15.1 Precipitation and Dissolution

Solubility equilibria are established when the dissolution and precipitation of a solute species occur at equal rates. These equilibria underlie many natural and technological processes, ranging from tooth decay to water purification. An understanding of the factors affecting compound solubility is, therefore, essential to the effective management of these processes. This section applies previously introduced equilibrium concepts and tools to systems involving dissolution and precipitation.

The Solubility Product

Recall from the chapter on solutions that the solubility of a substance can vary from essentially zero (insoluble or sparingly soluble) to infinity (miscible). A solute with finite solubility can yield a saturated solution when it is added to a solvent in an amount exceeding its solubility, resulting in a heterogeneous mixture of the saturated solution and the excess, undissolved solute. For example, a saturated solution of silver chloride is one in which the equilibrium shown below has been established.

AgCl (s) precipitation ⇌ dissolution Ag^{+} (a q) + Cl^{-} (a q)

In this solution, an excess of solid AgCl dissolves and dissociates to produce aqueous Ag⁺ and Cl– ions at the same rate that these aqueous ions combine and precipitate to form solid AgCl (Figure 15.2). Because silver chloride is a sparingly soluble salt, the equilibrium concentration of its dissolved ions in the solution is relatively low.

Two beakers are shown with a bidirectional arrow between them. Both beakers are just over half filled with a clear, colorless liquid. The beaker on the left shows a cubic structure composed of alternating green and slightly larger grey spheres. Evenly distributed in the region outside, 11 space filling models are shown. These are each composed of a central red sphere with two smaller white spheres attached in a bent arrangement. In the beaker on the right, the green and grey spheres are no longer connected in a cubic structure. Nine green spheres, 10 grey spheres, and 11 red and white molecules are evenly mixed and distributed throughout the liquid in the beaker. — Figure 15.2Silver chloride is a sparingly soluble ionic solid. When it is added to water, it dissolves slightly and produces a mixture consisting of a very dilute solution of Ag⁺ and Cl– ions in equilibrium with undissolved silver chloride.

The equilibrium constant for solubility equilibria such as this one is called the solubility product constant, K $_{s p}$ , in this case

AgCl (s) ⇌ Ag^{+} (a q) + Cl^{-} (a q) K_{sp} = [Ag^{+} (a q)] [Cl^{-} (a q)]

Recall that only gases and solutes are represented in equilibrium constant expressions, so the K $_{s p}$ does not include a term for the undissolved AgCl. A listing of solubility product constants for several sparingly soluble compounds is provided in Appendix J.

Example 15.1Writing Equations and Solubility Products

Write the dissolution equation and the solubility product expression for each of the following slightly soluble ionic compounds:

(a) AgI, silver iodide, a solid with antiseptic properties

(b) CaCO₃, calcium carbonate, the active ingredient in many over-the-counter chewable antacids

(d) Mg(NH₄)PO₄, magnesium ammonium phosphate, an essentially insoluble substance used in tests for magnesium

(e) Ca₅(PO₄)₃OH, the mineral apatite, a source of phosphate for fertilizers

Solution

$(a) AgI (s) ⇌ Ag^{+} (a q) + I^{-} (a q) (b) CaCO_{3} (s) ⇌ Ca^{2+} (a q) + CO_{3}^{2-} (a q) (c) Mg (OH)_{2} (s) ⇌ Mg^{2+} (a q) + 2OH^{-} (a q) (d) Mg (NH_{4}) PO_{4} (s) ⇌ Mg^{2+} (a q) + NH_{4}^{+} (a q) + PO_{4}^{3-} (a q) (e) Ca_{5} (PO_{4}) 3 OH (s) ⇌ 5Ca^{2+} (a q) + 3PO_{4}^{3-} (a q) + OH^{-} (a q) K_{sp} K_{sp} K_{sp} K_{sp} K_{sp} = = = = = [Ag^{+}] [I^{-}] [Ca^{2+}] [CO_{3}^{2-}] [Mg^{2+}] [OH^{-}]^{2} [Mg^{2+}] [NH_{4}^{+}] [PO_{4}^{3-}] [Ca^{2+}]^{5} [P O_{4}^{3-}]^{3} [OH^{-}]$

