Concept:
Chemistry (Organic Chemistry) - Heterocyclic Compounds.
Step 1: Analyze the structure of Pyrrole.
Pyrrole is a 5-membered heterocyclic aromatic organic compound. Its chemical formula is $C_4H_5N$, meaning its ring contains four carbon atoms and one nitrogen atom.
Step 2: Analyze the structure of Piperidine.
Piperidine is a 6-membered heterocyclic non-aromatic amine. Its chemical formula is $C_5H_{11}N$, consisting of a fully saturated six-membered ring containing one nitrogen atom.
Step 3: Analyze the structure of Pyridine.
Pyridine is a 6-membered heterocyclic aromatic organic compound. Its chemical structure is highly related to benzene, with one methine group (=CH-) replaced by a nitrogen atom, giving it the formula $C_5H_5N$.
Step 4: Analyze the structure of Pyran.
Pyran is a 6-membered heterocyclic non-aromatic ring. Unlike the previous compounds, its ring consists of five carbon atoms and one oxygen atom (formula $C_5H_6O$). It does not contain nitrogen.
Step 5: Compare the findings and conclude.
By evaluating the molecular composition of all four given options, we can clearly identify the heteroatoms present in their respective rings.
Pyrrole, Piperidine, and Pyridine all specifically feature a nitrogen atom embedded within their ring structures.
Pyran, on the other hand, contains an oxygen atom as its sole heteroatom and completely lacks nitrogen. Therefore, Pyran is the only molecule from the list that satisfies the condition of not containing nitrogen.
$$
\therefore \text{The correct answer is Option D: Pyran.}
$$