Rotational Kinetic Energy of Cl2?

[XianForce]

Homework Statement

In a crude model of a rotating diatomic molecule of chlorine (Cl2), the two Cl atoms are 2.00 10^-10 m apart and rotate about their center of mass with angular speed ω = 3.80 10^12 rad/s. What is the rotational kinetic energy of one molecule of Cl2, which has a molar mass of 70.0 g/mol?

Homework Equations

1/2 * m * v² (Kinetic Energy)

v/2 * K_B * T (Internal Energy of a molecule)

The Attempt at a Solution

I attempted to use the equation for kinetic energy, substituting r * ω for v, but my web assign says that this is wrong. Nothing like this was taught in class and the book does not say much, so I'm at a loss for where to go.

 

[ehild]

The rotational energy of a rigid body (like the Cl₂ molecule) is E_rot=1/2 Iω², where I is the moment of inertia and ω is the angular speed of rotation.

The Cl₂ molecule can be considered as two point masses d distance apart, rotating around a bisector of the connecting line. So the moment of inertia is 1/2 md^2.

There are two mutually perpendicular axis of rotation so the molecule has got two rotational degrees of freedom.

ehild

 

[XianForce]

So basically: 1/4 * 1 mol /(6.022 * 10²³) * (70 * 10^-3) kg/mol * (780 m/s)² = 1.768 * 10^-20 J , right? But Web Assign keeps telling me that's wrong, so where am I making the mistake?

 

[ehild]

Explain your calculation. What is that 780 m/s?

ehild

 

[XianForce]

Nevermind, I figured it out. It's m (d/2)^2, not 1/2 * md^2

 

[ehild]

Nevermind, I figured it out. It's m (d/2)^2, not 1/2 * md^2

Well done!

ehild