In the button cells widely used in watches and other devices the following reaction takes place :
`Zn_((S))+Ag_(2)O_((S))+H_(2)O_((l)) to Zn_((aq))^(2+)+2Ag_((S))+2OH_((aq))^(-)`
Determine `Delta_(r)G^(@) and E^(Theta)` cell for the reaction.

Explanation

(a) Calculation of standard reduction potential `E_(cell)^(Theta)` :
The following reaction is carried out in button cell.
`Zn_((S))+Ag_(2)O_((S)) +H_(2)O_((l)) to Zn_((aq))^(2+) +2Ag_((S))+2OH_((aq))^(-)`
Oxidation : `Zn_((S)) to Zn_((aq))^(2+)+2e^(-)`
`therefore E_(L)^(Theta)=E_(Zn^(2+)|Zn)^(Theta)=-0.76V`
Reduction : `Ag_(2)O_((S))+2e^(-) +H_(2)O_((l)) to 2Ag_((S))+2OH_((aq))^(-)`
`therefore E_(R)^(Theta)=E_(Ag_(2)O|Ag)^(Theta)=0.344V`
`therefore DeltaE_(cell)^(Theta)=E_(R)^(Theta)-E_(L)^(Theta)=E_(Ag_(2)O|Ag)^(Theta)-E_(Zn^(2+)|Zn)^(Theta)`
`=0.344-(-0.76)`
`+1.104V`
(b) Calculation of `Delta_(r)G^(@)`, `Delta_(r)G^(@)=-nFE_(cell)^(Theta)|" Where, "n=2" mol "`, `E_(cell)^(Theta)=1.104V`, `F=96500" C "mol^(-1)`
`therefore Delta_(r)G^(@)=-(2mol)xx(96500" C "mol^(-1))xx(1.104V)`
`=-213072CV`
`=-213072J`
`=-2.13xx10^(5)J`
`=-213.072kJ`
`=-213kJ`