Calculate the standard cell potentials of galvanic cell in which the following reactions take place:
(i) `2Cr (s) + 3Cd^(2+) (aq) to 2Cr^(3+) (aq) + 3Cd`
(ii) `Fe^(2+)(aq) + Ag^(+)(aq) to Fe^(3+)(aq) +Ag (s)`
Given: `E_(Cr^(3+),Cr) = -0.74 V, E_(Cd^(2+),Cd)^(@) = -0.04 V, E_(Ag^(+),Ag) = 0.80 V, E_(Fe^(3+),Fe^(2+))^(@) = 0.77 V`.
Calculate the `Delta_(r)G^(@)` and equilibrium constant of the reactions.

Explanation

Using the following relations and substituting the values, we get
(i) `E_(cell)^(@) = E_("cathode")^(@) -E_("anode")^(@) = -0.40 V -(-0.74 V) = +0.34` V
`Delta_(r)G^(@) =-nFe_("cell")^(@) =-6 mol xx 96500 C mol^(-1) = -196.86 kJ mol^(-1)`
`=-19600 C V mol^(-1) = -19860 J mol^(-1) = -196.86 kJ mol^(-1)`
`-Delta_(r)G^(@) =2.303 RT log K`
or 196860 = `2.303 xx 8.314 xx 298 log K`
or log K = 34.5014
(ii) `E_("cell")^(@) = +0.80 V - 0.77 v = 0.03 V`
`Delta_(r)G^(@) =-nFE_("cell")^(@) =-(1 mol ) xx (96500 C mol^(-1)) xx (0.03 V)`
`K = "Antilog" (0.5074) = 3.22`