Answer
$ K =e^{RT\div nFE^{\circ}cell} $
Work Step by Step
$ \Delta G^{\circ} =-nFE^{\circ}cell$ Equation (1)
Where,
$ \Delta G^{\circ} = standard\ free\ energy\ change $
n= number of electrons involved in the cell reaction
F = Faraday's constant
$ E^{\circ}{cell} $ = Standard cell EMF
$ \Delta G^{\circ} =-RT lnK$ Equation (2)
R = Universal gas constant
T = Absolute temparature
K = Equilibrim constant of the cell reaction
Combining equation (1) and (2) we have
$ -nFE^{\circ}cell =-RT lnK$
$lnK =RT\div nFE^{\circ}cell$
Taking exponentials on both sides we have
$ K =e^{RT\div nFE^{\circ}cell} $
