Positive deviation from ideal solution

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. 

The thermodynamics of mixing upon formation of the bilayered surface aggregates (admicelles) was studied as well as that associated with mixed micelle formation for the system. Ideal solution theory was obeyed upon formation of mixed micelles, but positive deviation from ideal solution theory was found at all mixture... 

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. 

Sketch the partial pressures above a solution in which both solute and solvent show positive deviation from ideal solution behavior. Using Raoult s law reference for both solute and solvent, sketch the activity coefficients for this solution. 

In Ex. 14.4 a plausibility argument was developedfrom the LLE equilibrium equations to demonstrate that positive deviations from ideal-solution behavior are conducive to liquid/Uquid phase splitting. 

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. 

Thermodynamic parameters for the mixing of dimyristoyl lecithin (DML) and dioleoyl lecithin (DOL) with cholesterol (CHOL) in monolayers at the air-water interface were obtained by using equilibrium surface vapor pressures irv, a method first proposed by Adam and Jessop. Typically, irv was measured where the condensed film is in equilibrium with surface vapor (V < 0.1 0.001 dyne/cm) at 24.5°C this exceeded the transition temperature of gel liquid crystal for both DOL and DML. Surface solutions of DOL-CHOL and DML-CHOL are completely miscible over the entire range of mole fractions at these low surface pressures, but positive deviations from ideal solution behavior were observed. Activity coefficients of the components in the condensed surface solutions were greater than 1. The results indicate that at some elevated surface pressure, phase separation may occur. In studies of equilibrium spreading pressures with saturated aqueous solutions of DML, DOL, and CHOL only the phospholipid is present in the surface film. Thus at intermediate surface pressures, under equilibrium conditions (40 > tt > 0.1 dyne/cm), surface phase separation must occur. 

Several other characteristics of regular solution theory are worth noting. The first is that the theory leads only to positive deviations from ideal solution behavior in the sense that yi > 1. This result can be traced back to the assumption of Eq. 9.6-7, which requires that (Avapf/)mi.x always be intermediate to Avapi/ the two pure components. Also, the solubility parameters are clearly functions of temperature since <5 0 as... 

When a mixture has all y, > 1, then > 0, and we say the mixture exhibits positive deviations from ideal-solution behavior. Inversely, if a mixture has all Yi < L then g < 0, and we say the mixture exhibits negative deviations from ideal-solution behavior. In some mixtures, the intermolecular forces are more complicated, causing some components to have y,- < 1 while others have y,- > 1. 

Mixtures that have a maximum in the Px curve exhibit positive deviations from ideal-solution behavior that is, the activity coefficients are greater than unity. Such mixtures are called positive deviants and their azeotropes are called positive azeotropes. Since such mixtures have minima in their Tx curves, those same azeotropes are also called minimum boiling-point azeotropes. Positive deviants usually occur when attractive intermolecular forces between molecules of the same species are stronger than those between molecules of different species. 

Usually, but not always, yT is the extreme (maximum or minimum) value assumed by 7/ for a component in a binary mixture. Hence, the 7,° are often used as measures of the magnitudes of nonidealities of binary liquid mixtures. Another measure is provided by gF or g /RT for the equimolar mixture for many binary solutions, this is near to the maximum (or minimum) value. For liquid solutions exhibiting positive deviations from ideal-solution behavior (activity coefficients greater than unity), a yl" of about 5 or an equimolar tFfRTof about 0.5 is considered large. ... 

An attempt to consider the effect of small amounts of carbon on the C-Cu-Fe liquid phase using the thermodynamic analysis was made in [1976Wag]. When the dependence of liquidus temperature on concentration is small it indicates considerable positive deviations from ideal solution in case of the C-Cu-Fe system somewhat larger amounts of carbon result in the formation of two liquid phases. 

Figure 8.6 shows that for the acetone-water system the liquid-phase activity coefficients are >1.00 for all possible mixtures. This is type II, positive deviation from ideal solution behavior (the logarithms of the activity coefficients are positive). Hgure 8.8 has the same format as Figure 8.7, and shows that type of deviation for mixtures of isopropanol and water. 

Figure 8.8a shows that for positive deviation from ideal solution behavior the partial pressure curves and the total pressure curve all bow upward, relative to the straight line connecting their endpoints, as Eq. 8.5 says they must. For this set of activity coefficients, the total pressure curve (at constant temperature) has a maximum. This corresponds in Figure 8.8d to a minimum in the boiling-point T-Xa curve. This is produces a minimum-boiling azeotrope. 

These mixtures need not be ideal solutions (e.g., acetone-water, see Chapters 8 and 9), but they will be closer to ideal solutions than those species pairs that do not form a single phase. In most (but not all ) of these cases the liquids form type II (see Section 8.4.2) interactions with each other (positive deviations from ideal solution, y,> 1.00), but the mutual repulsion is not strong enough to form two phases. 

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