An aqueous solution contains an unknown concentration of ${\mathrm{Ba}}^{2+}$. When $50 \mathrm{mL} \mathrm{of} \mathrm{a} 1 \mathrm{M}$ 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 ${\mathrm{Ba}}^{2+}$?

• A

  $1.0\times {10}^{-10}\mathrm{M}$
• B

  $5\times {10}^{-9}\mathrm{M}$
• C

  $2\times {10}^{-9}\mathrm{M}$
• Correct answer
  D

  $1.1\times {10}^{-9}\mathrm{M}$

Hence, the correct answer is option: 'D'.