Question

You are investigating the effect of strong base on the solubility of zinc hydroxide, Zn(OH)₂ (s).

(Ksp= 3 x 10^{- 15} for Zn(OH)₂ (s))

You prepare 1.0 L solution of 0.10M NaOH and add excess zinc hydroxide, Zn(OH)₂ (s).

Instead of suppresing the solubility, you observe extra solubility.

Your research advisor tells you that zinc ions react with four hydroxide ions in a solution to form the complex ion Zn(OH)₄^2- (aq).

(K_f = 2 x 10 ¹⁵ for Zn(OH)₄^2- (aq))

Calculate the pH of your solution.

Answer 1

Zn(OH)₂ = Zn²⁺ + 2OH^-                   ; K_sp = 3 x 10^{- 15}
Zn²⁺ + 4OH^- = [Zn(OH)₄]^2- ;                 K_f = 2 x 10 ¹⁵
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Zn(OH)₂ + 2OH^- = [Zn(OH)₄]^2-            ; K_reaction = K_sp*K_f = 6

               Zn(OH)₂                     +             2OH^-      =             [Zn(OH)₄]^2-             

Initial:    (solid)                                  0.1 M                    0

At eqm:                                              0.1 - 2x                 x

K_reaction = 6 = [Zn(OH)₄]^2-/[OH-]²

or, x/(0.1-2x)² = 6

or, 24x² - 3.4x + 0.06 = 0

or, x = 0.021, 0.121

but, x = 0.121 is not acceptable. when, x = 0.121, [OH-] = 0.1-2x = negative value, which is impossible

so, x = 0.021

[OH-] = 0.1-2x

= 0.058

pOH = -logx

= 1.24

pH = 12.76