Positive deviation

Figure 4-4. Representation of vapor-liquid equilibria for a binary system showing moderate positive deviations from Raoult s law.

Figure 4 shows experimental and predicted phase equilibria for the acetonitrile/benzene system at 45°C. This system exhibits moderate positive deviations from Raoult s law. The high-quality data of Brown and Smith (1955) are very well represented by the UNIQUAC equation. 

Figure 5 shows the isothermal data of Edwards (1962) for n-hexane and nitroethane. This system also exhibits positive deviations from Raoult s law however, these deviations are much larger than those shown in Figure 4. At 45°C the mixture shown in Figure 5 is only 15° above its critical solution temperature. Again, representation with the UNIQUAC equation is excellent.

The P-radiation was shown to cause the positive deviation from the background level (approx. 3 times) before the earthquake. 

Solubility Properties. Fats and oils are characterized by virtually complete lack of miscibility with water. However, they are miscible in all proportions with many nonpolar organic solvents. Tme solubiHty depends on the thermal properties of the solute and solvent and the relative attractive forces between like and unlike molecules. Ideal solubiHties can be calculated from thermal properties. Most real solutions of fats and oils in organic solvents show positive deviation from ideaHty, particularly at higher concentrations. Determination of solubiHties of components of fat and oil mixtures is critical when designing separations of mixtures by fractional crystallization. 

It has been found (7,9) that Z) > 0, ie, the maximum of an asymmetrical dye, X, is shifted to the short-wavelength region with respect to the arithmetical mean of the parent dye maxima. The phenomenon has been named a deviation (7). The positive deviations in PMDs are explained by the bond order alternation within the polymethine chain caused by different contributions of both end groups to the dye energetic stabiUty (7,9,10). The deviation reaches its maximum at Tqi > 45° and Tqi < 45° if the end groups have > 45° and 4>q2 > 45°, or < 45° and 4>q2 < 45°, then the... 

To force the naturally more volatile component i overhead, the solvent should either behave essentially ideally with component j and cause positive deviations from Raoult s Law for component i (7 1 and 7 > 1), or behave essentially ideally with component i and cause negative deviations from... 

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

HBSA + HBD HBAD + HBD Always positive deviations, HBSA -1- HBD often limited miscibility H-bonds broken and formed dissociation of HBSA or HBAD liquid most important effect... 

HBSA + HBSA HBSA-1- HBAD HBSA-1- HBA HBAD -1- HBAD HBAD + HBA Usually positive deviations some give maximum-boiling azeotropes H-bonds broken and formed... 

An activity coefficient greater than 1.0 for a solute in solution is generally considered to be a positive deviation from Raonlt s law ... 

Inspection of Fig. 14(a) reveals that Ap > 0 in the corner while Ap < 0 at the tip. The positive deviation indicates that the two walls forming the wedge squeeze the hard spheres into the corner this effect is more pronounced for smaller values of 7. Around a tip, on the other hand, the hard spheres are spatially less constrained so that the fluid is more disordered, as in the corresponding planar case, so that Ap < 0. 

Figure 8-5. Chloroform (l)-methanol (2) system at 50°C. Azeotrope formed by positive deviations from Raoult s Law (dashed lines). Data of Sesonke, dissertation, University of Delaware, used by permission. Smith, B.D., Design of Equilibrium Stage Processes, McGraw-Hill New York, (1963), all rights reserved.

At very high pressures, methane behaves quite differently. Above 150 atm, the ratio V,JV increases, becoming 1 at about 350 atm. Above that pressure, methane shows a positive deviation from the ideal gas law ... 

Positive deviations of molar conductivity from the values calculated for the ideal system correspond to the interaction of ionic and associated components of the system. Dissolution of KF in TaF5 and the solution generated as a result, cause the dissociation of the (TaF5)n polyanionic structure in to separate groups, leading to the ionization of the system, which undoubtedly leads in turn to an increase in its conductivity. 

These equations suggest that a plot of M vs conversion should be linear. A positive deviation from the line predicted by eq. 16 indicates incomplete usage of transfer agent (T) while a negative deviation indicates that other sources of polymer chains are significant (e.g. the initiator). 

Let us now focus attention on the common case where all three binaries exhibit positive deviations from Raoult s law, i.e., afj- > 0 for all ij pairs. If Tc for the 1-3 binary is far below room temperature, then that binary is only moderately nonideal and a13 is small. We must now choose a gas which forms a highly nonideal solution with one of the liquid components (say, component 3) while it forms with the other component (component 1) a solution which is only modestly nonideal. In that event,... 

To minimize the pressure requirement, //2,i should be small [gas (2) readily soluble in liquid (1)], and a12 should be large and positive (the 1-2 binary is highly nonideal with positive deviations from Raoult s law). 

Figure 8.17 Vapor fugacity for component 2 in a liquid mixture. At temperature T, large positive deviations from Raoult s law occur. At a lower temperature, the vapor fugacity curve goes through a point of inflection (point c), which becomes a critical point known as the upper critical end point (UCEP). The temperature Tc at which this happens is known as the upper critical solution temperature (UCST). At temperatures less than Tc, the mixture separates into two phases with compositions given by points a and b. Component 1 would show similar behavior, with a point of inflection in the f against X2 curve at Tc, and a discontinuity at 7V...

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. 

Deviations from Raoult s law can make it impossible to separate liquids by distillation. The temperature-composition diagrams for mixtures of ethanol and benzene and of acetone and chloroform show why. A positive deviation from Raoult s law means that the attractive forces between solute and solvent are lower than those between the molecules of the pure components. As a result, the boiling point of the mixture is lower than that predicted by Raoult s law. For some pairs of components, the boiling point of the mixture is in fact lower than the boiling point of either constituent (Fig. 8.41). A mixture for which the lowest boiling temperature is below... 

FIGURE 8.40 A graphical illustration of the variation in the vapor pressures of (a) a mixture of ethanol and benzene and (b> a mixture of acetone and chloroform. Note that the mixture in part (ai shows a vapor-pressure maximum and therefore displays a positive deviation front Raoult s law. The one in part (hi shows a minimum and hence displays a negative deviation from Raoult s law. 

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