Step 1: Recall reaction with sodium metal.
Sodium metal reacts with compounds containing active hydrogen atoms (such as –OH or –COOH groups), liberating hydrogen gas.
Step 2: Analyse each compound.
(A) Ethanol (\(\mathrm{CH_3CH_2OH}\)): Contains an –OH group, reacts with sodium to form sodium ethoxide and hydrogen gas.
(B) Phenol (\(\mathrm{C_6H_5OH}\)): Contains phenolic –OH group, reacts with sodium to give sodium phenoxide.
(C) Dimethyl ether (\(\mathrm{CH_3OCH_3}\)): Does not contain an –OH group or acidic hydrogen, hence does not react with sodium.
(D) Acetic acid (\(\mathrm{CH_3COOH}\)): Contains –COOH group, reacts vigorously with sodium.
Step 3: Conclusion.
Dimethyl ether does not react with sodium metal because it lacks an active hydrogen atom.