Standard reduction potential for `Cu^(2+)|Cu` is `+0.34V`. Calculate the reduction potential at pH = 14 for the above couple. `K_(sp)` of `Cu(OH)_(2)` is `1.0xx10^(-19)`.

Explanation

Given, `E_(Cu^(2+)|Cu)^(@)(aq)=+0.34V`
`Cu(OH)_(2)(s)rarr Cu^(2+)(aq)+2OH^(-)(aq), K_(sp)=[Cu^(2+)][OH^(-)]^(2)`
Given, `pH=14, [H^(+)]=10^(-14)M, [OH^(-)]=1M`
`K_(sp)" of "Cu(OH)_(2)=1.0xx10^(-19)`
`therefore" "1.0xx10^(-19)=[Cu^(2+)][OH^(-)]^(2)`
`"or, "[Cu^(2+)][1]^(2)=1.0xx10^(-19)" "[because Cu^(2+)+2e rarr Cu]`
`therefore" "[Cu^(2+)]=10^(-19)M`
`therefore" "E_(Cu^(2+)|Cu)^(@)=E_(Cu^(2+)|Cu)^(@)-(0.059)/(2)log.(1)/([Cu^(2+)])`
`therefore" "E_(cu^(2+)|Cu)=0.34-(0.059)/(2)log.(1)/(10^(-19))=-0.22V.`