## 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