निम्नलिखित सेलों की 298 K पर नर्नस्ट समीकरण एवं emf लिखिए ।
(i) `Mg_((s))|Mg^(2+)(0*001M)||Cu^(2+)(0*0001 M)|Cu_((s))`
(ii) `Fe_((s))|Fe^(2+)(0*001M)||H^(+)(1M)|H_(2(g))(1"bar")|Pt_((s))`
(iii) `Sn_((s))|Sn^(2+)(0*050M)||H^(+) (0*020 M)|H_(2(g))(1"bar")|Pt_((s))`
(iv) `Pt_((s))|Br_(2(l))|Br^(-)(0*010M)||H^(+)(0*030M)|H_(2(g))(1"bar")|Pt_((s))`.

Explanation

(i) ` Mg + Cu^(2+) to Mg^(2+) + Cu`
`E_(cell)^(o) = E_(Cu^(2+)//Cu)^(o) - E_(Mg^(2+)//Mg)^(o) `
` = 0*34 - (-2*37) = 2*71 V`
` :. n = 2`
अब , ` E_(cell) = E_(cell)^(o) - (0*0591)/n log. ([Mg^(2+)])/([Cu^(2+)])`
` E_(cell) = 2 * 71 - (0*0591)/2 log. (10^(-3))/(10^(-4))`
` = 2 * 71 - 0*02955 = 2 * 68V`
(ii) `E_(cell)^(o) = E_(H^(+)//H_(2)) - E_(Fe^(2+)//Fe)`
` = 0*0 - (- 0*44) = + 0 * 44.`
अब , `E_(cell) = E_(cell)^(o) - (0*0591)/n log. ([Fe^(2+)])/([H^(+)]^(2))`
`E_(cell) = 0*44 - (0*0591)/2 log .(10^(-3))/1^(2)`
` = 0 * 44 - (0*0591)/2 xx (-3)`
` = 0 * 44 + 0 *0887 = 0*528 V`
(iii) `E_(cell)^(o) = E_(H^(+)//H_(2))^(o) - E_(Sn^(2+)//Sn)^(o) `
` = 0*0 - (-0*14) = + 0 * 14 V`
अब , `E_(cell) = E_(cell)^(o) - (0*0591)/n log .([Sn^(2+)])/([H^(+)]^(2))`
` E_(cell) = 0*14 - (0*0591)/2 log. (0*05)/((0*02)^(2))`
` = 0*14 - (0*0591)/2 log 125 = 0*078V`
(iv) ` E_(cell)^(o) = E_(H^(+)//H_(2))^(o) - E_(Br^(-)//Br_(2))^(o) `
` = 0 - 1 * 08 = - 1 * 08 V`
अब , `E_(cell) = E_(cell)^(o) - (0*0591)/n log. 1/([Br^(-)]^(2)[H^(+)]^(2))`
` = - 1*08 - (0*0591)/2 log . 1/([0*01]^(2)[0*03]^(2))`
` = - 1*08 - (0*0591)/2 log (1*111 xx 10^(7))`
` = - 1*08 - (0*0591)/2 (7 * 0457)`
` = - 1 * 08 - (0*0591)/2 (7 * 04 57)`
` = - 1 * 08 - 0*208 = - 1 * 288 V`