`2M` solution of `Na_(2)CO_(3)` is boiled in a closed container with excess of `CaF_(2)`. Very small amount of `CaCO_(3)` and `NaF` are formed. If `K_(sp)` of `CaCO_(3)` is `x` and molar solubility of `CaF_(2)` is `y`, find the molar after cocentration of `F^(Theta)` in the resulting solution after equilibrium is attained.

Explanation

`{:(,Na_(2)CO_(3)+,CaF_(2)(s)hArr,2NaF(aq)+,CaCO_(3)(s)),(t=0,2,-,0,-),(t=eq,2-a,-,2a,-):}`
where is very small
For `CaCO_(3),K_(sp)=x=[Ca^(2+)][CO_(3)^(2-)]=[Ca^(2+)]xx2( :.CO_(3)^(2-)` mainly coming from `Na_(2)CO_(3)`
`[Ca^(2+)]=(x)/(2)`
For `CaF_(2),K_(sp)=4y^(3)=((x)/(2))[F^(-)]^(2)rArr [F^(-)]=sqrt((8y^(3))/(x))`