In qualitative analysis,the metals of group $I$ can be separated from other ions by precipitating them as chloride salts. $A$ solution initially contains $Ag^{+}$ and $Pb^{2+}$ at a concentration of $0.10 \, M$. Aqueous $HCl$ is added to this solution until the $Cl^{-}$ concentration is $0.10 \, M$. What will the concentrations of $Ag^{+}$ and $Pb^{2+}$ be at equilibrium? ($K_{sp}$ for $AgCl = 1.8 \times 10^{-10}$,$K_{sp}$ for $PbCl_2 = 1.7 \times 10^{-5}$)

• A
  $[Ag^{+}] = 1.8 \times 10^{-7} \, M, [Pb^{2+}] = 1.7 \times 10^{-6} \, M$
• B
  $[Ag^{+}] = 1.8 \times 10^{-11} \, M, [Pb^{2+}] = 8.5 \times 10^{-5} \, M$
• C
  $[Ag^{+}] = 1.8 \times 10^{-9} \, M, [Pb^{2+}] = 1.7 \times 10^{-3} \, M$
• D
  $[Ag^{+}] = 1.8 \times 10^{-11} \, M, [Pb^{2+}] = 1.7 \times 10^{-4} \, M$