K $_{s p}$ and Solubility

The K $_{s p}$ of a slightly soluble ionic compound may be simply related to its measured solubility provided the dissolution process involves only dissociation and solvation, for example:

M_{p} X_{q} (s) ⇌ p M^{m+} (a q) + q X^{n-} (a q)

For cases such as these, one may derive K $_{s p}$ values from provided solubilities, or vice-versa. Calculations of this sort are most conveniently performed using a compound’s molar solubility, measured as moles of dissolved solute per liter of saturated solution.

Example 15.5Determination of K $_{s p}$ from Gram Solubility

Many of the pigments used by artists in oil-based paints (Figure 15.3) are sparingly soluble in water. For example, the solubility of the artist’s pigment chrome yellow, PbCrO₄, is 4.6 $\times$ 10–6 g/L. Determine the solubility product for PbCrO₄.

Figure 15.3Oil paints contain pigments that are very slightly soluble in water. In addition to chrome yellow (PbCrO₄), examples include Prussian blue (Fe₇(CN)₁₈), the reddish-orange color vermilion (HgS), and green color veridian (Cr₂O₃). (credit: Sonny Abesamis)

Solution

Before calculating the solubility product, the provided solubility must be converted to molarity:

[PbCrO_{4}] = \frac{4.6 \times 10 ^{- 6} g PbCrO _{4}}{1 L} \times \frac{1 mol PbCrO _{4}}{323.2 g PbCrO _{4}} = \frac{1.4 \times 10 ^{- 8} mol PbCrO _{4}}{1 L} = 1.4 \times 10^{- 8} M

Using Barium Sulfate for Medical Imaging

Various types of medical imaging techniques are used to aid diagnoses of illnesses in a noninvasive manner. One such technique utilizes the ingestion of a barium compound before taking an X-ray image. A suspension of barium sulfate, a chalky powder, is ingested by the patient. Since the K $_{s p}$ of barium sulfate is 10.08 $\times$ 10–10, very little of it dissolves as it coats the lining of the patient’s intestinal tract. Barium-coated areas of the digestive tract then appear on an X-ray as white, allowing for greater visual detail than a traditional X-ray (Figure 15.4).

Figure 15.4A suspension of barium sulfate coats the intestinal tract, permitting greater visual detail than a traditional X-ray. (credit modification of work by “glitzy queen00”/Wikimedia Commons)

Medical imaging using barium sulfate can be used to diagnose acid reflux disease, Crohn’s disease, and ulcers in addition to other conditions.

Visit this website for more information on how barium is used in medical diagnoses and which conditions it is used to diagnose.

Predicting Precipitation

The equation that describes the equilibrium between solid calcium carbonate and its solvated ions is:

CaCO_{3} (s) ⇌ Ca^{2+} (a q) + CO_{3}^{2-} (a q) K_{s p} = [Ca^{2 +}] [CO_{3}^{2 -}] = 8.7 \times 10^{- 9}

It is important to realize that this equilibrium is established in any aqueous solution containing Ca²⁺ and CO₃2– ions, not just in a solution formed by saturating water with calcium carbonate. Consider, for example, mixing aqueous solutions of the soluble compounds sodium carbonate and calcium nitrate. If the concentrations of calcium and carbonate ions in the mixture do not yield a reaction quotient, Q $_{s p}$ , that exceeds the solubility product, K $_{s p}$ , then no precipitation will occur. If the ion concentrations yield a reaction quotient greater than the solubility product, then precipitation will occur, lowering those concentrations until equilibrium is established (Q $_{s p}$ = ). The comparison of to to predict precipitation is an example of the general approach to predicting the direction of a reaction first introduced in the chapter on equilibrium. For the specific case of solubility equilibria:

Q $_{s p}$ < K $_{s p}$ : the reaction proceeds in the forward direction (solution is not saturated; no precipitation observed)

Q $_{s p}$ > K $_{s p}$ : the reaction proceeds in the reverse direction (solution is supersaturated; precipitation will occur)

This predictive strategy and related calculations are demonstrated in the next few example exercises.

