[johnnyjohn993123]

Use activities to calculate the molar solubility of Zn(OH)2 in the solution that results when you mix 40 mL of 0.250 M KOH with 60.0 mL of 0.0250 M ZnCI₂

ZnCl₂ + 2KOH Zn(OH)₂ + 2KCl

Given Ksp for Zn(0H)₂ = 3.0x10^-16

Accourding to my stoich

in order to consume all 1.5mmol of ZnCl2 , 3mmol of KOH must react. Therefore there will be a remaining 7mmol of OH^- in the solution or that is 0.07 M OH^-

which can be substituted in [Zn²⁺][0.07]² = Ksp

calculating my γ for my activity coefficient given that I have 0.03M ionic strength (from my stoich -KCl)
where α= 0.3
both K⁺ and Cl^- would give me 0.8406 as an activity coefficient

Ksp'= Ksp/(0.8406)(0.8406)
ksp'= 4.26x10^-16
[Zn²⁺][0.07]²=Ksp'
[Zn²⁺]= 8.66x10^-14M

but the right answer was 2.8x10^-13M whats wrong with my solution please help

[mjc123]

Your ionic strength is wrong. What are ALL the ions present after precipitation of Zn(OH)₂ (you can ignore Zn²⁺), and what is the concentration of each?
I don't know about your γ calculation as I don't know the equation you're using, and have forgotten it from long ago.
Why do you write Ksp' = Ksp/(0.846)²? What is the order of Ksp?

[johnnyjohn993123]

i dont know whether to use 0.1 M of ionic strength or 0.03M inoic strength ? Like what is my basis of getting my KCl concentration? 40mL of 0.250M KOH to have 0.1M KCl conc. or 60mL 0.0250M ZnCl2 to have 0.03M KCl.   

I was using the Debye Huckel equation for Y and Ksp = Ksp' γ_K⁺ γ_Cl^-

[johnnyjohn993123]

well I do think my ionic strength is 0.03 because that will be the concentration of KCl in the solution .. I mean what else could it be?

[mjc123]

What else do you have in your solution? (You said it earlier.)

[johnnyjohn993123]

oKay now Im good <3 thanks for helping though. As always :")