Chemistry Solubility Math Question

Question

A saturated solution of unknown metal hydroxide M(OH)₂ has a measured pH of 8.93. Determine the value of K_sp for the compound.

Answer 1

Since this is a Ksp problem, you should write down the Ksp expression and from there, see what you know or what you an deduce, and what is being asked for.

M(OH)₂(s) <==> M²⁺ (aq) + 2OH^-(aq)

Kso = [M²⁺][OH^-]²

We are asked to find the Ksp, so that means we must know (or be able to determine) [M²⁺] and [OH^-]. Well, from the given pH of 8.93, we can find the pOH and then the [OH^-].

pH + pOH = 14

pOH = 14 - pH = 14 - 8.93 = 5.07

[OH^-] = 1x10^-5.07 = 8.51x10^-6 M

[M²⁺] = 1/2 (8.51x10^-6) = 4.26x10^-6 M (1/2 because M(OH₎₂ => M²⁺ + 2OH^-)

Ksp = (4.26x10^-6)(8.93x10^-6)²

Ksp = 3.40x10^-16