The standard cell potential of the above reaction is: [2025]

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Solution

Q.
For the given cell

${Fe}^{2 +}_{(aq)} + {Ag}^{+}_{(aq)} \to {Fe}^{3 +}_{(aq)} + {Ag}_{(s)}$

The standard cell potential of the above reaction is:

Given:

${Ag}^{+} + e^{-} \to Ag$ $E^{θ} = x V$

${Fe}^{2 +} + 2 e^{-} \to Fe$ $E^{θ} = y V$

${Fe}^{3 +} + 3 e^{-} \to Fe$ $E^{θ} = z V$ [2025]

1 $x + 2 y - 3 z$

2 $x + 2 y$

3 $x + y - z$

4 $y - 2 x$

Ans.
(1)

${Ag}^{+} + e^{-} \to Ag-I (Δ G_{1} = - n F E_{1} = - 1 F x)$

${Fe}^{2 +} + 2 e^{-} \to Fe-II (Δ G_{2} = - n F E_{2} = - 2 F y)$

${Fe}^{3 +} + 3 e^{-} \to Fe-III (Δ G_{3} = - n F E_{3} = - 3 F z)$

$I + II - III$ gives the required equation:

${Fe}^{2 +} + {Ag}^{+} \to {Fe}^{3 +} + Ag-IV$

$Δ G_{4} = Δ G_{1} + Δ G_{2} - Δ G_{3} = - 1 F x - 2 F y + 3 F z$

$- n F E_{4} = - 1 F x - 2 F y + 3 F z$

$- I F E_{4} = - 1 F x - 2 F y + 3 F z$

$E_{4} = x + 2 y - 3 z$

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