Degrees of freedom and triatomic gas

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Discussion Overview

The discussion centers on the degrees of freedom of a non-linear triatomic gas molecule, exploring the contributions from translational, rotational, and vibrational motions. Participants examine how these degrees of freedom are counted and the implications for understanding gas behavior at different temperatures.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the calculation of 6 degrees of freedom, suggesting it should be 7 based on their understanding of translational, rotational, and vibrational contributions.
  • Another participant proposes that there are 3 translational degrees, 3 from rotation about each atom, and 1 from the rotation of the three atoms about the center of the equilateral triangle.
  • Some participants assert that a triatomic molecule generally has 9 degrees of freedom, with 3 translational, 3 rotational, and 3 vibrational modes, noting that the "6 degrees of freedom" often cited neglects vibrational modes that are typically inactive at room temperature.
  • One participant mentions that the vibrational mode may couple with a flexing mode, suggesting that this coupling could be considered a single mode rather than two separate modes.
  • Another example is provided, indicating that CS2 has 10 observed degrees of freedom, highlighting variability in different molecules.

Areas of Agreement / Disagreement

Participants express differing views on the correct count of degrees of freedom for triatomic molecules, with some asserting 9 degrees of freedom while others suggest variations based on temperature and molecular structure. The discussion remains unresolved regarding the exact contributions of vibrational modes.

Contextual Notes

The discussion includes assumptions about temperature effects on vibrational modes and the specific molecular arrangements that may influence the degrees of freedom. There is also a lack of consensus on how to treat coupled modes in the context of degrees of freedom.

anigeo
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i wonder how can a non linear triatomic gas molecule have 6 degrees of freedom.As per me three of those will come from translational motion,two from rotational and two from vibrational modes.so it should be 7.
could you please tell me where am i going wrong.
note:the triatomic gas molecule has the arrangement of an equilateral triangle.
 
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there will be 3 from translation
3 from rotation about each atom
and 1 from from rotation of 3 atoms about center of equilateral triangle
 
A triatomic molecule has 9 degrees of freedom, in general.
There are 3 translational modes, 3 rotational and 3 vibrational.
The "6 degrees of freedom" triatomic molecule neglects the vibration modes, which usually are not active at room temperature.

Same as for diatomic gas (6 degrees of freedom) the vibration mode does not contribute to heat capacity at room temperature so the gas has only 5 active modes.
 
thanx nasu.
i think i got it
 
nasu said:
A triatomic molecule has 9 degrees of freedom, in general.
There are 3 translational modes, 3 rotational and 3 vibrational.
The "6 degrees of freedom" triatomic molecule neglects the vibration modes, which usually are not active at room temperature.

In general, yes, but not always. The vibrating mode is often coupled with a flexing mode (KE of libration), and many authorities prefer to consider this coupling as a single mode with a KE of kT rather than two modes with 1/2 kT each.

CS2, for instance, has 10 observed degrees of freedom.
 

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