(a) Calculate `DeltaG^(@)` and log `K_( c)` for the following reaction at 298 K :
`2Cr(s) + 3Fe^(2+) (aq) to 2Cr^(3+) (aq) + 3Fe (s)`
(b) (b) Using the E° values of A and B, predict which is better for coating the surface of iron `[E^(@)(Fe^(2+)//Fe) = -0.44 V]` to prevent corrosion and why?
Given : `E_(A^(2+)//A)^(@) = -2.37 V: E_(B^(2+)//B)^(@) = -0.14 V`

Explanation

(a) Given that `E_("cell")^(@) = +0.30 V, F = 96500 C mol^(-1)`
`2Cr (s) to 2Cr^(3+) + 6e^(-)`
`3Fe^(2+)(aq) + 6e^(-) to 3Fe (s)`
Thus, n=6
Apply the relation:
`Delta_(r)G^(@) =-n xx F xx E_("cell")^(@)`
or `Delta_(r)G^(@)=-6 xx 96500 C mol^(-1) xx 0.30 V = -173700 J mol^(-1)` or `-173.7 kJ mol^(-1)`
`log K_( c) = (nE_("cell")^(@))/0.059`
or `log K_( c) = (6 xx 0.30)/0.059`
or `log K_( c) = 30.5`
(b) A is better for coating the surface of iron. This is because E° value for A is more negative than that of Fe. Therefore A has greater tendency for oxidation than Fe. Thus A will oxidise in preference to Fe and protect it from corrosion.