Vapor pressure negative deviation

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 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... 

As these negative deviations become more extreme, the vapor-pressure curve may exhibit a minimum ... 

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). 

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 results are plotted in Fig. 3. As can be seen, with the Raoult s law reference, the acetone-chloroform system shows negative deviation from ideal behavior. This is unusual and is due to there being some tendency to form hydrogen bonds between acetone and chloroform. Note that as the system approaches either of the pure components, the vapor-pressure curve of that component becomes tangent to its Raoult s law line. 

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. 

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). 

Px relation of Raoult s law, and the system therefore exhibits negative deviations. When the deviations become sufficiently large relative to the difference between the two pure-species vapor pressures, the Px curve exhibits a minimum, as illustrated in Fig. 12.96 for the chloroform/tetrahydrofuran system at 30°C. This figure shows that the Py curve also has a minimum at the same point. Thus at this point where x - y the dew-point and bubble-point curves are tangent to the same horizontal line. A boiling liquid of this composition produces a vapor of exactly the same composition, and the liquid therefore does not change in composition as it evaporates. No separation of such a constant-boiling solution is possible by distillation. The term azeotrope is used to describe this state. 

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.

Any solution that obeys Raoult s law is called an ideal solution. One might say that Raoult s law is to solutions what the ideal gas law is to gases. As with gases, ideal behavior for solutions is never perfectly achieved, but is sometimes closely approached. Nearly ideal behavior is often observed when the solute-solute, solvent-solvent, and solute-solvent interactions are very similar. That is, in solutions where the solute and solvent are very much alike, the solute simply acts to dilute the solvent. However, if the solvent has a special affinity for the solute, such as if hydrogen bonding occurs, the tendency of the solvent molecules to escape will be lowered more than expected. In such cases the observed vapor pressure will be lower than the value predicted by Raoult s law there is a 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. 

Solutions of A and B have vapor pressures less than ideal (see Fig. 17.11), so this plot shows negative deviations from Raoult s law. Negative deviations occur when the intermolecular forces are stronger in solution than in pure solvent and solute. This results in an exothermic enthalpy of solution. The only statement that is false is e. A substance boils when the vapor pressure equals the external pressure. Since XB = 0.6 has a lower vapor pressure at the temperature of the plot than either pure A or pure B, one would expect this solution to require the highest temperature for the vapor pressure to reach the external pressure. Therefore, the solution with XB =... 

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. 

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. 

FIGURE 11.10 In an ideal solution, a graph of solvent vapor pressure Pi versus mole fraction of solvent Xi is a straight line. Nonideal solutions behave differently examples of positive and negative deviations from the ideal solution are shown. The vapor pressure of pure solvent is P°. 

FIGURE 11.15 Vapor pressures above a mixture of two volatile liquids. Both ideai (biue lines) and non-ideai behaviors (red curves) are shown. Positive deviations from ideal solution behavior are illustrated, although negative deviations are observed for other nonideal solutions. Raoult s and Henry s laws are shown as dilute solution limits for the nonideal mixture the markers explicitly identify regions where Raoult s law and Henry s law represent actual behavior. 

In order to better demonstrate whether a system follows Raoult s law, a diagram of the phase equilibrium called T-x-y should be plotted. This plot (Figure 2) shows the equilibrium temperatures at which either a liquid solution will start bubbling (bubble curve) or a vapor mixture starts condensing (dew curve). The two systems with their experimental data and the calculation curve of the ideal solution is shown in Figure 2. In Figure 2, the system of hexane-benzene at the pressure of 101.33 kPa [10] and the system of ethylacetate-benzene [11] show negative deviations from RaoulTs law. 

But this is not the entire story. As we saw with heats of solution, if the solution is not ideal, the intermolecular forces between molecules will be changed. Either less energy or more energy will be required for molecules to break the intermolecular bonds and leave the surface of the solution. This means that the vapor pressure of a nonideal solution will deviate from the predictions made by Raoult s law. We can make a general prediction of the direction of the deviation based upon heats of solution. If the heat of solution is negative, stronger bonds are formed, fewer molecules are able to break free from the surface and there will be a negative deviation of the vapor pressure from Raoult s law. The opposite will occur for a positive heat of solution. 

The deviation of vapor pressure from Raoult s law can be represented graphically by comparing the mole fractions of solvents with their vapor pressures. Graph 1 below shows only the partial pressure of the solvent as its mole fraction increases. As predicted by Raoult s law, tire relationship is linear. Graph 2 shows the vapor pressure of an ideal solution and the individual partial pressures of each solvent. Notice that the partial pressures add at every point to equal the total pressure. This must be true for any solution. Graph 3 and 4 show the deviations of nonideal solutions. The straight lines are the Raoult s law predictions and the curved lines are the actual pressures. Notice that the partial pressures still add at every point to equal the total pressure. Notice also that a positive heat of solution leads to an increase in vapor pressure, and a negative heat of solution, to a decrease in vapor pressure. 

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