A copper - silver cell is set up . The copper ion concentration in it is 0.10 M. concetration of silver ion is not known . The cell potential measured 0.422 V. determine the concentration of silver ion in the cell.
Given : `E_(Ag+//Ag)^(@)=+0.80V,E_(Cu^(2+)//Cu)^(@)=+0.34V.`

Explanation

The cell can be represented as:
`Cu(s)|Cu^(2+)(aq)||Ag^(+)(aq)|Ag(s)`
`thereforeE_(cell)^(@)=E_("cathode")^(@)-E_("anode")^(@)=0.80-0.34=0.46V`
`thereforeE_(cell)=E_(cell)^(@)-(0.059)/(n)log(([Cu^(2+)(aq)])/([Ag^(+)(aq)]^(2)))`
`therefore0.422=0.46-(0.059)/(2)log((0.1)/([Ag^(+)(aq)]^(2)))`
`=(0.10)/([Ag^(+)]^(2)))="antilog"(1.288)`
`=(0.10)/([Ag^(+)]^(2))=19.41implies[Ag^(+)]=7.1xx10^(-2)M`