1. Tardigrade
  2. Question
  3. Chemistry
  4. In 1 L saturated solution of AgCl [Ksp (AgCl) = 1.6 × 10 - 1 0 ], 0.1 mole of CuCl [ K sp = 1.0 × 10 - 6 ] is added. The resultant concentration of Ag+ in the solution is 1.6 × 10 - x The value of 'x' is

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Q. In $1 \,L$ saturated solution of $AgCl [K_{sp} (AgCl) = 1.6 \times 10^{ - 1 0 } ], $
$0.1$ mole of $CuCl [ K_{ sp } = 1.0 \times 10^{ - 6 } ] $ is added. The resultant concentration of $Ag^+ $ in the solution is $ 1.6 \times 10^{ - x} $ The value of '$x$' is

IIT JEEIIT JEE 2011Equilibrium

Solution:

It is a case of simultaneous solubility of salts with a common ion. Here, solubility product of $CuCl$ is much greater than that of $AgCl$, it can be assumed that $Cl-$ in solution comes mainly from $CuCl$
[$Cl^- ] = \sqrt{ K_{sp } \, ( CuCl) } = 10^{ - 3 } $ M
Now, for $AgCl, K_{ s p } = 1.6 \times 10^{ - 10 } = [Ag^+ ] \, [ Cl^ - ] $
= $ [ Ag^+ ] \times 10^{ - 3 } $
$\Rightarrow [ Ag^+ ] = 1.6 \times 10^{ - 7 } $