Nonideal Two-Component Liquid Solutions

Notice that Aj j G and Aj j S satisfy the general equation AmixG = - T A ,ixS 

With A ixff = 0 for an ideal solution, this equation simplifies to 

There is usually one other requirement for the mking of ideal solutions  

Of all requirements for an ideal solution, it is probably equation 7.30 that is most easily demonstrated to fail for most real liquid solutions. Most people are familiar with the example of pure water and pure alcohol. If 1.00 L of pure water is mixed with 1.00 L of pure alcohol, the resulting solution will be somewhat less than 2.00 L in volume. 

Even simple two-component mixtures are not ideal, as suggested by the comment about Amix V for solutions. Molecules in a liquid interact with each other, and molecules interact differently with liquid molecules of another species. These interactions cause deviations from Raoult s law. If the individual vapor pressures are higher than expected, the solution shows a positive deviation from Raoulfs law. If the individual vapor pressures are lower than expected, then the solution shows a negative deviation from Raoult s law. The liquid-vapor phase diagrams for each case show some interesting behavior. 

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Physical Equilibria and Solvent Selection. In nrder lor two separale liquid phases to exist in equilibrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy. G. nf a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in iwo phases. For the binary system containing only components A and B. the condition for the formation of two phases is... 

In order to indicate the fact that the value of G as given by equation (42.1) applies to the constituent 2, i.e., the solute, a subscript 2 is sometimes included. However, this is usually omitted, for in the great majority of cases it is understood that the apparent molar property refers to the solute. It i.s seen from equation (42.1) that o is the apparent contribution of 1 mole of the component 2 to the property G of the mixture. If the particular property were strictly additive for the two components, e.g., volume and heat content for ideal gas and liquid solutions, the value of 4>q would be equal to the actual molar contribution, and hence also to the partial molar value. For nonideal systems, however, the quantities are all different. 

An important first step in any model-based calculation procedure is the analysis and type of data used. Here, the accuracy and reliability of the measured data sets to be used in regression of model parameters is a very important issue. It is clear that reliable parameters for any model cannot be obtained from low-quality or inconsistent data. However, for many published experimentally measured solid solubility data, information on measurement uncertainties or quality estimates are unavailable. Also, pure component temperature limits and the excess GE models typically used for nonideality in vapor-liquid equilibrium (VLE) may not be rehable for SEE (or solid solubility). To address this situation, an alternative set of consistency tests [3] have been developed, including a new approach for modehng dilute solution SEE, which combines solute infinite dilution activity coefficients in the hquid phase with a theoretically based term to account for the nonideality for dilute solutions relative to infinite dilution. This model has been found to give noticeably better descriptions of experimental data than traditional thermodynamic models (nonrandom two liquid (NRTE) [4], UNIQUAC [5], and original UNIversal Eunctional group Activity Coefficient (UNIEAC) [6]) for the studied systems. 

Some solutions contain not only a volatile solvent, but also a volatile solute. In this case, both the solvent and the solute contribute to the overall vapor pressure of the solution. A solution like this may be an ideal solution (in which case its behavior follows Raoult s law at all concentrations for both the solvent and the solute) or it may be nonideal (in which case it does not follow Raoult s law). An ideal solution is similar in concept to an ideal gas. Just as an ideal gas follows the ideal gas law exactly, so an ideal solution follows Raoult s law exactly. In an ideal solution, the solute-solvent interactions are similar in magnitude to the solute-solute and solvent-solvent interactions. In this type of solution, the solute simply dilutes the solvent and ideal behavior is observed. The vapor pressure of each of the solution components is described by Raoult s law throughout the entire composition range of the solution. For a two-component solution containing liquids A and B, we can write ... 

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. 

However, two types of systems are sufficienfry important that we can use them almost exclusively (1) liquid aqueous solutions and (2) ideal gas mixtures at atmospheric pressure, hr aqueous solutions we assume that the density is 1 gtcvc , the specific heat is 1 cal/g K, and at any solute concentration, pressure, or temperature there are -55 moles/hter of water, hr gases at one atmosphere and near room temperature we assume that the heat capacity per mole is R, the density is 1/22.4 moles/hter, and aU components obey the ideal gas equation of state. Organic hquid solutions have constant properties within 20%, and nonideal gas solutions seldom have deviations larger than these. 

