Step 1: Understanding the Question:
The question asks us to identify the correct statement regarding the structural nature and chemical formula of the organic compound known as tropone.
Step 2: Key Formula or Approach:
Tropone (or 2,4,6-cycloheptatrien-1-one) is a well-known non-benzenoid aromatic compound. It contains a seven-membered ring with three conjugated double bonds and a carbonyl group. To determine its formula, we count the number of carbon, hydrogen, and oxygen atoms in its cyclic conjugated framework.
Step 3: Detailed Explanation:
The ring of tropone consists entirely of carbon atoms, which means it is a homocyclic (or carbocyclic) compound, completely ruling out the heterocyclic options (A and D).
Even though it exhibits aromatic character due to the polarization of the carbonyl group ($C^{\delta +}-O^{\delta -}$) creating a stable $6\pi$-electron aromatic tropylium-like ring cation, it does not contain a benzene ring. Therefore, it is classified specifically as a non-benzenoid aromatic compound.
Counting the atoms in its structure:
The ring has 7 carbon atoms: 6 alkene carbons and 1 carbonyl carbon, giving 7 carbons total ($C_7$).
The 6 alkene carbons each have one hydrogen atom attached, giving 6 hydrogens total ($H_6$).
There is exactly 1 oxygen atom double-bonded to the ring ($O$).
Thus, its molecular formula is $C_7H_6O$. This matches perfectly with option (C).
Step 4: Final Answer:
Tropone is a non-benzenoid aromatic compound with the molecular formula $C_7H_6O$, corresponding to option (C).