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A solution of 0.1M in Cl^– and 10^–4 $\large MCrO_4^{ - 2}$ . If solid AgNO₃ is gradually added to this solution, what will be the concentration of Cl^– when Ag₂CrO₄ begins to precipitate? $\large [{K_{sp}}(AgCl)\, = \,{10^{ - 10}}{M^2};$ $\large {K_{sp}}(A{g_2}Cr{O_4})\, = \,{10^{ - 12}}{M^3}\,]$ ]

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10^-6 M

10^-5 M

10^-4M

10^-9 M

answer is A.

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Detailed Solution

Concentration of Ag⁺ when AgCl begins to precipitate,

$= \frac{{{K_{sp}}}}{{\left[ {C{l^ - }} \right]}} = \frac{{{{10}^{ - 10}}}}{{{{10}^{ - 1}}}} = {10^{ - 9}}$

Concentration of Ag⁺ when Ag₂CrO₄ begins to precipitate,

$= \sqrt {\frac{{{K_{sp}}}}{{\left[ {CrO_4^{ - 2}} \right]}}} = \sqrt {\frac{{{{10}^{ - 12}}}}{{{{10}^{ - 4}}}}} = {10^{ - 4}}$

When Ag₂CrO₄ begins to precipitate, the equilibrium of undissolved AgCl and dissolved AgCl still exists.

${K_{IP}} = {K_{SP}} \Rightarrow \left[ {A{g^ + }} \right]\left[ {C{l^ - }} \right] = {10^{ - 10}}$

$\Rightarrow \left[ {C{l^ - }} \right] = {10^{ - 6}}$

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