What Is the Average Kinetic Energy of Ethane at 410K?

[chemman218]

Homework Statement

Find the average kinetic energy in kJ/mol (including all degrees of freedom) of one mole of ethane at 410K.

Homework Equations

1/2Mu^s = kT/2
u= avg. velocity
E=n/2kT
N=degrees of freedom

The Attempt at a Solution

C2H6 degrees of freedom - 3n-6 = 18

(18/2)(1.380x10^-23 j/k)(410K)= 5.09e^20J

not sure how to get to KJ/mol from here.

 

[dextercioby]

You should first check your arithmetics. Powers of 10, to be exact. Then comes the physics.

 

[chemman218]

Okay, thanks for the note on converting j to kj. My main question is how do I know how many degrees of freedom to use in order to complete the equation.
My professor sent us an equation to use:

the total internal
energy is (3+J)/2RT where J is the number of rotational degrees of
freedom in the molecule.

I calculated the degrees of freedom to be 18 due to 3n-6. But that was not correct. Do I just use the rotational degrees of freedom or all degrees of freedom? Thanks.

 

[chemman218]

Got it! Thanks for the help

 

[Nickie]

I would first clarify the units used in the given information. The temperature is given in Kelvin (K) and the kinetic energy equation uses Joules (J) as the unit for energy. To convert J to kJ (kilojoules), we need to divide by 1000. Additionally, the given degrees of freedom (18) is not the same as the number of moles (1 mol) in the question. We need to divide by Avogadro's number (6.022x10^23 mol^-1) to get the kinetic energy per mole.

Therefore, the average kinetic energy in kJ/mol of one mole of ethane at 410K can be calculated as:

(18/2)(1.380x10^-23 J/K)(410 K) / 1000 / (6.022x10^23 mol^-1) = 4.24 kJ/mol

This means that, on average, each molecule of ethane in a sample of one mole at 410K has a kinetic energy of 4.24 kJ/mol. It is important to note that this is an average value and the actual kinetic energies of individual molecules may vary.