In solutions containing two or more ions that may form insoluble compounds with the same counter ion, an experimental strategy called selective precipitation may be used to remove individual ions from solution. By increasing the counter ion concentration in a controlled manner, ions in solution may be precipitated individually, assuming their compound solubilities are adequately different. In solutions with equal concentrations of target ions, the ion forming the least soluble compound will precipitate first (at the lowest concentration of counter ion), with the other ions subsequently precipitating as their compound’s solubilities are reached. As an illustration of this technique, the next example exercise describes separation of a two halide ions via precipitation of one as a silver salt.

The Role of Precipitation in Wastewater Treatment

Solubility equilibria are useful tools in the treatment of wastewater carried out in facilities that may treat the municipal water in your city or town (Figure 15.6). Specifically, selective precipitation is used to remove contaminants from wastewater before it is released back into natural bodies of water. For example, phosphate ions $(PO_{4}^{3-})$ are often present in the water discharged from manufacturing facilities. An abundance of phosphate causes excess algae to grow, which impacts the amount of oxygen available for marine life as well as making water unsuitable for human consumption.

Figure 15.6Wastewater treatment facilities, such as this one, remove contaminants from wastewater before the water is released back into the natural environment. (credit: “eutrophication&hypoxia”/Wikimedia Commons)

One common way to remove phosphates from water is by the addition of calcium hydroxide, or lime, Ca(OH)₂. As the water is made more basic, the calcium ions react with phosphate ions to produce hydroxylapatite, Ca₅(PO4)₃OH, which then precipitates out of the solution:

Common Ion Effect

Compared with pure water, the solubility of an ionic compound is less in aqueous solutions containing a common ion (one also produced by dissolution of the ionic compound). This is an example of a phenomenon known as the common ion effect, which is a consequence of the law of mass action that may be explained using Le ChÂtelier’s principle. Consider the dissolution of silver iodide:

AgI (s) ⇌ Ag^{+} (a q) + I^{-} (a q)

This solubility equilibrium may be shifted left by the addition of either silver(I) or iodide ions, resulting in the precipitation of AgI and lowered concentrations of dissolved Ag⁺ and I–. In solutions that already contain either of these ions, less AgI may be dissolved than in solutions without these ions.

This effect may also be explained in terms of mass action as represented in the solubility product expression:

K_{sp} = [Ag^{+}] [I^{-}]

The mathematical product of silver(I) and iodide ion molarities is constant in an equilibrium mixture regardless of the source of the ions, and so an increase in one ion’s concentration must be balanced by a proportional decrease in the other.

Key Concepts and Summary

The equilibrium constant for an equilibrium involving the precipitation or dissolution of a slightly soluble ionic solid is called the solubility product, K $_{s p}$ , of the solid. For a heterogeneous equilibrium involving the slightly soluble solid M $_{p}$ X $_{q}$ and its ions M $^{m +}$ and Xn–:

M_{p} X_{q} (s) ⇌ p M^{m+} (a q) + q X^{n-} (a q)

the solubility product expression is:

K_{sp} = [M^{m+}]^{p} [X^{n-}]^{q}

The solubility product of a slightly soluble electrolyte can be calculated from its solubility; conversely, its solubility can be calculated from its K $_{s p}$ , provided the only significant reaction that occurs when the solid dissolves is the formation of its ions.

A slightly soluble electrolyte begins to precipitate when the magnitude of the reaction quotient for the dissolution reaction exceeds the magnitude of the solubility product. Precipitation continues until the reaction quotient equals the solubility product.

