To identify the acidic radical present in a salt, a student performs the following steps:
Upon adding \(\text{AgNO}_3\), a pale yellow precipitate is formed which is soluble with difficulty in \(\text{NH}_4\text{OH}\) (ammonium hydroxide) solution. This behavior suggests the presence of the bromide ion \(\text{Br}^−\). Here's the reasoning:
Given the choices and explanations, the presence of bromide ion \(\text{Br}^−\) is confirmed by the formation of a pale yellow precipitate which is soluble with difficulty in \(\text{NH}_4\text{OH}\). Therefore, the correct answer is: \(\text{Br}^−\)
The reactions with \( \text{Ag}^+ \) ions produce different colored precipitates depending on the halide present:
\[ \text{Ag}^+ + \text{I}^- \rightarrow \text{AgI} \quad (\text{Yellow ppt.}) \]
\[ \text{Ag}^+ + \text{Cl}^- \rightarrow \text{AgCl} \quad (\text{White ppt.}) \]
\[ \text{Ag}^+ + \text{Br}^- \rightarrow \text{AgBr} \quad (\text{Pale yellow ppt.}) \]
Since a pale yellow precipitate was obtained, it indicates the presence of \( \text{Br}^- \) ions.