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Electrolytic Cell

Construct gal...

Question

Construct galvanic cells from the following pairs of half cells and calculate their emf at $25^{o} C .$

$F e^{3 +} (a q, 0.1 M), F e^{2 +} (a q, 1 M) | P t (s); E_{F e^{3 +} / F e^{2 +}}^{0} = 0.77 V$

$A g (s) | A g C l (s) ∣ C l^{-} (a q, 0.001 M); E_{A g C l / A g}^{0} = 0.22 V$

E_{c e l l} = 0.567 V

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E_{c e l l} = 0.313 V

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E_{c e l l} = 0.023 V

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E_{c e l l} = 1.13 V

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Solution

The correct option is B $E_{c e l l} = 0.313 V$
For the half - cell reaction,
From the standard reduction potential values we can see $A g (s)$ will act as anode in the galvanic cell.
Applying nearst eq. for individual half cells:
$F e^{3 +} (a q) + e^{-} ⇌ F e^{2 +} (a q)$
By Nernst equation,

$E_{F e^{3 +} / F e^{2 +}} = E_{F e^{3 +} / F e^{2 +}} - \frac{0.0591}{1} l o g \frac{[F e^{2 +}]}{[F e^{3 +}]}$

$= 0.77 - \frac{0.0591}{1} l o g \frac{1}{0.1} = 0.71 V$

And, for the half - cell reaction,

$A g C l (s) + e^{-} ⇌ A g (s) + C l^{-} (a q)$

$E_{C l^{-} / A g C l / A g} = E_{C l^{-} / A g C l / A g}^{0} - \frac{0.0591}{1} l o g [C l^{-}$

$E_{C l^{-} / A g C l / A g} = 0.22 - \frac{0.0591}{1} l o g 0.001$

$E_{C l^{-} / A g C l / A g} = 0.22 - \frac{0.0591}{1} l o g 10^{- 3}$

$E_{C l^{-} / A g C l / A g} = 0.22 + \frac{3 \times 0.0591}{1}$

$E_{C l^{-} / A g C l / A g} = 0.397 V$

$∴$ Cell may be represented as

$A g (s) | A g C l (s) ∣ C l^{-} (a q) ∣∣ F e^{3 +} (a q), F e^{2 +} (a q) | P t (s)$

$E_{c e l l} = reduction potential of RHS electrode - reduction potential of LHS electrode$

$E_{c e l l} = 0.71 - 0.397 E_{c e l l} = 0.313 V$

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Similar questions

25^{o} C .

C d^{2 +} (a q, 1 M) ∣ C d (s); E_{C d^{2 +} / C d}^{0} = - 0.40 V

H g_{2} C l_{2} (s) ∣ H g (l) ∣ C l^{-} (a q, 0.1 M); E_{C l^{-} / H g_{2} C l_{2} / H g}^{0} = 0.28 V

25^{o} C

P t (s) | F e^{2 +} (a q, 0.1 M), F e^{3 +} (a q, 0.01 M); E_{F e^{3 +} / F e^{2 +}}^{0} = + 0.77 V

Z n (s) | Z n^{2 +} (a q) | | M^{x +} (a q) | M (s)

$M^{x +} (a q / M (s))$	$A u^{3 +} (a q) / A u (s)$	$A g^{+} / A g (s)$	$F e^{3 +} (a q) / F e^{2 +} (a q)$	$F e^{2 +} (a q) / F e (s)$
$E_{M^{x +} / M^{/ (V)}}^{o}$	$1.40$	$0.80$	$0.77$	$- 0.44$

E_{Z n^{2 +} / Z n}^{o} = - 0.76 V

E_{c e l l}^{o}

298 K

E_{N i^{2 +} (a q) / N i (s)}^{\circ} = - 0.24 V

E_{F e^{2 +} (a q) / F e (s)}^{\circ} = - 0.44 V

F_{2} (g) + 2 e^{-} \to 2 F^{-} (a q); E^{0} = 2.87 V C l_{2} (g) + 2 e^{-} \to C l^{-} (a q); E^{0} = 1.36 V F e^{3 +} (a q) + e^{-} \to F e^{2 +} (a q); E^{0} = 0.77 V

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