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

Let the concentration of silver ion be C mol `L^(-1)`
The cell reactions may be represented as:
`" "Cu(s) to Cu^(2+)(aq) +2e^(-)`
`ul(" "Ag^(+)(aq)+e^(-) to Ag(s)"]" xx 2" ")`
Net-reaction:
`Cu(s)+2Ag^(+)(aq) to Cu^(2+)(aq) +2Ag (s) (n =2)`
`E_("cell")^(Theta)=0.80-0.34=0.46V`
Using Nernst equation,
`E_("cell")=E_("cell")^(Theta)-(0.059)/(2)"log"([Cu^(2+)])/([Ag^(+)]^(2))`
or `0.422 =0.46 -0.02955 "log"([0.1])/([C]^(2))`
or `0.422 -0.46= -0.02955 [log 0.1-2log C]`
or `-0.038=-0.02955(-1-2logC)`
or `-0.038=0.02955(1+2logC)`
or `(1+2logC)= (-0.038)/(0.02955)= -1.286`
or `2logC= -2.286 or log C= -1.143`
or `log C= bar(2).857`
Taking antilogarithm, we have `C=0.07194" mol L"^(-1)`