Is My Calculation for Hydrogen Molecule Speed Correct?

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SUMMARY

The discussion centers on calculating the speed of a hydrogen molecule based on its total random kinetic energy at 300 K. The correct formula for total random kinetic energy is KE (total) = 1.5nRT, yielding 3738.42 J/mol for 1 mol of hydrogen. The user initially calculated the mass of one mole incorrectly as 0.001 kg instead of the correct 0.00202 kg, leading to an erroneous speed calculation of 2734.3811 m/s instead of the correct 1.93 km/s. The error highlights the importance of accurately determining molecular mass in kinetic energy calculations.

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  • Understanding of the Ideal Gas Law and its application in thermodynamics.
  • Familiarity with kinetic energy formulas in physics.
  • Knowledge of molecular weights and their significance in calculations.
  • Basic proficiency in unit conversions, particularly between grams and kilograms.
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  • Review the Ideal Gas Law and its implications for molecular behavior.
  • Study the derivation and application of the kinetic energy formula in different contexts.
  • Learn about molecular weights and how to accurately calculate them for diatomic molecules.
  • Explore unit conversion techniques to ensure accuracy in scientific calculations.
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Students in chemistry and physics, educators teaching thermodynamics, and anyone involved in molecular physics calculations will benefit from this discussion.

Steveku
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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
 
Physics news on Phys.org
The mass of one mole will be 2.02 g, since there are two hydrogen atoms in one hydrogen gas molecule.
 

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