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The standard reduction potentials of Cu^...

The standard reduction potentials of `Cu^(2+)//Cu` and `Ag^(+)//Ag` electrodes are 0.337 volt and 0.799 volt respectively. Construct a galvanic cell using these electrodes so that its standard e.m.f. is positive. For what concentration of `Ag^(+)`, will the e.m.f. of the cell at `25^(@)C` be zero if the concentration of `Cu^(2+)` is 0.01 M.

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Given, `E_(Cu^(2+)//Cu)^(@)=0.337` volt and `E_(Ag^(+)//Ag)^(@)=0.799` volt. The standard emf will be positive if `Cu//Cu^(2+)` is anode and `Ag^(+)//Ag` is cathode. The cell can be represented as :
`Cu|Cu^(2+)||Ag^(+)|Ag`
The cell reaction is,
`cu+2Ag^(+) rarr Cu^(2+)+2Ag`
`E_(cell)^(@)=` Oxid. potential of anode + Red. potential of cathode
`=-0.337+0.799`
`=0.462` volt
Applying the Nernst equation,
`E_(cell)=E_(cell)^(@)-0.0591/2"log" ([Cu^(2+)])/([Ag^(+)]^(2))`
or `"log" ([Cu^(2+)])/([Ag^(+)]^(2))=(0.462xx2)/0.0591=15.6345`
`([Cu^(2+)])/([Ag^(+)]^(2))=4.3102xx10^(15)`
`[Ag^(+)]^(2)=0.01/(4.3102xx10^(15))`
`=0.2320xx10^(-17)`
`=2.320xx10^(-18)`
`[Ag^(+)]=1.523xx10^(-9) M`
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