An unknown inorganic compound `(X)` gave the following reactions:
(i) The compound `(X)` on heating gave a residue, oxygen and oxide of nitrogen.
An aqueous solution of compound `(X)` on addition to tap water gave a turbidity which did not dissolve in `HO_(3+)`
(iii) The turbidity dissolved in `NH_(4)OH` .
Identify the compound `(X)` and gives equation for the reaction (i),(ii) & (iii)`

Explanation

To identify the unknown inorganic compound \(X\) and provide the equations for the reactions described, we will analyze each part of the question step by step.

### Step 1: Identify the compound \(X\)

From the first statement, we know that when compound \(X\) is heated, it gives a residue, oxygen, and oxides of nitrogen. This suggests that \(X\) is likely a nitrate compound, as heating nitrates typically produces nitrogen oxides and oxygen.

### Step 2: Write the equation for the first reaction

The most common nitrate that fits this description is silver nitrate (\(AgNO_3\)). When heated, silver nitrate decomposes as follows:

\[ 2 \, AgNO_3 (s) \rightarrow 2 \, Ag (s) + 2 \, NO_2 (g) + O_2 (g) \]

### Step 3: Analyze the second statement

The second statement indicates that an aqueous solution of compound \(X\) (which we suspect is \(AgNO_3\)) when added to tap water gives turbidity. This turbidity is likely due to the formation of a precipitate, which occurs when chloride ions from tap water react with silver ions.

### Step 4: Write the equation for the second reaction

When \(AgNO_3\) is added to tap water (which contains chloride ions, \(Cl^-\)), it forms a white precipitate of silver chloride (\(AgCl\)):

\[ AgNO_3 (aq) + Cl^- (aq) \rightarrow AgCl (s) + NO_3^- (aq) \]

### Step 5: Analyze the third statement

The third statement mentions that the turbidity (the precipitate \(AgCl\)) dissolves in \(NH_4OH\) (ammonium hydroxide). This indicates the formation of a soluble complex.

### Step 6: Write the equation for the third reaction

When \(AgCl\) reacts with \(NH_4OH\), it forms a soluble complex of silver with ammonia:

\[ AgCl (s) + 2 \, NH_3 (aq) \rightarrow [Ag(NH_3)_2]^+ (aq) + Cl^- (aq) \]

### Conclusion

Based on the above analysis, we can conclude that the unknown compound \(X\) is silver nitrate (\(AgNO_3\)). The reactions can be summarized as follows:

1. **Heating of \(AgNO_3\)**:
\[ 2 \, AgNO_3 (s) \rightarrow 2 \, Ag (s) + 2 \, NO_2 (g) + O_2 (g) \]

2. **Reaction with tap water**:
\[ AgNO_3 (aq) + Cl^- (aq) \rightarrow AgCl (s) + NO_3^- (aq) \]

3. **Dissolution in \(NH_4OH\)**:
\[ AgCl (s) + 2 \, NH_3 (aq) \rightarrow [Ag(NH_3)_2]^+ (aq) + Cl^- (aq) \]