Question

50 mL of solution containing ${10}^{-3}$ mole of ${Ag}^{+}$ is mixed with 50 ml. Of a 0.1 m HCI solution how much ${Ag}^{+}$ remains in solution? $(K_{sp}of{A}_{g}C1=1.0\times {10}^{-10})$

• A. $2.0\times {10}^{-9}$
• B. $2.0\times {10}^{-7}$
• C. $2.0\times {10}^{-8}$
• D. $2.0\times {10}^{-10}$

Answer 1

Answer: (A)

$2.0\times {10}^{-9}$

Let the solubility be $s$ in presence of $HCl$ solution.

$AgCl\rightleftharpoons A{g}^{+}+C{l}^{-}$

$\therefore s\times (S+C_{C{l}^{-}}\text{from HCl})=K_{sp}$

or, $S\times C_{C{l}^{-}}=K_{sp}$ (since $s<<C_{C{l}^{-}}\text{from HCl})$

or, $S\times \left(\frac{0.1}{2}\right)=K_{sp}=1\times {10}^{-10}$

or, $S=2\times {10}^{-9}$