Question

50 $ml$ of a solution containing ${10}^{-3}mol$ of $A{g}^{+}$ is mixed with 50 $ml$ of a 0.1 $M$ HCl solution. How much $A{g}^{+}$ concentration remains in solution? $(K_{sp}\text{of}AgCl=1.0\times {10}^{-10})$

• A. $2.5\times {10}^{-9}$
• B. $2.5\times {10}^{-7}$
• C. $2.5\times {10}^{-8}$
• D. $2.5\times {10}^{-10}$

Answer 1

The correct option is C $2.5\times {10}^{-8}$

$\underset{\underset{1\times {10}^{-3}mol}{\downarrow }}{A{g}^{+}}+\underset{\underset{5\times {10}^{-3}mol}{\downarrow }}{C{l}^{-}}\to AgCl\left(s\right)$
Millimoles of $HCl=50ml\times 0.1M$
$=5.0mmol=5.0\times {10}^{-3}mol$
$\left[H^{+}\right]=\left[C{l}^{-}\right]=5\times {10}^{-3}mol$
All of the silver reacts with the chloride ions and then starts to dissociate to form silver ions again.
$\left[C{l}^{-}\right]=4\times {10}^{-3}mol$ after the reaction.
$\left[A{g}^{+}\right]=\frac{1.0\times {10}^{-10}}{4.0\times {10}^{-3}}=2.5\times {10}^{-8}mol$