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Solid \( \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} \) is gradually dissolved in \( 1.0 \times 10^{-4} \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3} \) solution. At what concentration of \( \mathrm{Ba}^{2+} \) will a precipitate begin to form ? \( \left(\mathrm{K}_{\mathrm{sp}}\right. \) for \( \left.\mathrm{BaCO}_{3}=5.1 \times 10^{-9}\right) \)
(1) \( 5.1 \times 10^{-5} \mathrm{M} \)
(2) \( 8.1 \times 10^{-8} \mathrm{M} \)
(3) \( 8.1 \times 10^{-7} \mathrm{M} \)
(4) \( 4.1 \times 10^{-5} \mathrm{M} \)
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