Solid $Ba(NO_3)_2$ is gradually added to a $1.0 \times 10^{-4} \, M \, Na_2CO_3$ solution. At what concentration of $Ba^{2+}$ will precipitation start? (Given $K_{sp}$ for $BaCO_3 = 5.1 \times 10^{-9}$)
- A$8.1 \times 10^{-8} \, M$
- B$8.1 \times 10^{-7} \, M$
- C$4.1 \times 10^{-5} \, M$
- D$5.1 \times 10^{-5} \, M$
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