Solid `Ba(NO_(3))` is gradually dissolved in a `1.0xx10^(-4) M Na_(2)CO_(3)` solution. At what concentrations of `Ba^(2+)`, will a precipitate begin to form?
(`K_(SP)` for `BaCO_(3)=5.1xx10^(-9)`)

Options

A. `4.1xx10^(-5)M`
B. `5.1xx10^(-5)M`
C. `8.1xx10^(-8)M`
D. `8.1xx10^(-7)M`

Answer

B

Explanation

`Ba(NO_(3))_(2)+Na_(2)CO_(3)rarrBaCO_(3)+2NaNO_(3)`
`:' [CO_(3)^(2-)]= [Na_(2)CO_(3)]= 1.0xx10^(-4)M`
`:. K_(SP[BaCO_(3)])= [Ba^(2+)][CO_(3)^(2-)]`
`:. 5.1xx10^(-9) = [Ba^(2+)]xx1.0xx10^(-4)`
`[Ba^(2+)]= 5.1xx10^(-5)M`