Solutions 10
- Page ID
- 204090
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Q2:
The number of degrees of freedom a molecule has is 3N, where N is the number of atoms. Three are translational and for non-linear molecules, three are rotational, leaving 3N-6 vibrational modes. For linear molecules there are only two rotational degrees of freedom, leaving 3N-5 vibrational modes.
| Molecule | Vibrational Modes |
| \(NH_3\) | 6 |
| \(C_6H_6\) | 30 |
| \(C_{10}H_8\) | 48 |
| \(CH_4\), | 9 |
| \(C_2H_2\) | 7 |
Q3:
The one mode of CO stretch is IR active. All but the symmetric stretch of \(CO_2\) are IR active. The one mode of HCl is also active.
Q4:
The vibrational frequency is given by \(\omega = \sqrt(\frac{k}{\mu})\), where \(\mu = \frac{m_1 m_2 }{m_1 + m_2}\). The masses are provided.
Q5:
The vibrational energy is given by \(E_\nu = \hbar \omega (\nu + \frac{1}{2})\).
Q6:
The corresponding wave number of \(D_2 O\) compared with \(H_2 O\) is smaller due to the increased reduced mass, resulting in a lower energy read.