Negative deviation from ideality

Figure 5.10 shows a plot of Vm/Vm versus pressure for methane at 25°C. Up to about 150 atm, methane shows a steadily increasing negative deviation from ideality, as might be expected on the basis of attractive forces. At 150 atm, Vm is only about 70% of V ,. 

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. 

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). 

These results shown in Figures 1 and 2 demonstrate the similarity of the effects of short-range forces on the properties of nonelectrolytes and concentrated electrolytes. One finds both positive and negative deviations from ideality and these effects may be ascribed to the difference between the intermolecular potential energy of attraction of unlike species to the mean of the corresponding potentials for pairs of like molecules. Previous discussion of these systems has focused on the hydration of the positive ion as the dominant effect, but we see in Figure 1 that... 

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. 

Having shown that ionic/nonionic surfactant mixtures show negative deviations from ideality (when both components are hydrocarbon—based) and fluorocarbon/hydrocarbon—based surfactant mixtures show positive deviations from ideality, what would a ionic fluorocarbon/nonionic hydrocarbon surfactant pair be expected to do In one example of this case (57). the electrostatic stabi1ization forces overcome the hydrophobic group phobicity effects and negative deviation from ideality is observed. 

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. 

The higher the negative deviation from ideality in monolayer formation, the lower the concentration required to attain a given surface tension below the CMC. The higher this deviation for micelle formation, the lower the CMC. Since the CMC is where the surface tension approximately levels out at near a minimum value, the minimum surface tension in such a system represents the relative enhancement of monolayer formation over micelle formation. This relative favorability of aggregate formation is often an important factor in many applications, as will be further discussed in this article. 

Nishikido (21) has done a systematic study o-f mixed sur-factant solubilization. In that study, solubilization in mixed systems was compared to that predicted by application o-f a linear mixing rule to the solubilizations in the pure surfactant component micelles. For example, in this "ideal case, a micelle composed of a 50/50 molar mixture of two surfactants would have a solubilization capacity which is an average of that of the two pure surfactants involved. A system showing negative deviation from ideality would have less solubilization than this ideal system a system having positive deviation from ideality would have more. 

When an ionic/nonionic surfactant mixture adsorbs on a metal oxide surface, the admicelle exhibits negative deviation from ideality (74). This means that the adsorption level is higher than it would be if the admicelle were ideal, at a specific surfactant concentration below the CMC. Above the CMC, the adsorption level is dictated by the relative enhancement of micelle formation vs. admicelle formation. In this region, the level of adsorption can be viewed as the result of the competition between micelles and admicelles for surfactant. In analogy, the surface tension above the CMC can be viewed as competition between the monolayer and micelles for surfactant. 

In designing surfactant systems, if adsorption of a given component is to be minimized, an additional surfactant should be added to the system above the CMC. This surfactant should be selected so that it forms micelles with high negative deviations from ideality, using the guidelines already discussed, and so that it tends not to adsorb on the solid of interest. This will be very specific to the particular solid and may require empirical experiments to specify the surfactant. 

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. 

Large negative deviations from ideality are well known when mixed micelles are formed between ionic and nonionic surfactants (11—15.21.24) Negative deviations from ideality have been reported for mixed ionic/nonionic admicelle formation (26), although the degree of nonideality was not quantified. Since this work has pointed out the similarities and differences between mixed micelles and admicelles, the study of these systems should elucidate this relationship even further and will be the subject of future publications. 

Thermodynamic activity coefficients can be determined from the phase equilibrium measurements, and they are a measure of deviations from Raoult s law. Data of the activity coefficients covering the whole range of liquid composition of IL + molecular solvent mixtures have been reported in the literature and discussed in sections 1.6,1.7, and 1.8 as the values obtained from the SLE, LLE, and VLE data. When a strong interaction between the IL and the solvent exists, negative deviations from ideality should be expected with the activity coefficients lower than one. 

The simulations suggest that negative deviations from ideality (corresponding to attractive interactions) are possible for ammonia, but not for a sample of gas consisting mostly of hydrogen. This is in fact what is observed experimentally. Atomistic simulations are by no means guaranteed to reproduce experimental data as well as in this case. Conceptually, however, such simulations tend to be akin to real experiments even when they fail. ... 

Figure 2.6 Representative T dependence of the second virial coefficient B(T), showing the strong negative deviations from ideality at small T, the weak positive deviations at high Tand the Boyle temperature (TBoyie — 750K for C02) where B(TBoylc) vanishes.

The results are plotted in Fig. 3. As can be seen, with the Raoult s law reference, the acetone-chloroform system shows negative deviation from ideal behavior. This is unusual and is due to there being some tendency to form hydrogen bonds between acetone and chloroform. Note that as the system approaches either of the pure components, the vapor-pressure curve of that component becomes tangent to its Raoult s law line. 

In systems with negative deviation from ideal behavior, maximum-boiling-point azeotropes can occur. This is illustrated in Fig. 8 for the chloroform-acetone system, treated in Example 1. This system shows negative deviation from ideal behavior due to the possibility of hydrogen bonds between chloroform and acetone, which cannot occur with the pure components. 

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. 

Figure 39.4 shows that if = 1 then a = X (i.e. the effective mole fraction corresponds to the actual mole fraction as made up) then we have ideal behaviour. As discussed before (Frame 33, Figure 33.2) both positive and negative deviations from ideality can occur in real liquid mixtures. 

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