`NH_(3)` solution was added to four semple solution in difference test tube and found the following observation about the precipitate.
a. White ppt which is solution in oxcess of `NH_(3)` solution
b.On heating which is white in cold but yellow on heating
c. The cation present in (b) forms white ppt , with hypo solution which give black ppt on heating
d. The cation present in (c ) forms soluble complex with excess of `NH_(3)` solution
White ppt in (c) and the soluble complex from white ppt with the type solution is//are

Options

A. `Pb(OH)_(2),[Pb(S_(2)O_(3))_(2)]^(2)`
B. `Ag_(2)O, [Ag(S_(2)O_(3))_(2)]^(2)`
C. `HgO.Hg(NH_(2))NO_(3),[Hg(S_(2)O_(3))_(2)]^(2-)`
D. None of these

Answer

To solve the given question step by step, we will analyze the observations and identify the cations involved in each step.

### Step 1: Analyze the Observations
We have four observations based on the addition of NH₃ to different sample solutions. Let's summarize them:
- **Observation (a)**: White precipitate which is soluble in excess NH₃.
- **Observation (b)**: White precipitate that turns yellow upon heating.
- **Observation (c)**: The cation present forms a white precipitate with hypo solution, which gives a black precipitate on heating.
- **Observation (d)**: The cation in (c) forms a soluble complex with excess NH₃.

### Step 2: Identify the Cations
1. **For Observation (a)**: The white precipitate that is soluble in excess NH₃ could be due to the presence of either **Lead (Pb²⁺)** or **Mercury (Hg²⁺)**. Both can form white precipitates with NH₃.

2. **For Observation (b)**: The white precipitate that turns yellow on heating suggests the presence of **Mercuric compounds**. Specifically, when mercuric oxide (HgO) is heated, it can turn yellow.

3. **For Observation (c)**: The cation that forms a white precipitate with hypo (sodium thiosulfate) and gives a black precipitate on heating can be **Mercury (Hg²⁺)** or **Lead (Pb²⁺)**.
- For **Mercury**: The reaction with hypo gives mercuric thiosulfate (HgS₂O₃), which on heating gives a black precipitate of mercuric sulfide (HgS).
- For **Lead**: The reaction with hypo gives lead thiosulfate (PbS₂O₃), which also gives a black precipitate of lead sulfide (PbS) on heating.

4. **For Observation (d)**: The soluble complex formed with excess NH₃ can be either **Mercury (Hg²⁺)** or **Lead (Pb²⁺)**. Both can form soluble complexes with thiosulfate ions.

### Step 3: Conclusion
Based on the observations and analysis:
- The white precipitate in observation (c) could be either **HgO** or **Pb(OH)₂**.
- The soluble complex formed in observation (d) could be **HgS₂O₃²⁻** or **PbS₂O₃²⁻**.

### Final Answer
The white precipitate in (c) can be either **HgO** or **Pb(OH)₂**, and the soluble complex formed in (d) can be either **HgS₂O₃²⁻** or **PbS₂O₃²⁻**. Therefore, the answer for the given question is both **Option A and Option C**.

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