MOLECULAR MAGNITUDES 281 



of a molecule under the condition that its neighbors 

 are stationary. 



Now Clausius showed that 



L'/I> = Y47rr 2 (7) 



where Z/ is this mean free path, r is the radius of the 

 molecule, and l/D is the cube root of the number of 

 molecules per c. c. As a matter of fact all the molecules 

 are in motion with different velocities, so that the 

 problem is not quite as simple as the case we have just 

 considered. The mean free path is shorter than L' and 

 is L'/\/2~. Hence if we express the diameter in terms 

 of the mean free path we have 



(2r) 2 = D*/7rV2L = l/W^VoL (8) 



Substituting for N its value of 60.65 X10 22 /22410 and 

 for L the value found above, we find for hydrogen 

 2r = 2.17XlO- 8 cm. Similarly for oxygen 2r = 2.99XlO~ 8 

 cm. 



There are other methods by which these molecular 

 magnitudes may be obtained. For example, the con- 

 stants of Van der Waals's equation furnish an indica- 

 tion of the molecular diameter. This method is not, 

 however, as accurate as some others, e.g. that of vis- 

 cosity discussed above, but it leads to results of the 

 same order of magnitude. For example, Van der Waals 

 found 2r for hydrogen to be 1.04X10" 8 cm., while a 

 more recent determination using the same method 

 more carefully gave 1.26X10" 8 cm. 



Knowing the mean free path and the average velocity 

 we may calculate the average number of collisions per 

 second as v/L. Thus for hydrogen there are about 



