How many Faradays are needed to reduce 1 mole of `MnO_(4)^(-)` to `Mn^(2+)`?

Options

A. 2
B. 5
C. 4
D. 3

Explanation

To determine how many Faradays are needed to reduce 1 mole of \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \), we can follow these steps:

### Step 1: Determine the oxidation states
The oxidation state of manganese in \( \text{MnO}_4^{-} \) is +7. In \( \text{Mn}^{2+} \), the oxidation state is +2.

### Step 2: Calculate the change in oxidation state
The change in oxidation state from +7 to +2 is:
\[ \text{Change} = +7 - (+2) = 5 \]
This means that manganese is reduced by gaining 5 electrons.

### Step 3: Relate electrons to Faradays
One Faraday corresponds to the charge of one mole of electrons, which is approximately 96485 Coulombs. Therefore, to reduce 1 mole of \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \), we need 5 moles of electrons.

### Step 4: Calculate the number of Faradays required
Since 1 mole of electrons corresponds to 1 Faraday, the number of Faradays needed to reduce 1 mole of \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \) is equal to the number of moles of electrons gained:
\[ \text{Number of Faradays} = 5 \]

### Final Answer
Thus, 5 Faradays are needed to reduce 1 mole of \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \).

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