Solubility product

A solid also becomes less water soluble (the solubility product decreases) when its crystals are purer, their structure is more ordered, their size increases, and as the crystals contain less water (less hydrated), but these effects are secondary to the solubility product. The solubility product decreases as crystals grow in size and lose waters of hydration and occluded or coprecipitated ions. The slow growth and recrystallization is much more pronounced in the mixture of ions in soil solutions than in the pure aqueous solutions of the chemistry laboratory. The solid-phase reactions are often exceedingly slow in soils compared to the formation rates of new, poorly crystalline material. Hence, soil-formed crystals tend to be small and amorphous and to contain many impurities. 

Solubility products measured in pure systems may not represent soil conditions very well. The impurities in solids affect their aqueous solubility soil minerals are characteristically impure. Nonetheless, predictions of soil solution concentrations usually assume the solubility products of pure minerals apply. The water molecule is ignored in stability constant and solubility product equations. The concentration of water is assumed to be unity because water is present in great excess and does not change significantly during the reaction. This assumption is good in all but the most concentrated aqueous solutions and in dry soils. 

An important type of equilibrium in solution involves a solid salt and its ions when the salt is in contact with its saturated solution. For example, consider the case of 

Here we shall neglect activity coefficient elTects, which will be introduced in equation (7.72). The equilibrium constant can then be written as 

The concentration of AgCI (s) is constant and is incorporated into the constant The constant known as the solubility product, has a characteristic value for each salt. If the solution is less than saturated, the product [Ag ] [CP] will be less than Ks, because equilibrium is not established. However, the product cannot be greater than Kg for any period of time. If solutions containing Ag and Cl ions are mixed, solid AgCl will rapidly precipitate out until the product [Ag ][CI ] has reached the value of Xj. 

In a saturated aqueous solution of AgCl, with no other substance present, the concentrations of Ag and Cl ions will be equal Since their product is X, the individual concentrations are which is therefore the solubility  

the solubility of AgCl in pure water is approximately 1.7 x 10 = 

Source All values are from Martell, A. E. Smith, R. M. Critical Stability Constants, Vol. 4. Plenum Press New York, 1976. I Unless otherwise stated, values 

734 Modern Analytical Chemistry Add Dissociation Constants—continued 

The problem with such determinations is to devise suitable electrodes and cells. One method is to use the sparingly soluble material as part of an electrode, e.g., to determine A Agci oii could employ a silver-silver chloride electrode. K gc then be measured approximately by coupling the electrode with a reference electrode and determining its potential. 

In order for Equation (6.45) to be used it is required to know E% and Ucv, the former must be determined, the latter assumed approximately equal to a  

An alternative method can present serious problems in that it is not always easy to devise a suitable cell. For the determination of. K Agci the following cell could be used 

This cell has also the further disadvantages that chlorine electrodes are difficult to use since chlorine attacks platinum while formation of HCl and HCIO can alter the composition of the solution. The e.m.f. of the cell is given by 

From which A Agci may be found when the standard potential of the silver and chlorine electrode are known. 

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Addition of acid will reduce the concentration of ", whilst in alkaline solution the concentration of will increase. Since, in order for precipitation to occur, the solubility product of the sulphide must be exceeded, i.e. 

Microcrystals of SrS04 of 30 A diameter have a solubility product at 25°C which is 6.4 times that for large crystals. Calculate the surface tension of the SrS04-H20 interface. Equating surface tension and surface energy, calculate the increase in heat of solution of this SrS04 powder in joules per mole. 

Aqueous ammonia can also behave as a weak base giving hydroxide ions in solution. However, addition of aqueous ammonia to a solution of a cation which normally forms an insoluble hydroxide may not always precipitate the latter, because (a) the ammonia may form a complex ammine with the cation and (b) because the concentration of hydroxide ions available in aqueous ammonia may be insufficient to exceed the solubility product of the cation hydroxide. Effects (a) and (b) may operate simultaneously. The hydroxyl ion concentration of aqueous ammonia can be further reduced by the addition of ammonium chloride hence this mixture can be used to precipitate the hydroxides of, for example, aluminium and chrom-ium(III) but not nickel(II) or cobalt(II). 

