Solubility product rule

In this chapter we discuss some of the properties of electrolyte solutions. In Sec. 12-1, the chemical potential and activity coefficient of an electrolyte are expressed in terms of the chemical potentials and activity coefficients of its constituent ions. In addition, the zeroth-order approximation to the form of the chemical potential is discussed and the solubility product rule is derived. In Sec. 12-2, deviations from ideality in strong-electrolyte solutions are discussed and the results of the Debye-Hiickel theory are presented. In Sec. 12-3, the thermodynamic treatment of weak-electrolyte solutions is given and use of strong-electrolyte and nonelectrolyte conventions is discussed. 

As a new rule of thumb [473], in 0.15 M NaCl (or KC1) solutions titrated with NaOH (or KOH), acids start to precipitate as salts above log (S/So) 4 and bases above log (S/.S o) 3. It is exactly analogous to the cliff 3-4 rule let us call the solubility equivalent the sdijf3-4 rule [473], Consider the case of the monopro-tic acid HA, which forms the sodium salt (in saline solutions) when the solubility product Ksp is exceeded. In additions to Eqs. (3.1) and (6.1), one needs to add the following reaction/equation to treat the case ... 

In propagating errors it is generally advisable to keep one or two extra digits in intermediate results, and round off only when you get to the final result. Applying this rule to the solubility product measurement, the mass of dissolved silver chloride is 0.888 0.0142 mg, and the formula weight of silver chloride is 143.3279 0.00042 g- mol"1. 

Treatment of an epoxide, namely methyl 2,3-anhydro-4,6-0-benzylidene-oi-D-allopyranoside (78, Scheme 21), with nitryl iodide using methanol as the solvent has been reported.123 Rather than the expected nitration, opening of the epoxide occurred to afford 30% of methyl 4,6-0-benzylidene-3-0-methyl-oi-D-glucopyranoside (79), 10% of methyl 4,6-0-benzylidene-2-0-methyl-a-D-altropyranoside (80), and a water-soluble material. The water-soluble material was later determined to be a mixture of the 2-0- (81) and 3-0-methyl (82) products, with the benzylidene acetal removed, a result consistent with a later study.124 Performing the reaction in the absence of the silver salt resulted solely in formation of the water-soluble product. The preponderance of the diequatorial product 81 is in violation of the Flirst-Plattner rule, which predicts more of the diaxial product. The authors explanation for the anti-Fiirst-Plattner addition is as follows. 

Precipitation of sulphides Hydrogen sulphide gas is a frequently used reagent in qualitative inorganic analysis. When hydrogen sulphide gas is passed into a solution, metal sulphides are precipitated. For this precipitation the rule mentioned above can be applied precipitation may take place only if the product of concentrations of metal ions and sulphide ions (taken at proper powers) exceed the value of the solubility product. While the concentration of metal ions usually does fall into the range of 1-10 3 mol 1, the concentration of sulphide ion may vary considerably, and can easily be selected by the adjustment of the pH of the solution to a suitable value. 

Iron of inorganic dissolved compounds (bicarbonates, sulfates, chlorides, fluosilicates, etc.) may enter into the dissolved form of iron of inorganic origin (Fcj"" ), but their existence is governed by an acid environment with a pH not higher than 3. As a rule the pH in sea water is close to 8 ( 0.5). Under these conditions iron compounds are easily hydrolyzed and converted into hydroxides, which form colloidal solutions in sea water. In appropriate conditions colloidal hydroxide condenses to clots of gel and converts to the suspended state. Therefore there are practically no ionic forms of iron (Fe "" proper). As early as 1937 Cooper (1937) concluded, on the basis of the solubility product and activity of ferrous and ferric iron ions and FeOH ions, that until equilibrium is reached sea water may contain about 10 jiig/1 of iron ions in true solution at pH = 8.5 the amount of ionic Fe in ferric form is still less—10 which corresponds to the extremely... 

Various theories have been advanced in explanation. Ostwald suggested that supersaturation took place, followed by precipitation, which cleared the immediate neighbourhood of the reactants, and it was therefore necessary for the silver nitrate to diffuse further before supersaturation was again reached. Hatsehek, however, shows that the periodic precipitation takes place in conditions which render supersaturation impossible. Williams and Mackenzie maintain that the silver chromate is precipitated according to the usual rules of the solubility product, and does not behave in any way as a protected colloid but as a crystalloid. More recent w ork suggests that whenever precipitation takes place, the precipitate first passes through the colloidal... 

