Negative deviation from ideal solution

In our discussion of (vapor + liquid) phase equilibria to date, we have limited our description to near-ideal mixtures. As we saw in Chapter 6, positive and negative deviations from ideal solution behavior are common. Extreme deviations result in azeotropy, and sometimes to (liquid -I- liquid) phase equilibrium. A variety of critical loci can occur involving a combination of (vapor + liquid) and (liquid -I- liquid) phase equilibria, but we will limit further discussion in this chapter to an introduction to (liquid + liquid) phase equilibria and reserve more detailed discussion of what we designate as (fluid + fluid) equilibria to advanced texts. 

When a mixture has all y, > 1, then > 0, and we say the mixture exhibits positive deviations from ideal-solution behavior. Inversely, if a mixture has all Yi < L then g < 0, and we say the mixture exhibits negative deviations from ideal-solution behavior. In some mixtures, the intermolecular forces are more complicated, causing some components to have y,- < 1 while others have y,- > 1. 

At the temperatures of the measurements, there is quite appreciable solubility of N in Th(l) and estimation of the term is attended by an appreciable uncertainty. Estimation of AGf by equation (7) is, however, useful for indicating the physical chemistry involved. Tentative rough estimates of AGf(ThN) at some representative but arbitrary temperatures as summarized in Table 4 are based upon an extrapolation of equation (6) and the assumption of a regular Th-ThN solution. The estimates indicate that there must be a very strong interaction between the Th and N atoms in the liquid Th-N solution giving rise to strong negative deviations from ideal solution and that the p st predominate in equation (7) at temperatures below... 

Solubilities of ammonia in ionic liquids, l-ethyl-3-methylimidazolium acetate ([EMIm]Ac), l-ethyl-3-methylimidazolium thiocyanate ([EMIm]SCN), l-ethyl-3-methylimidazolium ethylsulfate ([EMImJEtOSOs), and N,N-dimethy- lethanolammonium acetate ([DMEA]Ac) were measured for the first time by A.Yokozeki and M.B. Shiflett [7] in 2007. Six mixture compositions of each binary system were involved from about 30 to 85 mole% of ammonia. Pressure-temperature-composition (P-T-x) data were claimed at isothermal conditions of 283, 298, 323, 348, and 373 K. The observed solubility of ammonia in ionic liquids is very high, and all cases show negative deviations from ideal solution behavior. Experimental P-T-x data were successfully correlated with the equation-of-state (EOS) model [8]. The experimental data and fitting results are shown in Figure 5 8. The opportunity for the absorption cycle application using the ammonia-RTIL system, replacing the traditional ammonia-water system, has been discussed [7]. 

Negative Deviations from Ideal Solution Behavior (Type III)... 

Figure 8.9 shows type III, the opposite of the type II behavior in Figure 8.8, for mixtures of acetone and chloroform. The activity coefficients (Figure 8.9b) for all possible mixtures are <1.00. This is called negative deviation from ideal solution behavior (the logarithms of the activity coefficients... 

Positive deviations from ideal behaviour for the solid solution give rise to a miscibility gap in the solid state at low temperatures, as evident in Figures 4.10(a)-(c). Combined with an ideal liquid or negative deviation from ideal behaviour in the liquid state, simple eutectic systems result, as exemplified in Figures 4.10(a) and (b). Positive deviation from ideal behaviour in both solutions may result in a phase diagram like that shown in Figure 4.10(c). 

Negative deviation from ideal behaviour in the solid state stabilizes the solid solution. 2so1 = -10 kJ mol-1, combined with an ideal liquid or a liquid which shows positive deviation from ideality, gives rise to a maximum in the liquidus temperature for intermediate compositions see Figures 4.10(h) and (i). Finally, negative and close to equal deviations from ideality in the liquid and solid states produces a phase diagram with a shallow minimum or maximum for the liquidus temperature, as shown in Figure 4.10(g). 

