Raoult’s law, deviation from

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). 

We derived equation (12.12) from equation (12.10) simply by saying that 7 could be introduced to take care of deviations from Raoult s Law. Deviations from Henry s Law are similarly accounted for by introducing 7// instead of 7/ , thus... 

Ideal Solutions and Raoult s Law Deviation from Ideality... 

Equation (1.5-11) is an expression for the difference between (he acinal bubble pressure P given by Eq. (1.5-10) aed the Ranult s Law bubble pressure PBL given by Eq. (1.5-9). To the extent that the approximate Eq. (1.5-10) is valid, Eq. (1.5-11) asserts diet deviations from Raoult s Law result from liquid-phase nonidealities liquid-phase activity coefficients greater than unity promore positive deviations from Raoult s Law. and liquid-phase activity coefficients less than unity promote negative deviations from Raonlt s Law. 

Ordinarily, solutions which exhibit positive deviations from Raoult s law are formed from their constituents with an absorption of heat. AHs is positive, therefore, and yA will be smaller at higher temperatures. For mixtures with negative deviations, the AHs is ordinarily negative. In both cases, therefore, the solutions ordinarily more nearly approach Raoult s law as the temperature is increased. Obvious exceptions to this rule are systems with lower critical solution temperatures, where, at least in the neighborhood of the lower C.S.T., the Raoult s law deviations become greater with increasing temperature. 

Figure 6.9 Partial Vapor Pressures of Ethanol (Component 2) and Diethyl Ether in a Solution at 20°C, Showing Positive Deviation from Raoult s Law. Drawn from data of J. Timmermans, Physicochemical Constants of Binary Systems, Vol. 2, Interscience Publishers, Inc., New York, 1959, p. 401.

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.

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-... 

Fig. 3. Binary activity coefficients for two component systems having (a) positive and (b) negative deviations from Raoult s law. Conditions are either...

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. 

Robbins chaii. Selecl candidate solvents from groups in the Robbins Chart (Table 13-15) that tend to give positive (or no) deviations from Raoult s law for the key component desired in the distillate and negative (or no) deviations for the other key. 

Pure-component vapor pressures can be used for predicting solu-bihties for systems in which RaoiilFs law is valid. For such systems Pa = Pa a, where p° is the pure-component vapor pressure of the solute andp is its partial pressure. Extreme care should be exercised when attempting to use pure-component vapor pressures to predict gas-absorption behavior. Both liquid-phase and vapor-phase nonidealities can cause significant deviations from the behavior predicted from pure-component vapor pressures in combination with Raoult s law. Vapor-pressure data are available in Sec. 3 for a variety of materials. 

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

In most cases, systems deviate to a greater or lesser extent from Raoult s law, and vapour pressures may be greater or less than the values calculated. In extreme cases (e.g. azeotropes), vapour pressure-composition curves pass through maxima or minima, so that attempts at fractional distillation lead finally to the separation of a constantboiling (azeotropic) mixture and one (but not both) of the pure species if either of the latter is present in excess. 

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). 

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. 

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