Solubility Problem - Involves Addition of Another Ion

[vertciel]

Homework Statement

How many moles of solid sodium fluoride should be added to 1.0 L of a saturated solution of barium fluoride, BaF₂, at 25^OC to raise the fluoride concentration to 3.0 x 10^-2 mol/L? The solubility product constant for BaF₂ is K_sp = 1.7 x 10^-6 at 25^OC.

The Attempt at a Solution

BaF₂ ---> Ba²⁺ + 2F^-

Initial Concentrations: 0, 0
Change: + x, + 2x

Therefore:

1.7 x 10^-6 = x(2x)²

x = 0.00752 M.

So: [F^-] = 0.01504 mol/2 L.

I thought to have the desired fluoride concentration, only 1.5 x 10^-2 mol would need to be added. However, the correct answer is

Spoiler

2.6 x 10^{-2 mol}

.

Thank you for your help!

 

[Borek]

What happens when you add F^- to the solution?