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The standard reduction potential of Cu^(...

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

Text Solution

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As `E_(Ag^+)^@, Ag` is more positive than `E_(cu^(2+))^@, Cu` the former will acts as cathode and the latter, anode. Thus the cell may be represented as
`Cu,Cu^(2+)||Ag^+, Ag`
Further, given that `[Cu^(2+)]=0.01M and E_(cell)=0` we have,
`E_(cell)=E_(Ag)^+, Ag-E_(cu)^(2+), Cu=0`
`{ E_(Ag^+)^@, Ag+ 0.0591/1 log[Ag^+]}- {E_(cu^(2+))^@, Cu+ 0.0591/2 log[Cu^(2+)]}=0`
or `{0.799+ 0.0591/2 log[Ag^+]}- {0.337+ 0.0591/2 log (0.01)}=0`
or `log[Ag^+]=-8.8172=overline9 .1828`
Taking antilog
`[Ag^+]=1.52 times 10^-9 M`
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