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A monomer is a small molecule that can bind to other similar molecules to form a larger and more complex structure called a polymer. Monomers have the ability to join together through chemical bonds and undergo a polymerization reaction to form long chains or three-dimensional networks.

To identify which of the given molecules can be used as a monomer, we need to know their structures and see if they can undergo polymerization reactions. 1. Ethanol (\(C_2H_5OH\)): Ethanol has the molecular formula \(C_2H_5OH\). It is a simple alcohol with an -OH (hydroxyl) group attached to one of its carbon atoms. Ethanol cannot undergo polymerization reactions and, therefore, is not considered a monomer. 2. Ethene (\(C_2H_4\), also called ethylene): Ethene has the molecular formula \(C_2H_4\). It is an alkene with a double bond between the two carbon atoms (\(C=C\)). This double bond can break easily to form single bonds, which can then bond with other ethene molecules. As a result, ethene can undergo polymerization reactions and is considered a monomer. 3. Methane (\(CH_4\)): Methane has the molecular formula \(CH_4\). It is the simplest alkane, with a single carbon atom bonded to four hydrogen atoms. Methane lacks any multiple bonds, functional groups, or reactive sites to undergo polymerization reactions. Therefore, methane is not considered a monomer.

Based on the molecular structures and reactivity of the given compounds, only ethene (ethylene) can be considered a monomer as it can undergo polymerization reactions to form polymers. Ethanol and methane cannot be used as monomers due to their lack of a reactive site or a functional group that allows them to undergo polymerization reactions.