Degree of Freedom Formula for Molecules with n Atoms

In summary, monatomic gases (He Ne Ar, the inert gasses) have 3 degrees of freedom of translation, rotation, and vibration. Diatomic gasses (O2 N2) have two identical atoms bonded together and have 5 degrees of freedom of translation, rotation, and vibration.
  • #1
kidia
66
0
Please I need help.

Can anybody can give me the formula for determine the number of degree of freedom of molecules undergoing translation,rotation and vibration of n number of atom.
 
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  • #2
it depends on what the molecules are. monatomic? (it's 3n.) diatomic? (it's 5n). more than that, i dunno.
 
  • #3
rbj can u clariyfy more if that 3n for monotomic and 5n for diatomic is for translation,rotation or vibration
 
  • #4
kidia said:
rbj can u clariyfy more if that 3n for monotomic and 5n for diatomic is for translation,rotation or vibration

sorry, kidia. they moved the thread but they didn't leave a little "moved" arrow behind.

for monatomic gases (He Ne Ar, the inert gasses), each molecule is a single atom and virtually all of the mass of the molecule is concentrated at the nucleus. they're a simple ball with the mass all concentrated at the center. even if you were to spin the ball, there would be very little rotational kinetic energy in that spin because the mass is all at the center. no moment of inertia. so these molecules have 3 degrees of freedom of translation, and only those three. up-down (z-axis), left-right (x-axis), and forward-backward (y-axis). no rotation or vibration.

diatomic gasses (O2 N2) have two identical atoms bonded together. for each atom, the mass is concetrated at the nucleus. so this structure is like a dumbell structure. besides the 3 translational motions (x, y, z-axis) that the monatomic gasses have, there are 2 more rotational degrees of freedom. imagine the dumbell lined up on the z-axis. there would be a non-zero moment of inertia along the x-axis and along the y-axis, but not along the z-axis.

it's obvious (due to symmetry) why the 3 translational degrees of freedom should be the same (contain the same average kinetic energy) and why the 2 identical rotational degrees of freedom contain the same average kinetic energy, but someone else will have to explain why the 2 rotational degrees of freedom contain the same amount of average kinetic energy per degree of freedom as the 3 translational degrees of freedom. can a real physicist explain that?
 
  • #5
thanx very much rbj I catch u.
 

1. What is the degree of freedom formula for molecules with n atoms?

The degree of freedom formula for molecules with n atoms is given by 3n - 6, where n is the number of atoms in the molecule. This formula is used to calculate the total number of possible ways the atoms in a molecule can vibrate or move.

2. How is the degree of freedom formula derived?

The degree of freedom formula is derived from the principles of classical mechanics and statistical mechanics. It takes into account the number of atoms in a molecule and the different types of motion that each atom can undergo, such as translational, rotational, and vibrational motion.

3. Why is the degree of freedom important in chemistry?

The degree of freedom is important in chemistry because it helps us understand the behavior and properties of molecules. It allows us to predict how molecules will interact and how they will behave under different conditions, such as changes in temperature or pressure.

4. Can the degree of freedom formula be applied to all molecules?

No, the degree of freedom formula is specifically applicable to non-linear molecules, which have more than two atoms. For linear molecules, the formula is 3n - 5, where n is the number of atoms.

5. How does the degree of freedom affect the energy of a molecule?

The degree of freedom has a direct impact on the energy of a molecule. The more degrees of freedom a molecule has, the higher its energy will be. This is because more degrees of freedom mean there are more ways for the molecules to move and vibrate, resulting in higher potential energy.

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