Solubility Equilibria

 

44)  (a) pH = 7.0          Ksp = 7.9 x 10-16

 

             [H+] = 10-pH = 10-7.0 = 1 x 10-7 M

             Kw = [H+] x [OH-] = 1.00 x 10-14

             [OH-] = Kw/[H+] = (1.00 x 10-14)/(1 x 10-7) = 1 x 10-7 M

       

                      Fe(OH)2(s) Fe2+(aq)   +   2OH-(aq)

             [ ]i                                      0                 1 x 10-7

             [ ]c                                   +x                  +x

             [ ]e                                     x                 1 x 10-7+x

 

             Ksp = [Fe2+] x [OH-]2

             7.9 x 10-16 = x · (1 x 10-7 + x)2 ≈ x · (1 x 10-7)2 = 1 x 10-14x

             [Fe2+] = 7.9 x 10-2 M

 

             s = 7.9 x 10-2 mol Fe2+/L x 1 mol Fe(OH)2/1 mol Fe2+ = 7.9 x 10-2 M

 

       (b) pH = 10.0          

 

             pH + pOH = 14.00

             pOH = 14.00 - pH = 14.00 - 10.0 = 4.0

             [OH-] = 10-pOH = 10-4.0 = 1 x 10-4 M

       

                      Fe(OH)2(s) Fe2+(aq)   +   2OH-(aq)

             [ ]i                                      0                 1 x 10-4

             [ ]c                                   +x                +2x

             [ ]e                                     x                 1 x 10-4+2x

 

             Ksp = [Fe2+] x [OH-]2

             7.9 x 10-16 = x · (1 x 10-4 + 2x)2 ≈ x · (1 x 10-4)2

             [Fe2+] = 7.9 x 10-8 M

 

             s = 7.9 x 10-8 mol Fe2+/L x 1 mol Fe(OH)2/1 mol Fe2+ = 7.9 x 10-8 M

 

       (c) pH = 12.0          

 

             pH + pOH = 14.00

             pOH = 14.00 - pH = 14.00 - 12.0 = 2.0

             [OH-] = 10-pOH = 10-2.0 = 1 x 10-2 M

       

                      Fe(OH)2(s) Fe2+(aq)   +   2OH-(aq)

             [ ]i                                      0                 1 x 10-2

             [ ]c                                   +x                +2x

             [ ]e                                     x                 1 x 10-2+2x

 

             Ksp = [Fe2+] x [OH-]2

             7.9 x 10-16 = x · (1 x 10-2 + 2x)2 ≈ x · (1 x 10-2)2

             [Fe2+] = 7.9 x 10-12 M

 

             s = 7.9 x 10-12 mol Fe2+/L x 1 mol Fe(OH)2/1 mol Fe2+ = 7.9 x 10-12 M