Kinetic-Molecular Theory
One of the greatest advances
in the history of the
Physical Sciences
Five Postulates of the KMT
• Molecules are in constant, random straight line motion
• Molecular collisions are elastic
• Average kinetic energy of molecules is proportional to
temperature
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Not all molecules have the same KE (see next slide)
Ave KE = 3/2 kT = 3/2 RT (for a mole of molecules)
k = Boltzmann’s constant = 1.38 x 10-23 J/K
R = 6.022 x 1023 k = 8.31 J/(mol K)
IGL assumption #1: molecular volume is negligible
IGL assumption #2: intermolecular attractions are
negligible
Maxwell-Boltzmann Distribution of Molecular Energies
Relative number of molecules
5_20
0ºC
500ºC
0
1000
2000
3000
4000
5000
Molecular speed (m/s)
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Houghton Mifflin Company. All rights reserved
5-20
Fun with Kinetic Energy
• Problem type #1:
Macroscopic KE = 1/2mv2
Microscopic KE = 3/2kT
Therefore 1/2mv2 = 3/2kT ----> velocity = √(3kT/mass)
= √(3RT/MW) per mole
Allows us to find molecular velocity as a function of mass, Temp
• Problem type #2:
Two molecules at the same Temp have same ave KE
Therefore, 1/2 m1v12 = 1/2 m2v22 ----> v1/v2 = √(m2/m1)
Provides a very slick method for estimating molecular weights
Calculating RMS velocities of molecules
(like #5.85 on Page 226)
• Uranium hexafluoride, UF6, is a white solid that sublimes at 57˚C
under normal atmospheric pressures. The compound is used to
separate the isotopes of uranium, U-235 and U-238, by effusion. At
57˚C, what is the RMS velocity, in m/s, of a molecule of UF6
containing U-235? Containing U-238?
• v235 = √(3RT/MW) = √[(3 x 8.31J/mol K x 330K) ÷ 349 g/mol]
= √23.6 kg m2/s2g
= √23,600 m2/s2
= 154 m/s (x 1mile/1600 m x 3600 s/hr = 346 mile/hr)
• v238 = √[(3 x 8,310 x 330) ÷ 352]
= 153 m/s
(NOT a very easy separation, thank goodness!)
Model of Gaseous Effusion
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Houghton Mifflin Company. All rights reserved
5-23
Rates and Times of Effusion
• Effusion: gas flows through a small hole
• Comparing rates (or times) of effusion allows
chemists to compare masses
• Rate of Eff1/Rate of Eff2 = Time2/Time1 = v1/v2 = √(m2/m1)
• Problems #89, #93 on Page 227