For the electrochemical cell,
`Mg(s)|Mg^(2+) (aq. 1M)||Cu^(2+) (aq. 1M)|Cu(s)`
the standard emf of the cell is 2.70 V at 300 K. When the concentration of `Mg^(2+)` is chaged 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 constant, ln (10) = 2.30)

Answer

10

Explanation

Cell reaction :
`Mg(s)+Cu^(2+) (aq) hArr Mg^(2+) (aq)+Cu(s)" "(n=2)`
when the concentration of ionic species is 1 M then `E=E^(@)`
`:. E^(@)=2.70 V`
Using Nernst equation :
`E=E^(@)-(RT)/(nF)"ln" ([Mg^(2+)])/([Cu^(2+)])`
`2.67=2.70-(RT)/(2F) log_(e) [x/1]`
`ln x=(0.03xx2)/300xxF/R=(0.03xx2xx11500)/(300)`
`=2.30=ln 10`
`x=10`