Positively deviation behavior

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 8.17 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...

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

The reason is that classical thermodynamics tells us nothing about the atomic or molecular state of a system. We use thermodynamic results to infer molecular properties, but the evidence is circumstantial. For example, we can infer why a (hydrocarbon + alkanol) mixture shows large positive deviations from ideal solution behavior, in terms of the breaking of hydrogen bonds during mixing, but our description cannot be backed up by thermodynamic equations that involve molecular parameters. 

Either a negative deviation or a positive deviation is regularly observed. In any phase diagram, composition is plotted against temperature. In this way, we can see how the interactions between phases change as the temperature changes and the behavior as each solid phase then melts. Either two-phase or three phase systems can be illustrated. This is shown in the following ... 

Figure 1.9 Vegard s law relating unit cell parameters to composition for solid solutions and alloys (a) ideal Vegard s law behavior (b) negative deviation from Vegard s law and (c) positive deviation from Vegard s law.

From Figures 3 and 6—9, the predicted total adsorptions For surFactant mixtures are higher than observed values. ThereFore, the mixed admicelles showed positive deviation From ideality at all compositions. This remarkable behavior has not been observed beFore because data oF the accuracy and range reported here has not (to our knowledge) previously been reported. Observation oF the expected ideal behavior For the CMC data indicate that this is probably not due to a peculiarity oF the surFactants used. 

Such behavior occurs when the two components either form an ideal mixture or are immiscible. Before drawing conclusions concerning molecular interactions (12, 13), it is clearly important to establish that homogeneous mixed films have been formed. Any deviation from line LM is, of course, indicative of both mixing and nonideality. In discussing such effects, we define any negative deviation from LM as a "condensation and any positive deviation as an "expansion. Our results fall into three distinct categories. 

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). 

There are differences in isotherm shape, and for DTAB the behavior is not amenable to a simple explanation. Of particular interest are plots of the amount adsorbed against the mean ionic activity of the surface active agent (including the counterion of the added electrolyte). In the case of DTAB all the data, including others at various salt concentrations up to 0.5M, lie on one line which, after an initial steep rise, is linear to the c.m.c. This indicates that for other than the initial strong adsorption at low concentrations (possibly because of specific interactions with the surface) the adsorption follows the law of mass action. For SDS a similar result is obtained except that positive deviations from the straight line occur below a — 4 X 10 3M for the cases (salt concentration < O.lAf) when there is a point of inflection in the isotherm. These deviations may reflect specific interactions of the DS" with the surface when the ions are adsorbed in parallel orientation. 

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. 

At higher pressures, (liquid + liquid) equilibrium is not present and the (solid-I-liquid) equilibria line shows large positive deviations from ideal behavior, but no phase separation. It is appropriate to describe the equilibrium at these pressures by saying that the (liquid + liquid) equilibrium curve has disappeared below the (solid + liquid) line. 

At p = 140 MPa (Figure 14.20d) the (liquid + liquid) equilibrium region has moved to the acetonitrile side of the eutectic. Increasing the pressure further decreases the (liquid + liquid) region, until at p= 175 MPa (Figure 14.20e), the (liquid + liquid) region has disappeared under a (solid + liquid) curve that shows significant positive deviations from ideal solution behavior. 

Deviations from log-linear behavior can still occur even if none of the above explanations is valid for your system [71-74], Deviations are typically at low and/or high concentrations of cosolvent. Typically, negative deviations are observed at low cosolvent concentrations and positive deviations are observed at high cosolvent concentrations. In Rubino and Yalkowsky s [72] review of this topic, deviations could not be consistently attributed to physical properties of the cosolvent-water mixtures or alterations in the solute crystal. They concluded that changes in the structure of the solvent play a role in deviation from expected log-linear solubilities. 

The Henry s law reference activity coefficients are plotted in Fig. 4. Note that this system shows positive deviation with respect to the ideally dilute behavior of Henry s law. 

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. 

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