Write the nernst equation and `e.m.f.` of the following cells at `298K` :
`Mg_((s))|Mg^(2+)(0.001 M)||Cu^(2+)(0.0001 M)|Cu_((s))`
(b) `Fe_((s))|Fe^(2+)(0.001 M)||H^(+)(1 M)|H_(2(g))(1"bar")|Pt_((s))`
(c) `Sn_((s))|Sn^(2+)(0.050 M)||H^(+)(0.020 M)|H_(2(g))(1"bar")|Pt_((s))`
(d) `Pt_((s))|Br_(2(l))|Br^(-)(0.010 M)||H^(+)(0.030 M)|H_(2(g))(1"bar")|Pt_((s))`
Given : `E_(OP)^(@)Mg = 2.36 V, E_(OP)^(@)Cu = -0.34 V`,
`E_(OP)^(@)Fe = 0.44 V, E_(OP)^(@)Sn = 0.14 V` and `E_(OP)^(@)Br_(2) = -1.09V` respectively.

Explanation

`E_(cell)^(@) = E_(OP_(Mg//Mg^(2+)))^(@)+E_(RP_(Cu^(2+)//Cu)) + (0.059)/(2)"log" ([Cu^(2+)])/ ([Mg^(2+)])`
`= 2.36 + 0.34 + (0.059)/(2)"log"(10^(-4))/(10^(-3))`
`= 2.67 V`
(b) `E_(cell)^(@) = E_(OP_(Fe//Fe^(2+)))^(@)+E_(RP_(2H^(+)//H_(2)))^(@) + (0.059)/(2)"log"[H^(+)]^(2)/([P_(H_(2))][Fe^(2+)])`
`= 0.44 + 0 + (0.059)/(2)"log"(1^(2))/((1) xx(0.001))`
`= 0.53 V`
(c) `E_(cell)^(@) = E_(OP_(Sn//Sn^(2+)))^(@)+E_(RP_(2H^(+)//H))^(@) + (0.059)/(2)"log"[H^(+)]^(2)/((P_(H_(2)))xx[Sn^(2+)])`
`= 0.44 + 0 + (0.059)/(2)"log"((0.02)^(2))/((1) xx(0.05))`
`= 0.08 V`
(d) `E_(cell)^(@) = E_(OP_(Br_(2)//Br^(-)))^(@)+E_(RP_(2H^(+)//H_(2)))^(@) + (0.059)/(2)"log"[H^(+)]^(2)/((P_(H_(2)))xx[Br^(-)]^(2))`
`= -1.09 + 0 + (0.059)/(2)"log"((0.03)^(2))/((1) xx(0.01)^(2))`
`= -1.06 V`