Vapor pressure positive deviation

For real solutions, the partial pressures PA, PB and total vapor pressure P deviate from the idealized limit (7.45a-c), with deviations of either sign. The following is an illustrative diagram for positive deviations (P > Fideal), showing the partial pressures (solid lines) and total pressure (heavy solid line) exceeding ideal values (dotted lines) ... 

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. 

Raoult s law applies to the vapor pressure of the mixture, so positive deviation means that the vapor pressure is higher than expected for an ideal solution. Negative deviation means that the vapor pressure is lower than expected for an ideal solution. Negative deviation will occur when the interactions between the different molecules are somewhat stronger than the interactions between molecules of the same... 

A series of works by Matsuda et al. composed perhaps the first systematic study to explore the physical foundation for such a mixing effect. Using PC/DME as a model system, they investigated the dependence of vapor pressure, dielectric constant, and viscosity on solvent composition, and they correlated these variations with ion conductions. It was found that the dielectric constant varied with solvent composition by following an almost linear relation, with slight positive deviations, while viscosity always showed a pronounced negative deviation from what a linear relation would predict (Figure 6b). For such binary solvent systems, approximate quantifications... 

Still more extreme positive deviations can finally lead to a maximum in the vapor-pressure curve ... 

In all the above discussions regarding liquid-vapor equilibria we have assumed that our representative systems were ideal, that is, there are no differences in attractions between molecules of different types. Few systems are ideal and most show some deviation from ideality and do not follow Raoult s law. Deviations from Raoult s law may be positive or negative. Positive deviations (for binary mixtures) occur when the attraction of like molecules, A-A or B-B, are stronger than unlike molecules, A-B (total pressure greater than that computed for ideality). Negative deviations result from the opposite effects (total pressure lower than that computed for ideality). A mixture of two liquids can exhibit nonideal behavior by forming an azeotropic mixture (a constant boiling mixture). 

A plot of 2 vs. -t2 for symmetrical systems (i.e., ii vo) is shown in Fig. 1 for a series of values of the heat lerm, It shows how the partial vapor pressure of a component of a binary solution deviates positively from Raoult s law more and mure as the components become more unlike in their molecular attractive forces. Second, the place of T in die equation shows that tlic deviation is less die higher the temperature. Third, when the heat term becomes sufficiently large, there are three values of U2 for the same value of ay. This is like the three roots of the van der Waals equation, and corresponds to two liquid phases in equilibrium with each other. The criterion is diat at the critical point the first and second partial differentials of a-i and a are all zero. 

Raoult s law applies to the vapor pressure of the mixture, so a positive deviation means that the vapor pressure is higher than expected for an ideal solution. 

B. Distillation and Purging. The great efficiency of fractional distillation for the removal of water from hydrocarbon and chlorocarbon solvents is often not well appreciated. The physical origin of this good separation is in part the large positive deviation of the water vapor pressure from Raoult s law because of the lack of affinity of water for these liquids. Typically, the distillation of a simple hydrocarbon solvent with a column of 100 plates and discarding the first two... 

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. 

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. 

Clearly, when B22 = B, the term in square brackets equals 1, and the pressure deviation from the Raoult s-law value has the sign of fin this is normally negative. When the virial coefficients are not equal, a reasonable assumption is that species 2, taken here as the heavier species (the one with the smaller vapor pressure) has the more negative second virial coefficient. This has the effect of making the quantity in parentheses negative and the quantity in square brackets < 1. However, if this latter quantity remains positive (the most likely case), the sign of fin still determines the sign of the deviations. 

FIGURE 3.10 Vapor pressure-composition curve ideal (dotted line) positive deviation (solid line) from Raoult s law. 

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.

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 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. 

Schematic vapor-pressure and boiling-point diagrams for systems showing (a) a strong positive deviation and (b) a strong negative deviation from Raoult s law.

Vapor pressure for a solution of two volatile liquids, (a) The behavior predicted for an ideal liquid-liquid solution by Raoult s law. (b) A solution for which PTota is larger than the value calculated from Raoult s law. This solution shows a positive deviation from Raoult s law. (c) A solution for which PTolai is smaller than the value calculated from Raoult s law. This solution shows a negative deviation from Raoult s law. 

If Pi exceeds the value given by equation (52a), then the p -X vapor-pressure curve is said to exhibit a positive deviation on the other hand, cases in which Pi < Xy are described as negative deviations. Molecular interpretations for the causes of positive and negative deviations are discussed in [18]. Typical vapor-pressure curves exhibiting positive deviations are shown in Figure A.l. 

Activity coefficients were determined for solutions of stearic acid in peanut oil (5). At low FFA concentration (<1%), positive deviations from theory resulting in activity coefficients around 1.5 were observed. At FFA concentration > 30%, the activity coefficients are close to one. This observation was explained by the presence of an association in the form of a fatty acid/triacylglycerol complex that is in equilibrium with the free fatty acids and the triacylglycerol molecules. A low fatty acid concentration favors this equilibrium to shift toward dissociation, which means that higher vapor pressures are measured at lower fatty acid concentrations. 

Very few liquid mixtures rigidly obey Raoult s law. Consequently, the vapor pressure data must be determined experimentally. Mixtures that deviate positively from this law give a total vapor pressure curve which lies above the theoretical straight line. Negative deviations fall below the line. In extreme cases, deviations are so large that a range of mixtures exhibits a higher or lower vapor pressure than either of the pure components. 

In a mixture of compounds, the total vapor pressure is approximately given by the sum of the products of the mole fractions x of the individual constituents and their vapor pressures at the given temperature (Raoult s law, Fig. 1-6). Thus, in any mixture, the vapor above the liquid will contain molecules of each of the species. Deviations from Raoult s law are rather common. Figure 1-7 shows the vapor pressure-composition curve for a mixture which shows positive... 

Fig. 1-7. Vapor pressure—composition relationship for o mixture having positive deviations from Raoult s law.

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