Slightly soluble solute solubility product constant

One way to establish equilibrium between a slightly soluble solid and its ions in solution is to stir the solid with water to form a saturated solution. As you might expect, the solubility of the solid, s, in moles per liter, is related to the solubility product constant, Ksp. In the case of barium sulfate dissolving in water we have... 

It is important to note that the solubility product relation applies with sufficient accuracy for purposes of quantitative analysis only to saturated solutions of slightly soluble electrolytes and with small additions of other salts. In the presence of moderate concentrations of salts, the ionic concentration, and therefore the ionic strength of the solution, will increase. This will, in general, lower the activity coefficients of both ions, and consequently the ionic concentrations (and therefore the solubility) must increase in order to maintain the solubility product constant. This effect, which is most marked when the added electrolyte does not possess an ion in common with the sparingly soluble salt, is termed the salt effect. 

Knowing the value of the solubility product constant can also allow us to predict whether or not a precipitate will form if we mix two solutions, each containing an ion component of a slightly soluble salt. We calculate the reaction quotient (many times called the ion product), which has the same form as the solubility product constant. We take into consideration the mixing of the volumes of the two solutions, and then compare this reaction quotient to the K.p. If it is greater than the Ksp then precipitation will occur until the ion concentrations reduce to the solubility level. 

The common-ion effect is an application of Le Chatelicr s principle to equilibrium systems of slightly soluble salts. A buffer is a solution that resists a change in pH if we add an acid or base. We can calculate the pH of a buffer using the Henderson-Hasselbalch equation. We use titrations to determine the concentration of an acid or base solution. We can represent solubility equilibria by the solubility product constant expression, Ksp. We can use the concepts associated with weak acids and bases to calculate the pH at any point during a titration. 

Consider the chemical equation for AgCl dissolved in water to make a saturated solution AgCl(s) <—> Ag1+(aq) + Cl1 (aq). At 298 K the solubility product constant is 1.8 x 10-10, which indicates that is a slightly soluble salt. There is a way of making AgCl even less soluble, via the common ion effect. Consider the following, when an ion that is already present is added to the solution, the equilibrium will shift to consume the increase in concentration of the ion. 

As before, the activity of the solid NaCl is a constant and is included in the equilibrium constant. In this case, in contrast with that of the nonelectrolyte, the equilibrium constant may not be equated to the solubility because the right-hand side of the equation contains the product of two concentration terms rather than a single concentration term. This equilibrium constant is called the solubility product constant Kjp. An added complexity arises in the illustration that we have chosen, because a saturated solution of NaCl happens to be quite concentrated. Hence the activity coefficients included in the equation may be quite different from those predicted by the Davies Equation, rendering attempts to describe quantitatively the solubility relationships of NaCl with the use of this equation difficult. The solubility product equilibrium just described is much more useful when applied to systems of slightly soluble electrolytes. 

Therefore, a thermodynamic equilibrium constant known as the solubility product constant K p is used for slightly soluble salts. This solubility product constant is useful for understanding the dissolution characteristics, because its value does not change in either acid or basic solutions under the same conditions of temperature, pressure and ionic strength. 

The solubility product constant, Kjp, is the equilibrium constant of a slightly soluble salt. To evaluate Ksp, consider this example. The solubility of AgCl in water is 1.3 X 10 mol/L at 25°C. The equation for the equilibrium between AgCl and its ions in solution is... 

The solubility product principle is generally valid only for saturated solutions in which the total concentration of ions of the slightly soluble compound is no more than about 0.01 M. Compounds with a less than lO" have extremely low solubility. Examine the table of solubility product constants in Appendix H. Which compound appears to be the most soluble Calculate its molar solubility. Which compound appears to be the least soluble Calculate its molar solubility. 

The solubility product constant, K p, of a slightly soluble ionic compound is expressed in terms of the molar concentrations of ions in the saturated solution. These ion concentrations are in turn related to the molar solubility of the ionic compound, which is the moles of compound that dissolve to give a liter of saturated solution. The next two examples show how to determine the solubility product constant from the solubility of a slightly soluble ionic compound. 

Calculating the solubility of a slightly soluble salt in a solution of a common ion Given the solubility product constant, calculate the molar solubility of a slightly soluble ionic compound in a solution that contains a common ion. (EXAMPLE 18.5)... 