These are practically insoluble in water, are not hydrolysed and so may be prepared by addition of a sufficient concentration of sulphide ion to exceed the solubility product of the particular sulphide. Some sulphides, for example those of lead(II), copper(II) and silver(I), have low solubility products and are precipitated by the small concentration of sulphide ions produced by passing hydrogen sulphide through an acid solution of the metal salts others for example those of zincfll), iron(II), nickel(II) and cobalt(II) are only precipitated when sulphide ions are available in reasonable concentrations, as they are when hydrogen sulphide is passed into an alkaline solution. 

The sodium salt of methyl red may be prepared by dissolving the crude product in an equal weight of 35 per cent, sodium hydroxide which has been diluted to 350 ml., hitoring, and evaporating under diminished pressure (Fig. II, 37, I). The resulting sodium salt forms orange leaflets. This water-soluble product is very convenient for use as an indicator. Incidentally, the toluene extraction is avoided. 

Then N-Boc-O-benzylserine is coupled to the free amino group with DCC. This concludes one cycle (N° -deprotection, neutralization, coupling) in solid-phase synthesis. All three steps can be driven to very high total yields (< 99.5%) since excesses of Boc-amino acids and DCC (about fourfold) in CHjClj can be used and since side-reactions which lead to soluble products do not lower the yield of condensation product. One side-reaction in DCC-promoted condensations leads to N-acylated ureas. These products will remain in solution and not reaa with the polymer-bound amine. At the end of the reaction time, the polymer is filtered off and washed. The times consumed for 99% completion of condensation vary from 5 min for small amino acids to several hours for a bulky amino acid, e.g. Boc-Ile, with other bulky amino acids on a resin. A new cycle can begin without any workup problems (R.B. Merrifield, 1969 B.W. Erickson, 1976 M. Bodanszky, 1976). 

ELECTROLYTES, EME, AND CHEMICAL EQUILIBRIUM TABLE 8.6 Solubility Product Constants Continued)... 

The equilibrium constant for this reaction is called the solubility product, Kjp, and is given as... 

Substituting the equilibrium concentrations into the solubility product expression (equation 6.33)... 

The most important types of reactions are precipitation reactions, acid-base reactions, metal-ligand complexation reactions, and redox reactions. In a precipitation reaction two or more soluble species combine to produce an insoluble product called a precipitate. The equilibrium properties of a precipitation reaction are described by a solubility product. 

Green, D. B. Rechtsteiner, G. Honodel, A. Determination of the Thermodynamic Solubility Product, Xsp, of Pbl2 Assuming Nonideal Behavior, /. Chem. Educ. 1996, 73, 789-792. 

The thermodynamic solubility product for Pbl2 is determined in this experiment by measuring its solubility at several ionic strengths. 

Solubility can often be decreased by using a nonaqueous solvent. A precipitate s solubility is generally greater in aqueous solutions because of the ability of water molecules to stabilize ions through solvation. The poorer solvating ability of nonaqueous solvents, even those that are polar, leads to a smaller solubility product. For example, PbS04 has a Ks of 1.6 X 10 in H2O, whereas in a 50 50 mixture of H20/ethanol the Ks at 2.6 X 10 is four orders of magnitude smaller. 

At the equivalence point, we know that the concentrations of Agi" and CL are equal. Using the solubility product expression... 

Before the equivalence point, the concentration of Cr04 is controlled by the solubility product of PbCr04. After the equivalence point, the concentration of Cr04 is determined by the amount of excess titrant added. Considering the reactions controlling the concentration of Cr04 , sketch the expected titration curve of pH versus volume of titrant. 

Potentiometric electrodes are divided into two classes metallic electrodes and membrane electrodes. The smaller of these classes are the metallic electrodes. Electrodes of the first kind respond to the concentration of their cation in solution thus the potential of an Ag wire is determined by the concentration of Ag+ in solution. When another species is present in solution and in equilibrium with the metal ion, then the electrode s potential will respond to the concentration of that ion. Eor example, an Ag wire in contact with a solution of Ck will respond to the concentration of Ck since the relative concentrations of Ag+ and Ck are fixed by the solubility product for AgCl. Such electrodes are called electrodes of the second kind. 

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