For the cell reaction,
`Mg|Mg^(2+) (aq.)||Ag^(+) (aq.)|Ag`
calculate the equilibrium constant at `25^(@)C` and maximum work that can be obtained by operating the cell.
`E_(Mg^(2+)//Mg)^(@)=-2.37` volt and `E_(Ag^(+)//Ag)^(@)=+0.80` volt

Explanation

The cell is :
`Mg|Mg^(2+) (aq) || Ag^(+) (aq) |Ag`
The cell reaction is :
`Mg (s) + 2 Ag^(+) (aq) to Mg^(2+) (aq) +2 Ag (s)`
Calculation of `E_(cell)^(Theta)`
`E_(cell)^(Theta) = E^(Theta) ` (cathode) `- E^(Theta)` (anode)
`E^(Theta) (Ag^(+) |Ag) - E^(Theta) (Mg ^(2+) |Mg)`
`= 0.80 - (- 2.37) = 3.17 V`.
Calculation of equilibrium constant .
`log K_(c) = (n E _(cell))/(0.059) ` at 298 K
`n = 2, E_(cell)^(Theta) = 3.17 V`
log `K_(c) = (2 xx 3017)/(0.059) = 107.457`
`K_(c) = 2.56 xx 10^(107)`
Calculation of maximum work that can be obtained from the cell . The maximum work obtained is equal to `Delta G^(Theta)` so that
`Delta G^(Theta) = - n FE_(cell)^(Theta)`
`n = 2 , F = 96500 C , E_(cell)^(Theta) = 3.17` V
`therefore " " Delta G^(Theta) = - 2 xx (96500 C) xx (3.17 V)`
`= -611 800 C V = -611 810 J (1 CV = 1 J)`
`therefore` Maximum work obtained = 611.8 kJ .