Question

What [Ag1+] is required to start precipitation of AgOH from a saturated solution of Mg(OH)2? Ksp = 2.4 ✕ 10-8 for AgOH and Ksp = 2.6 ✕ 10-11 for Mg(OH)2

Answer 1

AgOH ==> Ag^+ + OH^-
Mg(OH)2 ==> Mg^2+ + 2OH^-

Ksp Mg(OH)2 = (Mg^2+)(OH^-)^2
Ksp AgOH = (Ag^+)(OH^-)

Calculate (OH^-) in a saturated solution of Mg(OH)2. That is
.........Mg(OHO2 ==> Mg^2+ + 2OH^-
I........solid........0.......0
C........solid........x.......2x
E........solid........x.......2x
Ksp = (Mg^2+)(OH^-)^2
Ksp = (x)(2x)^2 = 4x^3
Solve for x = (Mg^2+) and twice that will be OH^-.
Then set up Ksp = (Ag^+)(OH^-). substitute OH and solve for (Ag^+).