Write the Nernst equation and emf of the following cells at 298 K:

(i) Mg(s)|Mg²⁺ (0.001M)||Cu²⁺ (0.0001 M)|Cu(s)

(ii) Fe(s)|Fe²⁺ (0.001M)||H⁺ (1M)|H₂(g)(1bar)| Pt(s)

(iii) Sn(s)|Sn²⁺ (0.050 M)||H⁺ (0.020 M)|H₂(g) (1 bar)|Pt(s)

(iv) Pt(s)|Br₂(l)|Br^–(0.010 M)||H⁺ (0.030 M)| H₂(g) (1 bar)|Pt(s).

E_cell = ?

(i) Mg + Cu^{2 +} → Mg^{2 +} + Cu (n = 2)

E⁰_Cu^{2 +} _/Cu ⁺ = 0.34V

E⁰_Mg^{2 +} _/Mg = - 2.37 V

E⁰_cell = E⁰_R - E⁰_L

E⁰_cell = 0.34 - ( - 2.37) → Equation 1

Using Nernst equation, we get,

→ Equation 2

Substituting Equation 1 in equation 2, we get,

∴ E_cell = 0.34 - ( - 2.37) -

= 2.71 -

= 2.71 - 0.02955

∴ E_cell = 2.68 V

The e.m.f of the cell, E_cell is 2.68 V

ii) Fe + 2H ⁺ → Fe^{2 +} + H₂ (n = 2)

E⁰_H ⁺ _/H2 = 0 V

E⁰_Fe^{2 +} _/Fe = - 0.44 V

E⁰_cell = E⁰_R - E⁰_L

E⁰_cell = 0 - ( - 0.44) → Equation 1

Using Nernst equation, we get,

→Equation 2

Substituting Equation 1 in equation 2, we get,

∴ E_cell = 0 - ( - 0.44) -

= 0.44 -

= 0.44 - 0.0887

∴ E_cell = 0.5287 V

The e.m.f of the cell, E_cell is 0.5287 V

iii) Sn + 2H ⁺ → Sn^{2 +} + H₂ (n = 2)

E⁰_H ⁺ _/H2 = 0 V

E⁰_Sn^{2 +} _/Sn = - 0.14V

E⁰_cell = E⁰_R - E⁰_L

E⁰_cell = 0 - ( - 0.14) → Equation 1

Using Nernst equation, we get,

→Equation 2

Substituting Equation 1 in equation 2, we get,

∴ E_cell = 0 - ( - 0.14) -

= 0.14 -

= 0.14 - 0.0295×2.0969

∴ E_cell = 0.08 V

The e.m.f of the cell, E_cell is 0.08 V

iv) 2Br ^- + 2H ⁺ → Br₂ + H₂ (n = 2)

E⁰_H ⁺ _/H2 = 0 V

E⁰_Br2/Br ^- = 1.08V

E⁰_cell = E⁰_R - E⁰_L

E⁰_cell = 0 - (1.08) → Equation 1

Using Nernst equation, we get,

→Equation 2

Substituting Equation 1 in equation 2, we get,

∴ E_cell = 0 - (1.08) -

= - 1.08 -

= - 1.08 - 0.208

∴ E_cell = 1.288 V

The e.m.f of the cell, E_cell is 1.288 V