To solve the problem, we need to analyze the behavior of the given cations (Co²⁺, Ni²⁺, Mn²⁺, and Zn²⁺) in the presence of hydrogen sulfide (H₂S) and ammonium hydroxide (NH₄OH). The goal is to avoid the precipitation of hydroxides of Ni²⁺, Co²⁺, and Mn²⁺ along with those of the third group cations.
### Step-by-Step Solution:
1. **Understanding the Group Reagents**:
- The group reagent is hydrogen sulfide (H₂S) in the presence of ammonium hydroxide (NH₄OH).
- H₂S reacts with the metal cations to form insoluble metal sulfides.
2. **Formation of Sulfides**:
- When H₂S is added to the solution containing Co²⁺, Ni²⁺, Mn²⁺, and Zn²⁺, these cations will precipitate as their respective sulfides.
- The sulfides of these metals are generally insoluble in NH₄OH.
3. **Effect of H₂S on NH₄OH**:
- The addition of H₂S increases the ionization of NH₄OH, which can be represented as:
\[
NH_4OH \rightleftharpoons NH_4^+ + OH^-
\]
- The presence of H₂S also shifts the equilibrium, affecting the concentration of hydroxide ions (OH⁻) in the solution.
4. **Black-Colored Salt (A)**:
- The black-colored salt (A) formed from the cations is likely a mixture of their sulfides.
- When treated with HCl and KClO₃, compound (B) is produced, which can be converted back to (A) with the evolution of H₂S gas.
5. **Treatment with KCN**:
- When salt (A) is treated with KCN, a buff-colored precipitate (C) is formed.
- This precipitate can dissolve in excess KCN to produce compound (D).
6. **Avoiding Precipitation of Hydroxides**:
- To avoid the precipitation of hydroxides of Ni²⁺, Co²⁺, and Mn²⁺ along with those of the third group cations, we need to reduce the concentration of OH⁻ ions in the solution.
- This can be achieved by adding excess NH₄Cl to the solution.
7. **Why NH₄Cl?**:
- NH₄Cl dissociates in solution to produce NH₄⁺ and Cl⁻ ions. The NH₄⁺ ions will shift the equilibrium of NH₄OH, reducing the concentration of OH⁻ ions.
- Since the solubility product of the hydroxides of the third group cations is lower than that of the fourth, fifth, and sixth groups, reducing OH⁻ concentration will prevent the precipitation of the hydroxides of Ni²⁺, Co²⁺, and Mn²⁺.
### Final Answer:
To avoid the precipitation of hydroxides of Ni²⁺, Co²⁺, and Mn²⁺ along with those of the third group cations, the solution should be treated with **excess NH₄Cl**.