The two liquid phases are necessarily nonideal solutions and their component equilibrium coefficients are best calculated from the activity coefficients in each phase (Section 1.3.5) ... 

Although the Murphree model contains an additional assumption (that the liquid leaving plate j is at its bubble-point temperature) over the modified Murphree model, the corresponding values of y 1 predicted by both models on the basis of the same sets coefficients n Li, nGi and points xylf yj+ lf i appear to be in almost perfect agreement for the two examples presented (see Tables 13-2 and 13-3). These examples were taken from Ref. 24. The number of transfer units for each film in these examples was taken to be independent of component identity just as they are for the existing correlations for binary mixtures which are given below. In Example 13-1 (the benzene-toluene system), the vapor and liquid phases closely approximate ideal solutions, but the liquid phase of the ethanol-water system in Example 13-2 is highly nonideal. 

If the top temperature is too cold and the bottom tenperature is too hot to allow sandwich conponents to exit at the rate they enter the column, they become trapped in the center of the column and accumulate there fKister. 20041. This accumulation can be quite large for trace conponents in the feed and can cause column flooding and development of a second liquid phase. The problem can be identified from the simulation if the engineer knows all the trace conponents that occur in the feed, accurate vapor-liquid equilibrium (VLE) correlations are available, and the simulator allows two liquid phases and one vapor phase. Unfortunately, the VLE may be very nonideal and trace conponents may not accumulate where we think they will. For example, when ethanol and water are distilled, there often are traces of heavier alcohols present. Alcohols with four or more carbons (butanol and heavier) are only partially miscible in water. They are easily stripped from a water phase (relative volatility 1), but when there is litde water present they are less volatile than ethanol. Thus, they collect somewhere in the middle of the column where they may form a second liquid phase in which the heavy alcohols have low volatility. The usual solution to this problem is to install a side withdrawal line, separate the intermediate component from the other components, and return the other components to the column. These heterogeneous systems are discussed in more detail in Chapter 8. 

From 7 4e it will be clear that if two liquids a and are partially immiscible their behaviour towards each other is necessarily nonideal. In the present section we consider, however, the behaviour of a third component (subscript i) which is present in each of the two liquid layers. If this substance is sufficiently dilute in each layer it may behave individuaUy as an ideal solute in both of them, even though the system as a whole is non-ideal. ... 

A solution in which the components have vapor pressures as given by Baoult s law is called an IDEAL SOLUTION. (An ideal solution has nothing to do with an ideal gas, except that each is described by an especially simple law.) Probably there are no exacdy ideal solutions, but many solutions are nearly ideal. C Hc and CCI4 illustrate a case in which two liquids form a slightly but measurably nonideal solution. 

Selection of appropriate thermodynamic model for the simulation of COj or SO2 in gas absorbers using water as a solvent is very important. Nonrandom two liquids (NRTL) activity coefficient model is chosen to explain the nonideal phase behavior of a liquid mixture between H2O and SO2. Henry s law option is also selected for the calculation of noncondensable supercritical gases such as Hj, CO, CO2, CH4, and Nj in a liquid mixture. In this example, NRTL was selected. Double click on NRTL01, the thermodynamic data modification window pops up. Click on Enter Data, vapor liquid equilibria (VLE) /(-values window pops up, and then click on Henry s law Enter Data as shown in Figure 7.3. Check use Henry s law for VLE of solute components. 

The thermodynamic model nsed is the nonrandom two liquid (NRTL), which can be used to describe vapor-liquid and liqnid-liquid equilibrium of strongly nonideal solutions. The NRTL model can handle any combination of polar and nonpolar compounds, up to very strong nonideality. In addition, many parameters for xylitol pure component were not available in the databanks of Aspen Plus and had to be acquired from the literature and from regression of experimental data (Table 12.1). 

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