Bromine is commercially prepared from sea water by displacement reaction
`Cl_(2)+2Br^(-)(aq.)to2Cl^(-)(aq.)+Br_(2)`
`Br_(2)` gas thus formed is dissolved into solution of `Na_(2)CO_(3)` and then pure `Br_(2)` iis obtained by treatment of the solution with :

Options

A. `Ca(OH)_(2)`
B. `NaOH`
C. `H_(2)SO_(4)`
D. `HI`

Explanation

To solve the problem of how to obtain pure bromine from the impure bromine produced in the reaction with sodium carbonate, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Reaction**:
- The initial reaction is given as:
\[ Cl_2 + 2Br^{-} \rightarrow 2Cl^{-} + Br_2 \]
- In this reaction, chlorine displaces bromine from bromide ions, resulting in the formation of bromine gas (\(Br_2\)).

2. **Dissolving Bromine in Sodium Carbonate**:
- The bromine gas produced is impure, so it is dissolved in a hot aqueous solution of sodium carbonate (\(Na_2CO_3\)).
- The reaction that occurs is:
\[ Br_2 + Na_2CO_3 \rightarrow NaBr + NaBrO_3 + CO_2 \]
- This reaction produces sodium bromide (\(NaBr\)), sodium bromate (\(NaBrO_3\)), and carbon dioxide (\(CO_2\)).

3. **Identifying the Need for Purification**:
- The goal is to obtain pure bromine (\(Br_2\)) from the sodium bromide formed in the previous step.
- To achieve this, we need to oxidize the bromide ions (\(Br^{-}\)) back to bromine gas (\(Br_2\)).

4. **Choosing the Correct Reagent**:
- We need a strong oxidizing agent to oxidize \(Br^{-}\) to \(Br_2\). The options provided are:
- Calcium hydroxide
- Sodium hydroxide
- Sulfuric acid
- Hydroiodic acid
- Among these, sulfuric acid (\(H_2SO_4\)) is known to be a strong oxidizing agent.

5. **The Reaction with Sulfuric Acid**:
- When sodium bromide (\(NaBr\)) is treated with sulfuric acid (\(H_2SO_4\)), the following reaction occurs:
\[ NaBr + H_2SO_4 \rightarrow Br_2 + Na_2SO_4 + H_2O \]
- In this reaction, bromide ions are oxidized to bromine gas, and sulfuric acid is reduced to sulfate ions.

6. **Conclusion**:
- Therefore, the pure bromine is obtained by treating the solution of sodium bromide with sulfuric acid (\(H_2SO_4\)).
- The correct answer is **sulfuric acid**.