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

Options

A. `4.1 xx 10^(-5) M`
B. `5.1 xx 10^(-5) M`
C. `8.1 xx 10^(-8) M`
D. `8.1 xx 10^(-7) M`

Answer

B

Explanation

`{:(Na_(2)CO_(3),rarr,2Na^(+),+,CO_(3)^(-2)),(1xx 10^(-4)M,,2 xx 10^(-4)M,,1 xx 10^(-4)M):}`
`K_(sp)[BaCO_(3)] = [Ba^(+2)][CO_(3)^(-2)]`
`5.1 xx10^(-9) = [Ba^(+2)] xx 1 xx 10^(-4)`
`[Ba^(+2)] = 5.1 xx 10^(-5) M`.