How many faradays are required to reduce ` 1` mol of `MnO_4^(-)` to `Mn^(2+)`?

Options

A. `1`
B. `2`
C. `3`
D. `5`

Explanation

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

### Step 1: Write the half-reaction for the reduction of \( \text{MnO}_4^{-} \)
The reduction of permanganate ion (\( \text{MnO}_4^{-} \)) to manganese ion (\( \text{Mn}^{2+} \)) can be represented as follows:

\[ \text{MnO}_4^{-} + 8 \text{H}^{+} + 5 \text{e}^{-} \rightarrow \text{Mn}^{2+} + 4 \text{H}_2\text{O} \]

### Step 2: Identify the number of electrons transferred
From the balanced half-reaction, we can see that 5 electrons (\( 5 \text{e}^{-} \)) are required to reduce 1 mole of \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \).

### Step 3: Relate the number of electrons to Faradays
1 Faraday is defined as the charge of 1 mole of electrons, which is approximately \( 96485 \) coulombs. Therefore, the number of Faradays required is equal to the number of moles of electrons transferred.

### Step 4: Calculate the number of Faradays
Since we need 5 moles of electrons to reduce 1 mole of \( \text{MnO}_4^{-} \):

\[ \text{Faradays required} = 5 \text{ moles of electrons} = 5 \text{ Faradays} \]

### Final Answer
Thus, the number of Faradays required to reduce 1 mole of \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \) is **5 Faradays**.

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