which compounds below that have a vibration that is infrared inactive. and indicate the specfic vibration that is infrared inactive.

1) acetone
2) 1-butyne
3) 2-butyne
4) water
5) chlorine

To determine which compounds have an infrared (IR) inactive vibration, we need to consider their molecular structures and the selection rules of IR spectroscopy. In IR spectroscopy, a molecule absorbs energy at specific frequencies that correspond to its vibrational modes. However, not all vibrations are detected by IR spectroscopy due to selection rules.

The main selection rule for IR activity is that for a vibration to be IR active, there must be a change in the dipole moment during the vibration. In simplistic terms, this means that the vibration causes a change in the symmetry of the molecule, leading to a change in the overall molecular dipole moment.

Now let's analyze each compound to determine their IR activity:

1) Acetone:
Acetone has a carbonyl group (C=O) which typically produces a strong IR absorption peak. The C=O stretching vibration is IR active as it results in a change in dipole moment, making acetone IR active.

2) 1-Butyne:
1-Butyne has a triple bond (C≡C) which contains two unique C-C stretching vibrations. Both C-C stretching vibrations in 1-butyne are IR active since they involve a change in dipole moment.

3) 2-Butyne:
2-Butyne also contains a triple bond (C≡C) with two unique C-C stretching vibrations. As with 1-butyne, both C-C stretching vibrations in 2-butyne are also IR active.

4) Water:
Water (H2O) has a bent molecular geometry, and the O-H bond can experience two fundamental vibrations: stretching and bending. The O-H stretching vibration is IR active since it involves a change in dipole moment. However, the bending vibration (H-O-H) is IR inactive because it does not result in a significant change in dipole moment.

5) Chlorine:
Chlorine (Cl2) is a diatomic molecule, and diatomic molecules have only one bond. As the Cl-Cl bond is not an internal vibration, it does not have any stretching or bending vibrations. Hence, there are no vibrations in chlorine that are IR active or inactive.

In summary, the compounds with vibrations that are IR inactive are water for the bending vibration (H-O-H) and chlorine since it does not have any internal vibrations. All other vibrations in acetone, 1-butyne, and 2-butyne are IR active.