Step 1: Understanding the Concept:
This problem pertains to the systematic qualitative analysis of inorganic salts, specifically identifying anions based on their reaction with concentrated acid and silver nitrate.
Step 2: Key Formula or Approach:
Correlate the physical observations (reddish-brown gas with Conc. $H_2SO_4$ and pale yellow precipitate with $AgNO_3$) to the standard confirmatory tests for halide ions.
Step 3: Detailed Explanation:
1. Reaction with Conc. $H_{2SO_{4}$:} Bromide salts react with concentrated sulphuric acid to liberate hydrogen bromide ($HBr$), which is subsequently oxidized by the acid to bromine gas ($Br_{2}$). Bromine is a reddish-brown gas.
Reaction: $2NaBr + 2H_{2}SO_{4} \rightarrow Na_{2}SO_{4} + Br_{2} \uparrow + SO_{2} + 2H_{2}O$.
(Note: Nitrates also give brown gas $NO_2$, but the next test differentiates it).
2. Reaction with $AgNO_{3$:} Aqueous solution of bromide ions reacts with silver nitrate to form Silver Bromide ($AgBr$), which is a pale yellow precipitate. This precipitate is partially soluble in dilute aqueous ammonia but soluble in concentrated ammonia.
Reaction: $Br^{-} + Ag^{+} \rightarrow AgBr \downarrow$ (pale yellow).
In contrast, $Cl^-$ gives a white ppt ($AgCl$), and $I^-$ gives a bright yellow ppt ($AgI$).
Step 4: Final Answer:
The observations perfectly correspond to the Bromide ion ($Br^{-}$).