Given the solubility product constant of a slightly soluble compound and the concentration of a solution having a common ion, calculate the solubility of the slightly soluble compound in the solution. 

The solubility product principle can be very useful when applied to solutions of slightly soluble substances. It cannothe applied to solutions of soluble substances. This is because the positive and negative ions attract each other, and this attraction becomes appreciable when the ions are close together. Sometimes it is necessary to consider two equilibria simultaneously. For example, if either ion hydrolyzes, the salt will be more soluble than predicted when only the solubility product constant is used. The solubility product is also sensitive to changes in solution temperature to the extent that the solubiUty of the dissolved substance is affected by such changes. All of these factors limit the conditions under which the solubility product principle can be applied. 

Ions of salts that are slightly soluble form saturated aqueous solutions at low concentrations. The solubility equilibrium expression for such salts yields a constant—the solubility product constant,... 

In Chapter 4, we learned that a precipitation reaction can occur upon the mixing of two solutions containing ionic compounds when one of the possible cross products—the combination of a cation from one solution and the anion from the other—is insoluble. In this chapter, however, we have seen that the terms soluble and insoluble are extremes in a continuous range of solubihty—many compounds are slightly soluble and even those that we categorized as insoluble in Chapter 4 actually have some limited degree of solubihty (they have very small solubility product constants). 

EXAMPLE 18-1 Writing Solubility Product Constant Expressions for Slightly Soluble Solutes... 

PRACTICE EXAMPLE B A handbook lists K p = 1 X 10 for calcium hydrogen phosphate, a substance used in dentifrices and as an animal feed supplement. Write (a) the equation for the solubility equilibrium and (b) the solubility product constant expression for this slightly soluble solute. 

Criteria for Precipitation and Its Completeness—To determine whether a slightly soluble solute will precipitate from a solution, the ion product, Qsp, is compared with the solubility product constant, K p. Q p is based on the initial ion concentrations in a solution. K p, on the other hand, is based on the equilibrium ion concentrations in a saturated solution. If Qgp > K p, precipitation will... 

The solubility of a substance is the concentration of its saturated solution. The solubility product constant, Kgp, is the equilibrium constant that describes the formation of a saturated solution of a slightly soluble ionic compound. It is the product of ionic concentrations, with each term raised to an appropriate power. 

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. 

For ionizing substances that are only slightly soluble, the concentrations of the ions multiply to a constant called the solubility product in a saturated solution. For a hypothetical compound CA, where the single cation is denoted by C and the anion by A, the solubility equation is... 

This relationship varies slightly because of the vertical fluctuation in the phosphorus content in the sea. For saline water systems, data on the solubility product of a calcium phosphate is difficult to obtain inasmuch as — aside from temperature and hydrostatic pressure — the solubility product is dependent on the type and amount of solutes present. The apparent dissociation constants of H3P04 are defined by the equations129,130 ... 

Chantooni and Kolthoff " derived equations which permit the calculation of hydration constants of cations and anions from the solubility products of slightly soluble salts in solutions of acetonitrile with various concentrations of water. The ionic solubility of a salt was determined by measuring the conductance. The water concentration of the acetonitrile solution was always less than 1 M. The total ionic solubility product was expanded in powers of the water concentration. The coefficients are related to the individual ionic hydration constants and were evaluated by... 

The least sophisticated but most convenient technique illustrating polymer fractionation is fractional precipitation, which is dependent on the slight change in the solubility parameter with molecular weight. Thus, when a small amount of miscible nonsolvent is added to a polymer solution at a constant temperature, the product with the highest molecular weight precipitates. This procedure may be repeated after the precipitate is removed. These fractions may also be redissolved and fractionally precipitated. The shape of the distribution curve is then constructed from the fractional amount of each sample after chain length determination. 

As an approximation, the dissolved portion of a slightly soluble salt dissociates completely into ions. In a saturated solution, the ions are in equilibrium with the solid, and the product of the ion concentrations, each raised to the power of its subscript in the compound s formula, has a constant value (Qsp = K p). The value of K p can be obtained from the solubility, and vice versa. Adding a common ion lowers an ionic compound s solubility. Adding HgO" (lowering the pH) increases a compound s solubility if the anion of the compound is that of a weak acid. If Qsp > K p for an ionic compound, a precipitate forms when two solutions, each containing one of the compound s ions, are mixed. Lakes bounded by limestone-rich soils form buffer systems that prevent harmful acidification by acid rain. 

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