Additional Equilibrium Concepts

In this chapter, we will extend the concepts of equilibrium that have been discussed in previous chapters. In Chapter 10 we discussed the concept of equilibrium in relation to saturated solutions in which an equilibrium was established between solvated ions and undissolved solute. In Chapter 11 we discussed the solubility of different salts when we looked at the formation of precipitates. In this chapter you will see the connection between these two ideas with the introduction of the solubility product constant, Ksp, which is a quantitative means of describing solubility equilibria. This measure helps to predict and explain the precipitation of different salts from solution. You will also see how the common-ion effect, temperature, and pH affect solubility. 

So far, you have learned about a number of different equilibrium constants, including Kp, Kc, Ka, Kb, and Kw. In this section, you will learn about another equilibrium constant, Ksp. If you recall from Chapter 10, when a soluble solute is placed into a solvent it will dissolve until the solution becomes saturated. At the point of saturation, an amount of solid solute exists in equilibrium with the surrounding solution. One thing you will learn in this chapter is that even when a substance is considered insoluble, a small amount of the substance will still dissolve. One of the insoluble substances you learned about in Chapter 10 was the bright yellow precipitate lead (II) iodide, Pbl2. If we assume for a moment that it is soluble in very small amounts (which it is), we can consider the equilibrium shown below  

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Schlenk equilibrium concept sot forth above, the magnesium halide component of tertiary alkyl Grignard reagents causes halohydria formation faster than the diaJkylmagnesium component can add. Spocial conditions have, howover. been found, which permit addition of (erf-butylmagnesium chloride to ethylene oxide (Eq. 818), giving a modest yield of the desired primary alcohol.1484 1101... 

Unfortunately, it seems to be difficult to teach this topic. Finley, Stewart and Yarroch [2] studied the level of difficulty of various themes in chemistry and reported the results of 100 randomly chosen teachers of chemistry from Wisconsin who chose chemical equilibrium as being clearly the most difficult theme overall. Berquist and Heikkinen [1] noted in addition Equilibrium, considered one of the more difficult chemical concepts to teach, involves a high level of students misunderstanding . One can therefore expect a large variety of misconceptions because of the difficulties in teaching this subject as well as for understanding it. 

If the reaction system considered is fast, the process can be satisfactorily described assuming reaction equilibrium. Here, a proper modeling approach is based on the nonreactive equilibrium-stage model, extended by the chemical equilibrium relationship. An alternative approach proposed by Davies and Jeffreys [13] includes two separate steps. First, the concentrations and flow rates of the leaving streams are calculated with the simple nonreactive equilibrium-stage model. Afterwards, the leaving concentrations are adapted by using an additional equilibrium reactor concept. However, the latter approach does not consider direct interactions between the chemical and thermodynamic equilibrium. 

In addition, the concept of the turning point (domain), which defines the transition between these two regimes, has to be introduced. Typically, the fast period is determined by the fast step(s), but strictly speaking the position of the turning point in time is determined by the fast parameters. The slow period is the obvious period of rate limitation. However, as a rule this limitation is accompanied by other phenomena such as quasi-equilibrium or QSS. 

The introduction of an additional parameter can be expected to give better agreement with experimental results. However, we have been concerned in this section with equilibrium concepts. Hence comparison needs to be made with experimental data obtained under as close to equilibrium conditions as possible. 

In the early 19th century (1803), Dalton proposed his atomic theory. In 1811, Amedeo Avogadro made clear the distinction between atoms and molecules of elementary substances, hi addition, the concepts of heat, energy, work, and temperature were developed. The first law of thermodynamics was set forth by Julius Robert von Mayer and the second law of thermodynamics was postulated by Rudolf Julius Emanuel Clausius and William Thomson (Lord Kelvin). Later in the century, Clausius, Ludwig Boltzmarm, and James Clerk Maxwell related the ideal gas law in terms of a kinetic theory of matter. This led to the kinetics of reactions and the laws of chemical equilibrium. 

There are two additional concepts which we can invoke to simplify Eq. (8.118) electroneutrality and a less familiar principle called Donnan equilibrium. Some relationships pertaining to these are developed below ... 

Impure metals and alloys exhibit all the structural features and crystal defects of the pure meteils already discussed. In addition, however, impure metals and alloys exhibit many structures which are not observed in pure metals, and which, in many instances, have an extremely important effect on the properties, particularly the corrosion resistance. However, before dealing with the structure of impure metals and alloys, it is necessary to consider the concept of metallurgical components, phases, constituents and equilibrium phase diagrams. 

The great importance of the solubility product concept lies in its bearing upon precipitation from solution, which is, of course, one of the important operations of quantitative analysis. The solubility product is the ultimate value which is attained by the ionic concentration product when equilibrium has been established between the solid phase of a difficultly soluble salt and the solution. If the experimental conditions are such that the ionic concentration product is different from the solubility product, then the system will attempt to adjust itself in such a manner that the ionic and solubility products are equal in value. Thus if, for a given electrolyte, the product of the concentrations of the ions in solution is arbitrarily made to exceed the solubility product, as for example by the addition of a salt with a common ion, the adjustment of the system to equilibrium results in precipitation of the solid salt, provided supersaturation conditions are excluded. If the ionic concentration product is less than the solubility product or can arbitrarily be made so, as (for example) by complex salt formation or by the formation of weak electrolytes, then a further quantity of solute can pass into solution until the solubility product is attained, or, if this is not possible, until all the solute has dissolved. 

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