Final answer:
Acetylene has 2 vibrational modes, benzene has 12, glycine has 12, and methanol has 4.
Step-by-step explanation:
(a) Acetylene, C₂H₂:
Acetylene has a triple bond between the two carbon atoms. Each carbon atom is attached to one hydrogen atom. The triple bond allows for two vibrational modes, one along the bond axis and one perpendicular to it.
(b) Benzene, C₆H₆:
Benzene has a ring structure with alternating double bonds and single bonds. The double bonds have a double bond character, allowing for a total of 12 vibrational modes.
(c) Glycine, C₂H₅NO₂:
Glycine has multiple functional groups, including a carboxylic acid and an amino group. These functional groups contribute to a total of 12 vibrational modes.
(d) Methanol, CH₄O:
Methanol has a single bond between the carbon and oxygen atoms. The methyl group also has three vibrational modes. Therefore, methanol has a total of 4 vibrational modes.