Questions about kinetic theory

[Steveku]

May you professors please check part b of my work because my answer does not match the answer in the back of the book. Thank you.

Question:
(a) What is the total random kinetic energy of all the molecules
in 1 mol of hydrogen at a temperature of 300 K? (b) With what
speed would a mole of hydrogen have to move so that the kinetic
energy of the mass as a whole would be equal to the total random
kinetic energy of its molecules?

Answer to part (a):
Since KE (total) = 1.5nRT, the total random kinetic energy is (1.5)(1)(8.314)(300) =
3738.42 J/mol

Answer to part (b):
The atomic weight of hydrogen is 1.01 grams per mole
So, the mass of one mole is 0.001 kg.

We have to find the velocity
By the kinetic energy formula,
KE = (.5)(m)(v)^2
(.5)(m)(v)^2 = 3738.42 J/mol
So, v = 2734.3811 m/s

However, the answer page in my booklet tells me that the correct answer for part b is 1.93 km/s. Please advise me and tell me what I did wrong. Thanks again.

Steve

 

[hage567]

The mass of one mole will be 2.02 g, since there are two hydrogen atoms in one hydrogen gas molecule.

 

[m2003]

, it is great that you are double-checking your work and seeking clarification. As a scientist, it is important to always question and verify our results. It is possible that there is a mistake in the answer key or in your calculations. I would suggest going back through your steps and checking your calculations to see if there were any errors. Additionally, you can reach out to your professor or classmates for further assistance. Remember, science is a collaborative field and it is okay to ask for help. Keep up the good work!