Final answer:
The carboxyl group is the functional group with two hydrogen bond donors and one hydrogen bond acceptor, due to its carbon-oxygen bond and an OH group on the same carbon atom.
Step-by-step explanation:
The functional group that has two hydrogen bond donors and one hydrogen bond acceptor is the carboxyl group. This functional group contains a carbon atom double-bonded to an oxygen (considered a hydrogen bond acceptor) and also bonded to an OH group. The two hydrogen atoms associated with the OH group can act as hydrogen bond donors, due to the presence of a hydrogen atom attached to an electronegative oxygen atom. Moreover, the oxygen atoms have lone pairs of electrons which allow them to be hydrogen bond acceptors.
In contrast, the amine group has a nitrogen atom that can donate a lone pair of electrons, making it a hydrogen bond acceptor, and it also has hydrogen atoms attached directly to the nitrogen, making it a hydrogen bond donor. The hydroxyl group consists of an oxygen atom bonded to a hydrogen atom and can act as both a hydrogen bond donor and acceptor. The carbonyl group, having a carbon atom double-bonded to an oxygen, is a hydrogen bond acceptor but does not have hydrogen atoms to donate for hydrogen bonding.