# Rotational Kinetic Energy and distribution of diatomic molecules

• merbear
So you need to multiply your answer by Avogadro's number. Also, make sure you are using the correct value for the degrees of freedom for a diatomic molecule in your calculation.For part C, you are on the right track with your equation, but you need to use the moment of inertia you calculated in part B and the correct value for the angular velocity. Remember that the molecule is rotating about either the x- or y-axis, so the angular velocity will be different for each axis.
merbear
[SOLVED] Rotational Kinetic Energy and distribution of diatomic molecules

a) Calculate the total rotational kinetic energy of the molecules in 1.00 mol of a diatomic gas at 300 K.

b) Calculate the moment of inertia of an oxygen molecule (O2) for rotation about either the x- or y-axis shown in the figure. Treat the molecule as two massive points (representing the oxygen atoms) separated by a distance 1.21×10-10m. The molar mass of oxygen atoms is 16 g/mol.

c) Find the rms angular velocity of rotation of an oxygen molecule about either an x- or y-axis

## Homework Equations

kT=2/3*<k>

where, k is boltzman constant and K is kinetic energy

I=mR^2

E(rot)= 1/2*I*angular velocity(for x)^2 + 1/2*I*angular velocity(for y)^2

## The Attempt at a Solution

To find the answer to the first part of the problem I used the first equation listed and got 6.21E-21 J, but that answer is incorrect. I do not know how else to approach the problem. I think it went wrong because K in that equation is the average kinetic energy and not the rotational kinetic energy, but I couldn't find another equation that would work.

For the second part I used I=mR^2. To find m, I took the molar mass and divided by avagadros number and I used the distance given for R.

my answer was: 3.89E-46 kg*m^2, but I don't think that was correct.

For the third part, I would think that you would use Vrms equals the squareroot of (3kT/m). But we are not given the temperature. So I don't know how to go about this part either.

I would really appreciate help on these three parts. Thank you!

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merbear said:
To find the answer to the first part of the problem I used the first equation listed and got 6.21E-21 J, but that answer is incorrect. I do not know how else to approach the problem. I think it went wrong because K in that equation is the average kinetic energy and not the rotational kinetic energy, but I couldn't find another equation that would work.
Look up the equipartion theorem. How many rotational degrees of freedom are there for a diatomic molecule?

For the second part I used I=mR^2. To find m, I took the molar mass and divided by avagadros number and I used the distance given for R.
What's the rotational inertia of a point mass? mR^2. But m must equal the mass of each atom and R the distance to the center. And you have two atoms, of course.

For the third part, I would think that you would use Vrms equals the squareroot of (3kT/m). But we are not given the temperature. So I don't know how to go about this part either.
Again, you are dealing with rotational motion here, so consider the answer to part 1. And the rotational KE is $1/2 I \omega^2$. I would assume the temperature is that given in part 1. (These questions all relate to the same situation.)

Still confused about Rotational Kinetic Energy and angular velocity

I was able to figure our the moment of inertia by using the equation I= 2mL^2

However, I tried Part A and C and I still can't figure it out.

For finding the rotational kinetic energy I used:

K(rot)= (f/2)*kT

When solving using f= 2 for the degrees of freedom, boltzman constant for k, and 300 K for temperature I get 4.14E-21 J. But when I input that into the program it comes up incorrect.

For part C, I think I am getting it wrong still because I am using an incorrect value for K(rot). I am using the equation: K(rot) = 1/2 I w^2.

Please let me know why my approach to part A was incorrect.

Thank you

For one thing, you are calculating the rotational energy per molecule, but the question asks for it per mole.

## 1. What is rotational kinetic energy?

Rotational kinetic energy is the energy possessed by an object due to its rotation around an axis. It is dependent on the object's moment of inertia and angular velocity.

## 2. How is rotational kinetic energy calculated?

The formula for calculating rotational kinetic energy is Erot = 1/2 * I * ω2, where Erot is rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity.

## 3. How does rotational kinetic energy relate to diatomic molecules?

In diatomic molecules, rotational kinetic energy is a form of internal energy that contributes to the overall energy of the molecule. It is dependent on the molecule's moment of inertia and rotational speed around its center of mass.

## 4. How is rotational kinetic energy distributed among diatomic molecules?

The distribution of rotational kinetic energy among diatomic molecules follows the Maxwell-Boltzmann distribution, which states that higher energy states are less probable than lower energy states. This distribution is influenced by factors such as temperature and molecular mass.

## 5. How does rotational kinetic energy affect the behavior of diatomic molecules?

The amount of rotational kinetic energy in a diatomic molecule affects its rotational motion and therefore contributes to its overall behavior, such as its ability to vibrate and interact with other molecules. Changes in rotational kinetic energy can also lead to changes in the molecule's physical and chemical properties.

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