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Molecular Mass and Molecular Speeds - I

Problem: Calculate the molecular speeds of the molecules of hydrogen, methane, and carbon dioxide at 300K! Plan: Use the equations for the average kinetic energy of a molecule, and the relationship between kinetic energy and velocity to calculate the average speeds of the three molecules.

Solution: EK =

for Hydrogen, H2 = 2.016 g/mol

3R 2 NA

x T = 1.5 x

    • 8.314

      J/mol K

    • 6.022

      x 1023 molecules/mol

x 300K =

EK = 6.213x10 - 21 J/molecule = 1/2 mu2

m=

2.016 x 10 -3

kg/mole

6 . 0 2 2 x 1 0 2 3 m o l e c u l e s / m o l e

= 3.348x10 - 27

kg/molecule

EK = 6.213x10 - 21 J/molecule = 1/2 mu2 = 1.674x10 - 27

kg/molecule (u2)

u = 1.926 x 103 (J/kg)1/2

= 1.926 x 103 m/s = 1,926 m/s

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