`K_(4)[Fe(CN)_(6)]` is used to test `Cu^(2+),Fe^(2+),Zn^(2+),Cd^(2+)`

Explanation

To analyze the reactions of `K_(4)[Fe(CN)_(6)]` (potassium ferrocyanide) with the ions `Cu^(2+)`, `Fe^(2+)`, `Zn^(2+)`, and `Cd^(2+)`, we can follow these steps:

### Step 1: Reaction with Copper Ion (Cu²⁺)
- When potassium ferrocyanide reacts with copper(II) ions, it forms a chocolate brown precipitate of copper(II) ferrocyanide.
- The balanced chemical equation is:
\[ Cu^{2+} + 2 K_4[Fe(CN)_6] \rightarrow Cu_2[Fe(CN)_6] + 8 K^+ \]
- The precipitate formed is of chocolate brown color.

### Step 2: Reaction with Ferrous Ion (Fe²⁺)
- When potassium ferrocyanide reacts with ferrous ions, it forms a white precipitate of ferrous ferrocyanide.
- The balanced chemical equation is:
\[ 2 Fe^{2+} + K_4[Fe(CN)_6] \rightarrow K_2[Fe_2(CN)_6] + 2 K^+ \]
- The precipitate formed is of white color.

### Step 3: Reaction with Zinc Ion (Zn²⁺)
- When potassium ferrocyanide reacts with zinc ions, it forms a white precipitate of zinc ferrocyanide.
- The balanced chemical equation is:
\[ Zn^{2+} + K_4[Fe(CN)_6] \rightarrow K_2[ZnFe(CN)_6] + 2 K^+ \]
- The precipitate formed is also white in color.

### Step 4: Reaction with Cadmium Ion (Cd²⁺)
- When potassium ferrocyanide is mixed with cadmium ions, no precipitate is formed.
- Therefore, the reaction can be summarized as:
\[ Cd^{2+} + K_4[Fe(CN)_6] \rightarrow \text{No precipitate} \]

### Summary of Precipitation Reactions:
1. **Copper (Cu²⁺)**: Chocolate brown precipitate of copper(II) ferrocyanide.
2. **Ferrous (Fe²⁺)**: White precipitate of ferrous ferrocyanide.
3. **Zinc (Zn²⁺)**: White precipitate of zinc ferrocyanide.
4. **Cadmium (Cd²⁺)**: No precipitate.