`Cu^(2+)(aq.)` is unstable in solution and under goes simultaneous oxidation and reduction according to the reaction
`2Cu^(+)(aq.)hArr Cu^(2+)(aq.)+Cu(s)`
Choose the correct `E^(@)` for the above reaction if
`E_(Cu^(2+))^(@)//Cu = 0.34 V and E_(Cu^(2+))^(@)//Cu^(+) = 0.15 V`

Options

A. `-0.38 V`
B. `+0.49 V`
C. `+0.38 V`
D. `-0.19 V`

Answer

C

Explanation

( c) `DeltaG^(@)=-nFE^(@)`
From given data,
`(i) Cu(s) to Cu^(2+)(aq) +2e^(-), DeltaG_(1)^(@)=-2(-0.34)xxF`
`(ii)Cu^(2+)(aq)+e^(-) to Cu^(+)(aq),DeltaG_(2)^(@)=-(0.15)xxF`
On addition,
`Cu(s) to Cu^(+)(aq)+e^(-), DeltaG_(3)^(@)=-1xxE^(@)xxF`
` and DeltaG_(3)^(@)=DeltaG_(1)^(@)+DeltaG_(2)^(@)`
`-n_(3)FE^(@)=-n_(1)FE_(1)^(@)-n_(2)FE_(2)`
`-E^(@)=-(-0.34)-1(0.15)`
`=(-2xx-0.34)+(-1xx0.15)`
`-E^(@)=+0.68-0.15=0.53`
` or E^(@)=-0.53V`
`Cu^(+)(aq) iff Cu^(2+)(aq)+e^(-),`
`DeltaG_(1)=-1xx(-0.15)xxF`
`Cu^(+)(aq)+e^(-) iff Cu(s),`
`DeltaG_(2)=-1xx(-0.53)xxF`
On adding above equation we get,
`2 Cu^(+) iff Cu^(2+)+Cu,DeltaG`
`DeltaG=DeltaG_(1)+DeltaG_(2)`
`-nFE^(@)=0.15F+(-0.53F)`
`-FE^(@)=-0.38 F`
`E^(@)=0.38V `
Thus, for the result reaction `E^(@)` value is 0.38 V