Write the Nernst equation and emf of the following cells at 298 K: (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)(1bar)| Pt(s) (iii) Sn(s)|Sn 2+ (0.050 M)||H + (0.020 M)|H 2 (g) (1 bar)|Pt(s) (iv) Pt(s)|Br 2 (l)|Br – (0.010 M)||H + (0.030 M)| H 2 (g) (1 bar)|Pt(s).

Question

Philoid · Accepted Answer

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

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).