In the following redox reactions, what is the value of $f$ ?
$I$ . $a M n O_{4}^{-} + b {F e}^{2 +} + c H^{+} ⟶ d {M n}^{2 +} + e {F e}^{3 +} + f H_{2} O$
$I I$ . $a {C r}_{2} O_{7}^{2 -} + b {F e}^{2 +} + c H^{+} ⟶ d {C r}^{3 +} + e {F e}^{3 +} + f H_{2} O$
$I I I$ . $a M n O_{4}^{-} + b H_{2} O_{2} + c H^{+} ⟶ d {M n}^{2 +} + e O_{2} + f H_{2} O$

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Solution

The balanced redox reactions are as shown
$I$ . $M n O_{4}^{-} + 5 {F e}^{2 +} + 8 H^{+} ⟶ {M n}^{2 +} + 5 {F e}^{3 +} + 4 H_{2} O$
The value of $f$ is 4.
$I I$ . ${C r}_{2} O_{7}^{2 -} + 6 {F e}^{2 +} + 14 H^{+} ⟶ 2 {C r}^{3 +} + 6 {F e}^{3 +} + 7 H_{2} O$
The value of $f$ is 7.
$I I I$ . $2 M n O_{4}^{-} + 5 H_{2} O_{2} + 6 H^{+} ⟶ 2 {M n}^{2 +} + 5 O_{2} + 8 H_{2} O$
The value of $f$ is 8.

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a M n O_{4}^{-} + b H_{2} O_{2} + c H^{+} \to d M n^{+ 2} + e O_{2} + f H_{2} O

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C H_{3} C H_{2} C H_{2} C H_{2} O H

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\begin{matrix} C o l u m n - I & C o l u m n - I I (M e t a l i o n) & (M a g n e t i c m o m e n t (B M)) (a) & C r^{3 +} & (p) & \sqrt{35} (b) & F e^{2 +} & (q) & \sqrt{30} (c) & N i^{2 +} & (r) & \sqrt{24} (d) & M n^{2 +} & (s) & \sqrt{15} (t) & \sqrt{8} \end{matrix}

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