At 298 K, $Δ G_{f}^{0} H_{2} O_{(l)}$ is $- 237 . 20 k J / m o l$ while that of its ionization into $H^{+}$ ion and $O H^{-}$ ion is $80 k J / m o l$ , then the EMF of the following cell at $298 K$ in the correct scientific notation is $+ A X 10^{B} V$ . ‘A’ Value is $H_{2 (g)} (1 b a r) | H^{+} (1 M) | | O H^{-} (1 M) | O_{2 (g)}, (1 b a r)$

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Detailed Solution

Cell reaction: $H_{2} (g) \to 2 H_{(a q)}^{+} + 2 e^{-}$
$\frac{1}{2} O_{2} + H_{2} O (l) + 2 e^{-} \to 2 O H_{(a q)}^{-}$
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$H_{2} (g) + \frac{1}{2} O_{2} (g) + H_{2} O (l) \to 2 H_{(a q)}^{+} + 2 O H_{(a q)}^{-}$
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$H_{2} (g) + \frac{1}{2} O_{2} (g) \to H_{2} O (l); Δ G^{\circ} = - 237.2 K J / m o l \to (1)$
$H_{2} O (l) \to + H_{(a q)}^{+} + H_{(a q)}^{-}; Δ G^{\circ} = + 80 K J / m o l \to (2)$
$(1) + (2) \times 2$ $H_{2} (g) + \frac{1}{2} O_{2} (g) \to H_{2} O (l)$ ; $Δ G^{\circ} = - 237.2 K J / m o l$
$2 H_{2} O (l) \to + 2 H_{(a q)}^{+} + 2 O H_{(a q)}^{-}$ ; $Δ G^{\circ} = + 160 K J / m o l$
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$H_{2} (g) + \frac{1}{2} O_{2} (g) + H_{2} O (l) \to 2 H_{(a q)}^{+} + 2 O H_{(a q)}^{-}$ $Δ G^{\circ} = - 77.2 K J / m o l$
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$Δ G^{\circ} = - n F E^{\circ}$

$- 77.2 \times 1000 = - 2 \times 96500 \times E^{\circ}$
$E^{\circ} = + 0.4 V = 4 \times 10^{- 1} V$