# Degree of freedom of CO?

1. Jun 27, 2014

### Hardik Batra

In my book showed that degree of freedom of CO(carbon monoxide) molecule is 7...

I think...
3 degree of freedom for translation motion and 2 degree of freedom for rotational motion. then total degree of freedom is 3 + 2 = 5.

But how it is 7 ?

Last edited: Jun 27, 2014
2. Jun 27, 2014

### jfizzix

There's 3 for translational,
2 for rotational,
and 2 for vibrational (since the bond between the C and O acts like a spring)

It seems weird that there should be two vibrational degrees, but there is vibrational potential energy and vibrational kinetic energy.

3. Jun 27, 2014

### Hardik Batra

CO molecule is diatomic like O2 and N2. And degree of freedom of this molecule is 5 (3 for translational and 2 for rotational = 5 ).

Then Why here O2 and N2 molecule does not possessed 7 degree of freedom like CO.
And why the bond between O2 and N2 does not act like spring.

At higher temp, degree of freedom of O2 and N2 gas is 7. Because of the high temp. vibrational energy comes into account.

But here CO molecule possessed 7 Degree of freedom is at normal temp or at higher temp?

Last edited: Jun 27, 2014
4. Jun 28, 2014

### klimatos

I believe that the two "vibrational" modes are vibration and libration. The true vibrational mode is akin to a spring compressing and expanding, while the librational mode is akin to that spring flexing back and forth.

5. Jun 29, 2014

### ehild

No, libration is restricted rotation, when an external torque opposes full rotation. No such exists in case of free diatomic molecules.
For any vibrational mode, Equipartition Principle assigns 2(1/2 kT) average energy, which corresponds to two degrees of freedom. The energy of a vibration mode is the sum of the kinetic energy and the potential energy. In case of translation and rotation, the potential energy is zero, therefore only 1/2 kT energy is assigned to the three translational directions, and also 1/2 kT energy for the rotation about an axis with moment of inertia I>0.
O2 and N2 also have vibrational degrees of freedom. But the vibration contributes to the heat capacity at high temperatures only, when kT exceeds the excitation energy of these modes.

ehild

Last edited: Jun 29, 2014