Consider the following electrode processes of a cell,
`Cl^- rightarrow 1/2 Cl_2 +e^-.
[MCl +e^- rightarrow M +Cl^-]`.
If EMF of the cell is -1.140 V and `E^@` value of the cell is -0.55V at 298K, the value of the equilibrium constant of the sparingly soluble salt MCl is in the order of

Options

A. `10 ^(-10)`
B. `10 ^(-8)`
C. `10 ^(-7)`
D. `10 ^(-11)`

Answer

A

Explanation

`MCI + e^(-) to M +Cl^(-) ` cathode ( reduction )
`Cl^(-) to (1)/(2) Cl_2 + e^(-) ` anode ( oxidation )
MCl ` to M + 1/2 Cl_2`
The `K_c` of the cell reaction is calculated from nemst equation ` E_(cell ) = E_("cell") ^@ -(0.059)/(n) log K_C`
`-1.140 =- 0.55 -(0.059 )/(1) log c`
`-0.59 =- 0.0559 log K_c`
`log K_(c) =(0.59 )/( 0.059)=10`
` therefore K_(c) = 10 ^(10)`
` K_(sp) ` is for M ` +1/2 Cl_2 to MCl to M^+ +CL^-`
` therefore K_(sp) =(1)/(K_(c))`
` =(1)/(10 ^(10))=10 ^(-10)`