However, if the B atom is bound into the solution because of negative interactions (i.e., n — ve) the vapour pressure of B above the alloy is less than if the mixing was ideal. In this circumstance there is a negative deviation from ideality and the plot of activity vs composition is as shown in Fig. 3.9(a). In the case where there are positive interactions (H + ve) there is a positive deviation from ideality as shown in Fig. 3.9(b), and the vapour pressure of B is greater than if mixing is ideal. 

Mixed Micelles Showing Negative Deviation -from Ideality. In an aqueous solution containing a mixture o-f Cll an ionic sur-factant and a nonionic sur-factant, or C21 an anionic sur-factant and a cationic sur-factant, or C33 a zwitterionic sur-factant and an anionic sur-factant, the CMC o-f the mixed sur-factant system exhibits a CMC which is substantially less than that predicted by Equation 1 (9.12.18-37). This means that the mixed micelle -formation is enhanced and that the mixing process in the micelle shows negative deviation -from ideality. This is demonstrated -for a cationic/nonionic system in Figure 1. 

Below the CMC, the surfactant mixing in monolayers composed of similarly structured surfactants approximately obeys ideal solution theory. This means that the total surfactant concentration required to attain a specified surface tension for a mixture is intermediate between those concentrations for the pure surfactants involved. For mixtures of ionic/nonionic or anionic/cationic surfactants, below the CMC, the surfactant mixing in the monolayer exhibits negative deviation from ideality (i.e., the surfactant concentration required to attain a specified surface tension is less than that predicted from ideal solution theory). The same guidelines already discussed to select surfactant mixtures which have low monomer concentrations when micelles are present would also apply to the selection of surfactants which would reduce surface tension below the CMC. 

In order to define a ionic/nonionic surfactant solution with high salinity/hardness tolerance, the following criterion should be followed. The mixed micelle should have as large of a negative deviation from ideality as possible. Surfactant mixture characteristics which result in this have already been discussed. The nonionic surfactant should have a high cloud point. Otherwise the amount of nonionic surfactant which can be added to the system is limited to low levels before phase separation occurs. If possible, a mixed ionic surfactant should be used for reasons Just discussed. There is no such benefit to using mixed nonionic surfactants, although this is not necessarily detrimental either. 

Show that the Gibbs-Duhem equation requires that in a binary solution, both solvent and solute must show positive deviation from ideal behavior or must both show negative deviation from ideal behavior. 

In solvents that are chemically similar to the solute (i.e., naphthalene/toluene), the experimental solubility of the solute is very close to the ideal value. Either negative or positive deviation from the ideal value occurs when the solute and the solvent are chemically dissimilar. The nonideal behavior results from the differences in the interactions between the solute and the solvent molecules (i.e., solute-solute, solvent-solvent, and solute-solvent). The sum of these interactions usually becomes positive, and having an incomplete mixing of all components results in a finite solubility of the solute in the solvent. These deviations from ideal solution behavior can be expressed by the activity coefficient of the nonideal solution. The activity, a2, of a solute in a nonideal solution is the product of concentration, x2, and the activity coefficient, y2, as ... 

Figure 12.18 is drawn for a species that shows positive deviations from ideality in the sense of the Lewis/ Randall rule. Negative deviations from ideality are also common, and in this case the /j-vs.-x, curve lies below the Lewis/Randall line. In Fig. 12.19 we show the composition dependence of the fugacity of acetone in two different binary solutions at 50°C. When the second component is methanol, acetone shows positive deviations from ideality. On the other hand, when the second component is chloroform, acetone shows negative deviations from ideality. The fugacity of pure acetone f—<— is of course the same regardless of the second component. However, Henry s constants, represented by the slopes of the two dotted lines, are very different for the two cases. 

Establish what equations must be satisfied. Ideal solutions or solutions exhibiting negative deviation from ideal behavior cannot form two liquid phases. Instead, strong positive deviation is necessary for two or more liquid phases to exist together. 

---