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An aqueous solution contains an unknown concentration of \( \mathrm{Ba}^{2+} \). When \( 50 \mathrm{~mL} \) of a \( 1 \mathrm{M} \) solution of \( \mathrm{Na}_{2} \mathrm{SO}_{4} \) is added, \( \mathrm{BaSO}_{4} \) just begins to precipitate. The final volume is \( 500 \mathrm{~mL} \). The solubility product of \( \mathrm{BaSO}_{4} \) is \( 1 \times 10^{-10} \). What is the original concentration of \( \mathrm{Ba}^{2+} \).
(1) \( 1.1 \times 10^{-9} \mathrm{M} \)
(2) \( 1.0 \times 10^{-10} \mathrm{M} \)
(3) \( 5 \times 10^{-9} \mathrm{M} \)
(4) \( 2 \times 10^{-9} \mathrm{M} \)
\( \mathrm{P} \)
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