Equilibrium - Hard

2\,\mathrm{M}

solution of

\mathrm{Na_2CO_3}

is boiled in a closed container with excess of

\mathrm{CaF_2}

. Very little amount of

\mathrm{CaCO_3}

and

\mathrm{NaF}

are formed. If the solubility product (

K_{sp}

) of

\mathrm{CaCO_3}

x

and molar solubility of

\mathrm{CaF_2}

y

, find the molar concentration of

[\mathrm{F}^-]

in the resulting solution after equilibrium is attained.