$8 \times 10^{- 6} M A g N O_{3}$ solution is gradually added in 1L of $10^{- 4} M K C l$ solution. Upto what volume of $A g N O_{3}$ solution being added (in L), precipitation of $A g C l$ will not take place? $(K_{s p} o f A g C l = 2 \times 10^{- 10})$

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Detailed Solution

$[C l^{-}] = 10^{- 4}$

Vol of $A g N O_{3}$ added = v

${[C l^{-}]}_{f i n a l} = \frac{10^{- 4} \times 1}{v + 1}$

$[A g^{+}] = \frac{8 \times 10^{- 6} \times v}{(v + 1)}$

For No ppt $k_{s p} > [A g^{+}] [C l^{-}]$

$\frac{10^{- 4} \times 8 \times 10^{- 6} v}{{(v + 1)}^{2}} = 2 \times 10^{- 10}$

$\frac{v}{{(v + 1)}^{2}} = \frac{1}{4}$

$v = 1$

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