Step 1: Understanding the Concept:
This question tests knowledge of qualitative analysis and characteristic colors of complex salts.
Potassium ferrocyanide, \(K_4[Fe(CN)_6]\), is an analytical reagent used to detect transition metal cations.
The reaction involves the formation of an insoluble metal ferrocyanide complex. The color of these precipitates is highly specific to the metal cation present.
Step 2: Detailed Explanation:
Let's analyze the reaction of each given cation with aqueous \(K_4[Fe(CN)_6]\):
1. Copper(II) ions (\(Cu^{2+}\)): When \(Cu^{2+}\) reacts with ferrocyanide, it forms copper(II) ferrocyanide.
The chemical equation is:
\[ 2Cu^{2+}(aq) + [Fe(CN)_6]^{4-}(aq) \rightarrow Cu_2[Fe(CN)_6] \downarrow \]
This precipitate has a distinct, characteristic chocolate brown color. This is a confirmatory test for copper in chemistry labs.
2. Iron(III) ions (\(Fe^{3+}\)): When \(Fe^{3+}\) reacts with ferrocyanide, it forms ferric ferrocyanide.
The chemical equation is:
\[ 4Fe^{3+}(aq) + 3[Fe(CN)_6]^{4-}(aq) \rightarrow Fe_4[Fe(CN)_6]_3 \downarrow \]
This precipitate is famously known as Prussian Blue due to its deep blue color.
3. Zinc(II) ions (\(Zn^{2+}\)): Reaction with ferrocyanide produces zinc ferrocyanide.
The chemical equation is:
\[ 2Zn^{2+}(aq) + [Fe(CN)_6]^{4-}(aq) \rightarrow Zn_2[Fe(CN)_6] \downarrow \]
This precipitate is white or grayish-white in appearance.
4. Calcium ions (\(Ca^{2+}\)): Calcium, being an alkaline earth metal, does not form a characteristic colored precipitate with this complexing reagent in dilute solutions.
Therefore, the only cation that matches the "chocolate brown" description is \(Cu^{2+}\).
Step 3: Final Answer:
The cation that gives a chocolate brown precipitate is \(Cu^{2+}\). This corresponds to option (B).