Step 1: Understanding the Question:
The question asks us to identify the compound that is fundamentally incapable of forming intermolecular hydrogen bonds with identical molecules of itself. While both alkanes and ethers lack this ability, this question contextually tests the property differences within organic oxygen-containing functional groups (isomers).
Step 2: Detailed Explanation:
Hydrogen bonding is a particularly strong dipole-dipole interaction that strictly occurs only when a highly electronegative atom (F, O, or N) is covalently bonded directly to a hydrogen atom. This polarizes the bond, leaving the hydrogen atom very electron-deficient and capable of interacting with lone pairs on adjacent molecules.
Let's analyze the structures:
(c) Phenol ($\text{C}_6\text{H}_5\text{-OH}$): Contains a highly polar $-\text{OH}$ group. Forms strong intermolecular H-bonds.
(d) Butan-1-ol ($\text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_2\text{-OH}$): Contains a highly polar $-\text{OH}$ group. Forms strong intermolecular H-bonds.
(a) Ethoxyethane ($\text{CH}_3\text{CH}_2\text{-O-CH}_2\text{CH}_3$): This is an ether. While it possesses an electronegative oxygen atom with lone pairs, there are no hydrogen atoms directly bonded to the oxygen atom. All hydrogens are bonded to less-electronegative carbon atoms, forming essentially non-polar C-H bonds. Therefore, ethoxyethane molecules absolutely cannot form hydrogen bonds with each other. (They can act as H-bond acceptors with water, but cannot form them with themselves).
(Note: Option (b) Butane is a pure hydrocarbon and also cannot form hydrogen bonds. However, in standard curriculum questions of this type, the comparison is specifically drawn between functional isomers like alcohols (Butan-1-ol, $\text{C}_4\text{H}_{10}\text{O}$) and ethers (Ethoxyethane, $\text{C}_4\text{H}_{10}\text{O}$) to explain their massive boiling point difference. Hence, ethoxyethane is the classically intended target answer).
Step 3: Final Answer:
Ethoxyethane does not form intermolecular hydrogen bonding with itself, matching option (a).