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
First, we need to find the oxidation state of manganese in \( \text{MnO}_4^{-} \). The oxidation state of oxygen is typically -2. So, for \( \text{MnO}_4^{-} \):

\[ \text{Let the oxidation state of Mn be } x. \]
\[ x + 4(-2) = -1 \quad \text{(since the overall charge is -1)} \]
\[ x - 8 = -1 \]
\[ x = +7 \]

Thus, the oxidation state of manganese in \( \text{MnO}_4^{-} \) is +7.

### Step 2: Determine the oxidation state of \( \text{Mn}^{2+} \)
In \( \text{Mn}^{2+} \), the oxidation state of manganese is +2.

### Step 3: Calculate the change in oxidation state
Now, we can calculate the change in oxidation state when \( \text{MnO}_4^{-} \) is reduced to \( \text{Mn}^{2+} \):

\[ \text{Change in oxidation state} = +7 - (+2) = +5 \]

This indicates that manganese is reduced by gaining 5 electrons.

### Step 4: Relate the number of moles of electrons to Faradays
According to Faraday's laws of electrolysis, the number of Faradays required is equal to the number of moles of electrons involved in the reaction. Since we need 5 moles of electrons to reduce 1 mole of \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \), we conclude:

\[ \text{Number of Faradays needed} = 5 \]

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

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