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What are the functional groups in $ C{H_3} - C{H_2} - OH $ and ?

Answer
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Hint: A functional group is a chemical moiety that is present in a molecule that causes the molecule’s characteristic chemical reaction. There are several functional groups like hydroxyl, carboxyl, aldehyde, ether, etc.

Complete answer:
Hydroxyl group $ - OH $ is for alcohol and the prefix used for this is hydroxy and the suffix used is -ol.
Alcohol is characterized by the presence of $ - OH $ , a group in them. As $ C{H_3} - C{H_2} - OH $ contains the $ - OH $ group, hence, it is alcohol and the functional group present in it is a hydroxyl group. The IUPAC name for the compound is ethanol.
Ether group $ R - O - R $ is for ethers and the prefix used for this is alkoxy and the suffix used is ether. Ether is characterized by the presence of $ R - O - R $ , a group in them. As $ C{H_3} - O - C{H_2} $ contains $ R - O - R $ a group, hence, it is ether and the functional group present in it is an ether group. The IUPAC name for the compound is diethyl ether.
Hence, the functional group in $ C{H_3} - C{H_2} - OH $ is hydroxyl ( $ - OH $ ) and in $ C{H_3} - O - C{H_2} $ is ether $ R - O - R $ .

Note:
The characteristic property of a molecule arises due to the presence of a functional group in it. There are various types of functional groups based on the atom present in it, like groups containing halogen, nitrogen, oxygen, sulfur, boron, phosphorus, metals, etc.