To obtain extra pure nitrogen gas (N₂), the most suitable method among the given options is heating barium azide, Ba(N₃)₂. Let's understand why:

Step 1: Analyze each option

Option 1: Heating NH₃ with CuO

Reaction: $2\mathrm{NH}{}_3+3\mathrm{CuO}\to 3\mathrm{Cu}+3H_{2}O+N_2$

This produces N₂, but it may contain traces of water vapor or other impurities, making it less pure.

Option 2: Heating Ba(N₃)₂

Reaction: $\mathrm{Ba}\left(N_3{}_2\right)\to \mathrm{Ba}+3N_2$

This decomposition yields pure N₂ gas without any other gaseous byproducts, ensuring high purity.

Option 3: Heating NH₄NO₃

Reaction: $\mathrm{NH}{}_4\mathrm{NO}{}_3\to N_{2}O+2H_{2}O$

This produces nitrous oxide (N₂O), not nitrogen gas (N₂).

Option 4: Heating (NH₄)₂Cr₂O₇

Reaction: $\left(\mathrm{NH}{}_4{}_2\right){\mathrm{Cr}}_2{O}_7\to {\mathrm{Cr}}_2{O}_3+4H_{2}O+N_2$

This produces N₂, but it also generates water vapor and chromium(III) oxide, which can contaminate the gas.

Step 2: Conclusion

Heating Ba(N₃)₂ is the best method because it cleanly decomposes to give only barium metal and nitrogen gas, resulting in extra pure N₂ without any gaseous impurities.

Related Topics & Formulae

Thermal Decomposition: Many azides, like barium azide, decompose on heating to produce nitrogen gas. The general reaction for metal azides is: $2\mathrm{MN}{}_3\to 2M+3N_2$, where M is a metal.

Purity Consideration: For laboratory preparation of pure gases, reactions that yield only the desired gas without other volatile products are preferred.