Y-X Diagram

In addition to the previously mentioned shortcut equations, plotting a McCabe-Thiele diagram is also a very useful tool. The equation for the equilibrium X-Y diagram and plotting of the operating lines are described next. 

In reference to distillation conditions, the azeotrope represents a point in the system where the relative volatilities reverse. This applies to either type of azeotrope, the direction of reversal is just opposite. For example in Figure 8-5 the lower portion of the x-y diagram shows that y, > Xj, while at the upper part, the yj < x,. In actual distilla-... 

Figure 8-19. X-y diagram for benzene in benzene-toluene mixture at 760 mm Hg total pressure, Example 8-5.

Simple Batch Distillation Constant a, with Trays or Packing, Constant BoUup, and with Reflux [129] Using x-y Diagram... 

The area under the curve between Xgo and is the value of the integrtil. Plot the equilibrium curve for the more volatile component on x - y diagram as shown in Figure 8-33. Then, select values of xd from the operating line hav ing the constant slope, L/V, from equation... 

Figure 8-37. x-y diagram for ethanol-water mixture, showing minimum reflux. Used by pemiission, Block, B. Chem. Eng. Feb. 6 (1961), p. 87. 

Note x and y ore Corresponding Equiiibrium Liquid and Vapor Voiues Obtained from x-y Diagram. 

V = volumetric flow rate for incoming fresh air Vjnin = minimum fresh air flow required based on slope of operating line L/V on x-y diagram x = mol fraction VOC contaminant in exiting water stream, usually aimed at meeting the environmental regulations... 

Vmin = Minimum fresh air flow based on slope of operating line, L/V, on x-y diagram V = Vapor flowrate, mols/hr or molar volume W = Bottoms product, or still bottoms, or ketde bottoms, mols also see B or mols/hr bottoms product or mols of residue or bottoms/unit time (Ponchon heat balance)... 

Figure 9-87. X-Y diagram for adicibatic absorption of HCl at 1 atmosphere. Reproduced by permission of the American Institute of Chemical Engineers, Oldershaw, C. F., Simenson, L, Brown, T. and Rad-cliffe, F. Trans. Sect. Chemical Engineering Progress, V. 43, No. 7 (1947) p. 371 all rights reserved.

Thus, by knowing aAB from vapor-liquid equilibrium and by specifying xA, A can be calculated. Figure 4.3a also shows a typical vapor-liquid equilibrium pair, where the mole fraction of benzene in the liquid phase is 0.4 and that in the vapor phase is 0.62. A diagonal line across the x-y diagram represents equal vapor and liquid compositions. The phase equilibrium behavior shows a curve above the diagonal line. This indicates that benzene has a higher concentration in the vapor phase than toluene, that is,... 

Solution To determine the location of the azeotrope for a specified pressure, the liquid composition has to be varied and a bubble-point calculation performed at each liquid composition until a composition is identified, whereby X = y,-. Alternatively, the vapor composition could be varied and a dew-point calculation performed at each vapor composition. Either way, this requires iteration. Figure 4.5 shows the x—y diagram for the 2-propanol-water system. This was obtained by carrying out a bubble-point calculation at different values of the liquid composition. The point where the x—y plot crosses the diagonal line gives the azeotropic composition. A more direct search for the azeotropic composition can be carried out for such a binary system in a spreadsheet by varying T and x simultaneously and by solving the objective function (see Section 3.9) ... 

The vapor-liquid x-y diagram in Figures 4.6c and d can be calculated by setting a liquid composition and calculating the corresponding vapor composition in a bubble point calculation. Alternatively, vapor composition can be set and the liquid composition determined by a dew point calculation. If the mixture forms two-liquid phases, the vapor-liquid equilibrium calculation predicts a maximum in the x-y diagram, as shown in Figures 4.6c and d. Note that such a maximum cannot appear with the Wilson equation. 

A mixture of benzene and toluene has a relative volatility of 2.34. Sketch the x-y diagram for the mixture, assuming the relative volatility to be constant. 

The system methanol-cyclohexane can be modeled using the NRTL equation. Vapor pressure coefficients for the Antoine equation for pressure in bar and temperature in Kelvin are given in Table 4.176. Data for the NRTL equation at 1 atm are given in Table 4.186. Assume the gas constant R = 8.3145 kIkmol 1-K 1. Set up a spreadsheet to calculate the bubble point of liquid mixtures and plot the x-y diagram. 

On an x-y diagram for Component i this is a straight line starting at the distillate composition with slope R/(R + 1) and which intersects the diagonal line at x,. ... 

In a mixture of methanol and water, methanol is the most volatile component. At a pressure of 1 atm, the relative volatility can be assumed to be constant and equal to 3.60. Construct the x—y diagram. 

A feed mixture of methanol and water containing a mole fraction of methanol of 0.4 is to be separated by distillation at a pressure of 1 atm. The overhead product should achieve a purity of 95 mole % methanol and the bottoms product a purity of 95 mole% water. Assume the feed to be saturated liquid. Using the x—y diagram constructed in Exercise 1 and the McCabe-Thiele construction ... 

For the unary diagram, we only had one component, so that composition was fixed. For the binary diagram, we have three intensive variables (temperature, pressure, and composition), so to make an x-y diagram, we must fix one of the variables. Pressure is normally selected as the fixed variable. Moreover, pressure is typically fixed at 1 atm. This allows us to plot the most commonly manipulated variables in a binary component system temperature and composition. 

The results of prediction over the entire range of liquid-phase composition are given in Table XII. The comparison of the prediction results with the observed values shown in the x-y diagram is shown in Figure 14. 

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