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Ethane (C2H6) is a non-linear molecule. Here's how to determine its degrees of freedom:
Translational: 3 degrees of freedom (movement along x, y, and z axes)
Rotational: 3 degrees of freedom (rotation around x, y, and z axes)
Vibrational: 3N - 6 = (3
8) - 6 = 18 degrees of freedom (where N is the number of atoms). However, some of these vibrations are degenerate, meaning they have the same frequency. Ethane has 9 unique vibrational modes.
Therefore, ethane has a total of 3 + 3 + 18 = 24 degrees of freedom.