Explanation:

Infrared (IR) spectroscopy is a technique that measures the absorption of infrared radiation by molecules. It provides information about the functional groups present in a molecule and can be used to identify and characterize compounds.

IR active and inactive molecules:
Not all molecules will show an infrared spectrum. Only molecules that have a change in dipole moment during vibration will absorb infrared radiation and produce an IR spectrum. These molecules are called IR active. On the other hand, molecules that do not have a change in dipole moment during vibration will not absorb infrared radiation and will not produce an IR spectrum. These molecules are called IR inactive.

Explanation of options:
a) H2 (Hydrogen gas):
- H2 is a diatomic molecule with a symmetrical linear structure.
- It does not have any polar bonds or a change in dipole moment during vibration.
- Therefore, H2 is IR inactive and will not show an infrared spectrum.

b) HCl (Hydrogen chloride):
- HCl is a polar molecule with a polar bond between hydrogen and chlorine.
- It has a change in dipole moment during vibration.
- Therefore, HCl is IR active and will show an infrared spectrum.

c) CH4 (Methane):
- CH4 is a tetrahedral molecule with a symmetrical structure.
- It does not have any polar bonds or a change in dipole moment during vibration.
- Therefore, CH4 is IR inactive and will not show an infrared spectrum.

d) H2O (Water):
- H2O is a bent molecule with a polar bond between oxygen and hydrogen.
- It has a change in dipole moment during vibration.
- Therefore, H2O is IR active and will show an infrared spectrum.

Conclusion:
Based on the explanation above, the molecule that will not show an infrared spectrum is H2 (option A) because it is IR inactive.