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A silver electrode is immersed in satura...

A silver electrode is immersed in saturated `Ag_(2)SO_(4(aq))`. The potential difference between the silver and the standard hydrogen electrode is found to be `0.711V` Determine `K_(SP)(AgSO_(4))`. Given `E_(Ag^(+)//Ag)^(@)=0799V`.

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The cell as described in the question is as follows:
`Pt, H_(2) ("1 atm") |H^(+) (1M) ||" satd. Solution of "Ag_(2)SO_(4)|Ag`
`H_(2) ("1 atm") to 2H^(+) +2e`
`2Ag^(+)+2e to 2Ag`
`=H_(2) ("1 atm") +2Ag^(+) to 2H^(+)+2Ag_((s))`
`q=([H^(2)]^(2))/([Ag^(+)]^(2)p_(H_(2)))=(1)/([Ag^(+)]^(2) xx 1)=(1)/([Ag^+]^2)`
`E_("cell")^(0)=E_(Ag^(+),Ag)^(0)-E_(H^(+), 1/2H_(2))^(0)`
`0.711 =0.799-(0.059)/(2) log""(1)/([Ag^(+)]^(2))`
`[Ag^(+)]=3.2 xx 10^(-2)`
`K_(sp)=[Ag^(+)]^(2) [SO_(4)^(-2)]=(3.2 xx 10^(-2))^(2) ((3.2 xx 10^(-2))/(2))=1.6 xx 10^(-5) M^(2)`
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