[johnnyjohn993]

Use activities to calculate the molar solubility of Zn(OH)2 in 0.0200M KCl
Ksp for Zn(OH)₂ = 3.00x10^-16 at 25°C
 
μ =1/2((0.0200×(1)²)+(0.0200x(-1)²))
μ= 0.0200M

given φ_x, nm
OH^- 0.35nm
Zn²⁺ 0.6nm

Invoking the Debye-Huckle equation in order to find the activity coefficient of the ions at a given μ.
-logγ_Zn²⁺=                                     0.51x2²xsqrt(0.0200)
                                           ______________________________
                                                1+ 3.3(0.6)xsqrt(0.0200)

γ_Zn²⁺=  0.595

-logγ_OH^-1=                                      0.51x(-1)²xsqrt(0.0200)
                                          ______________________________
                                                  1+ 3.3(0.35)xsqrt(0.0200)

γ_OH^-1=0.867

Using the formula
Ksp =K'sp x (γ_Zn²⁺)(γ_OH^-1)²

K'sp =       3.00x10^-16
              ______________________
               (0.595) (0.867)²

K'sp=     6.71x10^-10

 Zn(OH)₂  Zn²⁺  + 2OH^-

K'sp=  s*(2s)²

 2.06x10^-15=  4s³

s= 5.5x10^-4 mol/L 


But the answer here is 5.5x10^-6 mol/L please help me see my mistakes.

[mjc123]

You divide 3e-16 by a quantity equal to 0.447 and get 6.71e-10! So s³ is out by a factor of 10⁶, and s by a factor of 100.