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Calculate the standard cell potential of...

Calculate the standard cell potential of the galvanic cell in which the following reaction takes place:
`Fe%(2+)(aq)+Ag^(+)(aq)rarrFe^(3+)(aq)+Ag(s)`
Calculate the `Delta_(r)G^(@)` and equilibrium constant of the reaction also.
`(E_(Ag^(+)|Ag)^(@)=0.80V, E_(Fe^(3+)|Fe^(2+))^(@)=0.77V)`

Text Solution

Verified by Experts

`{:("Anode reaction : "Fe^(2+)(aq)rarrFe^(3+)(aq)+e),("Cathode reaction :"Ag^(+)(aq)+erarrAg(s)),(bar("Cell reaction :"Fe^(2+)(aq)+Ag^(+)(aq)rarrFe^(3+)(aq)+Ag(s)" ")):}`
So, for the cell reaction, n = 1.
`E_("cell")^(@)=E_("cathode")^(@)-E_("anode")^(@)=E_(Ag^(+)|Ag)^(@)-E_(Fe^(3+)|Fe^(2+))^(@)`
`=(0.80-0.77)V=0.03V`
`therefore" "Delta_(r)G^(@)=-nFE^(@)=-1xx96500xx0.03J=-2895J`
Equilibrium constant `(K_(eq))` is related with `Delta_(r)G^(@)` by the equation `Delta_(r)G^(@)=-RT ln K_(eq)`
`therefore" "-2895=-8.314xx298xx2.303 log K_(eq)`
or, `K_(eq)=3.216`
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