Degrees of Freedom for a Triatomic Molecule

AI Thread Summary
A triatomic molecule arranged in a straight line has 5 degrees of freedom, accounting for 3 translational and 2 rotational motions. When arranged in a V-shape, such as in water (H2O), it has 6 degrees of freedom due to an additional rotational axis. The distinction is made because rotation along the axis of the molecule is disregarded in the linear arrangement. The discussion confirms that the shape of the molecule significantly impacts its degrees of freedom. Understanding these concepts is crucial for analyzing the behavior of triatomic gases.
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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:
 
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