Degrees of Freedom for a Triatomic Molecule

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SUMMARY

A triatomic molecule arranged in a straight line possesses 5 degrees of freedom, comprising 3 translational and 2 rotational motions. In contrast, when arranged in a V-shape, such as in water (H2O), the molecule exhibits 6 degrees of freedom due to an additional rotational axis. This conclusion is based on the established principles of molecular motion, where vibrational motion is disregarded for this analysis. The discussion confirms that the arrangement of atoms significantly influences the total degrees of freedom in triatomic molecules.

PREREQUISITES
  • Understanding of molecular motion types: translational, rotational, and vibrational.
  • Familiarity with the concept of degrees of freedom in thermodynamics.
  • Knowledge of the Molar Heat Capacity equation: Cv = f/2(R).
  • Basic principles of molecular geometry and its impact on motion.
NEXT STEPS
  • Research the implications of degrees of freedom on the heat capacity of gases.
  • Learn about the differences in degrees of freedom for various molecular geometries.
  • Explore the role of vibrational motion in polyatomic molecules.
  • Investigate the application of the equipartition theorem in thermodynamics.
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Students and professionals in chemistry and physics, particularly those studying thermodynamics, molecular dynamics, and gas behavior in relation to molecular structure.

vineroon
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Homework Statement



A triatomic molecule consists of 3 atoms arranged along a straight line. The molecules can
translate and rotate but not vibrate. How many degrees of freedom are associated with this molecule?

Homework Equations



Molar Heat Capacity of Gases:
Cv = f/2(R)

f - degrees of freedom

The Attempt at a Solution



I figured that a triatomic gas would have the same translational motion as that of a monoatomic and diatomic molecule and it would have perhaps more axes of rotational motion than diatomic molecules. And from seeing that diatomic molecules have 5 degrees of freedom after ignoring vibrational motion, I am assuming that you can drop vibrational motion for triatomic molecules as well.

Would I be correct in concluding that a triatomic molecule has 6 degrees of freedom? I came to this conclusion by one more rotational axis. I'm not sure this is correct, however.

Any help would be greatly appreciated.
 
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Update:

I don't know if this is correct, but my guess is that there are 5 degrees of rotational and translational freedom. This would be because they are arranged in a straight line.

If they were arranged in a V-shape (such as H2O gas), the degrees of freedom would be 6, correct? If they are in a straight line it is only 5 because rotation on the axis of the molecules would have to be disregarded. However, since the V-shape offsets one of the molecules, there could be an extra axis of rotation.

I would appreciate it greatly if someone could affirm this. :smile:
 
Yeah it is 6

http://arasaraja.blogspot.com"


vineroon said:
Update:

I don't know if this is correct, but my guess is that there are 5 degrees of rotational and translational freedom. This would be because they are arranged in a straight line.

If they were arranged in a V-shape (such as H2O gas), the degrees of freedom would be 6, correct? If they are in a straight line it is only 5 because rotation on the axis of the molecules would have to be disregarded. However, since the V-shape offsets one of the molecules, there could be an extra axis of rotation.

I would appreciate it greatly if someone could affirm this. :smile:
 
Last edited by a moderator:

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