Azeotropes infinite-dilution / -values

At that azeotrope, compute the infinite-dilution -value for one of the missing species. 

Given a ternary azeotrope and a fourth species in the mixture, compute its infinite-dilution /(-value at this ternary azeotrope. Increase the amount of the fourth species, keeping the /(-values for the other three equal to each other. Stop where the fourth /(-value passes near 1 or shows a minimum or maximum along the trajectory being traced out. Solve directly for the four-species azeotrope. Stop searching this trajectory when it hits a side of the composition space. 

The most common method for screening potential extractive solvents is to use gas—hquid chromatography (qv) to determine the infinite-dilution selectivity of the components to be separated in the presence of the various solvent candidates (71,72). The selectivity or separation factor is the relative volatihty of the components to be separated (see eq. 3) in the presence of a solvent divided by the relative volatihty of the same components at the same composition without the solvent present. A potential solvent can be examined in as htfle as 1—2 hours using this method. The tested solvents are then ranked in order of infinite-dilution selectivities, the larger values signify the better solvents. Eavorable solvents selected by this method may in fact form azeotropes that render the desired separation infeasible. 

From the isothermal vapor-liquid equilibrium data for the ethanol(l)/toluene(2) system given in Table 1.11, calculate (a) vapor composition, assuming that the liquid phase and the vapor phase obey Raoult s and Dalton s laws, respectively, (b) the values of the infinite-dilution activity coefficients, Y and y2°°, (c) Van Laar parameters using data at the azeotropic point as well as from the infinite-dilution activity coefficients, and (d) Wilson parameters using data at the azeotropic point as well as from the infinite-dilution activity coefficients. 

So that an azeotrope with acetone does not form, the alcohol used must have a high enough boiling point. This requirement is reliably established only if vapor-liquid equilibrium data for at least two, preferably three, of the members of the series with acetone are known. The Pierotti-Deal-Derr method (4) (discussed later) or the Tassios-Van Winkle method (5) can be used in this case. In the latter method a log-log plot of y°i vs. P°i should yield a straight line. Figure 1 presents results for n-alco-hols and benzene from the isobaric (760 mm Hg) data of Wehe and Coates (6). Reliable infinite dilution activity coefficients are established for the other n-alcohols from data for at least two, and preferably three, of them. These y° values are used with equations like those of Van Laar or Wilson (7) to generate activity coefficients at intermediate compositions and to check for an existing azeotrope or a difficult separation (x-y curve close to the 45° line). 

We can predict azeotropic behavior as follows from infinite-dilution /T-values. Using a flowsheeting system, we perform a bubble-point calculation for each species in the mixture. Assuming a mixture contains the species A, B, C, and D, we wish to compute the infinite-dilution L-values for three of the species in the remaining one. For example, we perform a flash calculation where A is dominant and B, C, and D are in trace amounts, using something like a feed composition of 0.99999, 0.000003333, 0.000003333, 0.000003334. It does not... 

Given infinite-dilution A"-values, we want next to examine each species pair where one is plentiful and the other is in trace amount. As an example. Fig. 5 shows how A -values vary for a binary mixture of acetone and chloroform versus composition. We see that the /if-value for a drop of chloroform (far left) is less than unity. The vapor composition Vc is less than that for the liquid, Xq. The K-value for a drop of acetone in chloroform is also less than unity. The mixture displays a maximum-boiling azeotrope. 

Example. Table I (each row conies from one of the above flash computations) lists infinite-dilution T-values that were computed for a mixture of acetone, chloroform, and benzene. The infinite-dilution T-value for acetone in chloroform is 0.6 and for chloroform in acetone is 0.4. Both are less than 1 a maximumboiling azeotrope must exist. For chloroform and benzene, the values are 1.5 and 0.4. These values do not suggest the existence of an azeotrope. We assume normal behavior. A similar conclusion is obtained for acetone and benzene where the T-values are 3.0 and 0.7, respectively. 

Mixtures may also form two or more liquid phases at equilibrium. For example, a 50/50 mol% liquid mixture of toluene in water will partition into a water-rich liquid phase and a toluene-rich liquid phase. We just used infinite-dilution /f-values as a means to predict azeotropic behavior. We can argue that we should use infinite-dilution liquid activity coefficients to alert us to the potential for liquid/liquid behavior. We do so as follows. 

If we have evaluated infinite-dilution A -values to test for the existence of azeotropes, we can use those numbers to get a quick estimate of the corresponding activity coefficients by noting that... 

We predicted their behavior earlier using infinite-dilution /f-values, with the results at 1 atm shown in Table VIII. Only the acetone and chloroform appear to display azeotropic behavior. With this information and that for pure species boiling points at the pressure of interest, we can sketch the ternary diagram for this mixture. We can also use a computer code to generate it, which was done for Fig. 25. We see that there is one maximum-boiling azeotrope between acetone and chloroform. 

A distillation boundary exits. We deduce this when attempting to explain the azeotropic behavior determined using infinite-dilution Af-values. 

As shown, the raffinate stream, Fn, leaving such an extractor essentially contains pentane and acetone plus a trace of water. This pentane-rich mixture can be separated in a distillation column, producing pentane as bottoms and a distillate which is limited to the minimum-boiling azeotrope between pentane and acetone. (The infinite-dilution F-values of 7.9 and 3.0 indicate that such an azeotrope exists.) Figure 36 gives the flowrates and relative concentrations between the major species of the streams entering and leaving the distillation column (labeled DI-2) fltat carries out this separation for the raffinate (pentane-rich) stream. 

Compute the infinite-dilution A -values for all pairs of species, as we did earlier to check for the existence of binary azeotropes. For this example, we would find that all three binary pairs display an azeotrope. 

Figure 43 shows these azeotropes as well as a ternary one we now wish to find. Starting at the ethanol/water binary azeotrope, the infinite-dilution f-value for toluene is 2.78. Allowing for two liquid phases, the above algorithm locates the ternary azeotrope without difficulty. If we do not allow for two liquid phases, computations indicate there is no ternary azeotrope. 

Example 5.8. For the ethanol (E)-n-hexane (H) system at 1 atm (101.3 kPa), a best fit of the Wilson equation using the experimental data of Sinor and Weber leads to infinite-dilution activity coefficients of ye = 21.72 and yH = 9.104 as discussed in Example 5.6. Neglecting the effect of temperature, use these values to determine teh and the in the NRTL equation. Then, estimate activity coefficients at the azeotropic composition Xe = 0.332. Compare the values obtained to those derived from experimental data in Example 5.6. 

Furthermore, poor results are obtained for the solubilities and activity coefficients at infinite dilution of alkanes or naphthenes in water. This was accepted by the developers of modified UNIFAC to achieve reliable VLE results, for example, for alcohol/water systems. The reason was that starting from experimental g -values of approx. 250000 for n-hexane in water at room temperature it was not possible to fit alcohol-water parameters which deliver y -values for hexanol in water of 800 and at the same time describe the azeotropic composition of ethanol and higher alcohols with water properly and obtain homogeneous behavior for alcohol-water systems up to C3-alcohols and heterogeneous behavior starting from C4-alcohols. To allow for a prediction of hydrocarbon solubilities in water an empirical relation was developed [61, 62], which allows the estimation of the solubilities of hydrocarbons in water and of water in hydrocarbons (see below). 

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