Write the cell reaction and calculate the e.m.f. of the following cell at $298$ K.
$S n (s) | S n^{2 +} (0.004 M) | | H^{+} (0.020 M) | H_{2} (g) (1 b a r) | P t (s)$ .
(Given: $E_{S n^{2 +} / S n}^{o} = - 0.14 V)$ .

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Solution

Oxidation at anode:
$S n (s) \to S n^{2 +} (a q) + 2 e^{-}$
Reduction at cathode:
$2 H^{+} (a q) + 2 e^{-} \to H_{2} (g)$
The cell reaction is
$S n (s) + 2 H^{+} (a q) \to S n^{2 +} (a q) + H_{2} (g)$
$E_{c e l l}^{o} = E_{S H E}^{o} - E_{S n | S n^{2 +}}^{o}$
$E_{c e l l}^{o} = 0.0 V - (- 0.14 V) = 0.14 V$
$E_{c e l l} = E_{c e l l}^{o} - \frac{0.0592}{n} l o g \frac{[S n^{2 +}] \times P_{H 2}}{[H^{+}]^{2}}$
$E_{c e l l} = 0.14 V - \frac{0.0592}{2} l o g \frac{0.004 M \times 0.987 a t m}{[0.020]^{2}}$
Note: 1 bar $= 0.987$ atm.
$E_{c e l l} = 0.111 V$

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Q. Write the Nernst equation and emf of the following cells at

298 K

:
(i)

M g (s) | M g^{+ 2} (0.001 M) ∥ C u^{+ 2} (0.0001 M) | C u (s)

.
(ii)

F e (s) | F e^{+ 2} (0.001 M) ∥ H^{+} (1 M) | H_{2} (g) (1 b a r) | P t (s)

(iii)

S n (s) | S n^{2 +} (0.050 M) ∥ H^{+} (0.020 M) | H_{2} (g) (1 b a r) | P t (s)

(iv)

P t (s) | B r_{2} (l) | B r^{-} (0.010 M) ∥ H^{+} (0.030 M) | H_{2} (g) (1 b a r) | P t (s)

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).

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

(i) $M g (s) | M g^{2 +} (0.001 M) | | C u^{2 +} (0.001 M) | C u (s)$

(ii) $F e (s) | F e^{2 +} (0.001 M) | | H^{+} (1 M) | H_{2} (g) (1 b a r) | P t (s)$

(iii) $S n (s) | S n^{2 +} (0.050 M) | | H^{+} (0.020 M) | H_{2} (g) (1 b a r) | P t (s)$

(iv) $P t (s) | B r_{2} (l) | B r^{-} (0.010 M) | | H^{+} (0.030 M) | H_{2} (g) (1 b a r | P t (s))$

$E_{(\frac{M g^{2 +}}{M g})}^{\circ} = - 2.37 V; E_{(\frac{C u^{2 +}}{C u})}^{\circ} = + 0.34 V; E_{(\frac{F e^{2 +}}{F e})}^{\circ} = - 0.44 V; E_{(\frac{S n^{2 +}}{S n})}^{\circ} = - 0.14 V; E_{(\frac{\frac{1}{B r_{2}}}{B r^{-}})}^{\circ} = + 1.08 V,$