7, 8] Numerical Values 7 



Mass of a molecule. The mass of a cubic centimetre of oxygen under 

 normal conditions* is '001429 gms., so that from the number just given 

 it follows that the mass of a molecule of oxygen is, to the same degree of 

 accuracy as before, equal to 3'5 x 10" 23 gms. The masses of other molecules 

 are of course in proportion to their chemical molecular-weights. That of 

 hydrogen, for instance, is about 2 - 2 x 10" 24 gms. 



Velocity. The velocity of the molecules is known with great accuracy. 

 For air at a temperature of 15 C. the average velocity is about 459 metres 

 per second. For hydrogen at C. it is about 1694 metres per second. As 

 regards velocities under other conditions it may be said that, roughly, the 

 mean velocity of a molecule of molecular weight m, at a temperature of 

 6 degrees Centigrade, is proportional to >/273 + 6, and is inversely pro- 

 portional to Jm. It is approximately independent of the density. A table 

 of velocities will be given later. 



If all the molecules were moving with a velocity equal to the average 

 velocity, the total distance described by the 4 x 10 19 molecules in a c.c. of 

 hydrogen at C. would be about 677 x 10 17 kilometres per second. The 

 actual distance, after allowing for the variation in the velocities of the 

 molecules, is, as will be seen without trouble, exactly equal to this. 



Size. It is a matter of some difficulty to determine or even to define the 

 size of a molecule. The trouble arises primarily from our ignorance of the 

 shape and other properties of the molecule. If the molecules were known to 

 be elastic spheres the question would be simple enough, and the size of the 

 molecule would be measured by the diameter of the sphere. If, however, 

 the molecules are assumed as a first approximation to be elastic spheres, 

 experiment leads to discordant results for the diameters of these spheres, 

 shewing that the original assumption is unjustifiable. The divergencies 

 arise not only from the fact that the shape of the molecules is not spherical, 

 but also from the fact that the molecules are surrounded by fields of force, 

 and in most experiments it is the extension of this field of force, rather 

 than that of the molecules themselves, with which we are concerned. 



If, however, we agree to regard the molecules as roughly represented by 

 elastic spheres, it is found that these spheres must be supposed in the case of 

 hydrogen to have a radius of about 10~ 8 cms. The size ought strictly to be 

 different for different molecules, and more exact figures will be given later, 

 but as the difference in size is hardly more than comparable with the error 

 introduced by the supposition that the molecules are elastic spheres, these 

 differences need not be discussed here. Regarding the molecule of hydrogen 

 as a sphere of radius 10~ 8 cms. the number of collisions per cubic centimetre 

 of hydrogen at C. is found to be about 2'4 x 10** per second. 



* Travers, Experimental Study of Gases, p. 133. 



