`Cl_(2)+OH^(-)rarrCl^(-)+ClO_(3)^(-)`
What is the coefficient for `OH^(-)` when this equation is balanced with the smallest interger coefficients ?

Options

A. 2
B. 3
C. 4
D. 6

Explanation

To balance the equation \( \text{Cl}_2 + \text{OH}^- \rightarrow \text{Cl}^- + \text{ClO}_3^- \) and find the coefficient for \( \text{OH}^- \) with the smallest integer coefficients, we can follow these steps:

### Step 1: Identify the oxidation and reduction half-reactions
In this reaction, chlorine undergoes both oxidation and reduction:
- **Oxidation half-reaction**: \( \text{Cl}_2 \) is oxidized to \( \text{ClO}_3^- \)
- **Reduction half-reaction**: \( \text{Cl}_2 \) is reduced to \( \text{Cl}^- \)

### Step 2: Write the oxidation half-reaction
The oxidation half-reaction can be written as:
\[ \text{Cl}_2 \rightarrow \text{ClO}_3^- \]
To balance the chlorine atoms, we need to multiply by 2:
\[ 2 \text{Cl}_2 \rightarrow 2 \text{ClO}_3^- \]

### Step 3: Balance oxygen with water
Since there are 6 oxygen atoms in \( 2 \text{ClO}_3^- \), we add 6 water molecules to the left side:
\[ 2 \text{Cl}_2 + 6 \text{H}_2O \rightarrow 2 \text{ClO}_3^- \]

### Step 4: Balance hydrogen with hydroxide ions
Now, we have 12 hydrogen atoms from 6 water molecules. To balance the hydrogen, we add 12 hydroxide ions to the right side:
\[ 2 \text{Cl}_2 + 6 \text{H}_2O \rightarrow 2 \text{ClO}_3^- + 12 \text{OH}^- \]

### Step 5: Write the reduction half-reaction
The reduction half-reaction is:
\[ \text{Cl}_2 + 2 \text{e}^- \rightarrow 2 \text{Cl}^- \]

### Step 6: Balance the number of electrons
To balance the electrons, we multiply the reduction half-reaction by 5 (since the oxidation half-reaction involves 10 electrons):
\[ 5 \text{Cl}_2 + 10 \text{e}^- \rightarrow 10 \text{Cl}^- \]

### Step 7: Combine the half-reactions
Now we can combine both half-reactions:
\[ 2 \text{Cl}_2 + 6 \text{H}_2O + 10 \text{e}^- \rightarrow 2 \text{ClO}_3^- + 12 \text{OH}^- + 10 \text{Cl}^- \]

### Step 8: Simplify the equation
After simplifying, we have:
\[ 3 \text{Cl}_2 + 6 \text{OH}^- \rightarrow 5 \text{Cl}^- + \text{ClO}_3^- + 3 \text{H}_2O \]

### Conclusion
The coefficient for \( \text{OH}^- \) in the balanced equation is **6**.