solubility and pH (word problem)

Question

A new herbicide- Herbigon is dissolved in 1 M acetic acid for technical reasons .Ksp of Herbigon = 8.10×10−6. The formula for Herbigon is X-acetate (where X= the cation of the salt that kills weeds) Since it is critical to have Herbigon dissolved, you are working on adjusting the pH so Herbigon will be soluble at the concentration needed to kill weeds. What pH must the solution have to yield a solution in which the concentration of X+ is 5.50×10−3M ? p-Ka of acetic acid = 4.76

Answer 1

Denote the chemical formulae of Herbigon and acetic acid as XAc and HAc respectively.

Consider : XAc(s) = X+(aq) + Ac-(aq)
At equilibrium, Ksp = [X+] [Ac-]
[Ac-] = Ksp/[X+] = (8.1 x 10-6)/(5.5 x10-3)
[Ac-] = 1.47 x 10-3 M

XAc dissociates to give X+(aq) and Ac-(aq) ions, and some Ac- ions are protonated to give HAc.
Hence [Ac-] + [HAc] = [X+]
[HAc] = (5.5 x 10-3) - (1.47 x 10-3) = 4.03 x 10-3 M

Consider : HAc = H+ + Ac-
pH = pKa + log([Ac-]/[HAc])
pH = 4.76 + log((1.47 x 10-3)/(4.03 x 10-3)
pH = 4.32