Discussion Forum

1)

 Consider the following electrode processes of a cell

 $Cl^{-} \rightarrow \frac{1}{2} Cl_{2}+e^{-}$

                                      $[MCl+e^{-} \rightarrow M+ Cl^{-}$]

If EMF of this cell is -1.140 V and $E^{0}$ value of the cell is -0.55 V  at 298 K, the value of the equilibrium constant of the sparingly soluble salt MCl is in the order of 

Answer:

Option A

Explanation:

$MCl+e^{-} \rightarrow  M+Cl^{-}$ cathode (reduction)

 $Cl^{-} \rightarrow  \frac{1}{2} Cl_{2}+e^{-}$   anode (oxidation)

  $MCl \rightarrow  M+ \frac{1}{2}Cl_{2}$

  The $K_{c}$ of the cell reaction is calculated  from 

Nernst equation    $E_{cell}= E^{0}_{cell}- \frac{0.059}{n} \log K_{c}$

 $-1.140=-0.55-\frac{0.059}{1} \log c$

 $-0.59=-0.059 \log K_{c}$

 $\log K_{c}= \frac{0.59}{0.059} =10$

$\therefore  K_{c}=10^{10}$

 $K_{sp}$ is for  $M+\frac{1}{2} Cl_{2} \rightarrow  MCl \rightarrow  M^{+}+Cl^{-}$

$\therefore$    $K_{sp}= \frac{1}{  K_{c}}$

 $=\frac{1}{10^{10}}=10^{-10}$