Key Equations

M_{p} X_{q} (s) ⇌ p M^{m+} (a q) + q X^{n-} (a q) K_{sp} = [M^{m+}]^{p} [X^{n-}]^{q}

The Solubility Product

AgCl (s) precipitation ⇌ dissolution Ag^{+} (a q) + Cl^{-} (a q)

The equilibrium constant for solubility equilibria such as this one is called the solubility product constant, K $_{s p}$ , in this case

AgCl (s) ⇌ Ag^{+} (a q) + Cl^{-} (a q) K_{sp} = [Ag^{+} (a q)] [Cl^{-} (a q)]

Example 15.1Writing Equations and Solubility Products

Write the dissolution equation and the solubility product expression for each of the following slightly soluble ionic compounds:

(a) AgI, silver iodide, a solid with antiseptic properties

(b) CaCO₃, calcium carbonate, the active ingredient in many over-the-counter chewable antacids

(d) Mg(NH₄)PO₄, magnesium ammonium phosphate, an essentially insoluble substance used in tests for magnesium

(e) Ca₅(PO₄)₃OH, the mineral apatite, a source of phosphate for fertilizers

Solution

K $_{s p}$ and Solubility

The K $_{s p}$ of a slightly soluble ionic compound may be simply related to its measured solubility provided the dissolution process involves only dissociation and solvation, for example:

M_{p} X_{q} (s) ⇌ p M^{m+} (a q) + q X^{n-} (a q)

Example 15.5Determination of K $_{s p}$ from Gram Solubility

Solution

Before calculating the solubility product, the provided solubility must be converted to molarity:

[PbCrO_{4}] = \frac{4.6 \times 10 ^{- 6} g PbCrO _{4}}{1 L} \times \frac{1 mol PbCrO _{4}}{323.2 g PbCrO _{4}} = \frac{1.4 \times 10 ^{- 8} mol PbCrO _{4}}{1 L} = 1.4 \times 10^{- 8} M

Using Barium Sulfate for Medical Imaging

Medical imaging using barium sulfate can be used to diagnose acid reflux disease, Crohn’s disease, and ulcers in addition to other conditions.

Visit this website for more information on how barium is used in medical diagnoses and which conditions it is used to diagnose.

Predicting Precipitation

The equation that describes the equilibrium between solid calcium carbonate and its solvated ions is:

CaCO_{3} (s) ⇌ Ca^{2+} (a q) + CO_{3}^{2-} (a q) K_{s p} = [Ca^{2 +}] [CO_{3}^{2 -}] = 8.7 \times 10^{- 9}

Q $_{s p}$ < K $_{s p}$ : the reaction proceeds in the forward direction (solution is not saturated; no precipitation observed)

Q $_{s p}$ > K $_{s p}$ : the reaction proceeds in the reverse direction (solution is supersaturated; precipitation will occur)

This predictive strategy and related calculations are demonstrated in the next few example exercises.

The Role of Precipitation in Wastewater Treatment

Common Ion Effect

AgI (s) ⇌ Ag^{+} (a q) + I^{-} (a q)

This effect may also be explained in terms of mass action as represented in the solubility product expression:

K_{sp} = [Ag^{+}] [I^{-}]

Key Concepts and Summary

M_{p} X_{q} (s) ⇌ p M^{m+} (a q) + q X^{n-} (a q)

the solubility product expression is:

K_{sp} = [M^{m+}]^{p} [X^{n-}]^{q}

Key Equations

M_{p} X_{q} (s) ⇌ p M^{m+} (a q) + q X^{n-} (a q) K_{sp} = [M^{m+}]^{p} [X^{n-}]^{q}

15.1 Precipitation and Dissolution

The Solubility Product

Ksp​ and Solubility

Predicting Precipitation

Common Ion Effect

Key Concepts and Summary

Key Equations

15.1 Precipitation and Dissolution

The Solubility Product

Ksp​ and Solubility

Predicting Precipitation

Common Ion Effect

Key Concepts and Summary

Key Equations

K $_{s p}$ and Solubility

K $_{s p}$ and Solubility