The values of the `x` and `y` in the following redox reaction.
`xCl_(2)+6overset(ө)OHrarrCl_(3)^(ө)+yCl^(ө)+3H_(2)O`

Options

A. `x=2,y=4`
B. `x=5,y=3`
C. `x=3,y=5`
D. `x=4,y=2`

Explanation

To find the values of \( x \) and \( y \) in the given redox reaction:

\[ x \text{Cl}_2 + 6 \text{OH}^- \rightarrow \text{ClO}_3^- + y \text{Cl}^- + 3 \text{H}_2\text{O} \]

we will follow these steps:

### Step 1: Identify the oxidation states
In the reaction, we need to identify the oxidation states of chlorine in the reactants and products:
- In \( \text{Cl}_2 \), the oxidation state of Cl is 0.
- In \( \text{ClO}_3^- \), the oxidation state of Cl is +5.
- In \( \text{Cl}^- \), the oxidation state of Cl is -1.

### Step 2: Determine the change in oxidation states
From the oxidation states:
- \( \text{Cl}_2 \) (0) is oxidized to \( \text{ClO}_3^- \) (+5).
- \( \text{Cl}_2 \) (0) is reduced to \( \text{Cl}^- \) (-1).

### Step 3: Balance the half-reactions
We can write the half-reactions for oxidation and reduction:
1. **Oxidation half-reaction**:
\[ \text{Cl}_2 \rightarrow \text{ClO}_3^- \]
For every 1 mole of \( \text{Cl}_2 \), 2 moles of \( \text{ClO}_3^- \) are formed.

2. **Reduction half-reaction**:
\[ \text{Cl}_2 \rightarrow \text{Cl}^- \]
For every 1 mole of \( \text{Cl}_2 \), 2 moles of \( \text{Cl}^- \) are formed.

### Step 4: Combine the half-reactions
To balance the overall reaction, we need to ensure that the number of electrons lost in oxidation equals the number of electrons gained in reduction.

### Step 5: Balance the reaction
From the video transcript, we find that the balanced reaction is:
\[ 3 \text{Cl}_2 + 6 \text{OH}^- \rightarrow 5 \text{Cl}^- + \text{ClO}_3^- + 3 \text{H}_2\text{O} \]

### Step 6: Identify the coefficients
Now, we can identify the coefficients:
- The coefficient of \( \text{Cl}_2 \) (which corresponds to \( x \)) is 3.
- The coefficient of \( \text{Cl}^- \) (which corresponds to \( y \)) is 5.

### Final Values
Thus, we have:
- \( x = 3 \)
- \( y = 5 \)

### Conclusion
The values of \( x \) and \( y \) in the given redox reaction are:
- \( x = 3 \)
- \( y = 5 \)