How many Faradays are required to reduce `1 mol of BrO_(3)^(-)` to `Br^(-)` in basic medium ?

Explanation

To determine how many Faradays are required to reduce 1 mole of \( \text{BrO}_3^{-} \) to \( \text{Br}^{-} \) in a basic medium, we can follow these steps:

### Step 1: Write the half-reaction for the reduction of \( \text{BrO}_3^{-} \)

The first step is to write the half-reaction for the reduction of bromate ion \( \text{BrO}_3^{-} \) to bromide ion \( \text{Br}^{-} \).

\[ \text{BrO}_3^{-} + \text{e}^{-} \rightarrow \text{Br}^{-} \]

### Step 2: Balance the oxygen atoms

In basic medium, we need to balance the oxygen atoms by adding water molecules to the side that has fewer oxygen atoms. Since there are 3 oxygen atoms in \( \text{BrO}_3^{-} \), we will add 3 water molecules to the right side of the equation.

\[ \text{BrO}_3^{-} + \text{e}^{-} \rightarrow \text{Br}^{-} + 3 \text{H}_2\text{O} \]

### Step 3: Balance the hydrogen atoms

Next, we need to balance the hydrogen atoms. Since we added 3 water molecules, we now have 6 hydrogen atoms on the right side. To balance this, we will add 6 hydroxide ions \( \text{OH}^{-} \) to the left side of the equation.

\[ \text{BrO}_3^{-} + 6 \text{OH}^{-} + \text{e}^{-} \rightarrow \text{Br}^{-} + 3 \text{H}_2\text{O} \]

### Step 4: Balance the charges

Now we need to balance the charges. The left side has a total charge of \( -1 + (-6) + (-1) = -8 \) and the right side has a total charge of \( -1 \). To balance the charges, we need to add 6 electrons to the left side:

\[ \text{BrO}_3^{-} + 6 \text{OH}^{-} + 6 \text{e}^{-} \rightarrow \text{Br}^{-} + 3 \text{H}_2\text{O} \]

### Step 5: Determine the number of Faradays required

From the balanced half-reaction, we can see that 6 electrons are required to reduce 1 mole of \( \text{BrO}_3^{-} \) to \( \text{Br}^{-} \). Since 1 mole of electrons corresponds to 1 Faraday, we need 6 Faradays to reduce 1 mole of \( \text{BrO}_3^{-} \).

### Final Answer

Thus, the number of Faradays required to reduce 1 mole of \( \text{BrO}_3^{-} \) to \( \text{Br}^{-} \) in basic medium is **6 Faradays**.

---