Liquid and Solid Mixtures of Nonelectrolytes

AYhen we substitute the expression of Eq. 9.3.25 for F) inEq. 9.3.18, we obtain a relation between the fugacity coefficient of constituent i and the function B,-  

The third column of Table 9.1 gives formulas for various partial molar quantities of constituent i in terms of B - and its temperature derivative. The formulas are the same as the approximate formulas in the third column of Table 7.5 for molar quantities of a pure gas, with B replacing the second virial coefficient B. 

Homogeneous liquid and sohd mixtures are condensed phases of variable composition. Most of the discussion of condensed-phase nuxtures in this section focuses on liquids. The same principles, however, apply to homogeneous solid mixtures, often called solid solutions. These solid mixtures include most metal alloys, many gemstones, and doped semiconductors. 

The relations derived in this section apply to mixtures of nonelectrolytes—substances that do not dissociate into charged species. Solutions of electrolytes behave quite differently in many ways, and will be discussed in the next chapter. 

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Equation 12.5.20 shows that the slope of the freezing-point curve, 7f versus xa, is zero when Xa/(1 -xa) is equal toa/b,orxA = a/ a+b)-, that is, when the liquid and solid have the same composition. Because (9/tA/9xA)r,p is positive, and Aso H at this composition is also positive, we see from the equation that the slope decreases as xa increases. Thus, the freezing-point curve has a maximum at the mixture composition that is the same as the composition of the solid compound. This conclusion applies when both components of the liquid mixture are nonelectrolytes, and also when one component is an electrolyte that dissociates into ions. 

We now leave pure materials and the limited but important changes they can undergo and examine mixtures. We shall consider only homogeneous mixtures, or solutions, in which the composition is uniform however small the sample. The component in smaller abundance is called the solute and that in larger abimdance is the solvent. These terms, however, are normally but not invariably reserved for solids dissolved in Kquids one liquid mixed with another is normally called simply a mixture of the two liquids. In this chapter we consider mainly nonelectrolyte solutions, where the solute is not present as ions. Examples are sucrose dissolved in water, sulfur dissolved in carbon disulfide, and a mixture of ethanol and water. Although we also consider some of the special problems of electrolyte solutions, in which the solute consists of ions that interact strongly with one another, we defer a full study until Chapter 5. The measures of concentration commonly encoimtered in physical chemistry are reviewed in Further information 3.2. 

In this volume, we will apply the principles developed in Principles and Applications to the description of topics of interest to chemists, such as effects of surfaces and gravitational and centrifugal fields phase equilibria of pure substances (first order and continuous transitions) (vapor + liquid), (liquid 4-liquid), (solid + liquid), and (fluid -f fluid) phase equilibria of mixtures chemical equilibria and properties of both nonelectrolyte and electrolyte mixtures. But do not expect a detailed survey of these topics. This, of course, would require a volume of immense breadth and depth. Instead, representative examples are presented to develop general principles that can then be applied to a wide variety of systems. 

In Chapter 4, we dealt with the thermodynamic, physical and chemical properties of pure liquids. However, in most instances solutions of liquids are used in chemistry and biology instead of pure liquids. In Chapter 5, we will examine the surfaces of mainly nonelectrolyte (ion-free) liquid solutions where a solid, liquid or gas solute is dissolved in a liquid solvent. A solution is a one-phase homogeneous mixture with more than one component. For a two-component solution, which is the subject of many practical applications, the major component of the solution is called the solvent and the dissolved minor component is called the solute. Liquid solutions are important in the chemical industry because every chemical reaction involves at least one reactant and one product, mostly forming a single phase, a solution. In addition, the understanding of liquid solutions is useful in separation and purification of substances. 

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