Production Principles

An important application of the solubility product principle is to the calculation of the solubility of sparingly soluble salts in solutions of salts with a common... 

Factor 1, which is concerned with the completeness of precipitation, has already been dealt with in connection with the solubility-product principle, and the influence upon the solubility of the precipitate of (i) a salt with a common ion, (ii) salts with no common ion, (iii) acids and bases, and (iv) temperature (Sections 2.6-2.11). 

The silver ions involved are derived from the silver chloride, and by the solubility product principle (Section 2.6), the activity of these ions will be governed by the chloride-ion activity... 

The solubility product principle states that the solubility product expression for a slightly soluble compound is the product of the concentrations of its constituent ions, each raised to the power that corresponds to the number of ions in one formula unit of the compound. The quantity, K, is constant at constant temperature for a saturated solution of the compound, when the system is at equilibrium. The significance of the solubility product is that it can be used to calculate the concentrations of the ions in solutions for such slightly soluble compounds. 

Horwitz, E. P., Extraction chromatography of actinides and selected fission products Principles and achievement of selectivity, in International Workshop on Application of Extraction Chromatography in Radionuclide Measurement (IRMM), Geel, Belgium, 1998, 27-37. 

The method consists in first converting the sulphate into the carbonate by boiling it with a concentrated solution of sodium carbonate, and then dissolving the carbonate in hydrochloric acid, thereby yielding a solution of the chloride. The conversion of solid strontium sulphate into solid strontium carbonate furnishes an interesting illustration of the solubility product principle, for the solubility of these two salts in pure water is as follows ... 

On the basis of this general discussion, we can now consider some direct applications of the solubility product principle to quantitative inorganic analysis. 

Precipitation and dissolution of metal hydroxides The solubility product principle can also be applied to the formation of metal hydroxide precipitates these are also made use of in qualitative inorganic analysis. Precipitates will be formed only if the concentrations of the metal and hydroxyl ions are momentarily higher than those permitted by the solubility product. As the metal-ion concentration in actual samples does not vary much (10—1 —10 3 mol -1 is the usual range), it is the hydroxyl-ion concentration which has the decisive role in the formation of such precipitates. Because of the fact that in aqueous solutions the product of hydrogen- and hydroxyl-ion concentrations is strictly constant (A = 10 14 at 25°C, cf. Section 1.18), the formation of a metal-hydroxide precipitate depends mainly on the pH of the solution. Using the solubility product principle, it is possible to calculate the (minimum) pH required for the precipitation of a metal hydroxide. 

Solubility of sparingly soluble salts of weak acids in strong mineral acids The solubility product principle enables us to give a simple explanation of this phenomenon, which is of relatively frequent occurrence in quantitative analysis. Typical examples are the solubilities of calcium oxalate or barium carbonate in hydrochloric acid. When dilute hydrochloric acid is added to a suspension of calcium oxalate, the following equilibria will occur simultaneously ... 

Fractional precipitation The calculation as to which of two sparingly soluble salts will be precipitated under given experimental conditions may be also made with the aid of the solubility product principle. An example of great practical importance is the Mohr method for the estimation of halides. In this process a solution of chloride ions is titrated with a standard solution of silver nitrate, a small quantity of potassium chromate being added to serve as an indicator. Here two sparingly soluble salts may be formed, viz. silver chloride (a white precipitate) and silver chromate (which is red) ... 

Example 3.19 Minimum energy dissipation in heat conduction Use the minimum entropy production principle to derive the relation for nonstationary heat conduction in an isotropic solid rod. 

Distributing the entropy production as evenly as possible along space and time would allow for the design and operation of an economic separation process. Dissipation equations show that both the driving forces and flows play the same role in quantifying the rate of entropy production. Therefore, the equipartition of entropy production principle may point out that the uniform distribution of driving forces is identical to the uniform distribution of flows. 

The above equation shows that the steady state is less dissipative for a specified duty in a finite time. This conclusion is in line with the minimum entropy production principle of Prigogine. 

Solubility Equilibria The Solubility Product Principle.—It was seen on page 133 that the chemical potential of a solid is constant at a definite temperature and pressure consequently, when a solution is saturated with a given salt Mv A, the chemical potential of the latter in the solution must also be constant, since the chemical potential of any substance present in two phases at equilibrium must be the same in each phase. It is immaterial whether this conclusion is applied to the undissociated molecules of the salt or to the ions, for the chemical potential is given by... 

The significance of the solubility product principle is that when a solution is saturated with a given salt the product of the activities, or approximately the concentrations, of its constituent ions must be constant, irrespective of the nature of the other electrolytes present in the solution. If the latter contains an excess of one or other of the ions of the saturating salt, this must be taken into consideration in the activity product. Consider, for example, a solution saturated with silver chloride then according to the solubility product principle. 

Suppose the addition of x moles per liter of a completely dissociated salt containing a common ion, e.g., the anion, reduces the solubility of the sparingly soluble salt from So to S for simplicity all the ions present may be assumed to be univalent. The concentrations of cations in the solution, resulting from the complete dissociation of the sparingly soluble salt, is S, while that of the anions is S + x it follows, therefore, by the approximate solubility product principle that... 

Activity Coefficients from Solubility Measurements.—The activity coefficient of a sparingly soluble salt can be determined in the presence of other electrolytes by making use of the solubility product principle. In addition to the equations already given, this principle may be stated in still another form by introducing the definition of the mean ionic concentration, i.e., c , which is equal to c+clr, into equation (109) this equation then becomes... 

Whenever the problem arises of finding the solubility of a salt in a solution in which there are already present either anions or cations of the salt itself, the solubility-product principle can be used. You must remember that the solubility-product principle applies only to saturated solutions of the salt. The product of the ion concentrations can of course have any value less than for an unsaturated solution. 

Solution. We can calculate the concentration of aluminum ion in the solution after treatment with aluminum sulfate without writing the equation for the hydrolysis reaction. It is required by the solubility-product principle that the product of ion concentrations for the precipitated substance Al(OH)3 be equal to the solubility product. The expression in this case is... 

Making use of the solubility-product principle, explain why a metal hydroxide such us ferric hydroxide, Fe(OH)., is much more soluble in an acidic solution than it is in a basic solution. 

The Fluctuation Relation has been used by Dewar to assist in establishing a basis maximum entropy production principle. The difficulties with this outside the linear response regime have recently been discussed by Bruers. ... 

CHAPTER 20 Ionic Equilibria III The Solubility Product Principle... 

Another application of the solubility product principle is the calculation of the maximum concentrations of ions that can coexist in solution. From these calculations we can determine whether a precipitate will form in a given solution. We compare Qgp (Section 17-4) with i p. 

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