Raoult’s law positive deviation from

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.

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. 

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.

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...

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... 

As the components in a liquid mixture become more chemically dissimilar, their mutual solubility decreases. This is characterized by an increase in their activity coefficients (for positive deviation from Raoult s Law). If the chemical dissimilarity, and the corresponding increase in activity coefficients, become large enough, the solution can separate into two-liquid phases. 

If, for example, a mixture of ethanol and water is distilled, the concentration of the alcohol steadily increases until it reaches 96 per cent by mass, when the composition of the vapour equals that of the liquid, and no further enrichment occurs. This mixture is called an azeotrope, and it cannot be separated by straightforward distillation. Such a condition is shown in the y — x curves of Fig. 11.4 where it is seen that the equilibrium curve crosses the diagonal, indicating the existence of an azeotrope. A large number of azeotropic mixtures have been found, some of which are of great industrial importance, such as water-nitric acid, water-hydrochloric acid, and water-alcohols. The problem of non-ideality is discussed in Section 11.2.4 where the determination of the equilibrium data is considered. When the activity coefficient is greater than unity, giving a positive deviation from Raoult s law, the molecules of the components in the system repel each... 

In Raoult s law at infinite dilution, the reference state is the pure liquid state. The activity coefficient at infinite dilution accounts for deviation from pure solute-solute interactions in solution. When positive deviations from Raoult s law occur, the partial pressure of the substance above the solution is greater than it is in an ideal solution,y 1, and the chromatographic retention time is decreased. 

FIGURE 8.43 A graphical illustration of the variation of the vapor pressures of a mixture of (a) ethanol and benzene, (b) acetone and chloroform. Note that the mixture in (a) shows a vapor-pressure maximum, and therefore displays a positive deviation from Raoult s law. The one in (b) shows a minimum, and hence displays a negative deviation from Raoult s law. 

The direction of a deviation from Raoult s law can be correlated with the enthalpy of mixing, AHmix, the enthalpy difference between the mixture and the unmixed components. The enthalpy of mixing of ethanol and benzene is positive—the mixing process is endothermic—and this mixture also shows a positive deviation from Raoult s law. The enthalpy of mixing of acetone and chloroform is negative—the mixing process is exothermic—and this mixture shows a negative deviation from Raoult s law. 

Solutions in which intermodular forces are stronger in the solution than in the pure components have negative deviations from Raoult s law and negative enthalpies of mixing they often form maximum-boiling azeotropes. Solutions in which intermodular forces are weaker in the solution than in the pure components have positive deviations from Raoult s law and positive enthalpies of mixing they often form minimum-boiling azeotropes. 

Mixtures approximating curve (2), in which the critical locus is almost linear, usually are formed when the components have similar critical properties and form very nearly ideal mixtures. A minimum in the critical locus, as in curve (3), occurs when positive deviations from Raoult s law occur that are fairly large, but do not result in a (liquid + liquid) phase separation. Some (polar + nonpolar) mixtures and (aromatic + aliphatic) mixtures show this type, of behavior. 

Figure 17.3b compares G at two temperatures for the (cyclohexane+ hexane) system. The positive G indicates positive deviations from Raoult s law. The effect of temperature on G is related to the if results through the equation1... 

The excess Gibbs free energies are positive for these systems, indicating positive deviations from Raoult s law as these polar and nonpolar molecules are mixed. But is negative over most of the concentration range for the first of these systems and over the entire concentration range for the second, indicating... 

TypeL Non-ideal solutions of this type show small deviations from ideal behaviour and total pressure remains always within the vapour pressures of the pure components, as shown in figure (8), in which the dotted lines represent ideal behaviour. It is observed that the total pressure of each component shows a positive deviation from Raoult s law. However, the total pressure remains within the vapour pressures of the pure constituents A and B. 

This behavior requires positive deviations from Raoult s law over part of the composition range and negative deviations over the remainder. Thus a plot of GE vs. x starts and ends with GE = 0 at A i = 0 and X] = 1 and shows positive values over part of the composition range and negative values over the remainder, with an intermediate crossing of the Xi axis. Because these deviations are usually quite small, the vapor pressures P 1 and P2sat must not be too different, otherwise the dewpoint and bubblepoint curves cannot exhibit extrema. 

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.

When the activity coefficient is greater than 1, a positive deviation from Raoult s law occurs. 

The data for furan/carbon tetrachloride at 30°C shown by Fig. 12.9c provide an example of a system that exhibits small positive deviations from Raoult s law. Ethanol/toluene is a system for which the positive deviations are sufficiently large to lead to a maximum in the Px curve, as shown for 65°C by Fig. 12.9d. Just as a mimimum on the Px curve represents an azeotrope, so does a maximum. Thus there are minimum-pressure and maximum-pressure azeotropes. In either case the vapor and liquid phases at the azeotropic state are of identical composition. 

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