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2.2.4 Mean velocity, free path and size of molecules

From the Maxwell–Boltzmann distribution law for molecular velocities, the mean square and mean velocities are

From the kinetic theory of gases, assuming that molecules interact like hard spheres, it follows that:

           η  =  (5/16σ2)(mkT/π)½     τ  =  l/ = 4η/5p

            l = m/(πρσ2√2)

where k = Boltzmann's constant          σ = molecular diameter

         T = absolute temperature          m = mass of molecule

          p = pressure                           l = mean free path

         ρ = density                             τ = mean time between collisions.

         η = viscosity

A more exact theory uses the Lennard–Jones intermolecular potential. (See Hirschfelder, Curtiss and Bird (1954).

Equations are obtained for viscosity and second virial coefficient, B (i.e. first order departure from the perfect gas law) from which the molecular diameter, σ, can be estimated more accurately than from the simple equation for viscosity given above.


Gas

/(m s−1)

l/nm

τ/ps

σ/pm

 

at 0 °C and atmospheric pressure

η

B

Argon   .    .    .    .    .    .    .

380

62.6

165

342

340

Benzene     .    .    .    .    .    .

272

148.2  

545

527

Carbon dioxide    .    .    .    .

362

39.0

108

390

407

Carbon monoxide     .    .    .

454

58.6

129

371

376

Chlorine    .    .    .    .    .    .

285

27.4

  96

440

Chloroform     .    .    .    .    .

220

161.0  

732

543

Ethylene.    .    .    .    .    .    .

454

34.3

  75

423

452

Helium  .    .    .    .    .    .    .

1202  

173.6  

144

258

256

Hydrogen   .    .    .    .    .    .

1694  

110.6  

  65

297

293

Methane    .    .    .    .    .    .

600

48.1

  80

380

382

Neon   .    .    .    .    .    .    .

535

124.0  

232

279

275

Nitrogen   .    .    .    .    .    .

454

58.8

130

375

370

Nitrous oxide .    .    .    .    .

362

38.7

107

388

459

Oxygen     .    .    .    .    .    .

425

63.3

149

354

358

Sulphur dioxide   .    .    .    .

300

27.4

  91

429


Reference

Hirschfelder, Curtiss and Bird (1954) Molecular Theory of Gases and Liquids, Wiley, New York.

J.T.R.Watson

 

 

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