Degrees of freedom and triatomic gas

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SUMMARY

A triatomic gas molecule typically has 9 degrees of freedom, comprising 3 translational, 3 rotational, and 3 vibrational modes. However, at room temperature, the vibrational modes are often inactive, leading to the consideration of only 6 degrees of freedom for practical calculations. This is similar to diatomic gases, which also exhibit 6 degrees of freedom when vibrational contributions are neglected. In some cases, such as CS2, additional degrees of freedom can be observed due to molecular coupling effects.

PREREQUISITES
  • Understanding of molecular structure and geometry, specifically equilateral triangle arrangements.
  • Familiarity with the concepts of translational, rotational, and vibrational motion in gases.
  • Knowledge of thermodynamics, particularly heat capacity and degrees of freedom.
  • Basic principles of kinetic theory as they apply to gas behavior.
NEXT STEPS
  • Research the specific heat capacity of triatomic gases at various temperatures.
  • Explore the concept of vibrational modes in molecular dynamics simulations.
  • Investigate the coupling of vibrational and flexing modes in complex molecules.
  • Study the degrees of freedom in other molecular structures, such as polyatomic gases.
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Students and professionals in physical chemistry, molecular physics, and thermodynamics, particularly those studying gas behavior and molecular dynamics.

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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