An inorganic compound `(X)` shows the following reactions :
(a) It is white solid, exists as dimer and fumes in moist air.
(b) It sublimes at `180^@ C` and forms monomer on heating to `400^@ C`.
( c) Its aqueous solution turns blue litmus red and gives a white precipitate with `AgNO_(3)` solution which is soluble in excess of `NH_(4) OH`.
(d) Addition of `NaOH` to the solution of `(A)` gives a white gelatinous precipitate which is, however, soluble on excess of `NaOH`.
Identify the compound `(A)`.

Options

A. `AI(OH)_(3)`
B. `AI_(2)CI_(6)`
C. `AI_(2)O_(3)`
D. `AI_(2)(SO_(4))_(3)`

Explanation

To identify the compound \( (X) \) based on the given reactions, let's analyze each piece of information step by step.

### Step 1: Analyze the Physical Properties
The compound \( (X) \) is described as:
- A white solid
- Existing as a dimer
- Fuming in moist air

**Interpretation**:
- The white solid suggests it could be a metal chloride.
- The dimeric nature indicates it might be a covalent compound, possibly a metal halide.
- Fuming in moist air suggests it releases a gas, likely an acid, when it reacts with water.

### Step 2: Sublimation and Heating Behavior
The compound sublimes at \( 180^\circ C \) and forms a monomer upon heating to \( 400^\circ C \).

**Interpretation**:
- Sublimation indicates that the compound transitions from solid to gas without passing through a liquid state, which is characteristic of covalent compounds.
- The formation of a monomer at higher temperatures suggests that the dimeric form is less stable at elevated temperatures.

### Step 3: Aqueous Solution Behavior
The aqueous solution of \( (X) \) turns blue litmus red and gives a white precipitate with \( AgNO_3 \) solution, which is soluble in excess \( NH_4OH \).

**Interpretation**:
- The solution turning blue litmus red indicates that it is acidic, suggesting the presence of \( HCl \) or another strong acid.
- The formation of a white precipitate with \( AgNO_3 \) indicates the presence of chloride ions, forming \( AgCl \), which is a white precipitate.
- The solubility of this precipitate in excess \( NH_4OH \) suggests the formation of a complex ion, likely \( [Ag(NH_3)_2]^+ \).

### Step 4: Reaction with Sodium Hydroxide
The addition of \( NaOH \) to the solution of \( (X) \) gives a white gelatinous precipitate, which is soluble in excess \( NaOH \).

**Interpretation**:
- The white gelatinous precipitate indicates the formation of aluminum hydroxide \( Al(OH)_3 \).
- The solubility in excess \( NaOH \) suggests the formation of a soluble aluminate ion, such as \( NaAlO_2 \).

### Step 5: Conclusion
Based on the above analysis, the compound \( (X) \) is identified as **Aluminum Chloride \( (AlCl_3) \)**, which exists as a dimer \( Al_2Cl_6 \) in solid form.

### Summary of Reactions:
1. **Dimeric Nature**: \( Al_2Cl_6 \) fuming in moist air forms \( Al(OH)_3 \) and \( HCl \).
2. **Sublimation**: Sublimes at \( 180^\circ C \) to form \( Al_2Cl_6 \) gas, which dissociates into \( AlCl_3 \) at \( 400^\circ C \).
3. **Acidic Solution**: Forms \( HCl \) in solution, turning blue litmus red and precipitating \( AgCl \) with \( AgNO_3 \).
4. **Reaction with \( NaOH \)**: Forms \( Al(OH)_3 \), which is soluble in excess \( NaOH \).