Help please with this precipitation exercise

[BeeG]

Knowing K_s=6⋅10⁻³⁸ for Fe(OH)₃ in neutral solutions, calculate the minimum pH of an acidic solution in order to completely dissolve 10 mg of Fe(OH)₃. Data: Volume = 0.1 L.​

I set out the equation for the equilibrium constant. having first calculated the concentration or iron ions (9.35899*10^-4 M), and left the hydroxide concentration as an unknown:

K_s = 9.35899*10^-4 M * 27 C³​

Solving for C, I get 1.334*10^-12 M, and so my guess is that the concentration of the hydronium ions must be the difference, as it has to neutralise the hydroxide ions in order to move the equilibrium towards the left. Doing this, I get 9.35899*10^-4 M concentration for hydronium ions, which corresponds to pH = 3.03.
Is this approach and solution correct?

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[Borek]

my guess is that the concentration of the hydronium ions must be the difference

Difference between what and what?

Do you know what the water autoionization is? You have calculated concentration of OH^-. What is pH of this solution?

 

[BeeG]

Difference between what and what?

Do you know what the water autoionization is? You have calculated concentration of OH^-. What is pH of this solution?

I do know what water autoionization is. I meant the difference between the initial hydroxide concentration, 9.35899*10^-4 M, and the needed concentration for Q = K_s, which is what I calculated as 'C'.

What the problem wants me to do, I think, is calculate the concentration of hydronium ions in an acid solution that I have to add to the one I already have in order to dissolve the precipitate.

Please help. I am at complete loss at what to do and cannot seem to find any guidance in my textbook.

 

[Chestermiller]

Is this the exact statement of the problem?

 

[Borek]

Question is a bit ambiguous.

My bet is that you are asked to find the final pH at which the solution will be stable (that is, precipitate will not form). Otherwise there is no way to find the answer without making assumptions about the strength of the acid present. Not to mention the fact pH can be buffered (in which case it doesn't change during the dissolution).

I gave you hints about how to proceed with such a case in my previous post.

Once you have that and assuming solution contains a strong (fully dissociated) acid it is trivial to calculate (just from the stoichiometry of the dissolution) by how much the initial pH should be lower - but as I said above, it requires an assumption that the acid is strong, and the question doesn't justify this assumption.