Answer
$E_{cell} \gt 0$, $ \Delta G \lt 0$, Cell reaction is spontaneous.
$E_{cell} \lt 0$, $ \Delta G \gt 0$, Cell reaction is non-spontaneous.
$E_{cell} = 0$, $ \Delta G= 0$, Cell reaction is at equilibrium.
Work Step by Step
$ \Delta G = -n F E_{cell}$
Where
$ \Delta G$ = Free energy change
n = number of electrons involved in cell reaction.
F = Faraday’s constant
$E_{cell}$ = Cell EMF
If $ \Delta G $ = negative ; Cell reaction is spontaneous.
If $ \Delta G $ = positive ; Cell reaction is non-spontaneous.
If $ \Delta G $ = 0 ; Cell reaction is at equilibrium.
$E_{cell} \gt 0$ means $E_{cell}$ is positive.
Then on substituting in the equation $ \Delta G = -n F E_{cell}$
$ \Delta G $ = negative and cell reaction is spontaneous.
$E_{cell} \lt 0$ means $E_{cell}$ is negative.
Then upon substituting in the equation $ \Delta G = -n F E_{cell}$
$ \Delta G $ = positive and cell reaction is non-spontaneous.
$E_{cell} = 0$
Then upon substituting in the equation $ \Delta G = -n F E_{cell}$
$ \Delta G $ = 0 and cell reaction is at equilibrium.
