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. The value of x is _____.
(given , `F/R = 11500 KV^(-1),` where F is the Faraday constant and R is the gas constants, 1n (10) = 2.30)`

Explanation

For the given cell ,
Anodic reaction : `M g_((s)) to M g^(2+)+2e^(-)`
Cathodic reaction : `Cu^(2++)+2e^(-) to Cu_((s))` and balanced reaction is `M g_((s))+Cu^(2+)(1M) to Cu((s)) + M g^(2+)(xM)`
`E_(cell)=E_(cell)^(@)-(Rt)/(nF)1nx/1implies E_(cell)=E_(cell)^(@)-T/((nF)/R)1n x`
`implies 2.67=2.70-200/(2xx11500)1nx implies 0.03=300/(2xx11500)1nx`
`implies 2.3 =1nx therefore x=10`