Consider the following reaction occuring in basic medium
`2MnO_(4)^(-) + Br^(-)(aq) to 2MnO_(2) (s) + BrO_(3)^(-) (aq)`
How the above reaction can be balanced further ?

Options

A. By adding `2 OH^(-)` ions on right side
B. By adding one `H_(2)O` molecule to left side
C. By adding `2H^(+)` ions on right side
D. Both (a) and (b)

Explanation

To balance the given reaction in a basic medium, we will follow these steps:

### Step 1: Write the unbalanced reaction
The unbalanced reaction is:
\[ 2 \text{MnO}_4^{-} + \text{Br}^{-} \rightarrow 2 \text{MnO}_2 (s) + \text{BrO}_3^{-} \]

### Step 2: Count the number of atoms on both sides
- **Left side:**
- Manganese (Mn): 2
- Oxygen (O): 8 (from 2 MnO4^-)
- Bromine (Br): 1

- **Right side:**
- Manganese (Mn): 2 (from 2 MnO2)
- Oxygen (O): 7 (2 from MnO2 and 5 from BrO3^-)
- Bromine (Br): 1

### Step 3: Balance the oxygen atoms
There are 8 oxygen atoms on the left and 7 on the right. To balance the oxygen atoms, we need to add hydroxide ions (OH^-) to the right side. Since we need 1 more oxygen atom, we add 2 OH^- ions to the right side.

The reaction now looks like:
\[ 2 \text{MnO}_4^{-} + \text{Br}^{-} \rightarrow 2 \text{MnO}_2 (s) + \text{BrO}_3^{-} + 2 \text{OH}^{-} \]

### Step 4: Balance the hydrogen atoms
Now, we have added 2 OH^- ions, which means we have introduced 2 hydrogen atoms on the right side. To balance the hydrogen atoms, we need to add 1 water molecule (H2O) to the left side.

The balanced reaction now becomes:
\[ 2 \text{MnO}_4^{-} + \text{Br}^{-} + 1 \text{H}_2\text{O} \rightarrow 2 \text{MnO}_2 (s) + \text{BrO}_3^{-} + 2 \text{OH}^{-} \]

### Step 5: Final check
- **Left side:**
- Manganese (Mn): 2
- Oxygen (O): 8 (from 2 MnO4^-) + 1 (from H2O) = 9
- Bromine (Br): 1
- Hydrogen (H): 2

- **Right side:**
- Manganese (Mn): 2
- Oxygen (O): 4 (from 2 MnO2) + 3 (from BrO3^-) + 2 (from 2 OH^-) = 9
- Bromine (Br): 1
- Hydrogen (H): 2

Both sides are now balanced.

### Final Balanced Reaction:
\[ 2 \text{MnO}_4^{-} + \text{Br}^{-} + \text{H}_2\text{O} \rightarrow 2 \text{MnO}_2 (s) + \text{BrO}_3^{-} + 2 \text{OH}^{-} \]

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