[sun725]

The solubility of Ca(OH)₂ in water is  1.11*10^-2 M at 25 C.
I'm asked what's the L_c (concentration solubility product) for Ca(OH)₂ in water at 25 C? Also I have to find the ionic strength and calculate via the Debye-Hückels limiting law the activity coefficients for Ca²⁺ in the solution at 25 C.

Ca(OH)₂(s)    Ca²⁺ + 2OH^-

[Ca²⁺] = 1.11 x 10^^-2 ; [OH^-] = 2(1.11 X 10^-2) = 2.22 x 10^-2

Ksp = [Ca²⁺][OH-]² = 1.11 x 10^-2(2.22 x 10^-2)² = 5.47 x 10^-6

Ionic Strength = I = 1/2Σ ci zi²

Where ci = concentration of ions; zi = charge of the ions:

Ionic strength = ½ [( 1.11 x 10^-2)2² + 2.22 x 10^-2)1²)
I = ½ [ 4.44 x 10^-2 + 2.22 x 10^-2)]
I = ½(6.66 x 10^-2) =
Ionic strength = 0.0333

And the activity coefficients:
log Y_HA =-0.509Z*(-2)²*sqrt 0.0333
log Y_HA =0.371

I really want to know if I have calculated this correctly or if I have missed something.

[mjc123]

The values of K_sp and I look OK, but these quantities have units - what are they? A number is a wrong answer.

The activity coefficient looks wrong. I have
log γ_± [what's HA?] = -0.509*|z₊z_-|*sqrt(I)
So your number is wrong, and the sign is wrong (γ is not going to be > 1). And you are asked for the activity coefficient, so convert log γ to γ.