Deviations from ideal solutions

Mixtures. A number of mixtures of the hehum-group elements have been studied and their physical properties are found to show Httle deviation from ideal solution models. Data for mixtures of the hehum-group elements with each other and with other low molecular weight materials are available (68). A similar collection of gas—soHd data is also available (69). 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

When deviations from ideal solution behavior occur, the changes in the deviations with mole fraction for the two components are not independent, and the Duhem-Margules equation can be used to obtain this relationship. The allowed combinations"1 are shown in Figure 6.10 in which p /p and P2//>2 are... 

Figure 6.10 Representative deviations from ideal solution behavior allowed by the Duhem-Margules equation. The dotted lines are the ideal solution predictions. The dashed lines giveP2IP2 (lower left to upper right), and p jp (upper left to lower right).

The extent of deviation from ideal solution behavior and hence, the magnitude and arithmetic sign of the excess function, depend upon the nature of the interactions in the mixture. We will now give some representative examples. 

In our discussion of (vapor + liquid) phase equilibria to date, we have limited our description to near-ideal mixtures. As we saw in Chapter 6, positive and negative deviations from ideal solution behavior are common. Extreme deviations result in azeotropy, and sometimes to (liquid -I- liquid) phase equilibrium. A variety of critical loci can occur involving a combination of (vapor + liquid) and (liquid -I- liquid) phase equilibria, but we will limit further discussion in this chapter to an introduction to (liquid + liquid) phase equilibria and reserve more detailed discussion of what we designate as (fluid + fluid) equilibria to advanced texts. 

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... 

The concept of ideal solutions (41) was used by the industry early in the period covered by this discussion. Hydrocarbons follow this type of behavior with reasonable accuracy at pressures somewhat above their vapor pressures. However, important divergences occur at higher pressures. Serious deviations from ideal solutions are experienced for components at reduced temperatures markedly greater than unity. Lewis (48) proposed a modified type of ideal solution by neglecting the volume of the liquid phase. This modification simplified the application of the concept. The Lewis generalization has been widely employed by the industry. 

Unfortunately such "effective molecular weight studies involve the major assumption that the whole deviation from ideal solutions is due to association and this assumption can only be controlled by some non-osmotic method such as the spectrophotoraetric one. Dolezalek s papers of the 19)0 era provide ample warning of the falsity of this assumption when indiscriminately applied however, where associative interaction is pronounced, comparison of spectroscopic and osmotic data shows that the careful evaluation of the latter leads to essentially correct results. 

The activity coefficient of component i, y, is a measure for the deviation from ideal solution behaviour... 

The thermodynamic quantity 0y is a reduced standard-state chemical potential difference and is a function only of T, P, and the choice of standard state. The principal temperature dependence of the liquidus and solidus surfaces is contained in 0 j. The term is the ratio of the deviation from ideal-solution behavior in the liquid phase to that in the solid phase. This term is consistent with the notion that only the difference between the values of the Gibbs energy for the solid and liquid phases determines which equilibrium phases are present. Expressions for the limits of the quaternary phase diagram are easily obtained (e.g., for a ternary AJB C system, y = 1 and xD = 0 for a pseudobinary section, y = 1, xD = 0, and xc = 1/2 and for a binary AC system, x = y = xAC = 1 and xB = xD = 0). 

It is unusual to find systems that follow the ideal solution prediction as well as does (benzene+ 1,4-dimethylbenzene). Significant deviations from ideal solution behavior are common. Solid-phase transitions, solid compound formation, and (liquid 4- liquid) equilibria often complicate the phase diagram. Solid solutions are also present in some systems, although limited solid phase solubility is not uncommon. Our intent is to look at more complicated examples. As we do so, we will see, once again, how useful the phase diagram is in summarizing a large amount of information. 

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. 

Chapters 17 and 18 use thermodynamics to describe solutions, with nonelectrolyte solutions described in Chapter 17 and electrolyte solutions described in Chapter 18. Chapter 17 focuses on the excess thermodynamic properties, with the properties of the ideal and regular solution compared with the real solution. Deviations from ideal solution behavior are correlated with the type of interactions in the liquid mixture, and extensions are made to systems with (liquid + liquid) phase equilibrium, and (fluid -I- fluid) phase equilibrium when the mixture involves supercritical fluids. 

