For the electrochemical cell, `Mg(s)|Mg^(2+)(aq,1 M)||Cu^(2+)(aq.1 M) Cu(s)`, the standard emf of the cell is 2.70 V at 300 K. When the concentration of `Mg^(2+)` is changed to x M, the cell potential changes to 2.67 V at 300 K. What is the value of x ?
(Given, F/R =11500 K `V^(-1)`,where F is the Faraday constant and R is the gas constant, the value of `"In"_((10))(10)=2.30)`.

Explanation

The cell reaction is :
`Mg(s)+Cu^(2+)(aq)rarr Mg^(2+)(aq)+Cu(s)`
According to Nernst equation
`E=E^(@)-(RT)/(2F)In([Mg^(2+)])/([Cu^(2+)])`
`E_(cell)^(@)=2.70 V,E_(cell)=2.67 V,Mg^(2+)=x M, Cu^(2+)=1 M`
`2.67=2.70-(Rxx300)/(2F)"In "x`
`-0.03=-(Rxx300)/(2F)"In "x or "In "x=((0.03)xx2)/(300)xx(F)/(R)`
In `Inx=(0.03xx2xx(11500))/(300)=2.3 or x=10`