To predict the 3D shape of a molecule like H3C-CH3, or ethane, we can use VSEPR theory (Valence Shell Electron Pair Repulsion theory). In ethane, the central carbon atoms are each bonded to three hydrogen atoms and one other carbon atom. The tetrahedral arrangement around each carbon atom minimizes repulsion between the electron pairs. Thus, the shape of ethane is generally described as tetrahedral, with bond angles close to 109.5 degrees.
To sketch the vibrational modes of H3C-CH3, we consider the different types of vibrations that can occur due to the bond stretching and bending between the atoms. Ethane has several vibrational modes, including symmetric stretching, asymmetric stretching, in-plane bending, and out-of-plane bending. Each of these vibrations can be visualized as the atoms moving in specific patterns: for example, in symmetric stretching, both C-H bonds on either side of a carbon atom stretch and compress simultaneously.
To illustrate these vibrational modes, you might use simple diagrams that show the positions of the carbon and hydrogen atoms during these vibrations. Each mode has a unique frequency and is often studied using techniques like infrared spectroscopy to analyze the molecular dynamics.