and the size of gaseous ions. 173 





1 



e 2 



w - 



zz 



— 





40 



a' 





1 



e 2 



w = 



= 



— 





156 



a ' 



where 7 = *57712, 



^O) = ^i°gr(i+a0. 



Tables by which we can calculate ty(oc) are given in De 

 Morgan's Differential and Integral Calculus, p. 587. 



From these tables I find the following values for the work w, 



e 2 

 a = b, w = '14 - , 

 a 



i 

 2a = b, 



Sa = b, 



Now the process of aggregation will stop when w becomes 

 less than the kinetic energy of the system, which at 0° C. is equal 

 to e 2 /r, when r= 1*3 x 10~ 6 . 



Thus, if a = 10~ 8 , the work required to separate a molecule 

 from an ion whose radius is 2a is greater than e 2 /r, but the work 

 required to separate a molecule from an ion whose radius is 3a 

 is less than e 2 /r; hence in this case the radius of the ion cannot 

 exceed three times the radius of the molecule. If a=10 _7 cm., 

 the work required to separate a molecule from an ion whose 

 radius is 2a is less than e 2 /r; hence in this case the radius of 

 the ion cannot exceed twice the radius of the molecule. The 

 larger the molecule the smaller will be the ratio of the size of 

 the ion to that of the molecule, with very large molecules it is 

 probable that the molecule and the ion are identical. The ions 

 in different gases will thus not differ so much in size as the 

 molecules of the gases. Since the kinetic energy is greater at 

 a high temperature than at a low one, the process of the aggre- 

 gation of molecules in the ion will stop at an earlier stage the 

 higher the temperature, so that the ions will be simpler at high 

 temperatures than at low ones. 



