Raoult’s law negative deviation from

Figure 4-6. Representation of vapor-liquid equilibria for a binary system showing strong negative deviations from Raoult s law.

Figure 7 shows a fit of the UNIQUAC equation to the iso-baric data of Nakanishi et al. (1967) for the methanol-diethyl-amine system this system also exhibits strong negative deviations from Raoult s law. The UNIQUAC equation correctly re-... 

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. 

Other approaches to account for various effects have been developed. Negative deviations from Raoult s law (i.e., y < 1) are frequently... 

Figure 8-6. Acetone (1)-Chloroform (2) system at 50°C. Azeotrope formed by negative 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.

Deviations in which the observed vapor pressure are smaller than predicted for ideal solution behavior are also observed. Figure 6.8 gives the vapor pressure of. (CHjCF XiN +. viCHCfi at T — 283.15 K, an example of such behavior,10 This system is said to exhibit negative deviations from Raoult s law. 

Figure 6.12 shows a graph of u and a2 as a function of mole fraction for mixtures of. yi H O +. Y2CCI4J12 at T = 308.15 K.. A Raoult s law standard state has been chosen for both components. The system shows negative deviation from Raoult s law over the entire range of composition, with it less than. Y and a2 less than. V2. so that all -r.i and 7R.2 are less than 1. 

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. 

The activity coefficients /a and may be smaller or larger than unity hence, the excess chemical potentials pi and pi may be negative or positive. Depending on the sign of pi, the solution is said to exhibit positive or negative deviations from Raoult s law. Similarly, positive or negative deviations from Henry s law can be noted (see Fig. 2.4). 

The maximum boiling point is that temperature corresponding to a definite composition of a Iwo-coinponenl or multicomponent system al which the boiling point of the system is a maximum. At this temperature the liquid and vapor have the same composition and the solution distills completely without change in temperature. Binary liquid systems that show negative deviations from Raoult s law have maximum boiling points. See Raoult s I xiw and Van t Hoff I,aw. 

Tf the components are, respectively, electron-donor and acceptor, or basic and acidic in the generalized sense of Gilbert Lewis, negative deviations from Raoult s law occur, with enhancement of solubility. 

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. 

The (pyridine + trichloromethane) system3 shown in Figure 14.2b is an example of one with negative deviations from Raoult s law. That is, the vapor pressures are lower and the boiling temperatures are higher than for the ideal solution. 

The (trichloromethane + acetone) system5 shown in Figure 14.2d has such large negative deviations from Raoult s law that a minimum occurs in the vapor... 

If the attraction between the A and B molecules is stronger than that between like molecules, the tendency of the A molecules to escape from the mixture will decrease since it is influenced by the presence of the B molecules. The partial vapor pressure of the A molecules is expected to be lower than that of Raoult s law. Such nonideal behavior is known as negative deviation from the ideal law. Regardless of the positive or negative deviation from Raoult s law, one component of the binary mixture is known to be very dilute, thus the partial pressure of the other liquid (solvent) can be calculated from Raoult s law. Raoult s law can be applied to the constituent present in excess (solvent) while Henry s law (see Section 3.3) is useful for the component present in less quantity (solute). 

The activity coefficient can measure the positive or negative deviation from Raoult s law ... 

At the molecular level, appreciable negative deviations from Raoult s law reflect stronger forces of intermolecular attraction in the liquid phase between unlike than between like pairs of molecules. Conversely, appreciable positive deviations result for solutions in which intermolecular forces between like molecules are stronger than between unlike. In this latter case the forces between like molecules may be so strong as to prevent complete miscibility, and the system then forms two separate liquid phases over a range of compositions. Systems of limited miscibility are treated in Sec. 13.9. 

Rathbun and Babb [20] suggested that Darkens equation could be improved by raising the thermodynamic correction factor PA to a power, n, less than unity. They looked at systems exhibiting negative deviations from Raoult s law and found n = 0.3. Furthermore, for polar-nonpolar mixtures, they found n = 0.6. In a separate study, Siddiqi and Lucas [22] followed those suggestions and found an average absolute error of 3.3 percent for nonpolar-nonpolar mixtures, 11.0 percent for polar-nonpolar mixtures, and 14.6 percent for polar-polar mixtures. Siddiqi, Krahn, and Lucas (ibid.) examined a few other mixtures and... 

On the basis of the Duhem-Margules equation, prove that if one component of a binary mixture exhibits positive (negative) deviations from Raoult s Law, the second must do likewise. (See S. Glasstone, "Thermodynamics for Chemists", D. Van Nostrand, New York, 1947, Chapter 14.)... 

Note further that as xx - 1, all curves in Fig. 3.13.3 merge with the one for which B - 0 this agrees with the experimental fact that Raoult s Law always holds in this range. Similarly, as xx - 0 one obtains a straight line region consistent with Henry s Law here the slope as xx - 0 varies with each solution. For B < 0 negative deviations from Raoult s Law are encountered, but for B > 0 one finds positive... 

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