Calculate the emf and `DeltaG` of cell reaction for the following cell at 25 °C :
`Mg(s) | Mg^(2+) (0.001 M) || Cu^(2+) (0.0001 M) + Cu(s)`
`[E_(Mg^(2+)//Mg)]^(@) = -2.37 V, E_(Cu^(2+)//Cu)^(@) =+0.34 V` and `1F = 96500C mol^(-1)`

Explanation

The following reactions take place in the cell:
`Mg(s) to Mg^(2+) (aq) + 2e^(-)`
`Cu^(2+) (aq) + 2e^(-) to Cu(s)`
`Mg(s) + Cu^(2+) (aq) to Mg^(2+) (aq) + Cu(s)`
Thus, n=2
Applying Nernst equation and substituting the values, we get
`E_("cell") = E_(Cu^(2+)//Cu)^(@) -E_(Mg^(2+)//Mg)^(@) -0.0591/2 log ([Mg^(2+)])/([Cu^(2+)])`
`=0.34 V - (-2.37 V) - 0.0591/2 log 0.001/0.0001`
`=2.71 V - 0.0591/2 log 10 = 2.71 V - 0.0295 V = 2.6805V`
`DeltaG` can be obtained as under:
`DeltaG = -nFE =-2 xx 2.6805 xx 96500`
`=-517336.5 J mol^(-1) = -517.34 kJ mol^(-1)`