An aqueous solution an unknown concentration of `Ba^(2+)` When 50mL of a 1 (M) solution of `Na_SO_4` is added `BaSO_4` just begins to precipitate. The final volume is 500mL. The solubility product of `BsSO_4` is `1xx10^(10)` What is the original concentration of `Ba^(2+)`

Options

A. `5xx10^(-9)(M)`
B. `2xx10^(-19)(M)`
C. `1.1xx10^(-9)(M)`
D. `1.0xx10^(-10)(M)`

Explanation

`[SO_2^(2-)]=(1xx50)/(500)=0.1(M)`
If concentration of `Ba^+`=x(M)
then `[Ba^(2+)][SO_4^(2-)]=K_(sp)=1xx10^(-10)`
or, `xxx0.1=1xx10^(-10)` or `x=10^(-9)`
Thus original concentration of `Ba^(2+)=(500xx10^(-9))/((500-50))`