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Some common solubility products are listed in [link] according to their K sp values, whereas a more extensive compilation of products appears in Appendix J . Each of these equilibrium constants is much smaller than 1 because the compounds listed are only slightly soluble. A small K sp represents a system in which the equilibrium lies to the left, so that relatively few hydrated ions would be present in a saturated solution.

Common Solubility Products by Decreasing Equilibrium Constants
Substance K sp at 25 °C
CuCl 1.2 × 10 –6
CuBr 6.27 × 10 –9
AgI 1.5 × 10 –16
PbS 7 × 10 –29
Al(OH) 3 2 × 10 –32
Fe(OH) 3 4 × 10 –38

Writing equations and solubility products

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

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

(b) CaCO 3 , calcium carbonate, the active ingredient in many over-the-counter chewable antacids

(c) Mg(OH) 2 , magnesium hydroxide, the active ingredient in Milk of Magnesia

(d) Mg(NH 4 )PO 4 , magnesium ammonium phosphate, an essentially insoluble substance used in tests for magnesium

(e) Ca 5 (PO 4 ) 3 OH, the mineral apatite, a source of phosphate for fertilizers

(Hint: When determining how to break (d) and (e) up into ions, refer to the list of polyatomic ions in the section on chemical nomenclature.)

Solution

(a) AgI ( s ) Ag + ( a q ) + I ( a q ) K sp = [ Ag + ] [ I ]

(b) CaCO 3 ( s ) Ca 2+ ( a q ) + CO 3 2− ( a q ) K sp = [ Ca 2+ ] [ CO 3 2− ]

(c) Mg ( OH ) 2 ( s ) Mg 2+ ( a q ) + 2OH ( a q ) K sp = [ Mg 2+ ] [ OH ] 2

(d) Mg ( NH 4 ) PO 4 ( s ) Mg 2+ ( a q ) + NH 4 + ( a q ) + PO 4 3− ( a q ) K sp = [ Mg 2+ ] [ NH 4 + ] [ PO 4 3− ]

(e) Ca 5 ( PO 4 ) 3 OH ( s ) 5Ca 2+ ( a q ) + 3PO 4 3− ( a q ) + OH ( a q ) K sp = [ Ca 2+ ] 5 [ P O 4 3− ] 3 [ OH ]

Check your learning

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

(a) BaSO 4

(b) Ag 2 SO 4

(c) Al(OH) 3

(d) Pb(OH)Cl

Answer:

(a) BaSO 4 ( s ) Ba 2+ ( a q ) + SO 4 2− ( a q ) K sp = [ Ba 2+ ] [ SO 4 2 ] ; (b) Ag 2 SO 4 ( s ) 2Ag + ( a q ) + SO 4 2− ( a q ) K sp = [ Ag + ] 2 [ SO 4 2− ] ; (c) Al ( OH ) 3 ( s ) Al 2+ ( a q ) + 3OH ( a q ) K sp = [ Al 3+ ] [ OH ] 3 ; (d) Pb(OH)Cl( s ) Pb 2+ ( a q ) + OH ( a q ) + Cl ( a q ) K sp = [ Pb 2+ ] [ OH ] [ Cl ]

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Now we will extend the discussion of K sp and show how the solubility product constant is determined from the solubility of its ions, as well as how K sp can be used to determine the molar solubility of a substance.

K sp And solubility

Recall that the definition of solubility is the maximum possible concentration of a solute in a solution at a given temperature and pressure. We can determine the solubility product of a slightly soluble solid from that measure of its solubility at a given temperature and pressure, provided that the only significant reaction that occurs when the solid dissolves is its dissociation into solvated ions, that is, the only equilibrium involved is:

M p X q ( s ) p M m+ ( a q ) + q X n− ( a q )

In this case, we calculate the solubility product by taking the solid’s solubility expressed in units of moles per liter (mol/L), known as its molar solubility    .

Calculation of K sp From equilibrium concentrations

We began the chapter with an informal discussion of how the mineral fluorite ( [link] ) is formed. Fluorite, CaF 2 , is a slightly soluble solid that dissolves according to the equation:

CaF 2 ( s ) Ca 2+ ( a q ) + 2F ( a q )

The concentration of Ca 2+ in a saturated solution of CaF 2 is 2.15 × 10 –4 M ; therefore, that of F is 4.30 × 10 –4 M , that is, twice the concentration of Ca 2+ . What is the solubility product of fluorite?

Solution

First, write out the K sp expression, then substitute in concentrations and solve for K sp :

CaF 2 ( s ) Ca 2+ ( a q ) + 2F ( a q )

A saturated solution is a solution at equilibrium with the solid. Thus:

K sp = [ Ca 2+ ] [ F ] 2 = (2.1 × 10 4 ) ( 4.2 × 10 4 ) 2 = 3.7 × 10 11

As with other equilibrium constants, we do not include units with K sp .

Check your learning

In a saturated solution that is in contact with solid Mg(OH) 2 , the concentration of Mg 2+ is 1.31 × 10 –4 M . What is the solubility product for Mg(OH) 2 ?

Mg(OH) 2 ( s ) Mg 2+ ( a q ) + 2OH ( a q )

Answer:

8.99 × 10 –12

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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