Chemistry Math Question?

Question

A saturated solution of unknown metal hydroxide M(OH)₂ has a measured pH of 8.13. Determine the value of K_sp for the compound.

Answer 1

M(OH)₂(s) ==> M²⁺(aq) + 2OH^-(aq)

From the pH = 8.13, we can find the [OH-].

pH = 8.13

pH + pOH = 14

pOH = 14 - 8.13

pOH = 5.87

[OH^-] = 1x10^-5.87 = 1.35x10^-6 M

Since [M²⁺] is 1/2 [OH^-], we have [M²⁺] = 1/2(1.35x10^-6) = 6.75x10^-7 M

Ksp = [M²⁺][OH^-]²

Ksp = (6.75x10^-7)(1.35x10^-6)²

Ksp = 1.2x10^-18