Which of the following reaction is correct for a given electrochemical cell at `25^(@)C`?
`(PtBr_(2)(g)Br^()(g)||Cl^(-)(aq) Cl_(2) (g)pt`

Options

A. `2Br^(-) (aq) + C1_(2) ((g))rightarrow2Cl^(-) (aq) + Br_(2) (g)`
B. `(Br(g)) + 2C1^(-)(aq)rightarrow 2Br^(-) (aq) + Cl_(2) (g)`
C. `Br_(2)(g)+ C1_(2) (aq) rightarrow Br^(-) (aq) + 2C1 ^(-) (g)`
D. `2Br^(-)((aq)) + 2C1^(-) ((aq)) to Br_(2) ((g)) + C1_(2) ((g))`

Explanation

To determine which reaction is correct for the given electrochemical cell at 25°C, we need to analyze the half-reactions involved and identify the oxidation and reduction processes.

### Step-by-Step Solution:

1. **Identify the Species Involved:**
The electrochemical cell consists of:
- Left side: \( \text{Br}_2(g) \) and \( \text{Br}^-(g) \)
- Right side: \( \text{Cl}^-(aq) \) and \( \text{Cl}_2(g) \)

2. **Determine Oxidation and Reduction:**
- **Oxidation:** This is the loss of electrons. In this cell, bromine (\( \text{Br}_2 \)) is likely to be oxidized to bromide ions (\( \text{Br}^- \)).
- **Reduction:** This is the gain of electrons. Chlorine ions (\( \text{Cl}^- \)) are likely to be reduced to chlorine gas (\( \text{Cl}_2 \)).

3. **Write the Half-Reactions:**
- For oxidation of bromine:
\[ \text{Br}_2(g) + 2e^- \rightarrow 2\text{Br}^-(g) \quad \text{(Oxidation)} \]
- For reduction of chlorine:
\[ 2\text{Cl}^-(aq) \rightarrow \text{Cl}_2(g) + 2e^- \quad \text{(Reduction)} \]

4. **Combine the Half-Reactions:**
To combine these half-reactions, we need to ensure that the number of electrons lost in oxidation equals the number of electrons gained in reduction. Here, both half-reactions involve 2 electrons:
\[ \text{Br}_2(g) + 2\text{Cl}^-(aq) \rightarrow 2\text{Br}^-(g) + \text{Cl}_2(g) \]

5. **Identify the Correct Reaction:**
From the options provided, we need to check which one matches the combined half-reaction. The correct reaction should show the oxidation of bromine and the reduction of chlorine.

### Conclusion:
The correct reaction for the electrochemical cell is:
\[ \text{Br}_2(g) + 2\text{Cl}^-(aq) \rightarrow 2\text{Br}^-(g) + \text{Cl}_2(g) \]