Positive deviation from ideality

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

The reason is that classical thermodynamics tells us nothing about the atomic or molecular state of a system. We use thermodynamic results to infer molecular properties, but the evidence is circumstantial. For example, we can infer why a (hydrocarbon + alkanol) mixture shows large positive deviations from ideal solution behavior, in terms of the breaking of hydrogen bonds during mixing, but our description cannot be backed up by thermodynamic equations that involve molecular parameters. 

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). 

According to Masse et al. (1966), this mixture shows slight positive deviations from ideality of activity values at P = 1180 °C, P = 1 bar. There are no experimental data on intracrystalline distribution. 

Immiscibility phenomena in silicate melts imply positive deviations from ideality in the mixing process. Ghiorso et al. (1983) developed a mixing model applicable to natural magmas adopting the components listed in table 6.12. Because all components have the same standard state (i.e., pure melt component at the T and P of interest) and the interaction parameters used do not vary with T, we are dealing with a regular mixture of the Zeroth principle (cf sections 2.1 and 3.8.4) ... 

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. 

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. 

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. 

The thermodynamics of mixing upon formation of the bilayered surface aggregates (admicelles) was studied as well as that associated with mixed micelle formation for the system. Ideal solution theory was obeyed upon formation of mixed micelles, but positive deviation from ideal solution theory was found at all mixture... 

From Figures 3 and 6—9, the predicted total adsorptions For surFactant mixtures are higher than observed values. ThereFore, the mixed admicelles showed positive deviation From ideality at all compositions. This remarkable behavior has not been observed beFore because data oF the accuracy and range reported here has not (to our knowledge) previously been reported. Observation oF the expected ideal behavior For the CMC data indicate that this is probably not due to a peculiarity oF the surFactants used. 

For systems exhibiting positive deviations from ideality of mixing, aggregate patches of different composition may form on the surface. If methods (e.g., spectroscopic) could be developed to detect the average size of these distincly different patches, this would give insight into the monolayer formation process. 

It would be of scientific interest to study the adsorption of mixed surfactant systems showing positive deviations from ideality, as has been discussed for mixed micelles and monolayers. 

Positive deviations from ideality were also depicted in Section 7.3.1 in the form of P-VBq curves. The full P-xB diagram in this case may have the following qualitative appearance ... 

At higher pressures, (liquid + liquid) equilibrium is not present and the (solid-I-liquid) equilibria line shows large positive deviations from ideal behavior, but no phase separation. It is appropriate to describe the equilibrium at these pressures by saying that the (liquid + liquid) equilibrium curve has disappeared below the (solid + liquid) line. 

At p = 140 MPa (Figure 14.20d) the (liquid + liquid) equilibrium region has moved to the acetonitrile side of the eutectic. Increasing the pressure further decreases the (liquid + liquid) region, until at p= 175 MPa (Figure 14.20e), the (liquid + liquid) region has disappeared under a (solid + liquid) curve that shows significant positive deviations from ideal solution behavior. 

Positive deviation from ideal behavior is the usual occurrence for solutions of volatile components, and it results either when solute-solute and solvent-solvent interactions are stronger than solute-solvent interactions or when the addition of the solute breaks up structure (usually due to hydrogen-bonding) in the solvent. A case of mildly positive deviation is illustrated by the diethyl ether-ethanol system shown in Fig. 5. Here, the resulting total vapor pressure of the solution increases continuously as the concentration of the more volatile component (diethyl ether) is increased. 

If positive deviation from ideal behavior becomes great enough, a solution may separate into two liquid phases. We say that the components of this system are partially miscible. An example of this behavior is the water-ethyl ether system, which separates into water-rich and ether-rich phases at room temperature. By contrast, water and ethanol are completely miscible and do not separate. A phase... 

Sketch the partial pressures above a solution in which both solute and solvent show positive deviation from ideal solution behavior. Using Raoult s law reference for both solute and solvent, sketch the activity coefficients for this solution. 

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 3.10 shows the vapor pressure/composition curve at a given temperature for an ideal solution. The three dotted straight lines represent the partial pressures of each constituent volatile liquid and the total vapor pressure. This linear relationship is derived from the mixture of two similar liquids (e.g., propane and isobutane). However, a dissimilar binary mixture will deviate from ideal behavior because the vaporization of the molecules A from the mixture is highly dependent on the interaction between the molecules A with the molecules B. If the attraction between the molecules A and B is much less than the attraction among the molecules A with each other, the A molecules will readily escape from the mixture of A and B. This results in a higher partial vapor pressure of A than expected from Raoult s law, and such a system is known to exhibit positive deviation from ideal behavior, as shown in Figure 3.10. When one constituent (i.e., A) of a binary mixture shows positive deviation from the ideal law, the other constituent must exhibit the same behavior and the whole system exhibits positive deviation from Raoult s law. If the two components of a binary mixture are extremely different [i.e., A is a polar compound (ethanol) and B is a nonpolar compound (n-hexane)], the positive deviations from ideal behavior are great. On the other hand, if the two liquids are both nonpolar (carbon tetrachloride/n-hexane), a smaller positive deviation is expected.

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