How to find Ksp?

Question

A student trying to determine the Ksp for Calcium hydroxide used 10.25 mL of

0.060 M HCl to neutralize the initial volume of 12.00 mL Ca(OH) 2 solution.

[OH^-]=0.0512 M

[Ca^2+]=0.0256 M

Ksp=?

Answer 1

The concern posed by @Luke W was a valid one as it wasn't clear what those concentrations are or how they were arrived at. Below is an explanation:

Ca(OH)₂(s) + 2HCl(aq) ==> CaCl₂(aq) + 2H₂O(l)

moles HCl used = 10.25 mls x 1 L / 1000 ml x 0.06 mol/L = 0.000615 mols mols HCl

moles Ca(OH)₂ present = 0.000615 mols HCl x 1 mol Ca(OH)₂ / 2 mols HCl = 0.000375 mols Ca(OH)₂

mols Ca²⁺ = 0.000375

mols OH- = 0.000615

Volume = 12.00 ml = 0.01200 L

Final [Ca²⁺] = 0.0256 M

Final [OH-] = 0.0512 M

The rest of the calculation is shown in the original answer by @Luke W.

Answer 2

The formula for the solubility product constant is Ksp=[A+]^a[B-]^b where A is the concentration of the cation and B is the concentration of the anion. The powers a and b represent the molar coefficients of the two. Therefore Ksp=(0.0256)^1*(0.0512)^2. This means Ksp=6.711*10^-5, assuming the concentrations of the ions are correct.