Solubility of BaF₂ in a solution of Ba(NO₃)₂ will be represented by the concentration term

${\mathrm{BaF}}_2\left(\mathrm{s}\right)\rightleftharpoons \underset{\mathrm{S}}{{\mathrm{BaF}}_2}\left(\mathrm{aq}\right)\to \underset{\mathrm{S}+\mathrm{C}}{{\mathrm{Ba}}^{+2}}\left(\mathrm{aq}\right)+\underset{2\mathrm{S}}{2{\mathrm{F}}^{-}(}\mathrm{aq})$

$\mathrm{B}\underset{\mathrm{S}}{\mathrm{a}{\left({\mathrm{NO}}_3\right)}_2}\left(\mathrm{s}\right)\to \underset{\mathrm{C}+\mathrm{S}}{{\mathrm{Ba}}^{+2}(\mathrm{a}}\mathrm{q})+2\underset{2\mathrm{C}}{{\mathrm{NO}}_3^{-}}(\mathrm{aq})$

Due to common ion effect ,the solubility of BaF₂ is highly suppressed.

C>>>S   OR C + S ~ C

K_sp = (S + C) x (2S)²

[F^-] = 2S

$\frac{{\mathrm{F}}^{-}}{2}=\mathrm{S}$