salts and solubility...?

Question

Calcium fluoride, CaF2, is a nearly insoluble salt with a Ksp= 3.9 x 10^-11 at 298K. Addition of which substance is most likely to increase the solubility of CaF2 at constant temperature??
a- NaF (Solid)
b- CaCl2 (solid)
c- HCl (aqueous)
d- H20
e- C2H5OH (liquid)

and why??

thanks!

Answer 1

d-H2O

The equilibrium is

CaF2 <> Ca2+ + 2F-

let x = moles/l CaF2 that dissolve we get x moles/L Ca2+ and 2x moles/L F-

Ksp = [Ca2+] [ F-]^2 = x(2x)^2 = 4x^3

x = 0.000214 M

x is the molar solubility = moles/L

If we add H2O molar solubility increases

Answer 2

c- HCl(aq)

CaF2(s) + 2H+ + 2Cl- ===> Ca2+ + 2HF + 2Cl-

HF is a weak acid, and the equilibrium shifts.