SOLUBILITY EQUILIBRIA


    The ions of insoluble salts are present as ions in solution but at relatively low concentrations.  An equilibrium is established between these ions and the solid salt and the concentration of these ions are determined by an equilibrium constant called the solubility product constant, Ksp.  Examples are:
                AgCl(s)  =  Ag+  +  Cl-                Ag2SO4(s)  =  2Ag+  +  SO42-

                    Ksp= [Ag+][Cl-]                        Ksp= [Ag+]2[SO42-]

    There are essentially two types of problems, those that ask for the solubility of the insoluble salt in water and those that ask for the solubility of the insoluble salt in the presence of a relatively large concentration of one of the ions of the salt or the ion common to the salt.  The equilibrium reaction indicates that the solubility of the salt is dramatically decreased when relatively large concentrations of the common ion (from another source) are present.  That is, the solubility of silver chloride is much less in a solution containing 0.10M sodium chloride than in pure water.

    An example: (1) What is the solubility of AgCl in water?  Ksp= 1.8 x 10-10

                    DESCRIBE:        AgCl(s)  =  Ag+  +  Cl-

                    DEFINE:            Ksp= [Ag+][Cl-]

                    ASSIGN:           [Ag+]  =  x      [Cl-] = x

                    PLUG IN:           1.8 x 10-10  =  (x)(x) = x2

                    SOLVE:              x = 1.34 x 10-5

                    RELATE:            x = moles of AgCl that dissolved = solubility of AgCl = x = 1.34 x 10-5

                                   (2) What is the solubility of AgCl in 0.10M KCl solution?

                    DESCRIBE:        AgCl(s)  =  Ag+  +  Cl-

                    DEFINE:            Ksp= [Ag+][Cl-]

                    ASSIGN:           [Ag+]  =  x      [Cl-] = 0.10 + x

                    PLUG IN:           1.8 x 10-10  =  (x)(0.10 + x) = 0.10x  after approximation

                    SOLVE:              x = 1.8 x 10-9       x is small compared to 0.10

                    RELATE:            x = moles of AgCl that dissolved = solubility of AgCl = x = 1.8 x 10-9

The solubility is smaller (1.8 x 10-9) in 0.10M KCl than in water (1.34 x 10-5).  Cl- is the common ion.

If one calculates the solubility of  Ag2SO4(s)  ( Ksp= 4.0 x 10-12) one finds that its solubility is greater than AgCl even though its Ksp is less.  The reason for this is silver sulfate produces three ions when it ionizes.

            (3) What is the soubility of Ag2SO4 in water?

                                        Ksp= [Ag+]2[SO42-]    4.0 x 10-12 = (x)(2x)2        x3 = 1.0 x 10-12        x = 1 x 10-4 .

            (4) If the solubility of an insoluble salt, MX, is 2.0 x 10-8  what is its Ksp?

                                       Ksp= [M+][X-] = (2.0 x 10-8 )(2.0 x 10-8) = 4.0 x 10-16 .

            (5) If the solubility of an insoluble salt, M2X, is 2.0 x 10-8  what is its Ksp?

                            M2X(s)  =  2M+  +  X2-           where [M+] = 2x and [X2-] = x = solubility
                          Ksp= [M+]2[X2-] =  (4.0 x 10-8 )2(2.0 x 10-8) = 32 x 10-24 .

        Some insoluble salts are bases so their solubility is controlled by the pH of the solution.
                Consider the base, Cd(OH)2,
                          Cd [OH-]2(s)  =  Cd+  +  2OH-  and its Ksp = 2.5 x 10-14.
    The solubility will change depending upon the pH of the solution. Suppose the solution is buffered at a
                           pH of 10. Then [OH-] = 1 x 10-4 and the solubility is determined:
                     Ksp = 2.5 x 10-14 =  [Cd2+][OH-]2 = x(1 x 10-4)2  and solving for x which is the solubility
                            gives an answer of 2.5 x 10-6.

    The solubility of  Cd(OH)2 in water is determined to be:
                         Ksp = 2.5 x 10-14 =  [Cd2+][OH-]2 = x(2x)2   and  4x3 = 2.5 x 10-14 to give x = 1.84 x 10-5.
                Since [OH-] = 2x ,  then [OH-] =  3.68 x 10-5 and pOH =  4.43.
                So pH = 14.00 - 4.43 = 9.57 in a saturated solution of  Cd(OH)2.