How many normal modes does the CO2 molecule have; What if the C and the O atoms were constrained to move in one dimensional:a)4 normal modes for free CO2 and 4 for constrained CO2b)3 normal modes for free CO2 and 2 for constrained CO2c)3 normal modes for free CO2 and 3 for constrained CO2d)4 normal modes for free CO2 and 2 for constrained CO2Correct answer is option 'D'. Can you explain this answer?

Question

Answer

**Answer:**

The CO2 molecule consists of one carbon atom (C) double-bonded to two oxygen atoms (O). Each atom has three degrees of freedom (DOF) - three dimensions in which it can move.

**Free CO2:**
In a free CO2 molecule, all atoms are free to move in three dimensions. However, there are certain constraints due to the nature of the molecule.

1. **Translation (3 DOF):** The molecule can move as a whole in three dimensions - x, y, and z. This is the movement of the center of mass of the molecule.
2. **Rotation (3 DOF):** The molecule can also rotate around three axes - x, y, and z. This involves the spinning motion of the molecule.
3. **Vibration (4 DOF):** The CO2 molecule has two O-C-O bending vibrations and one symmetric O-C-O stretching vibration. These vibrations involve the stretching and bending of the bonds between the atoms.

Therefore, a free CO2 molecule has a total of 3 + 3 + 4 = 10 normal modes.

**Constrained CO2:**
If the C and O atoms were constrained to move in only one dimension, certain degrees of freedom would be lost.

1. **Translation (1 DOF):** The molecule can only move along the constrained dimension.
2. **Rotation (1 DOF):** The molecule can still rotate around the unconstrained axes (y and z).
3. **Vibration (2 DOF):** The CO2 molecule still retains its two O-C-O bending vibrations, but loses the symmetric O-C-O stretching vibration since the atoms cannot move in the constrained direction.

Therefore, a constrained CO2 molecule has a total of 1 + 1 + 2 = 4 normal modes.

Hence, the correct answer is option 'D' - 4 normal modes for free CO2 and 2 normal modes for constrained CO2.

Answer

For free CO2 there are 4 modes because 1) stretching,2) compression, 3) bending in plane of paper 4) bending out of the plane of paper. But if C and O move only in 1D then only stretching and compression is allowed so there is 2 mode.

Similar Chemistry Doubts

Consider the equation 2 H2 + O2 → 2 H2O, what does the 2 in the coefficient of H2O molecule represent?

Which of the following statements regarding mass spectrometry is wrong?

At constant volume, for a fixed number of moles of a gas, the pressure of the gas increases with an increase in temperature due to

A compound with molecular formula C4H4O has all the four carbon atoms and the oxygen atom in the ring. It also has two double bonds. The compound is: Correct answer is 'heterocyclic and aromatic'. Can you explain this answer?

Top Courses for Chemistry

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams