Step 1: Analyze the first observation.
Test: Salt + Conc. H\(_2\)SO\(_4\) \(\rightarrow\) Reddish brown gas.
This is a characteristic test for the bromide ion (Br\(^-\)). The concentrated sulfuric acid first oxidizes HBr (formed initially) to bromine gas (Br\(_2\)), which has a reddish-brown color.
The reactions are:
\[ \text{Br}^- + \text{H}_2\text{SO}_4 \rightarrow \text{HBr} + \text{HSO}_4^- \]
\[ 2\text{HBr} + \text{H}_2\text{SO}_4 \rightarrow \text{Br}_2 \text{(red-brown gas)} + \text{SO}_2 + 2\text{H}_2\text{O} \]
Nitrate ion (NO\(_3\)\(^-\)) also gives a reddish-brown gas (NO\(_2\)) with conc. H\(_2\)SO\(_4\), especially upon adding copper turnings, but the second test will confirm the anion.
Step 2: Analyze the second observation.
Test: Aqueous solution of salt + AgNO\(_3\) solution \(\rightarrow\) Pale yellow precipitate.
This test with silver nitrate is used to identify halide ions.
- AgCl (from Cl\(^-\)) is a curdy white precipitate.
- AgBr (from Br\(^-\)) is a pale yellow precipitate, which is sparingly soluble in ammonium hydroxide.
- AgI (from I\(^-\)) is a bright yellow precipitate, which is insoluble in ammonium hydroxide.
The observation of a pale yellow precipitate strongly indicates the presence of the bromide ion (Br\(^-\)).
Step 3: Conclusion.
Both tests are consistent with the presence of the bromide ion (Br\(^-\)) as the anion A\(^-\).
Step 4: Final Answer.
The anion present in the salt BA is Br\(^-\).