Equilibrium curve, determination

Subject to the condition that Eq. 42 holds true, the result in Eq. 44 is of general validity however, it cannot in general be used for predictive purposes, since the value of a is in general not known. However, in the instantaneous reaction limit, ot can be calculated from the requirement that equilibrium should prevail at the interface, i.e., one obtains Eq.8. Furthermore, since the molarity at the interface is the same as in the bulk, the value of a can simply oe read off an equilibrium curve determined at the bulk-liquid value of the molarity. 

E] Use s BoUes Fair (Ref. 75) data base to determine new effective area to use with Onda et al. (Ref. 126) correlation. Same definitions as 5-28-D. P = total pressure, atm Mq = gas, molecular weight m = local slope of equilibrium curve Lf /Gf = slope operating line Z = height of packing in feet. 

FIG. 13-101 Determination of minimum reflux for equilibrium curve with inflection. 

The design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

Specifying P determines the v-l-e relationship (equilibrium) curve from experimental data. 

The equilibrium curve can be drawn with sufficient accuracy to determine the stages above the feed by plotting the concentrations at increments of 0.1. The diagram would normally be plotted at about twice the size of Figure 11.7. 

For a binary mixture under constant pressure conditions the vapour-liquid equilibrium curve for either component is unique so that, if the concentration of either component is known in the liquid phase, the compositions of the liquid and of the vapour are fixed. It is on the basis of this single equilibrium curve that the McCabe-Thiele method was developed for the rapid determination of the number of theoretical plates required for a given separation. With a ternary system the conditions of equilibrium are more complex, for at constant pressure the mole fraction of two of the components in the liquid phase must be given before the composition of the vapour in equilibrium can be determined, even for an ideal system. Thus, the mole fraction yA in the vapour depends not only on X/ in the liquid, but also on the relative proportions of the other two components. 

If, for example, a mixture of ethanol and water is distilled, the concentration of the alcohol steadily increases until it reaches 96 per cent by mass, when the composition of the vapour equals that of the liquid, and no further enrichment occurs. This mixture is called an azeotrope, and it cannot be separated by straightforward distillation. Such a condition is shown in the y — x curves of Fig. 11.4 where it is seen that the equilibrium curve crosses the diagonal, indicating the existence of an azeotrope. A large number of azeotropic mixtures have been found, some of which are of great industrial importance, such as water-nitric acid, water-hydrochloric acid, and water-alcohols. The problem of non-ideality is discussed in Section 11.2.4 where the determination of the equilibrium data is considered. When the activity coefficient is greater than unity, giving a positive deviation from Raoult s law, the molecules of the components in the system repel each... 

For packed columns (k ga)/G represents a useful value for the efficiency, and the performance of a packed column is commonly represented by the simple term HG, where a low value of HG corresponds to an efficient column. If HG is known, the necessary height of a column is found from equation 11.154, since NG is determined from the change in concentration required and the shape of the equilibrium curve. Application of this technique is discussed in Chapter 12 and reference may also be made to Volume 1, Chapter 10. 

With increasing P and T, the equilibrium curve of equation 5.129 reaches an invariant condition, determined by the appearance of silicate melt T = 835 °C, P = 0.45 kbar Wones and Dodge, 1977). 

Selected entries from Methods in Enzymology [vol, page(s)] Computer programs, 240, 312 infrared S-H stretch bands for hemoglobin A, 232, 159-160 determination of enzyme kinetic parameter, 240, 314-319 kinetics program, in finite element analysis of hemoglobin-CO reaction, 232, 523-524, 538-558 nonlinear least-squares method, 240, 3-5, 10 to oxygen equilibrium curve, 232, 559, 563 parameter estimation with Jacobians, 240, 187-191. 

Diffusion-type models are two-parameter models, involving kt or Ds and La, while BDST models are one-parameter models, involving only 0, as gmax is an experimentally derived parameter. The determination of La requires the whole experimental equilibrium curve, and in case of sigmoidal or other non-Langmiur or Freundlich-type isotherms, these models are unusable. From this point of view, BDST models are more easily applied in adsorption operations, at least as a first approximation. 

The equilibrium curve also can be transformed into these coordinates. These transformations are useful for graphical determinations of numbers of theoretical trays rather than for determination of numbers of transfer units. Example 13.13 employs both sets of units. 

For determination of phenol distribution coefficients the extraction proceeded for 15 minutes in order to reach equilibrium. The time required to reach equilibrium was determined by making five replicate injections of the headspace onto the SFC system. The first injection was after the extraction had proceeded for 15 minutes at 50°C and 100 atm. Following the equilibration time, four further injections at ten minute intervals were made, after which the pressure inside the extraction apparatus was increased and the system was again allowed to equilibrate (i.e. 15 minutes). The five replicate injection process was then repeated. The amount of phenol in each injection was then noted by referring to an external phenol standard calibration curve. As the total volume of the system was known, the amount of phenol in the SF could be calculated. The amount of phenol in the aqueous phase could then be calculated by mass balance. 

Step 1. The first step in the procedure is to determine the key component equilibrium curve slope M. This is for one component only. You must choose a light key and a heavy key component for this tray efficiency calculation. Select components that are keys in the fractionator split. A single K = Y/X equilibrium value is to be applied to absorbers and strippers as this M value. The change of Y per the change of X is sought out for the light key component. 

Equations (7.11) and (7.12) may be used to determine the pounds of solute at any point on the respective equilibrium curve, including the entrance and exit points of the extractor. KD may also be calculated from ... 

Figure 8.22. Equilibrium curves for the reaction CaC03 + SiC>2 —> CaSiC>3 + Si02 at a CO2 pressure of 1 atm and at a CO2 pressure equal to total pressure on the system. At P-T values between the two CO2 pressure extremes, caicite and quartz are stable. Heavy solid line is experimentally determined and dashed lines are extrapolated or theoretical. (After Barth, 1962.)...

To obtain the number of ideal stages in the contactor, one starts by plotting the point y +1 (which is the feed composition of the gas) on the operating line this defines x N. This corresponds to solving the material balance given by Eq. (24) to determine x N. Next, one draws a vertical line from the point (x N, y +1) to the equilibrium curve this defines y N. This corresponds to solving the equilibrium relationship to determine yfN. From the point... 

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