A. Balanced Equation:
The balanced equation for the reaction is as follows:

2Cu(NO3)2(s) → 2CuO(s) + 4NO2(g) + O2(g)

B. Identification of Gas X:
The brown gas X is nitrogen dioxide (NO2).

C. Type of Reaction:
The reaction is a decomposition reaction.

Explanation:
1. Decomposition Reaction:
A decomposition reaction is a type of chemical reaction in which a compound breaks down into simpler substances. In this case, copper (II) nitrate (Cu(NO3)2) decomposes upon heating to form copper oxide (CuO), oxygen gas (O2), and nitrogen dioxide gas (NO2).

2. Copper (II) Nitrate:
Copper (II) nitrate is a blue-colored powder. When it is heated, it decomposes to give copper oxide, oxygen gas, and nitrogen dioxide gas. The blue color of copper (II) nitrate disappears during the reaction.

3. Copper Oxide:
Copper oxide is a black solid that forms during the decomposition of copper (II) nitrate. It is the product of the reaction and can be observed as a black residue in the boiling tube.

4. Oxygen Gas:
Oxygen gas is released during the decomposition of copper (II) nitrate. It is a colorless and odorless gas. The production of oxygen gas can be confirmed by the relighting of a glowing splint when introduced into the boiling tube.

5. Nitrogen Dioxide Gas:
The brown gas X formed during the reaction is nitrogen dioxide (NO2). Nitrogen dioxide is a reddish-brown gas with a pungent odor. It is formed as one of the products of the decomposition of copper (II) nitrate.

Overall, the reaction can be summarized as the decomposition of copper (II) nitrate into copper oxide, oxygen gas, and nitrogen dioxide gas. The blue color of copper (II) nitrate disappears, and a black residue is formed in the boiling tube. Oxygen gas is evolved, and the presence of nitrogen dioxide gas is indicated by its brown color and pungent odor.