Nonideal behavior interaction effects

Since activity coefficients have a strong dependence on composition, the effect of the solvent on the activity coefficients is generally more pronounced. However, the magnitude and direc tion of change is highly dependent on the solvent concentration, as well as the liquid-phase interactions between the key components and the solvent. The solvent acts to lessen the nonideahties of the key component whose liquid-phase behavior is similar to the solvent, while enhancing the nonideal behavior of the dissimilar key. 

Chemical and physical nonlinearities are caused by interactions among the components of a system. They include such effects as peak shifting and broadening as a function of the concentration of one or more components in the sample. Instrumental nonlinearities are caused by imperfections and/or nonideal behavior in the instrument. For example, some detectors show a... 

Should the macromolecules interact with each other, then d In yildcj does not vanish. In actual experience, its value is almost always positive, largely because of excluded volume effects. Then, c,[0 In Jt/dc,] will then increase in magnitude as Cj increases and r decreases. Thus, the downward curvature shown in curve B of Figure 21.3 is typical of nonideal behavior. 

Seawater has high concentrations of solutes and, hence, does not exhibit ideal solution behavior. Most of this nonideal behavior is a consequence of the major and minor ions in seawater exerting forces on each other, on water, and on the reactants and products in the chemical reaction of interest. Since most of the nonideal behavior is caused by electrostatic interactions, it is largely a function of the total charge concentration, or ionic strength of the solution. Thus, the effect of nonideal behavior can be accoimted for in the equilibrium model by adding terms that reflect the ionic strength of seawater as described later. 

This large increase in the solvent power of ethylene on compression to 100 bar cannot be attributed to a hydrostatic pressure effect on the vapor pressure of naphthalene, since the pressure effect is explicitly accounted for in the exponential term in equation 1.1. Instead, the large difference in experimental and calculated naphthalene solubility at high pressures is associated with the nonideal behavior of ethylene as it is compressed to liquid-like densities in its critical region. It is the strength of the interactions between solvent and solute molecules that fixes the solubility depending of course on whether the solvent molecules are in close enough proximity to interact. Chapters 3 and 5 delve more deeply into intermolecular interactions and solubility behavior. 

Figure 13.14 Nonideal behavior of strong electrolyte solutions. The van t Hoff factors (i) for various ionic solutes in dilute (0.05 m) aqueous solution show that the observed value dark blue) is always lower than the expected value [light blue). This deviation is due to ionic interactions that, in effect, reduce the number of free ions in solution. The deviation is greatest for multivalent ions.

Colligative properties are related to the number of dissolved solute particles, not their chemical nature. Compared with the pure solvent, a solution of a nonvolatile nonelectrolyte has a lower vapor pressure (Raoult s law), an elevated boiling point, a depressed freezing point, and an osmotic pressure. Colligative properties can be used to determine the solute molar mass. When solute and solvent are volatile, the vapor pressure of each is lowered by the presence of the other. The vapor pressure of the more volatile component is always higher. Electrolyte solutions exhibit nonideal behavior because ionic interactions reduce the effective concentration of the ions. 

In the foregoing sections, the mixtures (solutions) were assumed to behave ideally. This implies that the molecules of solute i interact with the solvent but not with each other. As a consequence, p,(X is determined by the dependence of the molar configuration entropy of i on resulting in Equation 3.30 (see Section 3.5). A mixture behaves ideally only when X, is sufficiently small. At higher mole fractions of i, deviation from ideality occurs due to excluded volume effects and/or interactions between the dissolved components (e.g., ions). Hence, the mole fraction of i, where nonideal behavior sets off, depends on the size and charge of the dissolved component(s). 

Activity ak- ti-vo-te (1530) A quantity which measures the parent or effective concentration (or, for a gas, partial pressure) of a species and which takes into account interparticle interactions which produce nonideal behavior. At low concentrations (or pressures) activity is essentially equal to concentration (or pressure). 

Nonsize-Exclusion Effects. To develop a reliable SEC method, one must not only ensure that enthalpic interactions are zero, but also must take into account or eliminate the following nonsize-exclusion effects that will lead to nonideal SEC behavior ... 

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. 

Section IV combines the thermochemistry from Section II with the shock behavior of Section III to describe detonation (reactive shock waves). This section begins with simple ideal detonation theory and then goes on to quantitative calculations of detonation interactions at interfaces with other materials, and then deals with nonideal effects, those that cannot be predicted by ideal theory, such as the effects of size and geometry. 

The ideal solution assumes equal strength of self- and cross-interactions between components. When this is not the case, the solution deviates from ideal behavior. Deviations are simple to detect upon mixing, nonideal solutions exhibit volume changes (expansion or contraction) and exhibit heat effects that can be measured. Such deviations are quantified via the excess properties. An important new property that we encounter in this chapter is the activity coefficient. It is related to the excess Gibbs free energy and is central to the calculation of the phase diagram. 

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