Thermal Decomposition of Inorganic Compounds to Generate Nitrogen Gas

To determine which compound(s) produce $\text{N}_2$ gas upon thermal decomposition at temperatures below $300^\circ\text{C}$, let us examine the thermal decomposition behavior of each given compound:

1. Option (A): $\text{NH}_4\text{NO}_3$ (Ammonium Nitrate) Upon mild heating (below $300^\circ\text{C}$, typically around $200^\circ\text{C}-260^\circ\text{C}$), ammonium nitrate undergoes decomposition to produce nitrous oxide ($\text{N}_2\text{O}$) and water vapor, rather than nitrogen gas: $\text{NH}_4\text{NO}_3 \xrightarrow{\Delta < 300^\circ\text{C}} \text{N}_2\text{O}\uparrow + 2\text{H}_2\text{O}$ (Note: $\text{N}_2$ is only formed in explosive/very high temperature reactions $>300^\circ\text{C}$.) Hence, Option (A) is incorrect.

2. Option (B): $(\text{NH}_4)_2\text{Cr}_2\text{O}_7$ (Ammonium Dichromate) Ammonium dichromate undergoes an intramolecular redox reaction upon heating at temperatures around $180^\circ\text{C}-200^\circ\text{C}$ to produce nitrogen gas, chromium(III) oxide, and water vapor: $(\text{NH}_4)_2\text{Cr}_2\text{O}_7 \xrightarrow{\Delta < 300^\circ\text{C}} \text{N}_2\uparrow + \text{Cr}_2\text{O}_3 + 4\text{H}_2\text{O}$ Hence, Option (B) is correct.

3. Option (C): $\text{Ba(N}_3)_2$ (Barium Azide) Azides of alkaline earth metals and alkali metals (such as $\text{Ba(N}_3)_2$ and $\text{NaN}_3$) decompose at moderate temperatures (around $160^\circ\text{C}-180^\circ\text{C}$) to give pure dinitrogen gas: $\text{Ba(N}_3)_2 \xrightarrow{\Delta < 300^\circ\text{C}} \text{Ba} + 3\text{N}_2\uparrow$ Hence, Option (C) is correct.

4. Option (D): $\text{Mg}_3\text{N}_2$ (Magnesium Nitride) Magnesium nitride is a thermally stable ionic solid that does not decompose at temperatures below $300^\circ\text{C}$ (its thermal decomposition requires temperatures well above $700^\circ\text{C}$). Hence, Option (D) is incorrect.

Correct Options: (B) and (C)