A solution is saturated with respect to `SrF_(2) K_(sp) = 7.9 xx 10^(-10)` and `SrCO_(3), K_(sp) = 7.0 xx 10^(-10)`. If the fluoride ion concentration is found to be `4.0 xx 10^(-2)M`. What is the concentration of carbonates ions.

Explanation

`SrF_(2) hArr Sr^(2+) (aq) +2F^(Θ) (aq)`
`K_(sp) = [Sr^(2+)] [F^(Θ)]^(2)`
`[Sr^(2+)] = (K_(sp))/([F^(Θ)]^(2)) = (7.9 xx 10^(10))/((4.0xx10^(-2))^(2))= 4.938 xx 10^(-7)M`
This concentration of `Sr^(2+)` ions should also satisfy the other equilibrium expression for `SrCO_(3)`
`SrCO_(3)(s) hArr Sr^(2+) (aq) +CO_(3)^(2-)(aq)`
`K_(sp) = [Sr^(2+)] [CO_(3)^(2-)]`
`[CO_(3)^(2-)] = (K_(sp))/([Sr^(2+)]) = (7.0 xx 10^(-10))/(4.938 xx 10^(-7)) =1.4 xx 10^(-3)`