To solve the problem, we need to analyze the information given step by step to identify the possible identity of the colorless solid A.
### Step 1: Identify the properties of solid A
- A is a colorless solid that dissolves in water.
- When dissolved, it gives a white precipitate B upon the addition of NaOH or NH₄OH.
**Hint:** Look for common salts that are soluble in water and can react with bases to form precipitates.
### Step 2: Determine the nature of precipitate B
- The precipitate B is formed when NaOH or NH₄OH is added.
- This precipitate B dissolves in excess NaOH but not in excess NH₄OH.
**Hint:** Consider the hydroxides that can form precipitates and their solubility in different conditions.
### Step 3: Analyze the behavior of precipitate B
- Since B dissolves in excess NaOH, it suggests that B is likely a metal hydroxide that can form soluble aluminate, zincate, or stannate ions.
- The fact that B does not dissolve in excess NH₄OH indicates that it is not an ammonium complex.
**Hint:** Think about metal hydroxides that are amphoteric (soluble in strong bases) but not soluble in ammonium hydroxide.
### Step 4: Precipitate C formation
- When BaCl₂ is added to the solution of A, it gives a white precipitate C that is insoluble in dilute HCl.
- This indicates that C is likely barium sulfate (BaSO₄), which is known to be insoluble in dilute acids.
**Hint:** Consider the sulfate salts that could be formed from the reaction of A with BaCl₂.
### Step 5: Identify possible candidates for A
1. **Al₂(SO₄)₃ (Aluminum sulfate)**:
- Forms Al(OH)₃ (B) when reacted with NaOH, which is a white precipitate.
- Al(OH)₃ dissolves in excess NaOH to form NaAlO₂.
- When reacted with BaCl₂, it forms BaSO₄ (C), which is insoluble in dilute HCl.
2. **ZnSO₄ (Zinc sulfate)**:
- Forms Zn(OH)₂ (B) when reacted with NaOH, which is a white precipitate.
- Zn(OH)₂ dissolves in excess NaOH to form Na₂ZnO₂.
- When reacted with BaCl₂, it also forms BaSO₄ (C), which is insoluble in dilute HCl.
3. **SnSO₄ (Tin(II) sulfate)**:
- Forms Sn(OH)₂ (B) when reacted with NaOH, which is a white precipitate.
- Sn(OH)₂ dissolves in excess NaOH to form Na₂SnO₂.
- When reacted with BaCl₂, it forms BaSO₄ (C), which is insoluble in dilute HCl.
### Conclusion
Since all three compounds (Al₂(SO₄)₃, ZnSO₄, and SnSO₄) fit the criteria outlined in the problem, the answer to the question is that A may be any of the following: Al₂(SO₄)₃, ZnSO₄, or SnSO₄.
**Final Answer:** All of the above (Al₂(SO₄)₃, ZnSO₄, SnSO₄) can be the colorless solid A.