Why does CO molecule have 7 degrees of freedom?

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Discussion Overview

The discussion centers on the degrees of freedom of the carbon monoxide (CO) molecule, specifically addressing why it is considered to have 7 degrees of freedom. Participants explore the contributions from translational, rotational, and vibrational motions, and compare CO with other diatomic molecules like O2 and N2.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that CO has 3 degrees of freedom for translational motion and 2 for rotational motion, totaling 5 degrees of freedom, questioning the additional 2 degrees.
  • Another participant asserts that CO has 3 translational, 2 rotational, and 2 vibrational degrees of freedom, explaining that the bond between carbon and oxygen behaves like a spring.
  • A different participant emphasizes that while CO has 5 degrees of freedom at normal temperature, O2 and N2 do not exhibit 7 degrees of freedom unless at higher temperatures where vibrational energy becomes significant.
  • Some participants discuss the nature of vibrational modes, distinguishing between true vibrational modes and librational modes, with one participant asserting that libration does not apply to free diatomic molecules.
  • Another participant mentions the Equipartition Principle, explaining how energy is distributed among translational, rotational, and vibrational modes, and notes that O2 and N2 also have vibrational degrees of freedom that contribute at high temperatures.

Areas of Agreement / Disagreement

Participants express differing views on the degrees of freedom of CO compared to O2 and N2, with no consensus on the conditions under which these degrees of freedom apply or the nature of vibrational modes.

Contextual Notes

The discussion includes assumptions about temperature effects on vibrational modes and the definitions of vibrational and librational motions, which remain unresolved.

Hardik Batra
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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 ?
 
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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.
 
jfizzix said:
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.

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

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.
 
klimatos said:
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.

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
 
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