[Spectrums]

For a saturated solution of an unknown metal hydroxide, M(OH)₂, 12.75 mL of this solution were required to neutralize 25.00 mL of 0.02 M HCl. Calculate the K_SP of the metal hydroxide.

I've tried the problem two different ways because I'm not sure whether I'm supposed to divide the concentration of M(OH)₂ by 2 to get the concentration of OH^- or if I should multiply it by 2.

M(OH)₂  M²⁺ + 2OH^-
This makes mole ratio 1 : 2.

Using C₁V₁=C₂V₂, the concentration of M(OH)₂ is:
C₁(12.75)=(0.02)(25.00)
= 0.039 M

From this I assumed that the concentration of M²⁺ was also 0.039 given the 1:1 mole ratio and the concentration of OH^- is 2 times the concentration of M(OH)₂ making it 0.078.

This makes the K_SP=[M²⁺][OH^-]²
= [0.039][0.078]²
= 2.373 x 10^-4

If the concentration of M(OH)₂ should be divided by 2 to get the concentration of OH^-, this makes the K_SP = [0.039][0.0195]²
= 1.483 x 10^-5

If neither of these are correct, could someone please point me in the right direction?

[AWK]

From this I assumed that the concentration of M2+ was also 0.039 given the 1:1 mole ratio and the concentration of OH- is 2 times the concentration of M(OH)2 making it 0.078.

Wrong - M(OH)₂ !!!
You titrated OH^-

[Spectrums]

From this I assumed that the concentration of M2+ was also 0.039 given the 1:1 mole ratio and the concentration of OH- is 2 times the concentration of M(OH)2 making it 0.078.

Wrong - M(OH)₂ !!!
You titrated OH^-

If the assumption regarding the concentration of M²⁺ is correct in it being equal to the concentration of M(OH)₂ but the assumption regarding the concentration of OH^- is wrong, wouldn't this make the second solution I posted correct? If not, can you give me some concrete advice on how to approach the problem?

[AWK]

the KSP = [0.039][0.0195]2

Also wrong - concetration of Me²⁺ is 0.0195 and you put is as concentration of OH^-

[Spectrums]

the KSP = [0.039][0.0195]2

Also wrong - concetration of Me²⁺ is 0.0195 and you put is as concentration of OH^-

So [OH^-] = [M(OH)₂] because OH^- is titrated & [M²⁺] = (0.5)[OH^-] because of 1:2 mole ratio?

[AWK]

So [OH-] = [M(OH)2]

False statement
So = 0.5[OH^-] = [M(OH)₂]

Titration of base with HCl is in fact
H⁺ + OH^- = H₂O
Since M(OH)₂ contains 2 hydroxyl group in stoichiometric unit of base then
concentration of M²⁺ = 0.5 times concentration of OH^-