Calculate the standard cell potentials of galvanic cell in which the following reactions take place `:`
`a. Cr(s) +3Cd^(2+)(aq) rarr 2Cr^(3+)(aq)+3Cd`
`b. Fe^(2+)(aq)+Ag^(o+)(aq)rarr Fe^(3+)(aq)+Ag(s)`
Calculate the `Delta_(r)G^(@)` and equilibrium constant of the reactions .

Explanation

(i). `E_(cell)^(@)=E_("cathode")^(@)-E_("anode")^(@)`
`=-40V-(-0.74V)=0*34V`
`Delta_(r)G^(@)=-nFE_(cell)^(@)`
`=-6xx96500C" "mol^(-1)xx0*34V`
`=-196860C" "V" "mol^(-1)`
`=-196860" J "mol^(-1)=-196.86" kJ "mol^(-1)`
`-Delta_(r)G^(@)=2*303RT" "log" "K`
or `log" "K=34*5014`
`K="antilog "34*5014=3*172xx10^(34)`
(ii). `E_(cell)^(@)=+0*80V-0*77V=+0*03`V
`Delta_(r)G^(@)=-FE_(cell)^(@)`
`=-1xx(96500" C "mol^(-1))xx(0*03V)`
`=-2895" C V "mol^(-1)=-2895" J "mol^(-1)`
`=-2*895" kJ "mol^(-1)`
`Delta_(r)G^(@)=-2*303" RT log "K`
`-2895=-2*303xx8*314xx298xxlog" "K`
or log `K=0*5074`
or `K="antilog "(0*5074)=3*22`.