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The standard reduction potential of the ...

The standard reduction potential of the `Ag^(o+)|Ag` electrode at `298K` is `0.799V`. Given that for `AgI,K_(sp)=8.7xx10^(-17)`, evaluate the potential of the `Ag^(o+)|Ag` electrode in a saturated solution of `AgI`.

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`Agl_((s)) Leftrightarrow Ag_((aq))^(+)+I_((aq))^(-)`
`K_(sp)=[Ag^(+)] [I^(-)]=[Ag^(+)]^(2)`
`[Ag^(+)]=sqrt(K_(sp))=sqrt(8.7 xx 10^(-17)) =9.33 xx 10^(-9)M`
`Ag^(+) +theta to Ag`
`E_(Ag^(+)//Ag)=E_(Ag^(+)//Ag)^(0)-(0.0591)/(1) log""(1)/([Ag^(+)])`
`=0.799 -0.0591 log (1)/((9.33 xx 10^(-8))=0.799 -0.475=0.324V`
`Ag to Ag^(+) +e" "E_(Ag//Ag^(+))^(0)=0.799V`
`AgI+e to Ag_((s))+I^(-)" "E_(I^(-)//AgI//Ag)^(0)=xV`
`="Net cell reaction AgI"_((s)) to [Ag^(+)] [I^(-)]" "E_("cell")^(0)=(0.799+x)`
`K=[Ag^(+)] [I^(-)]=K_(sp)`
`E_("cell") =E_("cell")^(0)-(0.0591)/(1) log K_(sp) (AgI)`
`=0.799V +x=0.0591 log 8.7 xx 10^(-17)`
`rArr 0.799V =-0.949 V`
`x=E_(I^(-)//AgI//Ag)^(0)=-0.150V`
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