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Home  >>  JEEMAIN and AIPMT  >>  Chemistry  >>  Redox Reactions
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The EMF of cell $Ag,AgCl$ in 0.1M $KCl\parallel sat\;NH_4NO_3\parallel 0.1M\;AgNO_3,Ag$ is $0.45\;volt$ at $25^oC$.Calculate solubility product & solubility of $AgCl(0.1M\; KCl$ is $85\% $dissociated & $0.1M$ $AgNO_3$ is $82\%$ dissociated)

$\begin{array}{1 1}(a)\;1.8\times 10^{-10},1.7\times 10^{-3}\\(b)\;1.7\times 10^{-10},1.8\times 10^{-3}\\(c)\;1.9\times 10^{-3},1.6\times 10^{-9}\\(d)\;1.2\times 10^{-9},1.6\times 10^{-3}\end{array}$

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Since at $25^o$C 0.1M $AgNO_3$ is 82% dissociated hence $Ag^+$ ion concentration $(C_2)$ on $AgNO_3$ side =$\large\frac{0.1\times 82}{100}$$=0.082mol\;dm^{-3}$
Let $C_1$ be concentration of $Ag^+$ ions on AgCl.Then assuming activity coefficient=1,the EMF of cell is
$0.45v=0.0591v\log 0.082mol\;dm^{-3}$
$C_1=2.008\times 10^{-9}mol\;dm^{-3}$
Since at $25^o$C KCl is 85% dissociated
$[Cl^-]=\large\frac{0.1\times 85}{100}=$$0.085mol\;dm^{-3}$
$K_{sp}$ of $AgCl=[Ag^+][Cl^-]$
$\Rightarrow 2.008\times 10^{-9}\times 0.085$
$\Rightarrow 1.7068\times 10^{-10}$
Solubility of AgCl =$\sqrt{solubility\;product\;of\;AgCl}$
$\Rightarrow \sqrt{1.7068\times 10^{-10}}$
$\Rightarrow 1.3\times 10^{-5}$
$\Rightarrow 1.3\times 10^{-5}mol\;dm^{-3}\times 143.5g\;mol^{-1}$
$\Rightarrow 1.875\times 10^{-3}g\;dm^{-3}$
Hence (b) is the correct answer.
answered Dec 12, 2013 by sreemathi.v

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