A solution is saturated with respect to `SrCO_(3)` and `SrF_(2)`. The `[CO_(3)^(2-)]` was found to be `1.2 xx 10^(-3)M`. The concnetration of `F^(Theta)` in the solution would be
Given `K_(sp)` of `SrCO_(3) = 7.0 xx10^(-10)M^(2)`,
`K_(sp) "of" SrF_(2) = 7.9 xx 10^(-10) M^(3)`,

Options

A. `1.3 xx 10^(-3)M`
B. `2.6 xx 10^(-2)M`
C. `3.7 xx 10^(-2)M`
D. `5.8 xx 10^(-7)M`

Answer

C

Explanation

The two `K_(sp)` values do not differ very much. So it is a case of simuoltansous equilibria, wher the concentration of any species can not be neglected.
`([cancel(Sr^(2+))][F^(Theta)]^(2))/([cancel(Sr^(2+))][CO_(3)^(2-)]) =(K_(sp)SrF_(2))/(K_(sp)SrCO_(3)) = (7.9xx10^(-10))/(7.0xx10^(-10)) = 1.128`
`:. [F^(Theta)]^(2) = 128 xx [CO+(3)^(2-)] = 1.128 xx 1.2 xx 10^(-3)`.
`= 13.5 xx 10^(-4)`
`:. [F^(Theta)] =(13.5 xx 10^(-4))^(1//2)`
` = 3.674 xx 10^(-2) ~~ 3.7 xx 10^(-2)M`.