. Adapted from Ref. [13] with permission. University Science Books, 1993.

Before leaving the nickel experiments, it may be well to refer to the experiments on hydrogen adsorption variously reported in the literature. As an example, the work of Maxted and Hassid (13) had as its main objective the measurement of the slow activated adsorption of hydrogen on reduced nickel oxide catalysts. It has been proved by the foregoing that the slow adsorption is actually absorption. When plotting their data as isobars, as was done in Fig. 9, the similarity between these isobars and those obtained with sintered nickel films is evident. 

Fig. 3.34 Relation between composition (phase), temperature, and pressure of As gas Pas for the Cia- As system (schematic). In this figure, the isobars, P, P, , are plotted.

Figures 1-5 present plots of the average absolute error in y vs. a 2 for the five ternary systems considered in this study. For three of the four isobaric systems, two sources of VLE data for the MeOH-water binary have been used to demonstrate the impact on the correlation of the ternary data. While the difference is not drastic, the better data of Ramalho et al. (18) also provide better correlation, as evidenced by Figures 1-3. The ensuing discussion is based on the latter data. Table III presents the optimum a 2 in the positive and negative regions. Considering the diversity of the systems studied—e.g., three involved...

We may treat this system two ways Hold temperature constant (isothermal conditions) and vary pressure and concentration, or hold pressure constant (isobaric conditions) and vary concentration and temperature. Both situations are shown in Figure 2.3. The plots in Figures 2.3a and 2.3b represent conditions for isothermal and isobaric treatments, respectively. 

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