`(NH_(4))_(2)Cr_(2)O_(7)` on heating liberates a gas. The same gas will be obtained by

Options

A. Heating `NH_(4)NO_(2)`
B. Heating `NH_(4)NO_(3)`
C. Heating `(NH_(4))_(2)SO_(4)`
D. Treatment `Mg_(3)N_(2)` with `H_(2)O`

Explanation

To solve the question regarding the gas liberated when `(NH4)2Cr2O7` (ammonium dichromate) is heated, we will follow these steps:

### Step 1: Identify the reaction of ammonium dichromate on heating
When ammonium dichromate is heated, it decomposes to produce nitrogen gas, water vapor, and chromium(III) oxide. The balanced equation for this reaction is:

\[ (NH_4)_2Cr_2O_7 \rightarrow Cr_2O_3 + N_2 + 4H_2O \]

### Step 2: Determine the gas produced
From the decomposition reaction, we can see that the gas produced is nitrogen gas (N₂).

### Step 3: Analyze the options given in the question
We need to check which of the given options also produces nitrogen gas when heated:

1. **Heating NH4NO2 (ammonium nitrite)**:
\[ NH_4NO_2 \rightarrow N_2 + 2H_2O \]
This reaction produces nitrogen gas.

2. **Heating NH4NO3 (ammonium nitrate)**:
\[ NH_4NO_3 \rightarrow N_2O + 2H_2O \]
This reaction produces nitrous oxide (N₂O), not nitrogen gas.

3. **Heating (NH4)2SO4 (ammonium sulfate)**:
\[ (NH_4)_2SO_4 \rightarrow 2NH_3 + H_2SO_4 \]
This reaction produces ammonia gas (NH₃) and sulfuric acid (H₂SO₄), not nitrogen gas.

4. **Treatment of Mg3N2 with H2O (magnesium nitride with water)**:
\[ Mg_3N_2 + 6H_2O \rightarrow 3Mg(OH)_2 + 2NH_3 \]
This reaction produces ammonia gas, not nitrogen gas.

### Step 4: Conclusion
From the analysis, the only option that produces nitrogen gas is the first option, heating ammonium nitrite (NH4NO2). Therefore, the answer to the question is:

**The same gas (nitrogen gas) will be obtained by heating NH4NO2.**

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