At basic pH values the rate of 3-MPA formation is reduced, but continues at measurable rates even at a pH value as high as 10. These results indicate that acrylate ion possesses significant reactivity, although the undissodated form is much more reactive. In the addic pH ranee, the rate of 3-MPA formation in seawater is similar to that in Milli-Q water, but at basic pH values, the rates in seawater are higher than those in Milli-Q water (Figure 4). In an ionic medium such as seawater, for reactions involving ions, the Bronsted-Bjerrum equation predicts that ionic interactions cause deviations from ideal-solution behaviour (Equation 5) (451. 

The deviations from ideal solution behavior are generally associated with a finite heat of solution. However, the properties of systems containing high molecular weight components, have shown extremely large deviations from the behavior to be expected of ideal solutions, even in cases where the heat of mixing was negligible. 

An alternative way of expressing the deviation from ideal solution behavior is by means of excess thermodynamic functions. These are defined as the difference between a thermodynamic property of a solution and the thermodynamic property it would have if it were an ideal solution ... 

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. 

The solutions are considered so dilute that the effect of ionic strength can be neglected (ideal solution). Mathematical expressions derived so far in this chapter use a molar concentration term. If the chemical activity deviates from ideal solution behavior, the ionization of a weak acid or weak base may be given in terms of activity rather than molar concentration to account for interactions in the real solution as follows ... 

There are many measurement techniques for activity coefficients. These include measuring the colligative property (osmotic coefficients) relationship, the junction potentials, the freezing point depression, or deviations from ideal solution theory of only one electrolyte. The osmotic coefficient method presented here can be used to determine activity coefficients of a 1 1 electrolyte in water. A vapor pressure osmometer (i.e., dew point osmometer) measures vapor pressure depression. 

In solvents that are chemically similar to the solute (i.e., naphthalene/toluene), the experimental solubility of the solute is very close to the ideal value. Either negative or positive deviation from the ideal value occurs when the solute and the solvent are chemically dissimilar. The nonideal behavior results from the differences in the interactions between the solute and the solvent molecules (i.e., solute-solute, solvent-solvent, and solute-solvent). The sum of these interactions usually becomes positive, and having an incomplete mixing of all components results in a finite solubility of the solute in the solvent. These deviations from ideal solution behavior can be expressed by the activity coefficient of the nonideal solution. The activity, a2, of a solute in a nonideal solution is the product of concentration, x2, and the activity coefficient, y2, as ... 

The molecular structure of binary HBD/HBA solvent mixtures is largely determined by intermolecular hydrogen bonding between the two components, which usually leads to pronounced deviations from ideal solution behaviour [306, 325-327]. Representative examples are trichloromethane/acetone [326] and trichloromethane/dimethyl sulfoxide mixtures [327], which readily form hydrogen-bonded 1 1 and 2 1 complexes, respectively, with distinct changes in their physical properties as a consequence. 

The qualitative phase behavior of hydrocarbon systems was described in the previous chapter. The quantitative treatment of these systems mil now be discussed and tire methods for calculating their phase behavior presented. It will became apparent that the liquid and vapor phases of mixtures of two or more hydrocarbons are in reality solutions (see below), so that it will be necessary to discuss the laws of solution behavior. Analogous to the treatment of gases, the behavior of a hypothetical fluid known as a perfect, or ideal, solution will be described. This will be followed by a description of actual solutions and tlie deviations from ideal solution behavior that occur. 

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. 

In addition to the short-range interactions between species in all solutions, long-range electrostatic interactions are found in electrolyte solutions. The deviation from ideal solution behavior caused by these electrostatic forces is usually calculated by some variation of the Debye-Huckel theory or the mean spherical approximation (MSA). These theories do not include terms for the short-range attractive and repulsive forces in the mixtures and are therefore usually combined with activity coefficient models or equations of state in order to describe the properties of electrolyte solutions. 

Deviations from ideal solution behavior have reduced the effective total molality from 0.060 to 0.050 mol kg . ... 

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. 

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