Question

Which of the following molecules may show a pure rotational spectrum in the microwave region: \(\mathrm{H}_{2}, \mathrm{HCl}, \mathrm{CH}_{4}, \mathrm{CH}_{3} \mathrm{Cl}, \mathrm{H}_{2} \mathrm{O}, \mathrm{NH}_{3}\).

Short answer

HCl, CH₃Cl, H₂O, NH₃ may show a pure rotational spectrum.

Step-by-step solution

Understand the requirement for microwave spectra

A molecule will show a pure rotational spectrum in the microwave region if it has a permanent dipole moment. Only molecules that possess a permanent dipole moment can interact with microwave radiation to exhibit rotational transitions.

Analyze each molecule for a dipole moment

Evaluate each molecule to determine whether it has a permanent dipole moment: - \(\mathrm{H}_{2}\) is homonuclear, thus no dipole.- \(\mathrm{HCl}\) is polar due to the electronegativity difference between H and Cl.- \(\mathrm{CH}_{4}\) is symmetrical and non-polar.- \(\mathrm{CH}_{3} \mathrm{Cl}\) is polar due to the C-Cl bond.- \(\mathrm{H}_{2} \mathrm{O}\) is polar.- \(\mathrm{NH}_{3}\) is polar.

Select molecules with permanent dipole moments

From the analysis, the molecules \(\mathrm{HCl}, \mathrm{CH}_{3} \mathrm{Cl}, \mathrm{H}_{2} \mathrm{O}, \mathrm{NH}_{3}\) have permanent dipole moments and can therefore show a pure rotational spectrum in the microwave region.

Key concepts

Permanent Dipole Moment

A permanent dipole moment is a condition in molecules where there is an uneven distribution of electrical charge. This typically happens when there are atoms with differing electronegativities within a molecule. When the molecules have a permanent dipole moment, it means one end of the molecule is slightly negative, while the other is slightly positive. This positive and negative end allows the molecule to interact with electromagnetic fields, such as microwave radiation in rotational spectroscopy.
Molecules without a permanent dipole moment, like homonuclear diatomics ( H_{2} ), do not produce a rotational spectrum since the charges are evenly balanced—resulting in no net dipole. So, when evaluating molecules for rotational spectroscopy, holding a permanent dipole moment is a key factor.

Rotational Spectrum

The rotational spectrum of a molecule involves the quantized rotational energy levels that can be identified when a molecule transitions between these levels, typically employing microwave radiation. Only molecules with a permanent dipole moment can exhibit a rotational spectrum. During this process, the rotational energy levels are determined by the moment of inertia, which depends on the mass and distribution of the atoms in the molecule.
When a molecule absorbs microwave radiation, it experiences a change in its rotational state. For instance, polar molecules like HCl and NH_{3} can absorb microwave radiation because of their dipole moments, making rotational spectrum analysis possible. This is crucial in understanding molecular structures and interactions through spectroscopic methods.

Molecular Polarity

Molecular polarity arises when there is a difference in electronegativity between atoms, causing an uneven distribution of electrons in a molecule. This uneven distribution results in partial positive and negative charges developing within the molecule. Such molecules are termed polar and are crucial in determining if a molecule can rotate to produce a rotational spectrum.
For example, HCl is a polar molecule because of the significant difference in electronegativity between hydrogen and chlorine. This polarity enables the molecule to interact with external fields, which is why it can exhibit a rotational spectrum. Recognizing the presence of molecular polarity is vital for predicting a molecule's behavior in various chemical processes.

Molecular Symmetry

Molecular symmetry can play a significant role in determining the presence of a permanent dipole moment in a molecule. Symmetrical molecules tend to be non-polar. This is because the symmetry leads to an even distribution of charges, which cancels out any potential dipole moments. Hence, they usually do not show a rotational spectrum.
For instance, CH_{4} (methane) is a highly symmetrical molecule resulting in its non-polar nature. This symmetry cancels out any dipole created by the individual bonds, preventing it from interacting with microwave radiation for rotational transitions. Understanding molecular symmetry is essential when predicting molecular polarity and analyzing molecular spectra.