The cell in which the following reactions occurs : `2Fe_((aq))^(3+)+2l_((aq))^(-) to 2Fe_((aq))^(2+)+I_(2(S))` has `E_(cell)^(Theta)=0.236V` at 298 K. calculate the standard Gibbs energy and the equilibrium constant of the cell reaction.

Explanation

(a) Cell reaction and calculation of `Delta_(r)G^(Theta)`:

Where, n=2 mol,
`F=96487" C "mol^(-1)`,
`E_(cell)^(Theta)=0.236V`
`therefore Delta_(r)G^(Theta)=-nFE_(cell)^(Theta)`
`=-(2mol)(96487" C "mol^(-1))(0.236V)`
`=-45542(V)`
`=-45542J`
=-45.542 kJ `~~-45.54kJ`
(b) Calculation of equilibrium constant `K_(c)`:
`therefore Delta_(r)G^(Theta)=-2.303RT" log "K_(c)`
`therefore -45542=-2.303xx8.314xx298xxlog" "K_(c)`
`therefore log" "K_(c)=(-45542)/(-2.303xx8.314xx298)`
`therefore log" "K_(c)=+7.9816`
`thereforeK_(c)="Antilog"(7.9816)`
`=9.586xx10^(7)`
`~~9.6xx10^(7)`