It should finally be remarked that dissociation constants generally depend, and often strongly depend, on temperature. The dissociation may either increase or decrease with temperature, and there are no general rules. The same holds for solubility products. 

From a knowledge of the solubility rules (see Section 4.2) and the solubility products listed in Table 16.2, we can predict whether a precipitate will form when we mix two solutions or add a soluble compound to a solution. This ability often has practical value. In industrial and laboratory preparations, we can adjust the concentrations of ions until the ion product exceeds K p in order to obtain a given compound (in the form of a precipitate). The ability to predict precipitation reactions is also useful in medicine. For example, kidney stones, which can be extremely painful, consist largely of calcium oxalate, CaC204 (K p = 2.3 X 10 ). The normal physiological concentration of calcium ions in blood plasma is about 5 mM (1 mM = 1 X 10 M). Oxalate ions ( 204 ), derived from oxalic acid present in many vegetables such as rhubarb and spinach, react with the calcium ions to form insoluble calcium oxalate, which can gradually build up in the kidneys. Proper adjustment of a patient s diet can help to reduce precipitate formation. Example 16.10 illustrates the steps involved in precipitation reactions. 

Therefore, the considerable advantages of the method with the use of two indicator electrodes can only be gained in some specific cases. Moreover, most oxides possess low-enough solubilities in halide melts and errors of the solubility product estimations are, as a rule, small enough. All the regularities which will be discussed in Part 7 were obtained using the simple method of solubility determination. 

As the name implies, a conditional solubility product is one whose value depends on solution conditions other than the presence of a common ion. Conditional solubility products are useful when determining the solubility of precipitates whose ions interact with solution constituents through reactions such as complexation or hydrolysis. This type of behavior is indeed the rule rather than the exception for the systems encountered in natural waters and treatment processes. Also, in many analytical measurements the total concentration of species is determined rather than the free ion concentration. 

The equilibrium-constant expression for the equilibrium between a solid and an aqueous solution of its component ions is written according to the rules that apply to any other equilibrium-constant expression. Remember, however, that solids do not appear in the equilibrium-constant expressions for heterogeneous equilibrium, j- (Section 15.4) Thus, the solubility-product expression for BaS04, which is based on Equation 17.15, is... 

From this equation we can develop rules of fractional precipitation, analogous to the rules of precipitation developed at the beginning of this chapter. Let us call the ratio of the concentrations of the two ions the ion ratio, (in analogy to the term in product used earlier). If the ion ratio is equal to the solubility product ratio, then simultaneous precipitation will occur. If the ion ration is greater than the solubility product ratio, then precipitation of the salt whose ion concentration is in the numerator will occur first. Conversely, if the ion ratio is smaller than the solubility product ratio, the salt whose ion concentration is in the denominator will precipitate first. 

Since the concentration of the non-dissociated oxide in the saturated solution, as a rule, is hardly determined, for practical purposes the solubility product, the magnitudes of PMeO (used below pP -logP),... 

As with any other equilibrium, the extent to which this dissolution reaction occurs is expressed by the magnitude of the equilibrium constant. Because this equilibrium equation describes the dissolution of a solid, the equilibrium constant indicates how soluble the solid is in water and is referred to as the solubility-product constant (or simply the solubility product). It is denoted K p, where sp stands for solubility product The equilibrium-constant expression for the equilibrium between a solid and an aqueous solution of its component ions (Ksp) is written according to the rules that apply to any other equilibrium-constant expression. Remember, however, that soUds do not appear in the equihbrium-constant expressions for heterogeneous equihbrium. ooo (Section 15.4) Thus, the solubihty-product expression for BaS04, which is based on Equation 17.15, is... 

Very careful control of pH can give selective precipitation although in practice this is very difficult. It is feasible to precipitate preferentially one metal over another. The best precipitant for this is hydroxide which is very sensitive to pH. The rule of thumb is that salts with the lowest solubility products will precipitate at the lowest pH with other salts being precipitated as the pH rises. Therefore it should be possible partially to separate chromium from manganese by precipitation with hydroxide. However, such careful control of pH may be impossible to carry out in a waste stream, and the chemistry is highly sensitive to other species in solution. 

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