Step 1: Understanding the Concept:
Metamerism is a type of structural isomerism that arises due to the unequal distribution of carbon atoms (alkyl groups) on either side of a polyvalent functional group.
A polyvalent functional group is one that is attached to more than one carbon atom, effectively sitting "inside" the carbon chain. Examples include the ether group (\(-O-\)), ketone group (\(-CO-\)), and secondary amine group (\(-NH-\)).
Monovalent groups like aldehydes (\(-CHO\)), carboxylic acids (\(-COOH\)), and primary alcohols (\(-OH\) at the end) cannot show metamerism.
Step 2: Detailed Explanation:
Let's evaluate each option:
1. Propanal (\(CH_{3}CH_{2}CHO\)): This is an aldehyde. The functional group is monovalent and always appears at the end of the chain. It cannot exhibit metamerism.
2. Propanone (\(CH_{3}COCH_{3}\)): This is a ketone, which is a polyvalent group. However, to show metamerism, a ketone must have at least four carbons so that the alkyl groups can be redistributed (e.g., Diethyl ketone vs. Methyl propyl ketone). Propanone has only 3 carbons, so only one arrangement is possible: methyl on both sides.
3. Methoxyethane (\(CH_{3}-O-C_{2}H_{5}\)): This is an ether. Ethers are the most classic examples of metamerism. While methoxyethane (3 carbons) doesn't have a metamer with 3 carbons (you need at least 4 carbons, like Ethoxyethane and Methoxypropane), the *class* of compound is what the question is targeting. Among the options, only ethers and ketones are polyvalent.
Wait, let's re-read carefully. The question asks which *can* show metamerism. Between an aldehyde, a small ketone, an alcohol, and an ether, the ether is the most correct functional class.
4. Ethanol (\(CH_{3}CH_{2}OH\)): This is a primary alcohol. The \(-OH\) group is monovalent. It cannot show metamerism.
Methoxyethane is an ether, and ethers are the primary functional group associated with metamerism in introductory organic chemistry.
Step 3: Final Answer:
Methoxyethane is the correct choice because it belongs to the ether family, which possesses the polyvalent functional group required for metamerism.
This is Option (C).