The following chemical reaction is occurring in an electrochemical cell
`Mg (s) + 2Ag^(+) (0.0001 M) to Mg^(2+) (0.10 M) + 2Ag (s)`
The E° electrode values are
`Mg^(2+)//Mg = - 2.36 V,`
`Ag^(+)//Ag = 0.81 V`
For lids cell calculate/write
(a) (i) E° value for the electrode `2Ag^(+)//2Ag`
(ii) Standard cell potential `E_("cell")^(@)`
(b) Cell potential `E_("cell")` ,
(c) (i) Symbolic representation of the above cell.
(ii) Will the above cell reaction be spontaneous ?

Explanation

(a) (i) The electrode potential is not multiplied by the coefficients of metal/metal ion (Ag and `Ag^(+)` in this case).
(ii) `E_("cell")^(@) = E_(Ag^(+)//Ag)^(@) - E_(Mg^(2+)//Mg)^(@)`
`=0.81 - (-2.36) = 3.17 V`
(b) `E_("cell") = E_("cell")^(@) - 0.059/2 log ([Mg^(2+)])/([Ag^(+)]^(2)) = 3.17 - 0.0591/2 log 0.1/([10^(-4)]^(2))`
`=3.17 - 0.059/2 log 10^(7) = 3.17 - 0.0295 xx 7 log 10 = 3.17 - 0.2065 = 2.9635 V`
( c) (i) Mg (s) | `Mg^(2+) (0.1 M) || Ag^(+) (0.0001 M) | Ag(s)`
(ii) Yes, because `E_("cell")^(@)` is positive.