Write the Nernst equation and `EMF` of the following cells at `298K :`
`a.` `Mg(s)|Mg^(2+)(0.001M)||Cu^(2+)(0.0001M)|Cu(s)`
`b.` `Fe(s)|Fe^(2+)(0.001M)|H^(o+)(1M)|H_(2)(g)(1 ba r)|Pt(s)`
`c.` `Sn(s)|Sn^(2+)(0.050M)||H^(o+)(0.020M)|H_(2)(g)(1 ba r)|Pt(s)`
`d.` `Pt(s)|Br_(2)(1)|Br^(c-)(0.010M)||H^(o+)(0.030M)|H_(2)(g)(1 ba r)|Pt(s)`

Explanation

(i) Cell reaction : `Mg(s)+Cu^(2+)(aq)toMg^(2+)(aq)+Cu(s)`
`E_(cell)^(@)=E_(cell)^(@)-(0.0591)/(2)"log"([Mg^(2+)])/([Cu^(2+)])=[0.34-(-2.37)]-(0.0591)/(2)"log"(10^(-3))/(10^(-4))`
`=2.71-0.02955=2.68" V"`
(ii) Cell reaction : `Fe(s)+2H^(+)(aq) to Fe^(2+)(aq)+H_(2)(g)`
`E_(cell)^(@)=E_(cell)^(@)-(0.0591)/(2)"log"([Fe^(2+)])/([H^(+)]^(2))=[0-(-0.44)]-(0.0591)/(2)"log"(10^(-3))/((1^(2)))`
`=0.44-(0.0591)/(2)xx(-3)=0=0.44+0.0887=0.523" V"`
(iii) Cell reaction : `Sn(s)+2H^(+)(aq)toSn^(2+)(aq)+H_(2)(g)`
`E_(cell)^(@)=E_(cell)^(@)-(0.0591)/(n)"log"([Sn^(2+)])/([H^(+)]^(2))=[0-(-0.14)]-(0.0591)/(2)"log"(0.05)/((0.02)^(2))`
`=0.14-(0.0591)/(2)xx(2.097)=0.14-0.0620=0.80" V"`
(iv) Cell reaction : `2Br^(-)+2H^(+) to Br_(2)+H_(2)`
`E_(cell)=E_(cell)^(@)-(0.0591)/(2)"log"(1)/([Br^(-)]^(2)[H^(+)]^(2))`
`=(0-1.08)-(0.0591)/(2)"log"(1)/((0.01)^(2)xx(0.03)^(2))=-1.08-(0.0591)/(2)"log"(1.111xx10^(7))`
`=-1.08-(0.0591)/(2)(7.0457)=-1.08-0.208=-1.288" V"`